Introduction

This Rmarkdown script contains the full results supporting the main paper (but very little interpretation). As described in detail in the README.md document, this script uses various types of input data (linguistic and genetic) and multiple methods of analysis.

Data

Tone

The data sources

WALS

WALS uses a categorical classification with 3 ordered categories ‘None’ < ‘Simple’ < ‘Complex.’ There are 513 languages with data.

None	Simple	Complex
301	127	85

Figure 1. Distribution of tone in WALS.

LAPSyD

LAPSyD gives both a categorical classification with 5 ordered categories ‘None’ < ‘Simple’ < ‘Complex,’ and the actual count of tones. There are 569 languages with data.

None	Marginal	Simple	Moderately complex	Complex
386	8	94	39	42

Figure 2. Distribution of tone in LAPSyD.

Figure 3. Distribution of tone counts in LAPSyD.

Dediu & Ladd (2007)

This uses a categorical classification with 2 (presence/absence) categories ‘No’ and ‘Yes.’ There are 60 languages with data.

No	Yes
30	30

Figure 4. Distribution of tone in Dediu & Ladd (2007)’s database.

PHOIBLE

PHOIBLE gives the actual count in 2030 languages with data.

0	1	2	3	4	5	6	7	8	9	10
1495	4	148	173	101	60	25	11	4	6	3

Figure 5. Distribution of tone in PHOIBLE.

WPHON

WPHON gives the actual count in 3160 languages with data.

0	1	2	3	4	5	6	7	8	9	10	11	12
2193	3	427	222	174	66	43	11	15	2	1	2	1

Figure 6. Distribution of tone in WPHON

Relationships between data sources

WALS - LAPSyD

languages with values in at least one classification: 724
shared languages: 358
language with values only in WALS: 155
language with values only in LAPSyD: 211

	None	Marginal	Simple	Moderately complex	Complex
None	229	2	1	0	0
Simple	4	4	59	12	4
Complex	1	0	2	16	24

Figure 7. Relationship between tone in WALS and LAPSyD.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
515.4	8	3.407e-106 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
515.4	NA	9.999e-05 * * *

WALS - Dediu & Ladd (2007)

languages with values in at least one classification: 550
shared languages: 23
language with values only in WALS: 490
language with values only in Dediu & Ladd (2007): 37

	No	Yes
None	12	1
Simple	0	5
Complex	0	5

Figure 8. Relationship between tone in WALS and Dediu & Ladd (2007)’s database.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
19.3	2	6.44e-05 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
19.3	NA	9.999e-05 * * *

LAPSyD - Dediu & Ladd (2007)

languages with values in at least one classification: 609
shared languages: 20
language with values only in LAPSyD: 549
language with values only in Dediu & Ladd (2007): 40

	No	Yes
None	12	0
Marginal	0	1
Simple	0	1
Moderately complex	0	2
Complex	0	4

Figure 9. Relationship between tone in LAPSyD and Dediu & Ladd (2007)’s database.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
20	4	0.0004994 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
20	NA	9.999e-05 * * *

PHOIBLE - WALS

languages with values in at least one classification: 2074
shared languages: 469
language with values only in PHOIBLE: 1561
language with values only in WALS: 44

	None	Simple	Complex
0	272	70	41
1	1	0	0
2	1	17	4
3	2	7	12
4	0	6	6
5	0	4	7
6	1	6	3
7	0	1	2
8	0	0	1
9	0	0	3
10	0	0	2

Figure 10. Relationship between tone in PHOIBLE and WALS (barplot).

Figure 11. Relationship between tone in PHOIBLE and WALS (boxplots).

Analysis of Variance Model
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
wa_tone	2	371.4	185.7	76.53	1.826e-29
Residuals	466	1131	2.427	NA	NA

	diff	lwr	upr	p adj
Simple-None	1.225	0.8137	1.637	3.976e-11
Complex-None	2.292	1.829	2.754	1.3e-11
Complex-Simple	1.066	0.5312	1.602	1.099e-05

PHOIBLE - LAPSyD

languages with values in at least one classification: 2132
shared languages: 467
language with values only in PHOIBLE: 1563
language with values only in LAPSyD: 102

	None	Marginal	Simple	Moderately complex	Complex
0	314	6	57	13	15
1	1	0	0	0	0
2	2	1	13	0	1
3	0	0	3	9	3
4	0	0	2	4	2
5	0	0	1	3	6
6	1	0	1	3	0
7	0	0	1	0	1
8	0	0	0	0	1
9	0	0	0	0	2
10	0	0	0	0	1

Figure 12. Relationship between tone in PHOIBLE and LAPSyD (barplot).

Figure 13. Relationship between tone in PHOIBLE and LAPSyD (boxplots).

Analysis of Variance Model
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
la_tone	4	368.3	92.06	61.43	1.324e-41
Residuals	462	692.3	1.499	NA	NA

	diff	lwr	upr	p adj
Marginal-None	0.2511	-1.03	1.532	0.9835
Simple-None	0.7475	0.3239	1.171	1.812e-05
Moderately complex-None	2.34	1.719	2.962	4.919e-12
Complex-None	2.84	2.219	3.462	4.874e-12
Simple-Marginal	0.4963	-0.8264	1.819	0.8425
Moderately complex-Marginal	2.089	0.6904	3.488	0.0004863
Complex-Marginal	2.589	1.19	3.988	5.735e-06
Moderately complex-Simple	1.593	0.8892	2.297	1.263e-08
Complex-Simple	2.093	1.389	2.797	4.965e-12
Complex-Moderately complex	0.5	-0.3381	1.338	0.4765

Figure 14. Relationship between tone in PHOIBLE and number of tones in LAPSyD (jittered for increased visibility).

Pearson’s product-moment correlation: `la_n_tones` and `ph_n_tones`
Test statistic	df	P value	Alternative hypothesis	cor
13.86	465	8.444e-37 * * *	two.sided	0.5406

Spearman’s rank correlation rho: `la_n_tones` and `ph_n_tones`
Test statistic	P value	Alternative hypothesis	rho
7516233	1.916e-39 * * *	two.sided	0.5572

PHOIBLE - Dediu & Ladd (2007)

languages with values in at least one classification: 2050
shared languages: 40
language with values only in PHOIBLE: 1990
language with values only in Dediu & Ladd (2007): 20

	No	Yes
0	20	7
1	0	0
2	1	3
3	0	3
4	0	2
5	0	3
6	0	0
7	0	0
8	0	1
9	0	0
10	0	0

Figure 15. Relationship between tone in PHOIBLE and Dediu & Ladd (2007)’s database (barplot).

Figure 16. Relationship between tone in PHOIBLE and Dediu & Ladd (2007)’s database (boxplots).

Welch Two Sample t-test: `ph_n_tones` by `dl_tone` (continued below)
Test statistic	df	P value	Alternative hypothesis
-4.264	19.13	0.0004133 * * *	two.sided

mean in group No	mean in group Yes
0.09524	2.421

WPHON - WALS

languages with values in at least one classification: 3188
shared languages: 485
language with values only in WPHON: 2675
language with values only in WALS: 28

	None	Simple	Complex
0	270	9	3
1	0	0	0
2	13	73	9
3	6	24	18
4	1	11	20
5	0	2	10
6	0	1	8
7	0	0	2
8	0	0	3
9	0	0	1
10	0	0	0
11	0	0	0
12	0	0	1

Figure 17. Relationship between tone in WPHON and WALS (barplot).

Figure 18. Relationship between tone in WPHON and WALS (boxplots).

Analysis of Variance Model
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
wa_tone	2	1094	546.8	490	7.358e-117
Residuals	482	537.9	1.116	NA	NA

	diff	lwr	upr	p adj
Simple-None	2.151	1.882	2.421	5.838e-11
Complex-None	3.954	3.633	4.276	5.838e-11
Complex-Simple	1.803	1.438	2.169	5.838e-11

WPHON - LAPSyD

languages with values in at least one classification: 3211
shared languages: 518
language with values only in WPHON: 2642
language with values only in LAPSyD: 51

	None	Marginal	Simple	Moderately complex	Complex
0	334	1	11	2	1
1	0	0	1	0	0
2	19	6	49	6	6
3	3	0	11	20	6
4	2	0	6	6	9
5	0	0	2	1	7
6	0	0	1	0	4
7	0	0	0	0	1
8	0	0	0	0	3
9	0	0	0	0	0
10	0	0	0	0	0
11	0	0	0	0	0
12	0	0	0	0	0

Figure 19. Relationship between tone in WPHON and LAPSyD (barplot).

Figure 20. Relationship between tone in WPHON and LAPSyD (boxplots).

Analysis of Variance Model
	Df	Sum Sq	Mean Sq	F value	Pr(>F)
la_tone	4	868.5	217.1	278.1	6.119e-127
Residuals	513	400.6	0.7808	NA	NA

	diff	lwr	upr	p adj
Marginal-None	1.561	0.6375	2.484	4.595e-05
Simple-None	1.97	1.672	2.267	2.014e-10
Moderately complex-None	2.732	2.304	3.16	2.014e-10
Complex-None	4.063	3.645	4.48	2.014e-10
Simple-Marginal	0.4092	-0.5438	1.362	0.7655
Moderately complex-Marginal	1.171	0.1699	2.173	0.01257
Complex-Marginal	2.502	1.505	3.499	3.885e-10
Moderately complex-Simple	0.7623	0.273	1.252	0.0002305
Complex-Simple	2.093	1.613	2.573	2.014e-10
Complex-Moderately complex	1.331	0.7601	1.901	4.023e-09

Figure 21. Relationship between tone in WPHON and number of tones in LAPSyD (jittered for increased visibility).

Pearson’s product-moment correlation: `la_n_tones` and `wp_tone`
Test statistic	df	P value	Alternative hypothesis	cor
31.51	516	2.475e-122 * * *	two.sided	0.8112

Spearman’s rank correlation rho: `la_n_tones` and `wp_tone`
Test statistic	P value	Alternative hypothesis	rho
3591376	2.359e-142 * * *	two.sided	0.845

WPHON - Dediu & Ladd (2007)

languages with values in at least one classification: 3176
shared languages: 44
language with values only in WPHON: 3116
language with values only in Dediu & Ladd (2007): 16

	No	Yes
0	22	1
1	0	0
2	1	6
3	0	7
4	0	4
5	0	0
6	0	1
7	0	2
8	0	0
9	0	0
10	0	0
11	0	0
12	0	0

Figure 22. Relationship between tone in WPHON and Dediu & Ladd (2007)’s database (barplot).

Figure 23. Relationship between tone in WPHON and Dediu & Ladd (2007)’s database (boxplots).

Welch Two Sample t-test: `wp_tone` by `dl_tone` (continued below)
Test statistic	df	P value	Alternative hypothesis
-8.362	22.18	2.64e-08 * * *	two.sided

mean in group No	mean in group Yes
0.08696	3.286

WPHON - PHOIBLE

languages with values in at least one classification: 3760
shared languages: 1430
language with values only in WPHON: 1730
language with values only in PHOIBLE: 600

	0	1	2	3	4	5	6	7	8	9	10
0	918	1	8	6	8	3	1	0	0	0	0
1	3	0	0	0	0	0	0	0	0	0	0
2	131	0	27	21	16	7	2	1	1	0	0
3	48	0	17	37	6	5	6	2	1	0	0
4	43	0	14	4	13	6	7	2	1	0	0
5	9	0	2	5	4	7	1	0	0	1	1
6	5	0	1	4	1	2	2	1	0	1	0
7	3	0	0	1	0	1	1	0	0	0	0
8	2	0	0	0	1	0	0	2	0	2	0
9	0	0	1	0	0	1	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	1	0	0	0	0	0
12	0	0	0	1	0	0	0	0	0	0	0

Figure 24. Relationship between tone in WPHON and PHOIBLE (barplot).

Figure 25. Relationship between tone in WPHON and PHOIBLE (scatterplot).

Pearson’s product-moment correlation: `wp_tone` and `ph_n_tones`
Test statistic	df	P value	Alternative hypothesis	cor
26.83	1428	9.157e-129 * * *	two.sided	0.579

Spearman’s rank correlation rho: `wp_tone` and `ph_n_tones`
Test statistic	P value	Alternative hypothesis	rho
1.97e+08	3.554e-138 * * *	two.sided	0.5959

Reconciliating the sources

Collapse LAPSyD 4-way

The 5-level coding in LAPSyD is too fine-grained, especially “Marginal” is very rare, and seemingly quite similar with “Simple” (rather than “None”) in its behaviour in the other data sets. On the other hand, “Moderately complex,” while quite similar with “Complex” (but not “Simple”), seems to have an identity of its own. Thus, I collapsed “Marginal” into “Simple,” resulting in a 4-way classification: “None” < “Simple” < “Moderately complex” < “Complex.”

The content of the sources

With this (and as a reminder), the sources contain the following information:

LAPSyD:
- 4-way classification for 569 languages: “None” (386), “Simple” (102), “Moderately complex” (39), “Complex” (42)
- counts for 569 languages: 0 (386), 1 (6), 2 (89), 3 (47), 4 (22), 5 (6), 6 (8), 7 (3), 9 (1), 11 (1)
WALS:
- 3-way classification for 513 languages: “None” (301), “Simple” (127), “Complex” (85)
Dediu & Ladd (2007):
- binary classification for 60 languages: “No” (30), “Yes” (30)
WPHON:
- counts for 3160 languages: 0 (2193), 1 (3), 2 (427), 3 (222), 4 (174), 5 (66), 6 (43), 7 (11), 8 (15), 9 (2), 10 (1), 11 (2), 12 (1)
PHOIBLE:
- counts for 2030 languages: 0 (1495), 1 (4), 2 (148), 3 (173), 4 (101), 5 (60), 6 (25), 7 (11), 8 (4), 9 (6), 10 (3)

The reconciliation rules

I designed a set of rules for deciding on a set of two “agreement” categorical classifications, based on a precedence of the sources and the patterns of (dis)agreement between them:

a binary classification: no tone (“No”) vs any form of tone (“Yes”), and
a 3-way classification: “None” < “Simple” < “Complex.”

More precisely, I preferred to use manually-curated categorical classifications to count sources, resulting in the following (rough) ordering: LAPSyD > WALS > Dediu & Ladd (2007) > WPHON > PHOIBLE.

For the sources that give actual numbers (i.e., counts of tones or tone symbols), we observe that 1 is very rare, probably signalling coding errors, marginal systems (“pitch-accent”) or theoretical arguments, so they can probably be safely collapsed it into 2, and then move everything “one step down” (i.e., 2 → 1, 3 → 2, etc) so we have a continuum of counts from 0 onward. With this, the pairwise correlations between the count sources become:

Figure 26. Relationships between counts after merging 1 into 2 and moving everything down by 1.

Thus, the main idea is to use LAPSyD wherever these data exists, followed by WPHON and finally PHOIBLE (thus with precedence LAPSyD > WPHON > PHOIBLE). Please note that the counts in WPHON and PHOIBLE are “corrected” to better map on those in LAPSyD and to “predict” missing data, using quadratic regression (i.e., the “corrected” counts are computed as WPHON_corr = 0.079 +0.919WPHON -0.04WPHON², and PHOIBLE_corr = 0.394 +0.68PHOIBLE -0.037PHOIBLE², respectively).

The “agreement” classifications

Distributions

Binary classification

# languages with data: 3798:

No	Yes
2541	1257

Figure 27. Distribution of the binary agreement classification of tone.

3-way classification

# languages with data: 3785:

None	Simple	Complex
2538	936	311

Figure 28. Distribution of the 3-way agreement classification of tone.

Counts

Rounded

# languages with data: 3785:

0	1	2	3	4	5	6	8	10
2544	516	524	114	56	26	3	1	1

Figure 29. Distribution of the agreement counts of tone.

Unrounded

# languages with data: 3785:

Figure 30. Distribution of the agreement counts of tone (unrounded).

Relationships with original sources

With WALS

Binary classification

	No	Yes
None	297	4
Simple	4	123
Complex	0	85

Figure 31. Relationship between tone in WALS and the agreement binary classification.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
480.7	2	4.049e-105 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
480.7	NA	9.999e-05 * * *

3-way classification

	None	Simple	Complex
None	298	3	0
Simple	4	119	4
Complex	1	2	82

Figure 32. Relationship between tone in WALS and the agreement 3-way classification.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
921	4	4.723e-198 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
921	NA	9.999e-05 * * *

With LAPSyD

Binary classification

	No	Yes
None	385	1
Simple	0	102
Moderately complex	0	39
Complex	0	42

Figure 33. Relationship between tone in LAPSyD and the agreement binary classification.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
564.4	3	5.148e-122 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
564.4	NA	9.999e-05 * * *

3-way classification

	None	Simple	Complex
None	386	0	0
Simple	0	102	0
Moderately complex	0	12	27
Complex	0	0	42

Figure 34. Relationship between tone in LAPSyD and the agreement 3-way classification.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
1028	6	7.755e-219 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
1028	NA	9.999e-05 * * *

Counts

Rounded

Figure 35. Relationship between tone in LAPSyD and the agreement counts.

Pearson’s product-moment correlation: `la_n_tones` and `n_tones`
Test statistic	df	P value	Alternative hypothesis	cor
Inf	567	0 * * *	two.sided	1

Spearman’s rank correlation rho: `la_n_tones` and `n_tones`
Test statistic	P value	Alternative hypothesis	rho
0	0 * * *	two.sided	1

Unrounded

Figure 36. Relationship between tone in LAPSyD and the agreement counts (unrounded).

Pearson’s product-moment correlation: `la_n_tones` and `n_tones_raw`
Test statistic	df	P value	Alternative hypothesis	cor
Inf	567	0 * * *	two.sided	1

Spearman’s rank correlation rho: `la_n_tones` and `n_tones_raw`
Test statistic	P value	Alternative hypothesis	rho
0	0 * * *	two.sided	1

With Dediu & Ladd (2007)

Binary classification

	No	Yes
No	30	0
Yes	0	30

Figure 37. Relationship between tone in Dediu & Ladd (2007) and the agreement binary classification.

Pearson’s Chi-squared test with Yates’ continuity correction: `cooc_tab`
Test statistic	df	P value
56.07	1	7.005e-14 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
60	NA	9.999e-05 * * *

3-way classification

	None	Simple	Complex
No	24	0	0
Yes	2	8	13

Figure 38. Relationship between tone in Dediu & Ladd (2007) and the agreement 3-way classification.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
39.61	2	2.502e-09 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
39.61	NA	9.999e-05 * * *

With PHOIBLE

Counts

Rounded

Figure 39. Relationship between tone in PHOIBLE and the agreement counts.

Pearson’s product-moment correlation: `ph_n_tones` and `n_tones`
Test statistic	df	P value	Alternative hypothesis	cor
41.42	2028	2.854e-272 * * *	two.sided	0.677

Spearman’s rank correlation rho: `ph_n_tones` and `n_tones`
Test statistic	P value	Alternative hypothesis	rho
358843117	0 * * *	two.sided	0.7426

Unrounded

Figure 40. Relationship between tone in PHOIBLE and the agreement counts (unrounded).

Pearson’s product-moment correlation: `ph_n_tones` and `n_tones_raw`
Test statistic	df	P value	Alternative hypothesis	cor
38.8	2028	9.067e-247 * * *	two.sided	0.6527

Spearman’s rank correlation rho: `ph_n_tones` and `n_tones_raw`
Test statistic	P value	Alternative hypothesis	rho
488625970	1.276e-243 * * *	two.sided	0.6495

With WPHON

Counts

Rounded

Figure 41. Relationship between tone in WPHON and the agreement counts.

Pearson’s product-moment correlation: `wp_tone` and `n_tones`
Test statistic	df	P value	Alternative hypothesis	cor
156	3158	0 * * *	two.sided	0.9408

Spearman’s rank correlation rho: `wp_tone` and `n_tones`
Test statistic	P value	Alternative hypothesis	rho
136411420	0 * * *	two.sided	0.9741

Unrounded

Figure 42. Relationship between tone in WPHON and the agreement counts (unrounded).

Pearson’s product-moment correlation: `wp_tone` and `n_tones_raw`
Test statistic	df	P value	Alternative hypothesis	cor
168.4	3158	0 * * *	two.sided	0.9486

Spearman’s rank correlation rho: `wp_tone` and `n_tones_raw`
Test statistic	P value	Alternative hypothesis	rho
689289938	0 * * *	two.sided	0.8689

Conclusions about tone

These three agreement tone codings were obtain using the full information from the 5 sources, but, of course, we have information about much fewer languages for this study, so that we end up using fewer languages here.

After this sub-setting, in summary, I used 5 primary sources:

WALS: categorical with 3 ordered categories ‘None’ < ‘Simple’ < ‘Complex,’
LAPSYD: categorical, recoded with 4 ordered categories ‘None’ < ‘Simple’ < ‘Moderately complex’ < ‘Complex’ by collapsing ‘Marginal’ into ‘Simple,’ and count, from 0 to 10 tones (mean 0.62 and median 0), by collapsing the original 1 tone into the original 2 tones and moving all tones one step down (i.e., original 2 tones become 1 tone),
Dediu & Ladd (2007): categorical with 2 (presence/absence) categories ‘No’ and ‘Yes,’
WPHON: count, from 0 to 11 tones (mean 0.67 and median 0), by collapsing the original 1 tone into the original 2 tones and moving all tones one step down (i.e., original 2 tones become 1 tone), and
PHOIBLE: count, from 0 to 9 tones (mean 0.66 and median 0), by collapsing the original 1 tone into the original 2 tones and moving all tones one step down (i.e., original 2 tones become 1 tone),

From these, I built 3 “agreement” combined and reconciled measures:

tone_binary: a binary (presence/absence) variable with categories ‘No’ and ‘Yes,’
tone_3way: a categorical variable with 3 ordered categories ‘None’ < ‘Simple’ < ‘Complex,’ and
n_tones: count, from 0 to 10 tones (mean 0.61 and median 0).

However, for the analyses reported here, I used the following variables:

tone1: this represents directly tone_binary and encapsulates the question “does the language use tone?” contrasting no tone (“No”) versus any type of tone system (“Yes”),
tone2: this is the dichotomisation of tone_3way into the question “does the language use a complex tone system?” contrasting complex tone systems (“Yes”) versus no tone and simple tone systems (“No”), and
tone counts: this is the n_tones, counting the number of tones/tone symbols in the language.

For counts, I will also use the unrounded (i.e., raw) “counts,” n_tones_raw, varying between 0 to 10 tones (mean 0.67 and median 0.0793991), to avoid any biases induced by numerically rounding to integer counts.

Distribution of retained tone data

Binary

# languages with data: 321:

No	Yes
251	70

Figure 43. Distribution of binary tone.

3-way

# languages with data: 314:

None	Simple	Complex
248	39	27

Figure 44. Distribution of 3-way tone.

Counts

# languages with data: 314:

0	1	2	3	4	5	6
249	26	23	6	5	3	2

Figure 45. Distribution of tone counts.

Counts (unrounded)

# languages with data: 314:

Figure 46. Distribution of tone counts (unrounded).

Intersection

There are 314 languages with data for binary, 3-way and counts.

ASPM-D and MCPH1-D population frequencies

I will denote the “derived” alleles of ASPM and MCPH1 (Microcephalin) as ASPM-D and MCPH1-D, respectively.

ASPM-D

ASPM-D this was originally defined in relation to “haplotype 63” and two of its polymorphic nonsynonymous sites in exon 18 in an open reading frame (ORF), A44871G and C45126A with the ancestral alleles, respectively, A and C, and the derived ones, G and A (Mekel-Bobrov et al., 2005, p. 1720). Later relevant publications (Patrick C. M. Wong, Chandrasekaran, & Zheng, 2012; Patrick C. M. Wong et al., 2020) however, use SNP rs41310927 with ancestral allele T and derived allele C. While most databases do contain info about this SNP, others do not, such that I also collected data about SNPs in very tight LD with it: rs41308365, rs3762271, rs41304071, rs147068597 and rs61819087 (the LD data was obtained from LDlink’s “LDproxy Tool” using all populations in that database).

Thus, I collected the following data:

Locus/SNP	“derived” allele	Datatbases	Position and LD to target
“haplotype 63”	“haplogroup D”	MB2005	the target
rs41310927	C	WONG2020, LDLink, gnomAD, dbSNP	the target
rs41308365	A	LDLink, gnomAD, dbSNP	chr1:197070707; D’=1.00, R²=1.00
rs3762271	T	LDLink, gnomAD, dbSNP, ALFRED	chr1:197070442; D’=1.00, R²=1.00
rs41304071	T	LDLink, dbSNP	chr1:197063352; D’=1.00, R²=1.00
rs147068597	A	LDLink	chr1:197058136; D’=1.00, R²=1.00
rs61819087	G	LDLink, dbSNP	chr1:197084857; D’=1.00, R²=1.00

where the databases are identified as:

Database	URL	Info	ID
Mekel-Bobrov et al. (2005)	https://science.sciencemag.org/content/309/5741/1720	The original source; 59 populations	MB2005
Patrick C. M. Wong et al. (2020)	https://advances.sciencemag.org/content/6/22/eaba5090	Massive experimental study in Cantonese speakers; 1 population	WONG2020
LDLink	https://ldlink.nci.nih.gov/?tab=home	“[…] a suite of web-based applications designed to easily and efficiently interrogate linkage disequilibrium in population groups”; 1000 genomes data in 32 individual and grouped populations	LDLink
gnomAD	https://gnomad.broadinstitute.org/	Genome Aggregation Database v2.1.1; very broad populations	gnomAD
dbSNP	https://www.ncbi.nlm.nih.gov/snp/	aggregation of info form multiple databases, mostly using very broad populations	dbSNP
1000 genomes	https://www.internationalgenome.org/	this info is included in other databases (gnomAD) so is not specifically used here	1KG
ALFRED	https://alfred.med.yale.edu/alfred/index.asp	The ALlele FREquency Database; lots of info in many populations; unfortunately, for ASPM only one SNP in strong LD with the target rs41310927 (rs3762271) is available	ALFRED

All SNPs

I ended up with frequency data about these loci in 170 unique samples coming from 127 unique meta-populations (such as “Han Chinese,” “Italians” or “Finnish”). After making sure the frequencies of these SNPs are very highly correlated (in those samples where they do co-occur), I computed their weighted average frequency (weighed by the number of sampled individuals).

Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
0	0.1012	0.2291	0.2416	0.3886	0.684

Figure 48. Distribution of the frequency of the “derived” allele of ASPM across the world.

Excluding “proxy” SNPs

Of these 7 SNPs, 5 are “proxy” SNPs (rs147068597, rs3762271, rs41304071, rs41308365, rs61819087), representing 289 unique samples (and 233237 total alleles) out of 396 (73%) unique samples (and 367519 total alleles; 63.5%) available for ASPM-D.

Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
0	0.0995	0.2073	0.2275	0.38	0.6

Figure 50. Distribution of the frequency of the “derived” allele of ASPM across the world, excluding the “proxy” SNPs.

Due to this high proportion of the data being represented by “proxy” SNPs, I also conducted separate analyses excluding these SNPs.

New samples

Moreover, 111 are new samples from 84 unique (meta)populations, compared to the 59 samples in 56 (meta)populations in the original Mekel-Bobrov et al. (2005). These new samples are distributed as:

Africa	Eurasia	America	Papunesia
12	90	5	4

and the corresponding new (meta)populations as:

Africa	Eurasia	America	Papunesia
12	63	5	4

Figure 51. Distribution of the “original” and “new” samples of ASPM-D across the world.

MCPH1-D

MCPH1-D was originally defined in relation to G37995C in exon 8 in an open reading frame (ORF) with the ancestral allele G, and the derived one C (Evans et al., 2005, p. 1717). Later relevant publications (Patrick C. M. Wong et al., 2020) however, use SNP rs930557 with ancestral allele G and derived allele C. While most databases do contain info about this SNP, others do not, such that I also collected info about the SNP rs1129706 which is in very tight LD with it (the linkage data was obtained from LDlink’s “LDproxy Tool” using all populations in that database).

Thus, I obtained the following data:

Locus/SNP	“derived” allele	Datatbases	Position and LD to target
G37995C	C	MB2005	the target
rs930557	C	WONG2020, LDLink, dbSNP	the target
rs1129706	G	ALFRED	chr8:6304814; D’=0.995, R²=0.936

All SNPs

I ended up with frequency data about these loci in 166 unique samples coming from 128 unique meta-populations. After making sure the frequencies of these SNPs are very highly correlated (in those samples where they do co-occur), I computed their weighted average frequency (weighted by the number of sampled individuals).

Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
0.0315	0.658	0.7986	0.7125	0.8652	1

Figure 53. Distribution of the frequency of the “derived” allele of MCPH1 across the world.

Excluding “proxy” SNPs

Of these 3 SNPs, 1 are “proxy” SNPs (rs1129706), representing 141 unique samples (and 13028 total alleles) out of 245 (57.6%) unique samples (and 107258 total alleles; 12.1%) available for MCPH1-D.

Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
0.033	0.5634	0.7737	0.6729	0.8357	1

Figure 55. Distribution of the frequency of the “derived” allele of MCPH1 across the world, excluding the “proxy” SNPs.

Due to this high proportion of the data being represented by “proxy” SNPs, I also conducted separate analyses excluding these SNPs.

New samples

Moreover, 107 are new samples from 85 unique (meta)populations, compared to the 59 samples in 56 (meta)populations in the original Evans et al. (2005). These new samples are distributed as:

Africa	Eurasia	America	Papunesia
12	86	5	4

and the corresponding new (meta)populations as:

Africa	Eurasia	America	Papunesia
12	64	5	4

Figure 56. Distribution of the “original” and “new” samples of MCPH1-D across the world.

The original Dediu & Ladd (2007) samples

These are the same for ASPM-D and MCPH1-D:

Africa	Eurasia	America	Papunesia
15	37	5	2

and the corresponding new (meta)populations as:

Africa	Eurasia	America	Papunesia
14	35	5	2

Figure 57. Distribution of the “original” and “new” samples of MCPH1-D across the world.

Putting tone and genes together

When combining the linguistic and genetic data, we are left with 175 unique samples in 129 unique (meta)populations speaking 321 unique “languages” (i.e., Glottolog codes) (from now on, denoted as 175:129:321), of which:

Information for	Number of samples:(meta)pops:languages	Missing samples:(meta)pops:languages
tone binary	175:129:321	0:0:0 = {} : {} : {}
tone 3-way	170:124:314	5:5:7 = {SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Burunge, Hazara, Mozabite, Oroqen, Xibe} : {buru1320, efee1239, gyel1242, haza1239, oroq1238, tumz1238, xibe1242}
tone counts	170:124:314	5:5:7 = {SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Burunge, Hazara, Mozabite, Oroqen, Xibe} : {buru1320, efee1239, gyel1242, haza1239, oroq1238, tumz1238, xibe1242}
ASPM-D	170:127:319	5:2:2 = {FINRISK, GenDan, GenNed5, KRGDB, Qatari} : {Dutch, Qatari} : {dutc1256, gulf1241}
MCPH1-D	166:128:320	9:1:1 = {gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish} : {Bulgarian} : {bulg1262}
ASPM-D & MCPH1-D	161:126:318	14:3:3 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari} : {Bulgarian, Dutch, Qatari} : {bulg1262, dutc1256, gulf1241}
tone binary & ASPM-D & MCPH1-D	161:126:318	14:3:3 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari} : {Bulgarian, Dutch, Qatari} : {bulg1262, dutc1256, gulf1241}
tone 3-way & ASPM-D & MCPH1-D	156:121:311	19:8:10 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari, SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Bulgarian, Burunge, Dutch, Hazara, Mozabite, Oroqen, Qatari, Xibe} : {bulg1262, buru1320, dutc1256, efee1239, gulf1241, gyel1242, haza1239, oroq1238, tumz1238, xibe1242}
tone counts & ASPM-D & MCPH1-D	156:121:311	19:8:10 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari, SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Bulgarian, Burunge, Dutch, Hazara, Mozabite, Oroqen, Qatari, Xibe} : {bulg1262, buru1320, dutc1256, efee1239, gulf1241, gyel1242, haza1239, oroq1238, tumz1238, xibe1242}

Some pair-wise differences in terms of samples:(meta)populations:languages with data:

Present in…	… but absent from	samples:(meta)pops:languages
tone binary	tone 3-way (and counts)	5:5:7 = {SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Burunge, Hazara, Mozabite, Oroqen, Xibe} : {buru1320, efee1239, gyel1242, haza1239, oroq1238, tumz1238, xibe1242}
tone binary	ASPM-D	5:2:2 = {FINRISK, GenDan, GenNed5, KRGDB, Qatari} : {Dutch, Qatari} : {dutc1256, gulf1241}
tone binary	MCPH1-D	9:1:1 = {gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish} : {Bulgarian} : {bulg1262}
tone binary	ASPM-D & MCPH1-D	14:3:3 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari} : {Bulgarian, Dutch, Qatari} : {bulg1262, dutc1256, gulf1241}
tone 3-way (and counts)	ASPM-D	5:2:2 = {FINRISK, GenDan, GenNed5, KRGDB, Qatari} : {Dutch, Qatari} : {dutc1256, gulf1241}
tone 3-way (and counts)	MCPH1-D	9:1:1 = {gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish} : {Bulgarian} : {bulg1262}
tone 3-way (and counts)	ASPM-D & MCPH1-D	14:3:3 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari} : {Bulgarian, Dutch, Qatari} : {bulg1262, dutc1256, gulf1241}

Stats

tone1 (is there tone?)

I kept only the entries with non-missing data for the tone1, ASPM-D and MCPH1-D, and if there are more than one possible languages or allele frequencies for a given sample, I only kept those entries that have different tone or allele data. The resulting dataset has 181 observations, distributed among 119 unique Glottolg codes in 35 families (ranging from a minimum of 1 language per family to a maximum of 48, with a mean 5.2 and median 2 languages per family) and 4 macroareas.

There are 161:126:119 unique samples:(meta)populations:languages retained, dropping 14:3:202 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari} : {Bulgarian, Dutch, Qatari} : {adze1240, ajie1238, amar1272, ambu1247, anei1239, apma1241, arak1252, arib1241, arop1243, aros1241, aulu1238, awtu1239, ayiw1239, baba1268, bahi1254, bann1247, bign1238, bili1260, boik1241, bulg1262, caro1242, cham1313, chek1238, chuu1238, dehu1237, dumb1241, dutc1256, east2443, east2447, fiji1243, futu1245, fwai1237, gapa1238, geez1241, gela1263, gilb1244, gulf1241, guma1254, hali1244, hang1263, hano1246, hmon1264, hoav1238, iaai1238, iatm1242, idak1243, idun1242, iris1253, iwam1256, juho1239, kaia1245, kair1263, kamb1297, kapi1249, kara1486, kaul1240, kela1255, kele1258, kiku1240, kili1267, kire1240, koko1269, kosr1238, kuan1247, kuan1248, kuma1276, kung1261, kwai1243, kwam1251, kwam1252, kwas1243, kwom1262, labu1248, lala1268, lame1260, lauu1247, lena1238, lese1243, lewo1242, long1395, loni1238, lonw1238, louu1245, lusi1240, maee1241, mais1250, male1289, malo1243, mana1295, mana1298, maor1246, mars1254, masa1299, matu1261, mbal1255, mbul1263, mehe1243, meke1243, mele1250, mina1269, ming1252, moch1256, moki1238, moks1248, mono1273, motl1237, motu1246, mudu1242, muri1260, muso1238, muss1246, muyu1244, naka1262, nali1244, nama1264, nami1256, natu1246, naur1243, ndon1254, neha1247, neng1238, ngan1300, niua1240, niue1239, nort2646, nort2836, nort2845, nuku1260, onto1237, paam1238, pate1247, patp1243, pile1238, ping1243, pohn1238, port1285, pulu1242, qima1242, raoo1244, rapa1244, renn1242, rotu1241, rovi1238, russ1264, saaa1240, saam1283, saka1289, sali1295, samo1305, sapo1253, scot1243, siar1238, siee1239, sina1266, sioo1240, sobe1238, sons1242, sout2642, sout2679, sout2807, sout2856, sout2866, sout2869, stan1318, sude1239, surs1246, tahi1242, tain1252, taki1248, tawa1275, tean1237, teop1238, tiga1245, tigr1271, tiri1258, toab1237, toba1266, toke1240, tong1325, tsot1241, tswa1253, tuam1242, tuml1238, tung1290, tuva1244, ulit1238, urav1235, urip1239, vinm1237, waim1251, wall1257, wata1253, west2500, west2519, woga1249, wole1240, xamt1239, xara1244, yabe1254, yess1239, yima1243, zulu1248}.

	Africa	Eurasia	America	Papunesia	Sum
No	9	100	4	7	120
Yes	27	26	6	2	61
Sum	36	126	10	9	181

Figure 58. Distribution of tone1.

Figure 59. Map of tone1.

Figure 60. Relationship between tone1, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%¹, ICC = 70.4%² (but generates warnings: Model is nearly unidentifiable: very large eigenvalue)
macroarea: R² = 23.3%, p_{macroarea/null} = 0.00082³
ASPM:
- by itself: R² = 10.0%, β = -1.00 ± 0.37, p_ASPM/null = 0.0041
- quadratic: R² = 10.7%, β_ASPM2 = -0.97 ± 0.38, p_ASPM2/ASPM = 0.6
- with macroarea: R² = 24.4%, β = -0.37 ± 0.45, p_{macroarea/ASPM} = 0.028, p_{ASPM/macroarea} = 0.42
MCPH1:
- by itself: R² = 9.4%, β = -1.04 ± 0.39, p_MCPH1/null = 0.0064
- quadratic: R² = 9.3%, β_MCPH12 = -1.01 ± 0.39, p_MCPH12/MCPH1 = 0.21
- with macroarea: R² = 24.1%, β = -0.39 ± 0.57, p_{macroarea/MCPH1} = 0.021, p_{MCPH1/macroarea} = 0.5
both alleles (no macroarea):
- ASPM + MCPH1: R² = 13.4%, β_ASPM = -0.72 ± 0.40, p_ASPM/MCPH1 = 0.074, β_MCPH1 = -0.62 ± 0.40, p_MCPH1/ASPM = 0.12, p_{ASPM+MCPH1/null} = 0.0049,
- interaction: R² = 13.2%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.86

Alleles on macroarea

To better understand this overlap between family, macroarea and the two “derived” alleles, I regressed (separately) the ASPM-D and MCPH1-D on the macroarea, using mixed-effects beta regression (after replacing all \(0.0\) values by \(10^{-7}\) and all \(1.0\) by \(1.0-10^{-7}\), respectively) with language family as random effect:

the alleles are very strongly clustered within families:
- ASPM: ICC = 100.0%
- MCPH1: ICC = 100.0%
macroarea predicts their distribution very strongly:
- ASPM: p = 3.4e-16, R² = 57.9%
- MCPH1: p = 3.1e-12, R² = 70.3%
separating Africa vs the rest of the world seems to drive most of this effect (both alleles have lower frequencies in Africa):
- ASPM: p = 2.3e-14, R² = 39.2%
- MCPH1: p = 3.2e-09, R² = 32.6%

Randomization

For these randomization analyses there are several important parameters:

Parameter	Meaning	Values
`permute`	what to permute?	`nothing` = the original data
		`tone` = permute the tone variable
		`alleles-together` = permute the two alleles together
		`alleles-independent` = permute the two alleles separately, i.e., each is independently permuted
`within`	how are the permutations constrained?	`unrestricted` = all the observations are freely permuted (i.e., there are no constraints, no structure in the data is preserved)
		`families` = only observations within the same language family are permuted (i.e., the structure of the families is preserved)
		`macroareas` = only observations within the same macroarea are permuted (i.e., the structure of the macroareas is preserved)
`macroarea`	how do we control for macroareas?	`none` = no control for macroareas at all
		`fixef` = as fixed effects

I performed 1000 independent replications of each of these parameter combinations, and below are the distributions of the permuted values versus the original ones (i.e., those obtained on the original, non-permuted data).

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	4%	6%	0%	4%	0%
unrestricted	none	alleles-together	0%	5%	4%	0%	5%	2%
unrestricted	none	alleles-independent	1%	6%	6%	0%	6%	1%
unrestricted	fixef	tone	0%	5%	5%	8%	5%	25%
unrestricted	fixef	alleles-together	68%	6%	7%	15%	4%	23%
unrestricted	fixef	alleles-independent	68%	5%	6%	16%	6%	20%
macroareas	none	tone	0%	95%	42%	4%	86%	28%
macroareas	none	alleles-together	26%	76%	10%	7%	59%	73%
macroareas	none	alleles-independent	32%	83%	20%	15%	66%	78%
macroareas	fixef	tone	0%	7%	7%	11%	6%	29%
macroareas	fixef	alleles-together	65%	5%	5%	19%	5%	35%
macroareas	fixef	alleles-independent	66%	4%	5%	20%	4%	35%
families	none	tone	2%	16%	2%	3%	14%	36%
families	none	alleles-together	2%	11%	3%	5%	5%	16%
families	none	alleles-independent	2%	16%	13%	10%	12%	20%
families	fixef	tone	1%	8%	3%	16%	11%	74%
families	fixef	alleles-together	66%	4%	5%	46%	2%	16%
families	fixef	alleles-independent	66%	3%	5%	37%	3%	22%

Regressions on 1000 permuted data. Each plot shows the original result (vertical dashed black line) and the distribution of the permutations for the three possible things to be permuted (colored curves) for each combination of permutation constraints (horizontal panels) and control for macroarea (vertical panels) in terms of the effect size β; ASPM-D is on the left and MCPH1-D on the right. The vertical dotted black thin line is at 0.0.

Restricted sampling

Figure 61. Results for 1000 restricted samplings. For ASPM-D (left): 100% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -81.1, mean = -0.81, p = 0), 82.7%, when controlling for the macroarea (t(999) = -32.0, mean = -0.45, p = 2.2e-155), and 82.2% when controlling for both macroarea and MCPH1 (t(999) = -30.5, mean = -0.45, p = 4.9e-145). For MCPH1-D (right): 100% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -107.4, mean = -0.59, p = 0), 68.7% when controlling for the macroarea (t(999) = -15.5, mean = -0.38, p = 3.9e-49), and 67.6% when controlling for both macroarea and ASPM (t(999) = -14.3, mean = -0.37, p = 1.7e-42).

`brms`

tone1 on ASPM-D and MCPH1-D in a mixed-effects Bayesian framework (using brms) with macroarea, language family and (meta)population as (nested) random effects. The ROPE is the region of practical equivalence around 0.0, usually [-0.1, 0.1] but may vary by regression type" the idea is that the HDI should have an as small intersection as possible with the ROPE. Another take is represented by the p_ROPE which is the proportion of the whole posterior distribution (i.e., 100%HDI) inside the ROPE; so, it can be interpreted like a “classic” p-value.

ASPM only:
- β = -0.69, 89%HDI = [-1.59, 0.25]
- posterior probability p(β<0) = 0.89 (evidence ratio = 7.9), p(β=0) = 0.73 (evidence ratio = 2.8)
- ROPE⁴ = [-0.18, 0.18], % HDI inside ROPE = 13.3%; p_ROPE = 0.118
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(71%:29%) K>]: moderate evidence for null against ASPM (BF=3.83), LOO=0.70 [SE=1.43], WAIC=0.92 [SE=1.19], KFOLD=4.48 [SE=3.46]⁵
MCPH1 only:
- β = -0.63, 89%HDI = [-1.66, 0.46]
- posterior probability p(β<0) = 0.83 (evidence ratio = 5), p(β=0) = 0.76 (evidence ratio = 3.2)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 15.2%; p_ROPE = 0.135
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(61%:39%) K>]: moderate evidence for null against MCPH1 (BF=3.17), LOO=-0.01 [SE=1.03], WAIC=0.45 [SE=0.77], KFOLD=2.33 [SE=2.31]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L= W=(79%:21%) K>]: moderate evidence for null against both (BF=9.56), LOO=1.30 [SE=1.53], WAIC=1.35 [SE=1.44], KFOLD=4.67 [SE=3.70]
- interaction:
  - posterior probability p(=0) = 0.82 (evidence ratio = 4.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 21.5%; p_ROPE = 0.134
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L> W=(46%:54%) K>]: moderate evidence for no interaction against with interaction (BF=3.06), LOO=0.88 [SE=0.81], WAIC=-0.14 [SE=0.46], KFOLD=6.05 [SE=3.43]
- ASPM (partial):
  - β = -0.61, 89%HDI = [-1.62, 0.32]
  - posterior probability p(β<0) = 0.84 (evidence ratio = 5.3), p(β=0) = 0.78 (evidence ratio = 3.6)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 17.6%; p_ROPE = 0.156
- MCPH1 (partial):
  - β = -0.46, 89%HDI = [-1.55, 0.78]
  - posterior probability p(β<0) = 0.75 (evidence ratio = 2.9), p(β=0) = 0.8 (evidence ratio = 4)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 19.4%; p_ROPE = 0.173

Figure 62. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 63. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 64. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 65. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Here, I try to disentangle the fact that macroarea is a very good predictor of tone1, but also of the frequency of the two alleles, from any effect that the alleles might have on tone1. For this, I conducted mediation analysis and path analysis, where I model the effect of macroarea on tone1 as partially mediated by the two alleles.

Please note that there are several technical issues with these approaches:

for mediation analysis, the method used (as implemented by function mediate in package mediation):
- cannot deal with a factor with several levels → I focused on the contrast between Africa and the rest of the world;
- cannot deal with language family as random effect → I use “flat” regressions throughout, but I did perform restricted sampling as well as a method to control for family.
to adress these issues, I also conducted Bayesian mediation analysis (using brms) with logistic regression for the outcome, beta regression for the “derived” allele frequencies, and family and (meta)population as random effects (the macroarea cannot be a random effect as it is the treatment as Africa vs the rest of the world).
for path analysis, the method used (as implemented by function sem with robust estimators in package lavaan):
- cannot deal with binary variables unless they are either converted to numeric (0 vs 1) or ordered (i.e., assume that there is an intrinsic ordering between the two values), affecting both the binary contrast between Africa and the rest of the world (coded as Africa=1, or ordered as “rest of the world” < “Africa”) and tone1 (coded as Yes=1, or No < Yes); I tested both codings separately;
- cannot deal with language family as random effect, but I did perform restricted sampling as well as a method to control for family.

Mediation analysis

Figure 66. Graphical representation of the mediation model for the two alleles considered separately. Blue = direct effect of macroarea on tone1; red = indirect effect mediatated by the alleles.

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.49 (0.33, 0.63), p=0, decomposed into:
average direct effect (ADE): 0.27 (0.08, 0.47), p=0.008, and
average indirect effect (ACME) mediated by ASPM-D: 0.22 (0.11, 0.34), p=0, mediating 44.9% (19.1%, 79.5%), p=0 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.25 ±0.16, p=7.7e-13, and
- effect of ASPM-D on tone: -0.90 ±0.24, p=0.00015.

For MCPH1-D:

TE: 0.50 (0.34, 0.65), p=0, decomposed into:
ADE: 0.55 (0.19, 0.75), p=0.002, and
ACME: -0.05 (-0.22, 0.25), p=0.49, mediating -14.7% (-51.3%, 56.8%), p=0.49 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.19 ±0.09, p=9.9e-59, and
- effect of MCPH1-D on tone: 0.20 ±0.38, p=0.6.

Restricted sampling

Figure 67. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM-D and MCPH1-D; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (solid), 0.05 (dashed) and 0.10 (dotted).

For ASPM-D:

TE: mean = 0.38, median = 0.38; 44.5% significant at α-level 0.05 and 72.8% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 134.2, p = 0;
ADE: mean = 0.28, median = 0.28; 8.2% significant at α-level 0.05 and 29.6% significant at α-level 0.10; 99.6% > 0.0; one-sample one-sided t-test vs 0: t(999) = 87.2, p = 0;
ACME: mean = 0.094, median = 0.091; 3.6% significant at α-level 0.05 and 20.1% significant at α-level 0.10; 99.5% > 0.0; one-sample one-sided t-test vs 0: t(999) = 61.4, p = 0;
β(Africa → allele): mean = -0.86, median = -0.87; 79.8% significant at α-level 0.05 and 96.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -211.9, p = 0;
β(allele → tone | Africa): mean = -0.61, median = -0.6; 10.2% significant at α-level 0.05 and 27.7% significant at α-level 0.10; 99.1% < 0.0; one-sample one-sided t-test vs 0: t(999) = -60.0, p = 0.

For MCPH1-D:

TE: mean = 0.38, median = 0.39; 44.3% significant at α-level 0.05 and 72.6% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 133.1, p = 0;
ADE: mean = 0.41, median = 0.44; 6.0% significant at α-level 0.05 and 18.9% significant at α-level 0.10; 96.9% > 0.0; one-sample one-sided t-test vs 0: t(999) = 74.0, p = 0;
ACME: mean = -0.029, median = -0.052; 0.1% significant at α-level 0.05 and 1.4% significant at α-level 0.10; 35.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = -6.2, p = 1;
β(Africa → allele): mean = -2.5, median = -2.5; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -884.5, p = 0;
β(allele → tone | Africa): mean = 0.42, median = 0.42; 0.2% significant at α-level 0.05 and 1.5% significant at α-level 0.10; 25.5% < 0.0; one-sample one-sided t-test vs 0: t(999) = 21.4, p = 1.

Given the low sample size N = 35 unique families, relatively few effect sizes are big enough to be significant for each individual analysis; however, there are many more significant ACMEs for ASPM-D than for MCPH1-D: 10.2% vs 0.2% (51.0 times) for α-level 0.05, and 27.7% vs 1.5% (18.5 times) for α-level 0.10.

`brms`

Figure 68. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 69. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 70. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

All data

With Africa and tone1 coded numerically, the model fits the data very well⁶ (χ²(1)=0.22, p=0.64; CFI=1.00, TLI=1.01, NNFI=1.01 and RFI=1.00):

Figure 71. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as numeric binary (tone_bin_num with Yes=1 and Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

## lavaan 0.6-8 ended normally after 25 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         8
##                                                       
##   Number of observations                           181
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 0.225
##   Degrees of freedom                                 1
##   P-value (Chi-square)                           0.635
## 
## Model Test Baseline Model:
## 
##   Test statistic                               371.522
##   Degrees of freedom                                 6
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.013
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -448.206
##   Loglikelihood unrestricted model (H1)       -448.094
##                                                       
##   Akaike (AIC)                                 912.413
##   Bayesian (BIC)                               938.000
##   Sample-size adjusted Bayesian (BIC)          912.664
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.154
##   P-value RMSEA <= 0.05                          0.704
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.005
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   tone_bin_num ~                                                        
##     Africa_num        0.390    0.166    2.351    0.019    0.065    0.716
##     ASPM_z           -0.144    0.035   -4.163    0.000   -0.212   -0.076
##     MCPH1_z           0.025    0.061    0.410    0.682   -0.095    0.145
##   ASPM_z ~                                                              
##     Africa_num       -1.249    0.111  -11.254    0.000   -1.467   -1.032
##   MCPH1_z ~                                                             
##     Africa_num       -2.190    0.081  -27.039    0.000   -2.349   -2.031
##    Std.lv  Std.all
##                   
##     0.390    0.330
##    -0.144   -0.305
##     0.025    0.053
##                   
##    -1.249   -0.500
##                   
##    -2.190   -0.877
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .tone_bin_num      0.165    0.015   10.844    0.000    0.135    0.195
##    .ASPM_z            0.746    0.074   10.144    0.000    0.602    0.890
##    .MCPH1_z           0.230    0.039    5.899    0.000    0.154    0.307
##    Std.lv  Std.all
##     0.165    0.740
##     0.746    0.750
##     0.230    0.232
## 
## R-Square:
##                    Estimate
##     tone_bin_num      0.260
##     ASPM_z            0.250
##     MCPH1_z           0.768

Likewise, with Africa and tone1 coded as ordered binary factors, the model also fits the data very well (χ²(1)=0.57, p=0.45; CFI=1.00, TLI=1.07, NNFI=1.07 and RFI=0.92):

Figure 72. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as ordered binary factors (tone_bin_ord with No < Yes, and Africa_ord with outside Africa < in Africa); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Restricted sampling

Here I use only the numerical coding.

Figure 73. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

models fits:
- 94.7% of the p-values are not significant
- mean(CFI) = 0.99, median(CFI) = 1, sd(CFI) = 0.01, IQR(CFI) = 0.02
- mean(TLI) = 0.97, median(TLI) = 0.99, sd(TLI) = 0.1, IQR(TLI) = 0.16
- mean(NNFI) = 0.97, median(NNFI) = 0.99, sd(NNFI) = 0.1, IQR(NNFI) = 0.16
- mean(RFI) = 0.9, median(RFI) = 0.92, sd(RFI) = 0.09, IQR(RFI) = 0.14
Africa → ASPM-D: mean = -0.87, median = -0.89, sd = 0.12, IQR = 0.17, 100.0% < 0; 98.7% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -2.2e+02, p = 0;
Africa → MCPH1-D: mean = -2.5, median = -2.5, sd = 0.086, IQR = 0.12, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -9e+02, p = 0;
Africa → tone1: mean = 0.43, median = 0.44, sd = 0.32, IQR = 0.46, 89.5% > 0; 12.8% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 41, p = 3.2e-219;
ASPM-D → tone1: mean = -0.11, median = -0.11, sd = 0.058, IQR = 0.089, 98.6% < 0; 36.2% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -62, p = 0;
MCPH1-D → tone1: mean = 0.041, median = 0.041, as = 0.11, IQR = 0.17, 36.7% < 0; 0.9% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 11, p = 1.

Machine Learning techniques

Here I apply various “machine learning” techniques to explore how well the macroarea and the two alleles predict tone1. For these techniques, in general I:

fit the model to the full data and estimate how well these modes fit, but also
repeatedly split the data into a training set the complementary test set; the first usually contains a random subset of 80% of the data and is used to fit the model, while the second, containing the remaining 20% of the data, is used to check how well the model generalizes to new data.

Thus, these techniques can:

quantify the amount of information about tone contained by macroarea and the alleles,
but also give an estimate of the relative importance of these variables as predictors.

Decision trees

Including macroarea

Using the frequency of the two alleles and the macroarea as predictors, the fit to the data is: accuracy = 77.3%, sensitivity = 71.7%, specificity = 79.3%, precision = 54.1%, and recall = 71.7%.

Figure 74. Decision tree on the full data using the two alleles and macroarea. ASPM.D = ASPM-D.

On the 100 training/testing sets, the fit is: accuracy = 77.1% ±6.6%, sensitivity = 71.6% ±15.2%, specificity = 79.3% ±6.8%, precision = 52.9% ±12.4%, recall = 71.6% ±15.2%.

Figure 75. The success of generalising to the testing sets from the training sets (yellow boxplots) compared to the success on the full data (red segments).

Excluding macroarea

When using the frequency of the two alleles only as predictors, the fit to the data is: accuracy = 75.1%, sensitivity = 75.0%, specificity = 75.2%, precision = 39.3%, and recall = 75.0%:

Figure 76. Decision tree on the full data using the two alleles only. ASPM.D = ASPM-D, MCPH1.D = MCPH1-D.

On the 100 training/testing sets,the fit is: accuracy = 70.1% ±7.6%, sensitivity = 61.3% ±19.1%, specificity = 76.2% ±8.7%, precision = 44.0% ±23.0%, recall = 61.3% ±19.1%.

Figure 77. The success of generalising to the testing sets from the training sets (yellow boxplots) compared to the success on the full data (red segments).

Random forests

I use two methods: random forests as implemented by randomForest() in package randomForest, and conditional random forests as implemented by cforest() in package partykit. As (conditional) random forests do internal bootstrapping, there is no need for the explicit training/testing set repeated refitting.

Including macroarea

When using the frequency of the two alleles and the macroarea as predictors, the models fit to the full data is:

random forests: accuracy = 77.7% ±0.8%, sensitivity = 68.9% ±1.9%, specificity = 81.6% ±0.4%, precision = 62.0% ±1.0%, recall = 68.9% ±1.9%,
conditional random forests: accuracy = 84.3% ±0.7%, sensitivity = 78.8% ±0.5%, specificity = 86.8% ±0.9%, precision = 73.0% ±2.0%, recall = 78.8% ±0.5%.

Figure 78. The success of the two random forest methods on the full data.

Figure 79. Variable importance using three methods: mean decrease in accuracy, mean decrease of the Gini coeficient, and unconditional importance. ASPM_freq_wavg = ASPM-D, MCPH1_freq_wavg = MCPH1-D.

Excluding macroarea

When using the frequency of the two alleles only, the models fit the full as:

random forests: accuracy = 70.7% ±1.0%, sensitivity = 56.3% ±1.4%, specificity = 78.6% ±0.8%, precision = 59.0% ±1.8%, recall = 56.3% ±1.4%,
conditional random forests: accuracy = 82.1% ±0.5%, sensitivity = 81.8% ±0.7%, specificity = 82.3% ±0.6%, precision = 60.5% ±1.6%, recall = 81.8% ±0.7%.

Figure 80. The success of the two random forest methods on the full data.

Figure 81. Variable importance using three methods: mean decrease in accuracy, mean decrease of the Gini coeficient, and unconditional importance. ASPM_freq_wavg = ASPM-D, MCPH1_freq_wavg = MCPH1-D.

Diachronic analyses

Here I try various analyses that explicitly take into account the diachronic nature of the processes.

The families with more than 2 tips are:

Figure 82. Phylogenies with tone1 (0=“No,” 1=“Yes,” ASPM-D and MCHP1-D for the families with at least 2 languages.

It can be seen that, unfortunately, there are very few families with more than 2 languages with data (17), and even for those with relatively many languages, there is very little variation in tone1 and in the frequencies of the two “derived” alleles. Unfortunately, combined with the issues concerning branch length for language family trees, this precludes the estimation of correlated evolution or phylogenetic regression methods.

tone2 (is there complex tone?)

I kept only the entries with non-missing data for the tone2, ASPM-D and MCPH1-D, and if there are more than one possible languages or allele frequencies for a given sample, I only kept those entries that have different tone or allele data. The resulting dataset has 180 observations, distributed among 118 unique Glottolg codes in 35 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 5.1 and median 2 languages per family) and 4 macroareas.

There are 156:121:118 unique samples:(meta)populations:languages retained, dropping 19:8:203 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari, SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Bulgarian, Burunge, Dutch, Hazara, Mozabite, Oroqen, Qatari, Xibe} : {adze1240, ajie1238, amar1272, ambu1247, anei1239, apma1241, arak1252, arib1241, arop1243, aros1241, aulu1238, awtu1239, ayiw1239, baba1268, bahi1254, bann1247, bign1238, bili1260, boik1241, bulg1262, buru1320, caro1242, cham1313, chek1238, chuu1238, dehu1237, dumb1241, dutc1256, east2443, east2447, efee1239, fiji1243, futu1245, gapa1238, geez1241, gela1263, gilb1244, gulf1241, guma1254, gyel1242, hali1244, hang1263, hano1246, haza1239, hmon1264, hoav1238, iaai1238, iatm1242, idak1243, idun1242, iris1253, iwam1256, juho1239, kaia1245, kair1263, kamb1297, kapi1249, kara1486, kaul1240, kela1255, kele1258, kili1267, kire1240, koko1269, kosr1238, kuan1247, kuan1248, kuma1276, kung1261, kwai1243, kwam1251, kwam1252, kwom1262, labu1248, lala1268, lame1260, lauu1247, lena1238, lewo1242, long1395, loni1238, lonw1238, louu1245, lusi1240, maee1241, mais1250, male1289, malo1243, mana1295, mana1298, maor1246, mars1254, masa1299, matu1261, mbal1255, mbul1263, mehe1243, meke1243, mele1250, mina1269, ming1252, moch1256, moki1238, moks1248, mono1273, motl1237, motu1246, mudu1242, muri1260, muso1238, muss1246, muyu1244, naka1262, nali1244, nami1256, natu1246, naur1243, ndon1254, neha1247, neng1238, ngan1300, niua1240, niue1239, nort2646, nort2836, nort2845, nuku1260, onto1237, oroq1238, paam1238, pate1247, patp1243, pile1238, ping1243, pohn1238, port1285, pulu1242, qima1242, raoo1244, rapa1244, renn1242, rotu1241, rovi1238, russ1264, saaa1240, saam1283, saka1289, sali1295, samo1305, sapo1253, scot1243, siar1238, siee1239, sina1266, sioo1240, sobe1238, sons1242, sout2642, sout2679, sout2807, sout2856, sout2866, sout2869, stan1318, sude1239, surs1246, tahi1242, tain1252, taki1248, tawa1275, tean1237, teop1238, tiga1245, tigr1271, tiri1258, toab1237, toba1266, toke1240, tong1325, tswa1253, tuam1242, tuml1238, tumz1238, tung1290, tuva1244, ulit1238, urav1235, urip1239, vinm1237, waim1251, wall1257, wata1253, west2500, west2519, woga1249, wole1240, xamt1239, xara1244, xibe1242, yabe1254, yess1239, yima1243, zulu1248}.

	Africa	Eurasia	America	Papunesia	Sum
No	28	105	9	9	151
Yes	9	18	1	1	29
Sum	37	123	10	10	180

Figure 83. Distribution of tone2.

Figure 84. Map of tone2.

Figure 85. Relationship between tone2, ASPM-D and MCPH1-D.

Please note that the distribution of this variable is very skewed, so the results might not be very solid…

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 95.6%
macroarea: R² = 2.0%, p_{macroarea/null} = 0.5
ASPM:
- by itself: R² = 1.3%, β = -0.87 ± 0.69, p_ASPM/null = 0.19
- quadratic: R² = 36.6%, β_ASPM2 = -3.46 ± 2.31, p_ASPM2/ASPM = 0.049
- with macroarea: R² = 2.6%, p_{macroarea/ASPM} = 0.8, p_{ASPM/macroarea} = 0.55
MCPH1:
- by itself: R² = 1.5%, β = -1.01 ± 0.73, p_MCPH1/null = 0.16
- quadratic: R² = 3.0%, β_MCPH12 = -1.17 ± 0.81, p_MCPH12/MCPH1 = 0.22
- with macroarea: R² = 2.4%, p_{macroarea/MCPH1} = 0.89, p_{MCPH1/macroarea} = 0.62
both alleles (no macroarea):
- ASPM + MCPH1: R² = 2.0%, β_ASPM = -0.56 ± 0.78, p_ASPM/MCPH1 = 0.47, β_MCPH1 = -0.68 ± 0.81, p_MCPH1/ASPM = 0.39, p_{ASPM+MCPH1/null} = 0.29,
- interaction: R² = 1.5%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.76

Randomization

Regressions with randomizations for *tone2*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	4%	4%	1%	6%	0%
unrestricted	none	alleles-together	31%	7%	6%	10%	6%	6%
unrestricted	none	alleles-independent	32%	7%	7%	9%	6%	4%
unrestricted	fixef	tone	0%	6%	6%	6%	7%	23%
unrestricted	fixef	alleles-together	84%	7%	7%	17%	7%	25%
unrestricted	fixef	alleles-independent	83%	9%	8%	16%	7%	21%
macroareas	none	tone	0%	4%	3%	1%	10%	1%
macroareas	none	alleles-together	40%	7%	5%	21%	6%	42%
macroareas	none	alleles-independent	44%	8%	6%	28%	10%	45%
macroareas	fixef	tone	0%	4%	4%	7%	4%	22%
macroareas	fixef	alleles-together	80%	8%	8%	28%	7%	38%
macroareas	fixef	alleles-independent	80%	9%	8%	25%	8%	37%
families	none	tone	31%	4%	4%	28%	1%	16%
families	none	alleles-together	20%	4%	5%	29%	1%	15%
families	none	alleles-independent	24%	4%	6%	25%	3%	22%
families	fixef	tone	45%	8%	9%	54%	4%	43%
families	fixef	alleles-together	80%	4%	6%	43%	3%	18%
families	fixef	alleles-independent	80%	5%	7%	34%	4%	24%

Restricted sampling

Figure 86. Results for 1000 restricted samplings. For ASPM-D (left): 99.6% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -77.3, mean = -0.61, p = 0), 99.8%, when controlling for the macroarea (t(999) = -75.6, mean = -0.96, p = 0), and 99.9% when controlling for both macroarea and MCPH1 (t(999) = -70.9, mean = -1.08, p = 0). For MCPH1-D (right): 72.9% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -21.7, mean = -0.16, p = 7.8e-86), 42.9% when controlling for the macroarea (t(999) = 9.6, mean = 0.30, p = 1), and 35.1% when controlling for both macroarea and ASPM (t(999) = 17.1, mean = 0.67, p = 1).

`brms`

ASPM only:
- β = -1.27, 89%HDI = [-2.73, 0.17]
- posterior probability p(β<0) = 0.93 (evidence ratio = 14), p(β=0) = 0.57 (evidence ratio = 1.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 6.1%; p_ROPE = 0.055
- comparison ‘null’ vs ‘ASPM’: [B= L> W=(53%:47%) K=]: anecdotal evidence for null against ASPM (BF=1.46), LOO=1.84 [SE=1.14], WAIC=0.10 [SE=1.16], KFOLD=-0.80 [SE=2.10]
MCPH1 only:
- β = -0.91, 89%HDI = [-2.38, 0.58]
- posterior probability p(β<0) = 0.85 (evidence ratio = 5.5), p(β=0) = 0.7 (evidence ratio = 2.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 10.9%; p_ROPE = 0.097
- comparison ‘null’ vs ‘MCPH1’: [B= L= W=(41%:59%) K<]: anecdotal evidence for null against MCPH1 (BF=1.63), LOO=0.25 [SE=0.64], WAIC=-0.36 [SE=0.73], KFOLD=-2.43 [SE=1.67]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L= W=(30%:70%) K=]: moderate evidence for null against both (BF=3.66), LOO=0.13 [SE=1.39], WAIC=-0.87 [SE=1.44], KFOLD=-1.33 [SE=2.11]
- interaction:
  - posterior probability p(=0) = 0.75 (evidence ratio = 3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 15.1%; p_ROPE = 0.134
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L> W=(57%:43%) K>]: moderate evidence for no interaction against with interaction (BF=3.65), LOO=1.16 [SE=1.00], WAIC=0.29 [SE=0.39], KFOLD=2.31 [SE=1.26]
- ASPM (partial):
  - β = -1.13, 89%HDI = [-2.71, 0.60]
  - posterior probability p(β<0) = 0.87 (evidence ratio = 6.8), p(β=0) = 0.66 (evidence ratio = 1.9)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 9%; p_ROPE = 0.08
- MCPH1 (partial):
  - β = -0.58, 89%HDI = [-2.21, 0.99]
  - posterior probability p(β<0) = 0.73 (evidence ratio = 2.7), p(β=0) = 0.75 (evidence ratio = 3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 13.7%; p_ROPE = 0.122

Figure 87. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 88. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 89. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 90. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.14 (-0.01, 0.30), p=0.078, decomposed into:
average direct effect (ADE): -0.05 (-0.20, 0.10), p=0.43, and
average indirect effect (ACME) mediated by ASPM-D: 0.19 (0.08, 0.31), p=0.004, mediating 133.8% (-419.6%, 802.0%), p=0.082 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.34 ±0.16, p=3.7e-15, and
- effect of ASPM-D on tone: -1.03 ±0.31, p=0.0011.

For MCPH1-D:

TE: 0.11 (-0.02, 0.27), p=0.12, decomposed into:
ADE: 0.12 (-0.21, 0.45), p=0.47, and
ACME: -0.01 (-0.29, 0.29), p=0.9, mediating -11.4% (-804.5%, 1112.4%), p=0.93 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.19 ±0.09, p=1.2e-61, and
- effect of MCPH1-D on tone: 0.03 ±0.45, p=0.94.

Restricted sampling

Figure 91. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM and MCPH1; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (solid), 0.05 (dashed) and 0.10 (dotted).

For ASPM-D:

TE: mean = 0.11, median = 0.12; 0.4% significant at α-level 0.05 and 2.3% significant at α-level 0.10; 89.6% > 0.0; one-sample one-sided t-test vs 0: t(999) = 39.7, p = 5.9e-208;
ADE: mean = 0.04, median = 0.039; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 67.3% > 0.0; one-sample one-sided t-test vs 0: t(999) = 16.0, p = 7.9e-52;
ACME: mean = 0.072, median = 0.07; 0.0% significant at α-level 0.05 and 0.1% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 78.5, p = 0;
β(Africa → allele): mean = -0.88, median = -0.89; 88.6% significant at α-level 0.05 and 98.7% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -249.8, p = 0;
β(allele → tone | Africa): mean = -0.58, median = -0.57; 0.0% significant at α-level 0.05 and 0.4% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -79.8, p = 0.

For MCPH1-D:

TE: mean = 0.11, median = 0.11; 0.2% significant at α-level 0.05 and 2.3% significant at α-level 0.10; 82.1% > 0.0; one-sample one-sided t-test vs 0: t(999) = 37.1, p = 1.3e-190;
ADE: mean = 0.13, median = 0.14; 0.0% significant at α-level 0.05 and 0.7% significant at α-level 0.10; 75.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 24.8, p = 2.3e-106;
ACME: mean = -0.028, median = -0.034; 0.0% significant at α-level 0.05 and 0.3% significant at α-level 0.10; 43.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = -5.4, p = 1;
β(Africa → allele): mean = -2.4, median = -2.4; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -927.9, p = 0;
β(allele → tone | Africa): mean = 0.26, median = 0.21; 0.0% significant at α-level 0.05 and 0.1% significant at α-level 0.10; 38.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = 11.3, p = 1.

`brms`

Figure 92. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 93. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 94. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

All data

Coding Africa and tone2 numerically, the model fit is: χ²(1)=0.36, p=0.55; CFI=1.00, TLI=1.01, NNFI=1.01 and RFI=0.99.

Figure 95. Path analysis model with standardised coefficients and significance stars. Here, we coded tone and macroarea (Africa vs non-Africa) as numeric binary (tone_complex_num with Yes=1 and Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

## lavaan 0.6-8 ended normally after 25 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         8
##                                                       
##   Number of observations                           180
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 0.361
##   Degrees of freedom                                 1
##   P-value (Chi-square)                           0.548
## 
## Model Test Baseline Model:
## 
##   Test statistic                               354.897
##   Degrees of freedom                                 6
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.011
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -407.836
##   Loglikelihood unrestricted model (H1)       -407.655
##                                                       
##   Akaike (AIC)                                 831.671
##   Bayesian (BIC)                               857.215
##   Sample-size adjusted Bayesian (BIC)          831.879
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.166
##   P-value RMSEA <= 0.05                          0.630
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.006
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                      Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   tone_complex_num ~                                                      
##     Africa_num         -0.051    0.139   -0.366    0.714   -0.322    0.221
##     ASPM_z             -0.108    0.026   -4.124    0.000   -0.159   -0.056
##     MCPH1_z            -0.005    0.050   -0.093    0.926   -0.102    0.093
##   ASPM_z ~                                                                
##     Africa_num         -1.338    0.101  -13.315    0.000   -1.535   -1.141
##   MCPH1_z ~                                                               
##     Africa_num         -2.189    0.072  -30.443    0.000   -2.330   -2.048
##    Std.lv  Std.all
##                   
##    -0.051   -0.056
##    -0.108   -0.292
##    -0.005   -0.013
##                   
##    -1.338   -0.542
##                   
##    -2.189   -0.887
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .tone_complx_nm    0.125    0.016    7.848    0.000    0.094    0.157
##    .ASPM_z            0.702    0.072    9.767    0.000    0.561    0.843
##    .MCPH1_z           0.212    0.037    5.748    0.000    0.140    0.284
##    Std.lv  Std.all
##     0.125    0.927
##     0.702    0.706
##     0.212    0.213
## 
## R-Square:
##                    Estimate
##     tone_complx_nm    0.073
##     ASPM_z            0.294
##     MCPH1_z           0.787

Coding Africa and tone2 as ordered binary factors, the model fit is: χ²(1)=0.98, p=0.32; CFI=1.00, TLI=1.01, NNFI=1.01 and RFI=0.79.

Figure 96. Path analysis model with standardised coefficients and significance stars. Here, we coded tone and macroarea (Africa vs non-Africa) as ordered binary factors (tone_complex_ord with No < Yes, and Africa_ord with outside Africa < in Africa); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Restricted sampling

Here I use here only the numerically-coded model.

Figure 97. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

It can be seen that:

the models fit are:
- 97.6% of the p-values are not significant
- mean(CFI) = 0.99, median(CFI) = 1, sd(CFI) = 0.01, IQR(CFI) = 0.01
- mean(TLI) = 0.98, median(TLI) = 0.99, sd(TLI) = 0.1, IQR(TLI) = 0.15
- mean(NNFI) = 0.98, median(NNFI) = 0.99, sd(NNFI) = 0.1, IQR(NNFI) = 0.15
- mean(RFI) = 0.9, median(RFI) = 0.92, sd(RFI) = 0.09, IQR(RFI) = 0.13
Africa → ASPM-D: mean = -0.89, median = -0.9, sd = 0.11, IQR = 0.15, 100.0% < 0; 99.8% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -2.5e+02, p = 0;
Africa → MCPH1-D: mean = -2.4, median = -2.4, sd = 0.079, IQR = 0.11, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -9.6e+02, p = 0;
Africa → tone2: mean = 0.039, median = 0.021, sd = 0.26, IQR = 0.37, 53.6% > 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 4.7, p = 1.2e-06;
ASPM-D → tone2: mean = -0.071, median = -0.071, sd = 0.027, IQR = 0.037, 99.8% < 0; 5.9% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -83, p = 0;
MCPH1-D → tone2: mean = -0.00016, median = -0.0016, as = 0.1, IQR = 0.14, 50.8% < 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -0.051, p = 0.48.

Machine Learning techniques

Decision trees

When using the frequency of the two alleles and the macroarea as predictors, the decision tree is trivial: it uniformly predicts just the majority value “No.”

Figure 98. Decision tree on the full data using the two alleles and macroarea.

accuracy = 83.9%, sensitivity = NA%, specificity = 83.9%, precision = 0.0%, and recall = NA%.

On the 100 training/testing sets: accuracy = 82.9% ±5.8%, sensitivity = 15.8% ±9.0%, specificity = 83.5% ±5.3%, precision = 0.8% ±4.4%, recall = 15.8% ±9.0%.

Figure 99. The success of generalising to the testing sets from the training sets (yellow boxplots) compared to the success on the full data (red segments).

Random forests

Including macroarea

random forests: accuracy = 84.2% ±0.5%, sensitivity = 58.4% ±11.2%, specificity = 84.9% ±0.4%, precision = 8.8% ±2.6%, recall = 58.4% ±11.2%
conditional random forests: accuracy = 87.2% ±0.7%, sensitivity = 97.5% ±4.8%, specificity = 86.9% ±0.7%, precision = 21.2% ±5.2%, recall = 97.5% ±4.8%

Figure 100. The success of the two random forest methods on the full data.

Figure 101. Variable importance using three methods: mean decrease in accuracy, mean decrease of the Gini coeficient, and unconditional importance.

Excluding macroarea

random forests: accuracy = 82.2% ±1.0%, sensitivity = 42.8% ±4.4%, specificity = 87.3% ±0.6%, precision = 30.3% ±3.5%, recall = 42.8% ±4.4%
conditional random forests: accuracy = 87.3% ±0.2%, sensitivity = 81.2% ±3.1%, specificity = 87.7% ±0.0%, precision = 27.6% ±0.0%, recall = 81.2% ±3.1%

Figure 102. The success of the two random forest methods on the full data.

Figure 103. Variable importance using three methods: mean decrease in accuracy, mean decrease of the Gini coeficient, and unconditional importance.

Tone counts

Here the imputed counts are rounded to the nearest integer; please see below for using the actually predicted values.

I kept only the entries with non-missing data for the tone counts, ASPM-D and MCPH1-D, and if there are more than one possible languages or allele frequencies for a given sample, I only kept those entries that have different tone or allele data. The resulting dataset has 184 observations, distributed among 121 unique Glottolg codes in 35 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 5.3 and median 2 languages per family) and 4 macroareas.

There are 156:121:121 unique samples:(meta)populations:languages retained, dropping 19:8:200 = {FINRISK, GenDan, GenNed5, gnomAD_asj, gnomAD_bgr, gnomAD_est, gnomAD_fin, gnomAD_jpn, gnomAD_kor, gnomAD_swe, gnomADexomes_AshkenaziJewish, gnomADgenomes_AshkenaziJewish, KRGDB, Qatari, SA001471N, SA001477T, SA001487U, SA001491P, SA001681Q} : {Bulgarian, Burunge, Dutch, Hazara, Mozabite, Oroqen, Qatari, Xibe} : {adze1240, ajie1238, amar1272, ambu1247, anei1239, apma1241, arak1252, arib1241, arop1243, aros1241, aulu1238, awtu1239, ayiw1239, baba1268, bahi1254, bann1247, bign1238, bili1260, boik1241, bulg1262, buru1320, caro1242, cham1313, chek1238, chuu1238, dehu1237, dumb1241, dutc1256, east2443, east2447, efee1239, fiji1243, futu1245, gapa1238, geez1241, gela1263, gilb1244, gulf1241, guma1254, gyel1242, hali1244, hang1263, hano1246, haza1239, hoav1238, iaai1238, iatm1242, idak1243, idun1242, iris1253, iwam1256, juho1239, kaia1245, kair1263, kamb1297, kapi1249, kara1486, kaul1240, kela1255, kele1258, kili1267, kire1240, koko1269, kosr1238, kuan1248, kuma1276, kung1261, kwai1243, kwam1251, kwam1252, kwom1262, labu1248, lala1268, lame1260, lauu1247, lena1238, lewo1242, long1395, loni1238, lonw1238, louu1245, lusi1240, maee1241, mais1250, male1289, malo1243, mana1295, mana1298, maor1246, mars1254, masa1299, matu1261, mbal1255, mbul1263, mehe1243, meke1243, mele1250, mina1269, ming1252, moch1256, moki1238, moks1248, mono1273, motl1237, motu1246, mudu1242, muri1260, muso1238, muss1246, muyu1244, naka1262, nali1244, nami1256, natu1246, naur1243, ndon1254, neha1247, neng1238, ngan1300, niua1240, niue1239, nort2646, nort2836, nort2845, nuku1260, onto1237, oroq1238, paam1238, pate1247, patp1243, pile1238, ping1243, pohn1238, port1285, pulu1242, qima1242, raoo1244, rapa1244, renn1242, rotu1241, rovi1238, russ1264, saaa1240, saam1283, saka1289, sali1295, samo1305, sapo1253, scot1243, siar1238, siee1239, sina1266, sioo1240, sobe1238, sons1242, sout2642, sout2679, sout2807, sout2856, sout2866, sout2869, stan1318, sude1239, surs1246, tahi1242, taki1248, tawa1275, tean1237, teop1238, tiga1245, tigr1271, tiri1258, toab1237, toba1266, toke1240, tong1325, tswa1253, tuam1242, tuml1238, tumz1238, tung1290, tuva1244, ulit1238, urav1235, urip1239, vinm1237, waim1251, wall1257, wata1253, west2500, west2519, woga1249, wole1240, xamt1239, xara1244, xibe1242, yabe1254, yess1239, yima1243, zulu1248}.

	Africa	Eurasia	America	Papunesia	Sum
0	9	98	4	7	118
1	10	6	5	1	22
2	16	3	0	2	21
3	2	5	0	0	7
4	0	8	1	0	9
5	1	4	0	0	5
6	0	2	0	0	2
Sum	38	126	10	10	184

Figure 104. Distribution of tone counts.

Figure 105. Distribution of tone counts across the world.

Figure 106. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

Regressions

I used a mixed-effects Poisson model.

`glmer`

All data

null model: R² = 0.0%, ICC = 100.0%
the Poisson model is not overdispersed: χ²(182) = 112.6, p = 1
macroarea: R² = 23.8%, p_{macroarea/null} = 0.013
ASPM:
- by itself: R² = 7.6%, β = -0.37 ± 0.19, p_ASPM/null = 0.061
- quadratic: R² = 17.9%, β_ASPM2 = -0.42 ± 0.21, p_ASPM2/ASPM = 0.12
- with macroarea: R² = 24.8%, p_{macroarea/ASPM} = 0.058, p_{ASPM/macroarea} = 0.66
MCPH1:
- by itself: R² = 9.9%, β = -0.46 ± 0.19, p_MCPH1/null = 0.016
- quadratic: R² = 10.9%, β_MCPH12 = -0.45 ± 0.19, p_MCPH12/MCPH1 = 0.19
- with macroarea: R² = 24.1%, p_{macroarea/MCPH1} = 0.15, p_{MCPH1/macroarea} = 0.64
both alleles (no macroarea):
- ASPM + MCPH1: R² = 15.7%, β_ASPM = -0.27 ± 0.20, p_ASPM/MCPH1 = 0.18, β_MCPH1 = -0.37 ± 0.19, p_MCPH1/ASPM = 0.043, p_{ASPM+MCPH1/null} = 0.022,
- interaction: R² = 15.4%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.86

Randomization

We performed 1000 independent replications:

Regressions with randomizations for tone *counts*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	18%	14%	4%	13%	2%
unrestricted	none	alleles-together	1%	2%	3%	0%	3%	0%
unrestricted	none	alleles-independent	1%	3%	4%	0%	3%	0%
unrestricted	fixef	tone	0%	23%	16%	33%	19%	30%
unrestricted	fixef	alleles-together	81%	2%	3%	16%	3%	12%
unrestricted	fixef	alleles-independent	81%	4%	3%	13%	4%	6%
macroareas	none	tone	0%	44%	19%	12%	31%	7%
macroareas	none	alleles-together	18%	36%	8%	6%	34%	20%
macroareas	none	alleles-independent	20%	34%	12%	7%	37%	19%
macroareas	fixef	tone	0%	31%	23%	33%	21%	35%
macroareas	fixef	alleles-together	79%	3%	4%	23%	4%	26%
macroareas	fixef	alleles-independent	81%	4%	4%	24%	4%	26%
families	none	tone	24%	19%	14%	28%	8%	8%
families	none	alleles-together	9%	16%	12%	32%	4%	4%
families	none	alleles-independent	10%	20%	20%	40%	8%	8%
families	fixef	tone	18%	7%	9%	63%	2%	54%
families	fixef	alleles-together	83%	4%	8%	61%	2%	5%
families	fixef	alleles-independent	82%	5%	7%	59%	2%	11%

Restricted sampling

Figure 107. Results for 1000 restricted samplings. For ASPM-D (left): 100% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -81.5, mean = -0.48, p = 0), 96.7%, when controlling for the macroarea (t(999) = -52.9, mean = -0.48, p = 4.6e-292), and 96.7% when controlling for both macroarea and MCPH1 (t(999) = -53.5, mean = -0.52, p = 5e-296). For MCPH1-D (right): 99.2% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -70.7, mean = -0.25, p = 0), 50.5% when controlling for the macroarea (t(999) = 2.8, mean = 0.05, p = 1), and 38.2% when controlling for both macroarea and ASPM (t(999) = 12.6, mean = 0.24, p = 1).

`brms`

ASPM only:
- β = -0.25, 89%HDI = [-0.64, 0.17]
- posterior probability p(β<0) = 0.84 (evidence ratio = 5.2), p(β=0) = 0.88 (evidence ratio = 7.5)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 21%; p_ROPE = 0.187
- comparison ‘null’ vs ‘ASPM’: [B> L= W>(71%:29%) K>]: moderate evidence for null against ASPM (BF=4.35), LOO=1.00 [SE=1.31], WAIC=0.89 [SE=0.89], KFOLD=4.18 [SE=3.39]
MCPH1 only:
- β = -0.24, 89%HDI = [-0.65, 0.25]
- posterior probability p(β<0) = 0.8 (evidence ratio = 4), p(β=0) = 0.89 (evidence ratio = 8.1)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 20.4%; p_ROPE = 0.182
- comparison ‘null’ vs ‘MCPH1’: [B> L> W>(65%:35%) K>]: moderate evidence for null against MCPH1 (BF=6.59), LOO=1.00 [SE=0.83], WAIC=0.63 [SE=0.61], KFOLD=1.49 [SE=1.40]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W>(83%:17%) K>>]: very strong evidence for null against both (BF=46.8), LOO=1.99 [SE=1.23], WAIC=1.58 [SE=1.08], KFOLD=9.05 [SE=3.68]
- interaction:
  - posterior probability p(=0) = 0.93 (evidence ratio = 13)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 33.8%; p_ROPE = 0.301
  - comparison ‘no interaction’ vs ‘with interaction’: [B>> L> W>>(68%:32%) K>]: strong evidence for no interaction against with interaction (BF=17.1), LOO=0.63 [SE=0.59], WAIC=0.77 [SE=0.30], KFOLD=2.09 [SE=1.95]
- ASPM (partial):
  - β = -0.22, 89%HDI = [-0.66, 0.16]
  - posterior probability p(β<0) = 0.81 (evidence ratio = 4.2), p(β=0) = 0.9 (evidence ratio = 8.6)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 24.2%; p_ROPE = 0.216
- MCPH1 (partial):
  - β = -0.21, 89%HDI = [-0.64, 0.23]
  - posterior probability p(β<0) = 0.78 (evidence ratio = 3.5), p(β=0) = 0.89 (evidence ratio = 8.1)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 22.4%; p_ROPE = 0.199

Figure 108. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 109. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 110. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.94 (0.40, 1.72), p=0, decomposed into:
average direct effect (ADE): -0.16 (-0.69, 0.30), p=0.48, and
average indirect effect (ACME) mediated by ASPM-D: 1.11 (0.63, 1.79), p=0, mediating 117.0% (76.3%, 223.9%), p=0 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.34 ±0.15, p=1.6e-15, and
- effect of ASPM-D on tone: -0.73 ±0.12, p=4.2e-10.

For MCPH1-D:

TE: 0.69 (0.32, 1.13), p=0, decomposed into:
ADE: 0.44 (-0.44, 1.38), p=0.32, and
ACME: 0.25 (-0.57, 1.06), p=0.53, mediating 36.6% (-95.5%, 197.0%), p=0.53 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.18 ±0.09, p=3e-62, and
- effect of MCPH1-D on tone: -0.12 ±0.17, p=0.5.

Restricted sampling

Figure 111. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM and MCPH1; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (dotted), 0.05 (solid) and 0.10 (dashed).

For ASPM-D:

TE: mean = 1.3, median = 1.3; 59.2% significant at α-level 0.05 and 72.5% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 79.3, p = 0;
ADE: mean = 0.73, median = 0.74; 19.4% significant at α-level 0.05 and 33.9% significant at α-level 0.10; 97.4% > 0.0; one-sample one-sided t-test vs 0: t(999) = 58.4, p = 0;
ACME: mean = 0.54, median = 0.5; 21.5% significant at α-level 0.05 and 44.6% significant at α-level 0.10; 98.4% > 0.0; one-sample one-sided t-test vs 0: t(999) = 53.7, p = 2.6e-297;
β(Africa → allele): mean = -0.89, median = -0.9; 87.0% significant at α-level 0.05 and 98.9% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -237.7, p = 0;
β(allele → tone | Africa): mean = -0.38, median = -0.36; 34.1% significant at α-level 0.05 and 51.0% significant at α-level 0.10; 98.2% < 0.0; one-sample one-sided t-test vs 0: t(999) = -66.8, p = 0.

For MCPH1-D:

TE: mean = 1.1, median = 1.1; 57.6% significant at α-level 0.05 and 70.0% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 83.9, p = 0;
ADE: mean = 3.9, median = 2; 16.4% significant at α-level 0.05 and 26.1% significant at α-level 0.10; 83.2% > 0.0; one-sample one-sided t-test vs 0: t(999) = 17.2, p = 1.3e-58;
ACME: mean = -2.8, median = -0.89; 5.2% significant at α-level 0.05 and 11.9% significant at α-level 0.10; 35.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = -12.3, p = 1;
β(Africa → allele): mean = -2.4, median = -2.4; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -915.3, p = 0;
β(allele → tone | Africa): mean = 0.13, median = 0.1; 5.7% significant at α-level 0.05 and 11.9% significant at α-level 0.10; 40.4% < 0.0; one-sample one-sided t-test vs 0: t(999) = 10.3, p = 1.

Given the low sample size N = 35 unique families, relatively few effect sizes are big enough to be significant; however, there are many more significant indirect effects (ACME) for ASPM-D than for MCPH1-D: 34.1% vs 5.7% (6.0 times) for α-level 0.05, and 51.0% vs 11.9% (4.3 times) for α-level 0.10.

`brms`

Figure 112. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 113. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 114. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

Please note that path analysis uses a linear model (so not a Poisson one) for the tone counts; also I only use the numeric coding for Africa.

All data

Coding Africa numerically, the model fits the data very well (χ²(1)=0.29, p=0.59; CFI=1.00, TLI=1.01, NNFI=1.01 and RFI=1.00):

Figure 115. Path analysis model with standardised coefficients and significance stars. Here, macroarea (Africa vs non-Africa) is coded as numeric binary (Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D..

## lavaan 0.6-8 ended normally after 28 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                         8
##                                                       
##   Number of observations                           184
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                                 0.292
##   Degrees of freedom                                 1
##   P-value (Chi-square)                           0.589
## 
## Model Test Baseline Model:
## 
##   Test statistic                               369.194
##   Degrees of freedom                                 6
##   P-value                                        0.000
## 
## User Model versus Baseline Model:
## 
##   Comparative Fit Index (CFI)                    1.000
##   Tucker-Lewis Index (TLI)                       1.012
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)               -663.138
##   Loglikelihood unrestricted model (H1)       -662.992
##                                                       
##   Akaike (AIC)                                1342.276
##   Bayesian (BIC)                              1367.995
##   Sample-size adjusted Bayesian (BIC)         1342.657
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.000
##   90 Percent confidence interval - lower         0.000
##   90 Percent confidence interval - upper         0.159
##   P-value RMSEA <= 0.05                          0.666
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.005
## 
## Parameter Estimates:
## 
##   Standard errors                           Robust.sem
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##   n_tones ~                                                             
##     Africa_num       -0.265    0.601   -0.441    0.659   -1.443    0.913
##     ASPM_z           -0.490    0.114   -4.291    0.000   -0.713   -0.266
##     MCPH1_z          -0.131    0.229   -0.571    0.568   -0.580    0.319
##   ASPM_z ~                                                              
##     Africa_num       -1.338    0.099  -13.477    0.000   -1.533   -1.144
##   MCPH1_z ~                                                             
##     Africa_num       -2.180    0.071  -30.517    0.000   -2.320   -2.040
##    Std.lv  Std.all
##                   
##    -0.265   -0.075
##    -0.490   -0.342
##    -0.131   -0.091
##                   
##    -1.338   -0.543
##                   
##    -2.180   -0.885
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
##    .n_tones           1.790    0.273    6.566    0.000    1.256    2.324
##    .ASPM_z            0.701    0.071    9.837    0.000    0.561    0.841
##    .MCPH1_z           0.216    0.036    5.943    0.000    0.145    0.287
##    Std.lv  Std.all
##     1.790    0.879
##     0.701    0.705
##     0.216    0.217
## 
## R-Square:
##                    Estimate
##     n_tones           0.121
##     ASPM_z            0.295
##     MCPH1_z           0.783

Restricted sampling

Figure 116. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

It can be seen that:

the models fits:
- 97.9% of the p-values are not significant
- mean(CFI) = 0.99, median(CFI) = 1, sd(CFI) = 0.01, IQR(CFI) = 0.01
- mean(TLI) = 0.99, median(TLI) = 1.01, sd(TLI) = 0.09, IQR(TLI) = 0.15
- mean(NNFI) = 0.99, median(NNFI) = 1.01, sd(NNFI) = 0.09, IQR(NNFI) = 0.15
- mean(RFI) = 0.91, median(RFI) = 0.93, sd(RFI) = 0.08, IQR(RFI) = 0.13
Africa → ASPM-D: mean = -0.88, median = -0.89, sd = 0.12, IQR = 0.16, 100.0% < 0; 99.9% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -2.3e+02, p = 0
Africa → MCPH1-D: mean = -2.4, median = -2.4, sd = 0.083, IQR = 0.12, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -9.1e+02, p = 0
Africa → tone counts: mean = 0.77, median = 0.83, sd = 1.1, IQR = 1.6, 74.9% > 0; 10.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 22, p = 2e-86
ASPM-D → tone counts: mean = -0.32, median = -0.31, sd = 0.16, IQR = 0.22, 98.7% < 0; 22.5% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -63, p = 0
MCPH1-D → tone counts: mean = 0.019, median = 0.034, as = 0.45, IQR = 0.65, 47.4% < 0; 3.3% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 1.3, p = 0.91

Unrounded (raw) imputed counts

I kept only the entries with non-missing data for the tone counts, ASPM-D and MCPH1-D, and if there are more than one possible languages or allele frequencies for a given sample, I only kept those entries that have different tone or allele data. The resulting dataset has 200 observations, distributed among 136 unique Glottolg codes in 37 families (ranging from a minimum of 1 language per family to a maximum of 51, with a mean 5.4 and median 2 languages per family) and 4 macroareas.

Figure 117. Distribution of tone counts (unrounded).

Figure 118. Distribution of tone counts (unrounded) across the world.

Figure 119. Relationship between tone counts (unrounded; colors) and the two alleles (frequency) by macroarea.

Power analysis

I use simulations for power analysis (as implemented by package simr), focusing on the effect of ASPM-D on tone1 using glmer, i.e. logistic regression with ASPM-D as fixed effect and controlling for language family (as random effect) and macroarea as fixed effect.

Observed power

The observed effect size of ASPM-D is β_ASPM-D = -0.4, p_ASPM-D = 0.41, with an ICC = 68.4% on 35 level-2 groups (families) and 181 observations (languages/samples). The observed (post-hoc) power 1 - β = %, 95%CI = .

Changing the number of languages

If we keep the families but change the number of languages per family:

Figure 120. Estimated power (with 95%) when changing the number of languages but keeping everything else constant.

Changing the number of families

If we change the number of families:

Figure 121. Estimated power (with 95%) when changing the number of language families but keeping everything else constant.

Changing the number of families and languages

If we change the number of families and the number of languages per family:

Figure 122. Estimated power when changing the number of language families and the number of languages per family, but keeping everything else constant. Color is proportional to power and the shape shows if the power is > 80%. The two vertical dotted lines are the approximate number of families in Ethnologue (blue, ~150) and Glottolog (black, ~420). The horizontal dotted lines are summaries of the number of languages in Glottolog: the mean (red, ~20), the median (black, 2) and the median excluding isolates (blue, 5); not shown is the maxmimum (~1400 in Atlantic-Congo).

Appendix I: Gaussian Process

Here I model language contact with a 2D Gaussian Process as suggested in, for example, McElreath (2020), using brms’s gp(). tone is regressed on ASPM-D and MCPH1-D with language family and (meta)population as (nested) random effects, and a 2D Gaussian process separately for each macroarea.

tone1

ASPM only:
- β = -0.88, 89%HDI = [-1.63, -0.06]
- posterior probability p(β<0) = 0.96 (evidence ratio = 25), p(β=0) = 0.59 (evidence ratio = 1.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 3.5%; p_ROPE = 0.065
- comparison ‘null’ vs ‘ASPM’: [B= L= W=(33%:67%) K=]: anecdotal evidence for null against ASPM (BF=1.3), LOO=-0.05 [SE=2.69], WAIC=-0.69 [SE=2.74], KFOLD=-1.21 [SE=3.41]
MCPH1 only:
- β = -1.03, 89%HDI = [-1.63, -0.45]
- posterior probability p(β<0) = 0.99 (evidence ratio = 1.7e+02), p(β=0) = 0.15 (evidence ratio = 0.17)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 0%; p_ROPE = 0.011
- comparison ‘null’ vs ‘MCPH1’: [B< L< W<(10%:90%) K=]: moderate evidence for MCPH1 against null (BF=0.301), LOO=-2.13 [SE=1.73], WAIC=-2.22 [SE=1.73], KFOLD=-2.02 [SE=2.70]
both alleles:
- comparison ‘null’ vs ‘both’: [B= L= W=(9%:91%) K=]: anecdotal evidence for both against null (BF=0.704), LOO=-1.87 [SE=2.93], WAIC=-2.34 [SE=2.95], KFOLD=-2.34 [SE=3.50]
- interaction:
  - posterior probability p(=0) = 0.87 (evidence ratio = 6.6)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 31.5%; p_ROPE = 0.28
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L>> W>(76%:24%) K>]: moderate evidence for no interaction against with interaction (BF=5.75), LOO=1.49 [SE=0.73], WAIC=1.16 [SE=0.66], KFOLD=2.70 [SE=2.09]
- ASPM (partial):
  - β = -0.58, 89%HDI = [-1.35, 0.20]
  - posterior probability p(β<0) = 0.88 (evidence ratio = 7.4), p(β=0) = 0.76 (evidence ratio = 3.2)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 15.7%; p_ROPE = 0.14
- MCPH1 (partial):
  - β = -0.85, 89%HDI = [-1.47, -0.25]
  - posterior probability p(β<0) = 0.99 (evidence ratio = 77), p(β=0) = 0.41 (evidence ratio = 0.69)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 0%; p_ROPE = 0.032

Figure 123. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right). Please note that I have cut the x-axis at 2.5 as the distributions of the sdgp and lscale have a few extreme outliers which would make the plots impossible to see.

Figure 124. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 125. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 126. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

tone2

ASPM only:
- β = -1.15, 89%HDI = [-2.12, -0.16]
- posterior probability p(β<0) = 0.97 (evidence ratio = 33), p(β=0) = 0.5 (evidence ratio = 1)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 0.6%; p_ROPE = 0.044
- comparison ‘null’ vs ‘ASPM’: [B= L= W=(41%:59%) K=]: anecdotal evidence for ASPM against null (BF=0.767), LOO=-0.34 [SE=1.58], WAIC=-0.34 [SE=1.59], KFOLD=-0.07 [SE=1.64]
MCPH1 only:
- β = -0.63, 89%HDI = [-1.27, -0.04]
- posterior probability p(β<0) = 0.95 (evidence ratio = 19), p(β=0) = 0.68 (evidence ratio = 2.1)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 6.5%; p_ROPE = 0.099
- comparison ‘null’ vs ‘MCPH1’: [B= L= W=(55%:45%) K=]: anecdotal evidence for null against MCPH1 (BF=2.14), LOO=0.06 [SE=1.58], WAIC=0.19 [SE=1.58], KFOLD=0.88 [SE=1.88]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L= W=(45%:55%) K=]: moderate evidence for null against both (BF=4.38), LOO=-0.23 [SE=1.82], WAIC=-0.19 [SE=1.81], KFOLD=0.17 [SE=1.92]
- interaction:
  - posterior probability p(=0) = 0.83 (evidence ratio = 4.7)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 22.4%; p_ROPE = 0.2
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L> W>(62%:38%) K>>]: moderate evidence for no interaction against with interaction (BF=6.35), LOO=0.53 [SE=0.37], WAIC=0.48 [SE=0.37], KFOLD=2.63 [SE=1.03]
- ASPM (partial):
  - β = -0.88, 89%HDI = [-1.96, 0.15]
  - posterior probability p(β<0) = 0.91 (evidence ratio = 10), p(β=0) = 0.68 (evidence ratio = 2.1)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 9.9%; p_ROPE = 0.092
- MCPH1 (partial):
  - β = -0.42, 89%HDI = [-1.04, 0.21]
  - posterior probability p(β<0) = 0.86 (evidence ratio = 6.3), p(β=0) = 0.83 (evidence ratio = 4.7)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 24.1%; p_ROPE = 0.214

Figure 127. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right). Please note that I have cut the x-axis at 2.5 as the distributions of the sdgp and lscale have a few extreme outliers which would make the plots impossible to see.

Figure 128. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 129. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 130. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Tone counts

ASPM only:
- β = -0.22, 89%HDI = [-0.66, 0.24]
- posterior probability p(β<0) = 0.78 (evidence ratio = 3.5), p(β=0) = 0.9 (evidence ratio = 8.9)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 23.7%; p_ROPE = 0.211
- comparison ‘null’ vs ‘ASPM’: [B> L>> W>>(90%:10%) K=]: moderate evidence for null against ASPM (BF=9.37), LOO=2.40 [SE=1.07], WAIC=2.20 [SE=1.01], KFOLD=1.54 [SE=1.62]
MCPH1 only:
- β = -0.41, 89%HDI = [-0.77, -0.08]
- posterior probability p(β<0) = 0.95 (evidence ratio = 21), p(β=0) = 0.7 (evidence ratio = 2.3)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 1.2%; p_ROPE = 0.058
- comparison ‘null’ vs ‘MCPH1’: [B> L> W>(93%:7%) K=]: moderate evidence for null against MCPH1 (BF=3.35), LOO=2.30 [SE=1.36], WAIC=2.53 [SE=1.30], KFOLD=1.72 [SE=1.79]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W>(97%:3%) K>]: strong evidence for null against both (BF=14), LOO=3.61 [SE=2.03], WAIC=3.47 [SE=1.89], KFOLD=3.27 [SE=2.59]
- interaction:
  - posterior probability p(=0) = 0.93 (evidence ratio = 12)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 33.7%; p_ROPE = 0.3
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L>> W>>(68%:32%) K>>]: moderate evidence for no interaction against with interaction (BF=6.73), LOO=1.03 [SE=0.44], WAIC=0.74 [SE=0.37], KFOLD=4.04 [SE=1.72]
- ASPM (partial):
  - β = -0.27, 89%HDI = [-0.67, 0.17]
  - posterior probability p(β<0) = 0.84 (evidence ratio = 5.4), p(β=0) = 0.88 (evidence ratio = 7.5)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 19.5%; p_ROPE = 0.174
- MCPH1 (partial):
  - β = -0.4, 89%HDI = [-0.72, -0.11]
  - posterior probability p(β<0) = 0.97 (evidence ratio = 29), p(β=0) = 0.67 (evidence ratio = 2)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 0%; p_ROPE = 0.049

Figure 131. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right). Please note that I have cut the x-axis at 2.5 as the distributions of the sdgp and lscale have a few extreme outliers which would make the plots impossible to see.

Figure 132. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 133. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Appendix II: Sensitivity to the prior

Here I explore the sensitivity to the prior of the brms models, focusing on each “derived” allele independently.

tone1

ASPM-D

All models show good mixing and convergence (not shown).

Comparing the posterior distribution for *ASPM*-D frequency (z-scored) for various prior distributions. The HDI is a 89%HDI; p(β<0) and p(β=0) show the posterior probability (and the evidence ratio, in parantheses); the ROPE is [-0.18, 0.18].
Prior name	Prior distribution	β	HDI	p(β<0)	p(β=0)	%HDI in ROPE	p_ROPE
default	student_t(3, 0, 3)	-0.70	[-1.52, 0.33]	0.89 (8.0)	0.73 (2.7)	13.3%	0.12
flat	normal(0, 10)	-0.74	[-1.63, 0.24]	0.9 (9.0)	0.89 (8.0)	13.1%	0.12
default_normal	normal(0, 5)	-0.70	[-1.60, 0.24]	0.89 (8.5)	0.8 (4.0)	13.8%	0.12
narrow_0	student_t(3, 0, 1)	-0.55	[-1.32, 0.23]	0.87 (7.0)	0.55 (1.2)	18.7%	0.17
verynarrow_0	student_t(3, 0, 0.1)	-0.05	[-0.28, 0.16]	0.62 (1.6)	0.49 (1.0)	91.1%	0.82
negative_default	student_t(3, -1, 3)	-0.75	[-1.71, 0.13]	0.91 (10.0)	0.73 (2.7)	11.4%	0.11
negative_narrow	student_t(3, -1, 1)	-0.82	[-1.60, -0.06]	0.96 (25.1)	0.47 (0.9)	4.0%	0.07
verynegative_default	student_t(3, -3, 3)	-0.87	[-1.83, 0.10]	0.94 (14.5)	0.79 (3.7)	8.3%	0.08
verynegative_narrow	student_t(3, -3, 1)	-1.33	[-2.44, -0.21]	0.98 (51.6)	0.8 (3.9)	0.0%	0.03
positive_default	student_t(3, 1, 3)	-0.62	[-1.52, 0.28]	0.87 (6.8)	0.76 (3.2)	14.0%	0.12
positive_narrow	student_t(3, 1, 1)	-0.34	[-1.13, 0.52]	0.74 (2.9)	0.74 (2.9)	25.7%	0.23
verypositive_default	student_t(3, 3, 3)	-0.55	[-1.39, 0.44]	0.84 (5.2)	0.86 (6.4)	17.8%	0.16
verypositive_narrow	student_t(3, 3, 1)	-0.23	[-1.12, 0.78]	0.66 (1.9)	0.97 (27.8)	25.0%	0.22
informative	student_t(3, -0.7, 3)	-0.72	[-1.64, 0.21]	0.9 (9.2)	0.73 (2.7)	13.0%	0.12

MCPH1-D

All models show good mixing and convergence (not shown).

Comparing the posterior distribution for *MCPH1*-D frequency (z-scored) for various prior distributions. The HDI is a 89%HDI; p(β<0) and p(β=0) show the posterior probability (and the evidence ratio, in parantheses); the ROPE is [-0.18, 0.18].
Prior name	Prior distribution	β	HDI	p(β<0)	p(β=0)	%HDI in ROPE	p_ROPE
default	student_t(3, 0, 3)	-0.65	[-1.69, 0.47]	0.84 (5.2)	0.75 (3.0)	14.3%	0.13
flat	normal(0, 10)	-0.68	[-1.76, 0.48]	0.85 (5.5)	0.9 (8.6)	13.6%	0.12
default_normal	normal(0, 5)	-0.67	[-1.76, 0.47]	0.84 (5.1)	0.83 (4.8)	14.9%	0.13
narrow_0	student_t(3, 0, 1)	-0.49	[-1.35, 0.46]	0.82 (4.4)	0.56 (1.3)	18.6%	0.17
verynarrow_0	student_t(3, 0, 0.1)	-0.04	[-0.25, 0.17]	0.59 (1.4)	0.52 (1.1)	94.0%	0.84
negative_default	student_t(3, -1, 3)	-0.73	[-1.79, 0.35]	0.87 (6.6)	0.75 (3.0)	12.6%	0.11
negative_narrow	student_t(3, -1, 1)	-0.80	[-1.74, 0.03]	0.93 (12.7)	0.57 (1.3)	7.5%	0.09
verynegative_default	student_t(3, -3, 3)	-0.85	[-1.93, 0.27]	0.9 (8.7)	0.8 (3.9)	11.5%	0.10
verynegative_narrow	student_t(3, -3, 1)	-1.31	[-2.51, -0.09]	0.97 (27.8)	0.84 (5.3)	2.1%	0.04
positive_default	student_t(3, 1, 3)	-0.61	[-1.64, 0.52]	0.81 (4.3)	0.77 (3.3)	15.6%	0.14
positive_narrow	student_t(3, 1, 1)	-0.22	[-1.26, 0.80]	0.63 (1.7)	0.75 (2.9)	23.6%	0.21
verypositive_default	student_t(3, 3, 3)	-0.47	[-1.56, 0.59]	0.77 (3.3)	0.87 (6.4)	18.1%	0.16
verypositive_narrow	student_t(3, 3, 1)	-0.06	[-1.39, 1.16]	0.55 (1.2)	0.96 (22.6)	19.9%	0.18
informative	student_t(3, -0.6, 3)	-0.66	[-1.83, 0.42]	0.83 (4.9)	0.74 (2.8)	13.0%	0.12

tone2

ASPM-D

All models show good mixing and convergence (not shown).

Comparing the posterior distribution for *ASPM*-D frequency (z-scored) for various prior distributions. The HDI is a 89%HDI; p(β<0) and p(β=0) show the posterior probability (and the evidence ratio, in parantheses); the ROPE is [-0.18, 0.18].
Prior name	Prior distribution	β	HDI	p(β<0)	p(β=0)	%HDI in ROPE	p_ROPE
default	student_t(3, 0, 3)	-1.30	[-2.72, 0.17]	0.93 (13.7)	0.56 (1.3)	6.3%	0.06
flat	normal(0, 10)	-1.76	[-3.44, 0.22]	0.95 (20.4)	0.71 (2.5)	3.8%	0.03
default_normal	normal(0, 5)	-1.50	[-3.04, 0.22]	0.94 (17.0)	0.63 (1.7)	5.3%	0.05
narrow_0	student_t(3, 0, 1)	-0.67	[-1.73, 0.40]	0.84 (5.4)	0.52 (1.1)	15.6%	0.14
verynarrow_0	student_t(3, 0, 0.1)	-0.03	[-0.23, 0.20]	0.55 (1.2)	0.5 (1.0)	94.4%	0.84
negative_default	student_t(3, -1, 3)	-1.42	[-2.85, 0.07]	0.95 (17.7)	0.55 (1.2)	4.9%	0.05
negative_narrow	student_t(3, -1, 1)	-1.05	[-1.98, 0.02]	0.96 (23.1)	0.44 (0.8)	4.3%	0.06
verynegative_default	student_t(3, -3, 3)	-1.76	[-3.33, -0.17]	0.98 (40.2)	0.54 (1.2)	0.2%	0.03
verynegative_narrow	student_t(3, -3, 1)	-1.89	[-3.12, -0.61]	0.99 (120.2)	0.57 (1.4)	0.0%	0.01
positive_default	student_t(3, 1, 3)	-1.21	[-2.58, 0.36]	0.91 (10.1)	0.64 (1.8)	7.9%	0.07
positive_narrow	student_t(3, 1, 1)	-0.45	[-1.81, 0.77]	0.7 (2.3)	0.7 (2.3)	19.6%	0.17
verypositive_default	student_t(3, 3, 3)	-1.14	[-2.60, 0.44]	0.89 (7.8)	0.77 (3.3)	9.1%	0.08
verypositive_narrow	student_t(3, 3, 1)	-0.40	[-1.94, 1.51]	0.68 (2.1)	0.94 (16.3)	14.2%	0.13
informative	student_t(3, -1.3, 3)	-1.48	[-2.94, 0.10]	0.95 (20.5)	0.53 (1.1)	3.9%	0.04

MCPH1-D

All models show good mixing and convergence (not shown).

Comparing the posterior distribution for *MCPH1*-D frequency (z-scored) for various prior distributions. The HDI is a 89%HDI; p(β<0) and p(β=0) show the posterior probability (and the evidence ratio, in parantheses); the ROPE is [-0.18, 0.18].
Prior name	Prior distribution	β	HDI	p(β<0)	p(β=0)	%HDI in ROPE	p_ROPE
default	student_t(3, 0, 3)	-0.93	[-2.41, 0.53]	0.85 (5.6)	0.68 (2.2)	10.6%	0.09
flat	normal(0, 10)	-1.23	[-3.11, 0.51]	0.88 (7.0)	0.83 (5.0)	8.2%	0.07
default_normal	normal(0, 5)	-1.07	[-2.60, 0.66]	0.86 (6.2)	0.75 (2.9)	9.2%	0.08
narrow_0	student_t(3, 0, 1)	-0.47	[-1.61, 0.68]	0.75 (3.0)	0.57 (1.3)	18.7%	0.17
verynarrow_0	student_t(3, 0, 0.1)	-0.01	[-0.25, 0.19]	0.53 (1.1)	0.5 (1.0)	93.8%	0.84
negative_default	student_t(3, -1, 3)	-1.05	[-2.58, 0.45]	0.88 (7.0)	0.66 (2.0)	8.8%	0.08
negative_narrow	student_t(3, -1, 1)	-0.89	[-1.98, 0.15]	0.92 (10.9)	0.5 (1.0)	8.1%	0.07
verynegative_default	student_t(3, -3, 3)	-1.31	[-2.88, 0.30]	0.92 (10.8)	0.73 (2.7)	6.7%	0.06
verynegative_narrow	student_t(3, -3, 1)	-1.73	[-3.11, -0.32]	0.98 (39.4)	0.75 (2.9)	0.0%	0.02
positive_default	student_t(3, 1, 3)	-0.81	[-2.25, 0.84]	0.81 (4.4)	0.72 (2.6)	12.2%	0.11
positive_narrow	student_t(3, 1, 1)	-0.08	[-1.36, 1.31]	0.53 (1.1)	0.69 (2.2)	19.5%	0.17
verypositive_default	student_t(3, 3, 3)	-0.67	[-2.30, 0.85]	0.77 (3.4)	0.82 (4.5)	13.8%	0.12
verypositive_narrow	student_t(3, 3, 1)	0.40	[-1.51, 2.62]	0.42 (0.7)	0.94 (14.7)	11.8%	0.10
informative	student_t(3, -0.9, 3)	-1.01	[-2.44, 0.46]	0.88 (7.5)	0.69 (2.2)	10.1%	0.09

Tone counts

ASPM-D

All models show good mixing and convergence (not shown).

Comparing the posterior distribution for *ASPM*-D frequency (z-scored) for various prior distributions. The HDI is a 89%HDI; p(β<0) and p(β=0) show the posterior probability (and the evidence ratio, in parantheses); the ROPE is [-0.10, 0.10].
Prior name	Prior distribution	β	HDI	p(β<0)	p(β=0)	%HDI in ROPE	p_ROPE
default	student_t(3, 0, 3)	-0.24	[-0.65, 0.16]	0.82 (4.7)	0.89 (8.1)	22.2%	0.20
flat	normal(0, 10)	-0.25	[-0.67, 0.16]	0.83 (5.0)	0.96 (23.4)	21.1%	0.19
default_normal	normal(0, 5)	-0.24	[-0.66, 0.16]	0.82 (4.7)	0.92 (12.1)	21.8%	0.19
narrow_0	student_t(3, 0, 1)	-0.22	[-0.63, 0.18]	0.81 (4.4)	0.75 (2.9)	23.4%	0.21
verynarrow_0	student_t(3, 0, 0.1)	-0.04	[-0.22, 0.14]	0.63 (1.7)	0.53 (1.1)	72.9%	0.65
negative_default	student_t(3, -1, 3)	-0.26	[-0.69, 0.15]	0.83 (5.0)	0.9 (8.5)	21.6%	0.19
negative_narrow	student_t(3, -1, 1)	-0.32	[-0.74, 0.07]	0.9 (8.9)	0.76 (3.2)	14.3%	0.14
verynegative_default	student_t(3, -3, 3)	-0.28	[-0.69, 0.14]	0.86 (6.2)	0.93 (12.3)	18.6%	0.17
verynegative_narrow	student_t(3, -3, 1)	-0.34	[-0.77, 0.09]	0.89 (8.4)	0.96 (27.0)	14.3%	0.13
positive_default	student_t(3, 1, 3)	-0.23	[-0.67, 0.16]	0.82 (4.6)	0.9 (9.1)	22.4%	0.20
positive_narrow	student_t(3, 1, 1)	-0.15	[-0.55, 0.27]	0.72 (2.6)	0.87 (6.5)	28.6%	0.25
verypositive_default	student_t(3, 3, 3)	-0.22	[-0.62, 0.21]	0.79 (3.9)	0.94 (15.3)	23.0%	0.20
verypositive_narrow	student_t(3, 3, 1)	-0.14	[-0.57, 0.27]	0.7 (2.3)	0.98 (58.0)	30.0%	0.27
informative	student_t(3, -0.2, 3)	-0.26	[-0.66, 0.14]	0.85 (5.6)	0.89 (7.8)	20.2%	0.18

MCPH1-D

All models show good mixing and convergence (not shown).

Comparing the posterior distribution for *MCPH1*-D frequency (z-scored) for various prior distributions. The HDI is a 89%HDI; p(β<0) and p(β=0) show the posterior probability (and the evidence ratio, in parantheses); the ROPE is [-0.10, 0.10].
Prior name	Prior distribution	β	HDI	p(β<0)	p(β=0)	%HDI in ROPE	p_ROPE
default	student_t(3, 0, 3)	-0.23	[-0.70, 0.20]	0.79 (3.7)	0.89 (7.9)	21.8%	0.19
flat	normal(0, 10)	-0.24	[-0.66, 0.24]	0.81 (4.3)	0.96 (22.7)	20.4%	0.18
default_normal	normal(0, 5)	-0.24	[-0.68, 0.24]	0.8 (4.0)	0.92 (11.4)	19.6%	0.17
narrow_0	student_t(3, 0, 1)	-0.21	[-0.65, 0.21]	0.79 (3.7)	0.72 (2.6)	21.9%	0.20
verynarrow_0	student_t(3, 0, 0.1)	-0.04	[-0.22, 0.16]	0.62 (1.6)	0.53 (1.1)	70.3%	0.63
negative_default	student_t(3, -1, 3)	-0.24	[-0.69, 0.22]	0.81 (4.3)	0.89 (7.8)	19.5%	0.17
negative_narrow	student_t(3, -1, 1)	-0.30	[-0.73, 0.11]	0.87 (6.8)	0.79 (3.8)	16.6%	0.15
verynegative_default	student_t(3, -3, 3)	-0.25	[-0.71, 0.19]	0.81 (4.4)	0.93 (12.7)	20.2%	0.18
verynegative_narrow	student_t(3, -3, 1)	-0.31	[-0.77, 0.14]	0.86 (5.9)	0.97 (31.5)	15.4%	0.14
positive_default	student_t(3, 1, 3)	-0.22	[-0.66, 0.23]	0.79 (3.8)	0.9 (8.8)	21.3%	0.19
positive_narrow	student_t(3, 1, 1)	-0.13	[-0.59, 0.32]	0.67 (2.1)	0.85 (5.6)	27.5%	0.24
verypositive_default	student_t(3, 3, 3)	-0.20	[-0.65, 0.25]	0.77 (3.3)	0.93 (13.8)	22.3%	0.20
verypositive_narrow	student_t(3, 3, 1)	-0.12	[-0.59, 0.37]	0.66 (1.9)	0.98 (52.4)	25.9%	0.23
informative	student_t(3, -0.2, 3)	-0.24	[-0.71, 0.17]	0.82 (4.5)	0.89 (7.9)	20.6%	0.18

Appendix III: Excluding the “proxy” SNPs

Here I conduct some of the analyses using only the actual “derived” loci for the two genes (i.e., excluding all the “proxy” SNPs used in the full analysis).

tone1

There are 108 observations, distributed among 75 unique Glottolg codes in 29 families (ranging from a minimum of 1 language per family to a maximum of 38, with a mean 3.7 and median 2 languages per family) and 4 macroareas.

There are 98:83:75 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
No	6	53	2	3	64
Yes	19	21	3	1	44
Sum	25	74	5	4	108

Figure 134. Distribution of tone1.

Figure 135. Map of tone1.

Figure 136. Relationship between tone1, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 53.2%
macroarea: p_{macroarea/null} = 0.046
ASPM:
- by itself: R² = 6.8%, β = -0.68 ± 0.38, p_ASPM/null = 0.065
- quadratic: R² = 7.0%, β_ASPM2 = -0.61 ± 0.43, p_ASPM2/ASPM = 0.71
- with macroarea: R² = 18.2%, p_{macroarea/ASPM} = 0.19, p_{ASPM/macroarea} = 0.64
MCPH1:
- by itself: R² = 8.5%, β = -0.79 ± 0.40, p_MCPH1/null = 0.042
- quadratic: R² = 9.5%, β_MCPH12 = -0.74 ± 0.39, p_MCPH12/MCPH1 = 0.28
- with macroarea: R² = 18.2%, p_{macroarea/MCPH1} = 0.26, p_{MCPH1/macroarea} = 0.68
both alleles (no macroarea):
- ASPM + MCPH1: R² = 11.0%, β_ASPM = -0.45 ± 0.40, p_ASPM/MCPH1 = 0.26, β_MCPH1 = -0.57 ± 0.42, p_MCPH1/ASPM = 0.16, p_{ASPM+MCPH1/null} = 0.068,
- interaction: R² = 11.4%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.62

Alleles on macroarea

the alleles are very strongly clustered within families:
- ASPM: ICC = 100.0%
- MCPH1: ICC = 100.0%
macroarea predicts their distribution very strongly:
- ASPM: p = 3.3e-05, R² = 39.1%
- MCPH1: p = 2.3e-09, R² = 74.1%
separating Africa vs the rest of the world seems to drive most of this effect (both alleles have lower frequencies in Africa):
- ASPM: p = 8.1e-05, R² = 24.1%
- MCPH1: p = 1.5e-07, R² = 49.5%

Randomization

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	5%	4%	3%	5%	1%
unrestricted	none	alleles-together	8%	6%	6%	9%	6%	5%
unrestricted	none	alleles-independent	8%	5%	6%	9%	5%	2%
unrestricted	fixef	tone	0%	7%	7%	29%	5%	33%
unrestricted	fixef	alleles-together	89%	6%	6%	34%	6%	28%
unrestricted	fixef	alleles-independent	86%	5%	5%	30%	5%	28%
macroareas	none	tone	0%	82%	14%	19%	71%	51%
macroareas	none	alleles-together	39%	30%	8%	27%	22%	56%
macroareas	none	alleles-independent	43%	35%	12%	34%	25%	59%
macroareas	fixef	tone	0%	5%	4%	26%	5%	33%
macroareas	fixef	alleles-together	86%	5%	5%	32%	5%	38%
macroareas	fixef	alleles-independent	86%	4%	5%	36%	4%	38%
families	none	tone	20%	13%	2%	10%	17%	46%
families	none	alleles-together	9%	6%	2%	16%	4%	21%
families	none	alleles-independent	13%	9%	7%	25%	8%	26%
families	fixef	tone	20%	6%	2%	33%	7%	65%
families	fixef	alleles-together	79%	1%	2%	35%	1%	19%
families	fixef	alleles-independent	84%	2%	3%	32%	1%	19%

Restricted sampling

Figure 137. Results for 1000 restricted samplings. For ASPM-D (left): 98.2% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -56.0, mean = -0.55, p = 1.2e-310), 56.3%, when controlling for the macroarea (t(999) = -7.6, mean = -0.10, p = 4e-14), and 54.3% when controlling for both macroarea and MCPH1 (t(999) = -7.3, mean = -0.10, p = 2.2e-13). For MCPH1-D (right): 100% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -88.1, mean = -0.54, p = 0), 58.4% when controlling for the macroarea (t(999) = -7.1, mean = -0.15, p = 9.9e-13), and 60% when controlling for both macroarea and ASPM (t(999) = -8.8, mean = -0.19, p = 3.8e-18).

`brms`

ASPM only:
- β = -0.53, 89%HDI = [-1.46, 0.31]
- posterior probability p(β<0) = 0.83 (evidence ratio = 5), p(β=0) = 0.8 (evidence ratio = 4.1)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 18.8%; p_ROPE = 0.168
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(61%:39%) K>]: moderate evidence for null against ASPM (BF=3.2), LOO=0.42 [SE=1.20], WAIC=0.46 [SE=1.07], KFOLD=1.90 [SE=1.88]
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(61%:39%) K>]: moderate evidence for null against ASPM (BF=3.2), LOO=0.42 [SE=1.20], WAIC=0.46 [SE=1.07], KFOLD=1.90 [SE=1.88]
MCPH1 only:
- β = -0.7, 89%HDI = [-1.91, 0.43]
- posterior probability p(β<0) = 0.84 (evidence ratio = 5.2), p(β=0) = 0.75 (evidence ratio = 3.1)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 13.2%; p_ROPE = 0.117
- comparison ‘null’ vs ‘MCPH1’: [B= L= W=(52%:48%) K>]: anecdotal evidence for null against MCPH1 (BF=2.89), LOO=0.27 [SE=0.87], WAIC=0.07 [SE=0.75], KFOLD=1.68 [SE=1.60]
- comparison ‘null’ vs ‘MCPH1’: [B= L= W=(52%:48%) K>]: anecdotal evidence for null against MCPH1 (BF=2.89), LOO=0.27 [SE=0.87], WAIC=0.07 [SE=0.75], KFOLD=1.68 [SE=1.60]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W=(69%:31%) K>]: strong evidence for null against both (BF=15.6), LOO=1.80 [SE=1.38], WAIC=0.82 [SE=1.28], KFOLD=2.78 [SE=1.76]
- interaction:
  - posterior probability p(=0) = 0.77 (evidence ratio = 3.3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 14.9%; p_ROPE = 0.132
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L= W=(44%:56%) K>>]: moderate evidence for no interaction against with interaction (BF=3.55), LOO=0.25 [SE=0.82], WAIC=-0.25 [SE=0.68], KFOLD=3.69 [SE=1.62]
- ASPM (partial):
  - β = -0.41, 89%HDI = [-1.33, 0.55]
  - posterior probability p(β<0) = 0.76 (evidence ratio = 3.1), p(β=0) = 0.82 (evidence ratio = 4.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 22.1%; p_ROPE = 0.197
- MCPH1 (partial):
  - β = -0.6, 89%HDI = [-1.74, 0.63]
  - posterior probability p(β<0) = 0.8 (evidence ratio = 4), p(β=0) = 0.77 (evidence ratio = 3.3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 15.7%; p_ROPE = 0.14

Figure 138. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 139. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 140. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 141. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.44 (0.24, 0.61), p=0, decomposed into:
average direct effect (ADE): 0.28 (0.04, 0.51), p=0.02, and
average indirect effect (ACME) mediated by ASPM-D: 0.16 (0.03, 0.30), p=0.022, mediating 35.7% (5.6%, 85.0%), p=0.022 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.22 ±0.20, p=1.2e-08, and
- effect of ASPM-D on tone: -0.63 ±0.27, p=0.022.

For MCPH1-D:

TE: 0.44 (0.24, 0.61), p=0, decomposed into:
ADE: 0.53 (0.10, 0.73), p=0.012, and
ACME: -0.09 (-0.29, 0.28), p=0.43, mediating -25.9% (-104.5%, 70.5%), p=0.43 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.08 ±0.11, p=1.7e-36, and
- effect of MCPH1-D on tone: 0.38 ±0.48, p=0.42.

Restricted sampling

Figure 142. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM-D and MCPH1-D; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (solid), 0.05 (dashed) and 0.10 (dotted).

For ASPM-D:

TE: mean = 0.32, median = 0.33; 15.6% significant at α-level 0.05 and 49.1% significant at α-level 0.10; 99.9% > 0.0; one-sample one-sided t-test vs 0: t(999) = 115.5, p = 0;
ADE: mean = 0.28, median = 0.28; 6.4% significant at α-level 0.05 and 24.7% significant at α-level 0.10; 99.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = 87.8, p = 0;
ACME: mean = 0.046, median = 0.044; 0.0% significant at α-level 0.05 and 1.8% significant at α-level 0.10; 79.3% > 0.0; one-sample one-sided t-test vs 0: t(999) = 30.0, p = 1.1e-141;
β(Africa → allele): mean = -0.82, median = -0.84; 69.4% significant at α-level 0.05 and 89.8% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -228.0, p = 0;
β(allele → tone | Africa): mean = -0.31, median = -0.29; 0.1% significant at α-level 0.05 and 4.3% significant at α-level 0.10; 78.7% < 0.0; one-sample one-sided t-test vs 0: t(999) = -28.3, p = 5.8e-130.

For MCPH1-D:

TE: mean = 0.33, median = 0.33; 15.8% significant at α-level 0.05 and 50.0% significant at α-level 0.10; 99.9% > 0.0; one-sample one-sided t-test vs 0: t(999) = 116.1, p = 0;
ADE: mean = 0.35, median = 0.39; 2.1% significant at α-level 0.05 and 12.3% significant at α-level 0.10; 95.6% > 0.0; one-sample one-sided t-test vs 0: t(999) = 65.5, p = 0;
ACME: mean = -0.029, median = -0.048; 0.1% significant at α-level 0.05 and 0.8% significant at α-level 0.10; 38.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = -6.5, p = 1;
β(Africa → allele): mean = -2.3, median = -2.3; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -953.8, p = 0;
β(allele → tone | Africa): mean = 0.34, median = 0.33; 0.2% significant at α-level 0.05 and 0.5% significant at α-level 0.10; 27.6% < 0.0; one-sample one-sided t-test vs 0: t(999) = 18.9, p = 1.

Given the low sample size N = 29 unique families, relatively few effect sizes are big enough to be significant for each individual analysis; however, there are many more significant ACMEs for ASPM-D than for MCPH1-D: 0.1% vs 0.2% (0.5 times) for α-level 0.05, and 4.3% vs 0.5% (8.6 times) for α-level 0.10.

`brms`

Figure 143. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 144. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 145. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

All data

With Africa and tone1 coded numerically, the model fit is: χ²(1)=0.00, p=0.96; CFI=1.00, TLI=1.03, NNFI=1.03 and RFI=1.00:

Figure 146. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as numeric binary (tone_bin_num with Yes=1 and Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Likewise, with Africa and tone1 coded as ordered binary factors, the model fit is: χ²(1)=0.01, p=0.94; CFI=1.00, TLI=1.66, NNFI=1.66 and RFI=1.00:

Figure 147. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as ordered binary factors (tone_bin_ord with No < Yes, and Africa_ord with outside Africa < in Africa); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Restricted sampling

Figure 148. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

models fits:
- 100% of the p-values are not significant
- mean(CFI) = 1, median(CFI) = 1, sd(CFI) = 0.01, IQR(CFI) = 0
- mean(TLI) = 1.04, median(TLI) = 1.06, sd(TLI) = 0.07, IQR(TLI) = 0.08
- mean(NNFI) = 1.04, median(NNFI) = 1.06, sd(NNFI) = 0.07, IQR(NNFI) = 0.08
- mean(RFI) = 0.94, median(RFI) = 0.96, sd(RFI) = 0.06, IQR(RFI) = 0.08
Africa → ASPM-D: mean = -0.83, median = -0.85, sd = 0.11, IQR = 0.14, 100.0% < 0; 95.6% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -2.4e+02, p = 0;
Africa → MCPH1-D: mean = -2.3, median = -2.3, sd = 0.077, IQR = 0.099, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -9.5e+02, p = 0;
Africa → tone1: mean = 0.45, median = 0.47, sd = 0.3, IQR = 0.44, 92.2% > 0; 12.4% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 47, p = 5.6e-253;
ASPM-D → tone1: mean = -0.057, median = -0.057, sd = 0.071, IQR = 0.11, 76.0% < 0; 10.8% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -25, p = 2.3e-110;
MCPH1-D → tone1: mean = 0.057, median = 0.064, as = 0.11, IQR = 0.16, 30.4% < 0; 0.9% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 16, p = 1.

tone2

The resulting dataset has 106 observations, distributed among 73 unique Glottolg codes in 29 families (ranging from a minimum of 1 language per family to a maximum of 37, with a mean 3.7 and median 2 languages per family) and 4 macroareas.

There are 93:78:73 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
No	17	58	5	4	84
Yes	9	13	0	0	22
Sum	26	71	5	4	106

Figure 149. Distribution of tone2.

Figure 150. Map of tone2.

Figure 151. Relationship between tone2, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 94.9%
macroarea: p_{macroarea/null} = 0.21
ASPM:
- by itself: R² = 3.7%, β = -1.78 ± 1.25, p_ASPM/null = 0.072
- quadratic: R² = 50.0%, β_ASPM2 = -8.21 ± 6.07, p_ASPM2/ASPM = 0.0044
- with macroarea: R² = 52.7%, p_{macroarea/ASPM} = 0.52, p_{ASPM/macroarea} = 0.33
MCPH1:
- by itself: R² = 3.3%, β = -1.30 ± 0.94, p_MCPH1/null = 0.13
- quadratic: R² = 24.3%, β_MCPH12 = -1.39 ± 0.93, p_MCPH12/MCPH1 = 0.06
- with macroarea: R² = 47.0%, p_{macroarea/MCPH1} = 0.43, p_{MCPH1/macroarea} = 0.52
both alleles (no macroarea):
- ASPM + MCPH1: R² = 5.1%, β_ASPM = -1.38 ± 1.32, p_ASPM/MCPH1 = 0.22, β_MCPH1 = -0.72 ± 1.03, p_MCPH1/ASPM = 0.48, p_{ASPM+MCPH1/null} = 0.15,
- interaction: R² = 6.9%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.69

Randomization

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	5%	6%	0%	6%	1%
unrestricted	none	alleles-together	20%	9%	8%	3%	9%	13%
unrestricted	none	alleles-independent	23%	9%	8%	2%	8%	9%
unrestricted	fixef	tone	0%	6%	6%	0%	6%	91%
unrestricted	fixef	alleles-together	60%	9%	9%	5%	8%	92%
unrestricted	fixef	alleles-independent	62%	9%	7%	3%	9%	94%
macroareas	none	tone	0%	19%	3%	0%	28%	13%
macroareas	none	alleles-together	46%	19%	4%	10%	24%	78%
macroareas	none	alleles-independent	48%	23%	8%	15%	25%	79%
macroareas	fixef	tone	0%	6%	6%	0%	5%	90%
macroareas	fixef	alleles-together	54%	6%	6%	13%	7%	73%
macroareas	fixef	alleles-independent	55%	7%	8%	15%	7%	79%
families	none	tone	6%	10%	5%	13%	3%	26%
families	none	alleles-together	18%	8%	8%	18%	0%	18%
families	none	alleles-independent	18%	8%	12%	19%	3%	23%
families	fixef	tone	6%	6%	9%	28%	3%	90%
families	fixef	alleles-together	70%	8%	6%	25%	10%	31%
families	fixef	alleles-independent	66%	10%	8%	17%	11%	35%

Restricted sampling

Figure 152. Results for 1000 restricted samplings. For ASPM-D (left): 87.8% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -38.2, mean = -0.27, p = 5.6e-198), 93%, when controlling for the macroarea (t(999) = -45.5, mean = -0.48, p = 9.2e-246), and 94.3% when controlling for both macroarea and MCPH1 (t(999) = -44.1, mean = -0.60, p = 9.5e-237). For MCPH1-D (right): 82.5% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -35.5, mean = -0.29, p = 2.7e-179), 13.3% when controlling for the macroarea (t(999) = 32.3, mean = 0.86, p = 1), and 12.6% when controlling for both macroarea and ASPM (t(999) = 30.9, mean = 1.08, p = 1).

`brms`

ASPM only:
- β = -1.33, 89%HDI = [-2.91, 0.32]
- posterior probability p(β<0) = 0.92 (evidence ratio = 11), p(β=0) = 0.57 (evidence ratio = 1.3)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 6.9%; p_ROPE = 0.061
- comparison ‘null’ vs ‘ASPM’: [B= L= W=(45%:55%) K=]: anecdotal evidence for null against ASPM (BF=1.26), LOO=0.33 [SE=1.05], WAIC=-0.20 [SE=0.94], KFOLD=-0.02 [SE=2.27]
- comparison ‘null’ vs ‘ASPM’: [B= L= W=(45%:55%) K=]: anecdotal evidence for null against ASPM (BF=1.26), LOO=0.33 [SE=1.05], WAIC=-0.20 [SE=0.94], KFOLD=-0.02 [SE=2.27]
MCPH1 only:
- β = -0.9, 89%HDI = [-2.89, 0.76]
- posterior probability p(β<0) = 0.8 (evidence ratio = 3.9), p(β=0) = 0.66 (evidence ratio = 2)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 10.1%; p_ROPE = 0.09
- comparison ‘null’ vs ‘MCPH1’: [B= L= W<(37%:63%) K=]: anecdotal evidence for null against MCPH1 (BF=1.69), LOO=0.55 [SE=0.68], WAIC=-0.51 [SE=0.47], KFOLD=-0.29 [SE=2.45]
- comparison ‘null’ vs ‘MCPH1’: [B= L= W<(37%:63%) K=]: anecdotal evidence for null against MCPH1 (BF=1.69), LOO=0.55 [SE=0.68], WAIC=-0.51 [SE=0.47], KFOLD=-0.29 [SE=2.45]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L= W=(30%:70%) K=]: moderate evidence for null against both (BF=3.62), LOO=-0.09 [SE=1.10], WAIC=-0.86 [SE=1.02], KFOLD=0.92 [SE=1.18]
- interaction:
  - posterior probability p(=0) = 0.7 (evidence ratio = 2.4)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 11.7%; p_ROPE = 0.104
  - comparison ‘no interaction’ vs ‘with interaction’: [B= L> W=(58%:42%) K>]: anecdotal evidence for no interaction against with interaction (BF=2.54), LOO=1.33 [SE=0.81], WAIC=0.34 [SE=0.41], KFOLD=3.94 [SE=2.20]
- ASPM (partial):
  - β = -1.22, 89%HDI = [-2.99, 0.53]
  - posterior probability p(β<0) = 0.88 (evidence ratio = 7), p(β=0) = 0.64 (evidence ratio = 1.7)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 8.6%; p_ROPE = 0.077
- MCPH1 (partial):
  - β = -0.59, 89%HDI = [-2.52, 1.43]
  - posterior probability p(β<0) = 0.7 (evidence ratio = 2.3), p(β=0) = 0.72 (evidence ratio = 2.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 12.7%; p_ROPE = 0.114

Figure 153. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 154. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 155. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 156. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.20 (0.01, 0.40), p=0.036, decomposed into:
average direct effect (ADE): 0.01 (-0.18, 0.25), p=0.96, and
average indirect effect (ACME) mediated by ASPM-D: 0.19 (0.02, 0.34), p=0.024, mediating 95.9% (-1.7%, 470.4%), p=0.052 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.34 ±0.18, p=7.4e-11, and
- effect of ASPM-D on tone: -0.86 ±0.39, p=0.028.

For MCPH1-D:

TE: 0.18 (-0.01, 0.39), p=0.064, decomposed into:
ADE: 0.30 (-0.15, 0.63), p=0.17, and
ACME: -0.12 (-0.39, 0.28), p=0.46, mediating -72.3% (-674.6%, 386.6%), p=0.5 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.08 ±0.10, p=7.6e-39, and
- effect of MCPH1-D on tone: 0.47 ±0.63, p=0.46.

Restricted sampling

Figure 157. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM-D and MCPH1-D; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (solid), 0.05 (dashed) and 0.10 (dotted).

For ASPM-D:

TE: mean = 0.15, median = 0.15; 0.7% significant at α-level 0.05 and 4.8% significant at α-level 0.10; 90.1% > 0.0; one-sample one-sided t-test vs 0: t(999) = 50.2, p = 7.1e-276;
ADE: mean = 0.13, median = 0.13; 0.1% significant at α-level 0.05 and 2.4% significant at α-level 0.10; 90.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = 46.1, p = 1.3e-249;
ACME: mean = 0.016, median = 0.016; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 71.4% > 0.0; one-sample one-sided t-test vs 0: t(999) = 19.0, p = 5e-69;
β(Africa → allele): mean = -0.88, median = -0.88; 93.2% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -433.7, p = 0;
β(allele → tone | Africa): mean = -0.097, median = -0.11; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 69.5% < 0.0; one-sample one-sided t-test vs 0: t(999) = -14.6, p = 3.1e-44.

For MCPH1-D:

TE: mean = 0.15, median = 0.15; 0.9% significant at α-level 0.05 and 4.8% significant at α-level 0.10; 90.1% > 0.0; one-sample one-sided t-test vs 0: t(999) = 49.6, p = 3.8e-272;
ADE: mean = 0.12, median = 0.12; 0.0% significant at α-level 0.05 and 0.1% significant at α-level 0.10; 81.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 28.7, p = 7e-133;
ACME: mean = 0.024, median = 0.023; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 55.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 5.7, p = 7.3e-09;
β(Africa → allele): mean = -2.3, median = -2.3; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -1219.2, p = 0;
β(allele → tone | Africa): mean = 0.033, median = 0.021; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 48.5% < 0.0; one-sample one-sided t-test vs 0: t(999) = 1.9, p = 0.97.

Given the low sample size N = 29 unique families, relatively few effect sizes are big enough to be significant for each individual analysis; however, there are many more significant ACMEs for ASPM-D than for MCPH1-D: 0.0% vs 0.0% (NaN times) for α-level 0.05, and 0.0% vs 0.0% (NaN times) for α-level 0.10.

`brms`

Figure 158. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 159. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 160. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

All data

With Africa and tone1 coded numerically, the model fit is: χ²(1)=0.03, p=0.86; CFI=1.00, TLI=1.03, NNFI=1.03 and RFI=1.00:

Figure 161. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as numeric binary (tone_complex_num with Yes=1 and Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Likewise, with Africa and tone1 coded as ordered binary factors, the model fit is: χ²(1)=0.07, p=0.79; CFI=1.00, TLI=1.61, NNFI=1.61 and RFI=0.97:

Figure 162. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as ordered binary factors (tone_complex_ord with No < Yes, and Africa_ord with outside Africa < in Africa); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Restricted sampling

Figure 163. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

models fits:
- 100% of the p-values are not significant
- mean(CFI) = 1, median(CFI) = 1, sd(CFI) = 0.01, IQR(CFI) = 0
- mean(TLI) = 1.04, median(TLI) = 1.05, sd(TLI) = 0.06, IQR(TLI) = 0.08
- mean(NNFI) = 1.04, median(NNFI) = 1.05, sd(NNFI) = 0.06, IQR(NNFI) = 0.08
- mean(RFI) = 0.94, median(RFI) = 0.95, sd(RFI) = 0.06, IQR(RFI) = 0.07
Africa → ASPM-D: mean = -0.88, median = -0.89, sd = 0.062, IQR = 0.084, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -4.5e+02, p = 0;
Africa → MCPH1-D: mean = -2.3, median = -2.3, sd = 0.056, IQR = 0.074, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -1.3e+03, p = 0;
Africa → tone1: mean = 0.12, median = 0.11, sd = 0.21, IQR = 0.3, 69.9% > 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 18, p = 5.9e-64;
ASPM-D → tone1: mean = -0.013, median = -0.013, sd = 0.028, IQR = 0.039, 67.2% < 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -14, p = 3.9e-41;
MCPH1-D → tone1: mean = -0.004, median = -0.0039, as = 0.09, IQR = 0.13, 51.1% < 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -1.4, p = 0.08.

Tone counts

The resulting dataset has 110 observations, distributed among 76 unique Glottolg codes in 29 families (ranging from a minimum of 1 language per family to a maximum of 37, with a mean 3.8 and median 2 languages per family) and 4 macroareas.

There are 93:78:76 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
0	6	52	2	3	63
1	6	6	3	0	15
2	12	2	0	1	15
3	2	3	0	0	5
4	0	6	0	0	6
5	1	3	0	0	4
6	0	2	0	0	2
Sum	27	74	5	4	110

Figure 164. Distribution of tone counts.

Figure 165. Distribution of tone counts across the world.

Figure 166. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 100.0%
the Poisson model is not overdispersed: χ²(108) = 68.4, p = 1
macroarea: p_{macroarea/null} = 0.22
ASPM:
- by itself: R² = 5.7%, β = -0.28 ± 0.23, p_ASPM/null = 0.22
- quadratic: R² = 9.6%, β_ASPM2 = -0.24 ± 0.23, p_ASPM2/ASPM = 0.41
- with macroarea: R² = 17.6%, p_{macroarea/ASPM} = 0.37, p_{ASPM/macroarea} = 0.62
MCPH1:
- by itself: R² = 10.2%, β = -0.40 ± 0.21, p_MCPH1/null = 0.064
- quadratic: R² = 12.8%, β_MCPH12 = -0.39 ± 0.21, p_MCPH12/MCPH1 = 0.31
- with macroarea: R² = 15.8%, p_{macroarea/MCPH1} = 0.78, p_{MCPH1/macroarea} = 0.76
both alleles (no macroarea):
- ASPM + MCPH1: R² = 14.0%, β_ASPM = -0.18 ± 0.24, p_ASPM/MCPH1 = 0.44, β_MCPH1 = -0.34 ± 0.22, p_MCPH1/ASPM = 0.11, p_{ASPM+MCPH1/null} = 0.13,
- interaction: R² = 14.0%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.9

Randomization

We performed 1000 independent replications:

Regressions with randomizations for tone *counts*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	18%	16%	15%	13%	4%
unrestricted	none	alleles-together	11%	4%	3%	6%	4%	0%
unrestricted	none	alleles-independent	10%	3%	4%	5%	3%	0%
unrestricted	fixef	tone	0%	24%	18%	26%	18%	34%
unrestricted	fixef	alleles-together	86%	3%	3%	15%	4%	19%
unrestricted	fixef	alleles-independent	84%	3%	4%	12%	3%	15%
macroareas	none	tone	0%	40%	20%	18%	33%	22%
macroareas	none	alleles-together	32%	15%	4%	16%	17%	25%
macroareas	none	alleles-independent	30%	12%	4%	18%	16%	23%
macroareas	fixef	tone	0%	34%	24%	33%	22%	38%
macroareas	fixef	alleles-together	85%	4%	5%	21%	4%	35%
macroareas	fixef	alleles-independent	86%	3%	4%	19%	4%	33%
families	none	tone	11%	6%	8%	49%	2%	6%
families	none	alleles-together	24%	10%	14%	66%	0%	3%
families	none	alleles-independent	26%	9%	15%	65%	0%	5%
families	fixef	tone	17%	7%	12%	67%	1%	49%
families	fixef	alleles-together	86%	2%	6%	58%	1%	3%
families	fixef	alleles-independent	83%	2%	6%	53%	1%	6%

Restricted sampling

Figure 167. Results for 1000 restricted samplings. For ASPM-D (left): 97.7% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -57.2, mean = -0.35, p = 8.7e-318), 88.4%, when controlling for the macroarea (t(999) = -35.2, mean = -0.31, p = 2.6e-177), and 88.5% when controlling for both macroarea and MCPH1 (t(999) = -36.1, mean = -0.33, p = 2.6e-183). For MCPH1-D (right): 99.9% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -77.4, mean = -0.31, p = 0), 50.8% when controlling for the macroarea (t(999) = 1.5, mean = 0.02, p = 0.93), and 44.1% when controlling for both macroarea and ASPM (t(999) = 7.5, mean = 0.10, p = 1).

`brms`

ASPM only:
- β = -0.2, 89%HDI = [-0.65, 0.24]
- posterior probability p(β<0) = 0.77 (evidence ratio = 3.3), p(β=0) = 0.9 (evidence ratio = 9.1)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 24.7%; p_ROPE = 0.22
- comparison ‘null’ vs ‘ASPM’: [B> L> W>(83%:17%) K>]: moderate evidence for null against ASPM (BF=6.54), LOO=1.59 [SE=0.82], WAIC=1.60 [SE=0.85], KFOLD=2.27 [SE=1.55]
MCPH1 only:
- β = -0.3, 89%HDI = [-0.79, 0.18]
- posterior probability p(β<0) = 0.84 (evidence ratio = 5.5), p(β=0) = 0.86 (evidence ratio = 6.2)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 15.8%; p_ROPE = 0.141
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(58%:42%) K>]: moderate evidence for null against MCPH1 (BF=5.03), LOO=0.07 [SE=0.70], WAIC=0.32 [SE=0.59], KFOLD=1.38 [SE=0.83]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W>(81%:19%) K>>]: very strong evidence for null against both (BF=67.8), LOO=1.39 [SE=0.84], WAIC=1.42 [SE=1.02], KFOLD=4.66 [SE=1.61]
- interaction:
  - posterior probability p(=0) = 0.9 (evidence ratio = 8.7)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 24%; p_ROPE = 0.214
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L= W=(58%:42%) K<]: moderate evidence for no interaction against with interaction (BF=8.92), LOO=0.36 [SE=0.71], WAIC=0.31 [SE=0.37], KFOLD=-6.87 [SE=3.51]
- ASPM (partial):
  - β = -0.17, 89%HDI = [-0.61, 0.24]
  - posterior probability p(β<0) = 0.74 (evidence ratio = 2.9), p(β=0) = 0.91 (evidence ratio = 9.7)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 27%; p_ROPE = 0.24
- MCPH1 (partial):
  - β = -0.27, 89%HDI = [-0.77, 0.20]
  - posterior probability p(β<0) = 0.82 (evidence ratio = 4.7), p(β=0) = 0.86 (evidence ratio = 6.3)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 17.3%; p_ROPE = 0.154

Figure 168. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 169. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 170. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.81 (0.19, 1.64), p=0.006, decomposed into:
average direct effect (ADE): -0.20 (-0.91, 0.42), p=0.53, and
average indirect effect (ACME) mediated by ASPM-D: 1.01 (0.49, 1.89), p=0, mediating 124.1% (61.9%, 380.1%), p=0.006 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.34 ±0.18, p=3.1e-11, and
- effect of ASPM-D on tone: -0.58 ±0.14, p=3.9e-05.

For MCPH1-D:

TE: 0.62 (0.13, 1.17), p=0.018, decomposed into:
ADE: 0.62 (-0.69, 2.13), p=0.35, and
ACME: 0.00 (-1.26, 1.27), p=1, mediating 0.3% (-277.8%, 294.1%), p=1 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.07 ±0.10, p=1e-39, and
- effect of MCPH1-D on tone: -0.01 ±0.22, p=0.96.

Restricted sampling

Figure 171. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM and MCPH1; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (dotted), 0.05 (solid) and 0.10 (dashed).

For ASPM-D:

TE: mean = 1.2, median = 1.1; 55.1% significant at α-level 0.05 and 65.0% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 72.9, p = 0;
ADE: mean = 0.91, median = 0.9; 32.4% significant at α-level 0.05 and 46.1% significant at α-level 0.10; 98.3% > 0.0; one-sample one-sided t-test vs 0: t(999) = 60.8, p = 0;
ACME: mean = 0.26, median = 0.22; 3.0% significant at α-level 0.05 and 11.2% significant at α-level 0.10; 78.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 25.7, p = 8.1e-113;
β(Africa → allele): mean = -0.89, median = -0.89; 92.1% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -447.7, p = 0;
β(allele → tone | Africa): mean = -0.18, median = -0.17; 6.5% significant at α-level 0.05 and 14.2% significant at α-level 0.10; 78.7% < 0.0; one-sample one-sided t-test vs 0: t(999) = -27.1, p = 3.3e-122.

For MCPH1-D:

TE: mean = 1.1, median = 1.1; 55.6% significant at α-level 0.05 and 64.9% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 74.9, p = 0;
ADE: mean = 0.79, median = 0.74; 1.1% significant at α-level 0.05 and 3.7% significant at α-level 0.10; 70.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = 15.0, p = 1.6e-46;
ACME: mean = 0.31, median = 0.36; 0.2% significant at α-level 0.05 and 2.9% significant at α-level 0.10; 60.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = 5.7, p = 8.9e-09;
β(Africa → allele): mean = -2.3, median = -2.3; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -1254.2, p = 0;
β(allele → tone | Africa): mean = -0.12, median = -0.13; 0.4% significant at α-level 0.05 and 2.7% significant at α-level 0.10; 67.5% < 0.0; one-sample one-sided t-test vs 0: t(999) = -13.5, p = 1.3e-38.

Given the low sample size N = 35 unique families, relatively few effect sizes are big enough to be significant; however, there are many more significant indirect effects (ACME) for ASPM-D than for MCPH1-D: 6.5% vs 0.4% (16.2 times) for α-level 0.05, and 14.2% vs 2.7% (5.3 times) for α-level 0.10.

`brms`

Figure 172. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 173. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 174. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

Please note that path analysis uses a linear model (so not a Poisson one) for the tone counts; also I only use the numeric coding for Africa.

All data

Coding Africa numerically, the model fits the data very well (χ²(1)=0.02, p=0.88; CFI=1.00, TLI=1.03, NNFI=1.03 and RFI=1.00):

Figure 175. Path analysis model with standardised coefficients and significance stars. Here, macroarea (Africa vs non-Africa) is coded as numeric binary (Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D..

Restricted sampling

Figure 176. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

It can be seen that:

the models fits:
- 100% of the p-values are not significant
- mean(CFI) = 1, median(CFI) = 1, sd(CFI) = 0, IQR(CFI) = 0
- mean(TLI) = 1.04, median(TLI) = 1.05, sd(TLI) = 0.06, IQR(TLI) = 0.07
- mean(NNFI) = 1.04, median(NNFI) = 1.05, sd(NNFI) = 0.06, IQR(NNFI) = 0.07
- mean(RFI) = 0.94, median(RFI) = 0.95, sd(RFI) = 0.05, IQR(RFI) = 0.07
Africa → ASPM-D: mean = -0.89, median = -0.89, sd = 0.064, IQR = 0.084, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -4.4e+02, p = 0
Africa → MCPH1-D: mean = -2.3, median = -2.3, sd = 0.057, IQR = 0.078, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -1.3e+03, p = 0
Africa → tone counts: mean = 0.45, median = 0.49, sd = 0.89, IQR = 1.2, 70.2% > 0; 3.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 16, p = 1.1e-51
ASPM-D → tone counts: mean = -0.16, median = -0.16, sd = 0.19, IQR = 0.26, 79.9% < 0; 7.3% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -27, p = 2.7e-122
MCPH1-D → tone counts: mean = -0.18, median = -0.18, as = 0.37, IQR = 0.51, 69.2% < 0; 0.1% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -16, p = 4.7e-49

Appendix IV: Excluding ambiguous samples

The correspondence between genetic samples and languages is given below (excluding the 139 samples that unambiguously correspond to a single language):

Genetic samples corresponding to more than 1 language.
pop_ID	n_languages	n_families	languages	families
SA004382R	144	1	’Are’are, Adzera, Äiwoo, Ajië, Amara, Aneityum, Araki, Aribwatsa, Arop-Lokep, Arosi, Aulua, Babatana, Bannoni, Big Nambas, Carolinian, Cemuhî, Cheke Holo, Chuukese, Dehu, Dumbea, East Ambae, East Futuna, East Uvean, Fijian, Futuna-Aniwa, Fwâi, Gapapaiwa, Gela, Gilbertese, Gumawana, Halia, Hano, Hawaiian, Hoava, Iaai, Iduna, Kairiru, Kapingamarangi, Kara (Papua New Guinea), Kaulong, Kela (Papua New Guinea), Kele (Papua New Guinea), Kilivila, Kokota, Kosraean, Kuanua, Kwaio, Kwamera, Labu, Lala, Lamenu, Lau, Lenakel, Lewo, Longgu, Loniu, Lonwolwol, Lou, Luangiua, Lusi, Maisin, Maleu-Kilenge, Manam, Maori, Marshallese, Matukar, Mbula, Mekeo, Mele-Fila, Minaveha, Mokilese, Mono-Alu, Motu, Muduapa, Musom, Mussau-Emira, Muyuw, Mwotlap, Nakanai, Nalik, Natügu, Nauru, Nehan, Nêlêmwa-Nixumwak, Nengone, Neve’ei, Niuafo’ou, Niuean, North Efate, North Marquesan, Nukuoro, Paama, Patep, Patpatar, Pingelapese, Pohnpeian, Port Sandwich, Puluwatese, Rapanui, Rennell-Bellona, Rotuman, Roviana, Sa’a, Saliba, Samoan, Saposa, Siar-Lak, Sie, Sinaugoro, Sio, Sobei, Sonsorol, South Efate, South Marquesan, Southwest Tanna, Sudest, Sursurunga, Tahitian, Takia, Tamambo, Tawala, Teanu, Teop, Tigak, Tirax, Tiri-Mea, To’abaita, Tobati, Tokelau, Tonga (Tonga Islands), Tuamotuan, Tumleo, Tungag, Tuvalu, Ulithian, Ura (Vanuatu), Uripiv-Wala-Rano-Atchin, Vaeakau-Taumako, Waima, Wanohe, Western Fijian, Woleaian, Xârâcùù, Yabem	Austronesian
SA001501H	23	4	Abau, Alamblak, Ambulas, Ap Ma, Awtuw, Bahinemo, Boikin, Chambri, Hanga Hundi, Iatmul, Iwam, Kaian, Kire, Kwoma, Manambu, Mehek, Murik (Papua New Guinea), Namia, Rao, Watam, Wogamusin, Yessan-Mayo, Yimas	Ap Ma, Lower Sepik-Ramu, Ndu, Sepik
SA001818S	9	1	Herero, Kuanyama, Kwambi, Mbalanhu, Ndonga, Ngandyera, Southern Sotho, Tswana, Zulu	Atlantic-Congo
SA004368V	7	1	Amharic, Awngi, Bilin, Geez, Qimant, Tigrinya, Xamtanga	Afro-Asiatic
SA004046O	6	1	Bukusu, Idakho-Isukha-Tiriki, Kisa, Masaaba, Saamia, Tsotso	Atlantic-Congo
SA001469U	5	3	East Taa, Hai//om-Akhoe, Nama (Namibia), North-Central Ju, South-Eastern Ju	Khoe-Kwadi, Kxa, Tuu
SA001467S	4	1	Eastern Maninkakan, Kita Maninkakan, Mandinka, Western Maninkakan	Mande
SA001819T	4	1	Gusii, Kamba (Kenya), Kikuyu, Meru	Atlantic-Congo
SA003646T	4	1	Eastern Maninkakan, Kita Maninkakan, Mandinka, Western Maninkakan	Mande
SA001476S	3	1	Eastern Balochi, Southern Balochi, Western Balochi	Indo-European
SA001478U	3	1	Eastern Balochi, Southern Balochi, Western Balochi	Indo-European
SA004365S	3	1	Kahe, Machame, Mochi	Atlantic-Congo
SA004371P	3	1	Modern Hebrew, South Levantine Arabic, Standard Arabic	Afro-Asiatic
ESTONIAN_VAR	2	1	Estonian, South Estonian	Uralic
MB2005_BakolaPygmy	2	1	Gyele, Kwasio	Atlantic-Congo
Qatari	2	1	Gulf Arabic, Standard Arabic	Afro-Asiatic
SA001466R	2	1	Efe, Lese	Central Sudanic
SA001474Q	2	1	South Levantine Arabic, Standard Arabic	Afro-Asiatic
SA001483Q	2	1	Mandarin Chinese, Yue Chinese	Sino-Tibetan
SA001486T	2	1	Central Mashan Hmong, Hmong Njua	Hmong-Mien
SA001493R	2	1	Lü, Tai Nüa	Tai-Kadai
SA001508O	2	1	English, Scots	Indo-European
SA002254N	2	1	South Levantine Arabic, Standard Arabic	Afro-Asiatic
SA002257Q	2	1	South Levantine Arabic, Standard Arabic	Afro-Asiatic
SA002262M	2	1	Central Pashto, Northern Pashto	Indo-European
SA003028N	2	1	Estonian, South Estonian	Uralic
SA004111H	2	1	English, Spanish	Indo-European
SA004238R	2	1	Lü, Tai Nüa	Tai-Kadai
SA004361O	2	1	Efe, Lese	Central Sudanic
SA004370O	2	1	Judeo-Yemeni Arabic, Modern Hebrew	Afro-Asiatic
SA004378W	2	1	English, Irish	Indo-European
SA004587Y	2	1	Mongolia Buriat, Russia Buriat	Mongolic-Khitan
SA004592U	2	1	Mandarin Chinese, Yue Chinese	Sino-Tibetan
SA004599B	2	1	Erzya, Moksha	Uralic
SA004603N	2	1	Church Slavic, Russian	Indo-European
SA004623P	2	1	Georgian, Mingrelian	Kartvelian

Even if it is very conservative (e.g., Church Slavic and Russian corresponding to SA004603N are very similar for tone, as are Modern Hebrew, South Levantine Arabic and Standard Arabic corresponding to SA004371P), I removed from this analysis all genetic samples that map to more than 1 language.

This results in 139 unique genetic samples corresponding to 103 (meta)populations, each mapping to a single language, distributed across 91 unique languages (i.e., it is still the case that more than one sample maps to the same language) in 4 macroareas:

Africa	Eurasia	America	Papunesia
16	109	10	4

tone1

There are 126 observations, distributed among 88 unique Glottolg codes in 30 families (ranging from a minimum of 1 language per family to a maximum of 37, with a mean 4.2 and median 2 languages per family) and 4 macroareas.

There are 126:100:88 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
No	2	79	4	4	89
Yes	14	17	6	0	37
Sum	16	96	10	4	126

Figure 177. Distribution of tone1.

Figure 178. Map of tone1.

Figure 179. Relationship between tone1, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 79.9%
macroarea: p_{macroarea/null} = 0.0027
ASPM:
- by itself: R² = 6.9%, β = -0.92 ± 0.54, p_ASPM/null = 0.094
- quadratic: R² = 6.3%, β_ASPM2 = -0.91 ± 0.52, p_ASPM2/ASPM = 0.77
- with macroarea: R² = 54.9%, p_{macroarea/ASPM} = 0.008, p_{ASPM/macroarea} = 0.48
MCPH1:
- by itself: R² = 7.1%, β = -1.01 ± 0.47, p_MCPH1/null = 0.032
- quadratic: R² = 7.2%, β_MCPH12 = -1.02 ± 0.47, p_MCPH12/MCPH1 = 0.9
- with macroarea: R² = 53.3%, p_{macroarea/MCPH1} = 0.018, p_{MCPH1/macroarea} = 0.45
both alleles (no macroarea):
- ASPM + MCPH1: R² = 10.6%, β_ASPM = -0.58 ± 0.60, p_ASPM/MCPH1 = 0.36, β_MCPH1 = -0.77 ± 0.48, p_MCPH1/ASPM = 0.1, p_{ASPM+MCPH1/null} = 0.065,
- interaction: R² = 10.0%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.56

Alleles on macroarea

the alleles are very strongly clustered within families:
- ASPM: ICC = 100.0%
- MCPH1: ICC = 100.0%
macroarea predicts their distribution very strongly:
- ASPM: p = 8.6e-05, R² = 48.8%
- MCPH1: p = 6.2e-10, R² = 77.6%
separating Africa vs the rest of the world seems to drive most of this effect (both alleles have lower frequencies in Africa):
- ASPM: p = 0.023, R² = 15.8%
- MCPH1: p = 3.1e-07, R² = 47.5%

Randomization

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	4%	4%	0%	5%	0%
unrestricted	none	alleles-together	6%	5%	5%	7%	6%	4%
unrestricted	none	alleles-independent	7%	6%	5%	7%	5%	2%
unrestricted	fixef	tone	0%	6%	5%	13%	7%	15%
unrestricted	fixef	alleles-together	70%	6%	5%	25%	6%	19%
unrestricted	fixef	alleles-independent	67%	6%	6%	24%	5%	16%
macroareas	none	tone	0%	72%	28%	24%	67%	7%
macroareas	none	alleles-together	30%	24%	8%	28%	20%	40%
macroareas	none	alleles-independent	35%	29%	14%	37%	25%	46%
macroareas	fixef	tone	0%	5%	5%	14%	6%	21%
macroareas	fixef	alleles-together	64%	4%	4%	24%	5%	28%
macroareas	fixef	alleles-independent	64%	5%	4%	27%	4%	26%
families	none	tone	44%	21%	5%	24%	16%	38%
families	none	alleles-together	18%	15%	6%	32%	6%	17%
families	none	alleles-independent	30%	27%	20%	49%	19%	27%
families	fixef	tone	27%	6%	4%	37%	4%	38%
families	fixef	alleles-together	70%	8%	6%	50%	3%	24%
families	fixef	alleles-independent	74%	8%	10%	52%	5%	35%

Restricted sampling

Figure 180. Results for 1000 restricted samplings. For ASPM-D (left): 100% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -137.3, mean = -1.04, p = 0), 99.5%, when controlling for the macroarea (t(999) = -76.0, mean = -0.95, p = 0), and 99.5% when controlling for both macroarea and MCPH1 (t(999) = -67.1, mean = -1.13, p = 0). For MCPH1-D (right): 100% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -100.4, mean = -0.78, p = 0), 92.4% when controlling for the macroarea (t(999) = -45.7, mean = -1.42, p = 1.4e-247), and 92.5% when controlling for both macroarea and ASPM (t(999) = -47.9, mean = -1.75, p = 3.3e-261).

`brms`

ASPM only:
- β = -1.17, 89%HDI = [-3.06, 0.82]
- posterior probability p(β<0) = 0.84 (evidence ratio = 5.2), p(β=0) = 0.66 (evidence ratio = 1.9)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 9%; p_ROPE = 0.08
- comparison ‘null’ vs ‘ASPM’: [B= L< W<(15%:85%) K=]: anecdotal evidence for null against ASPM (BF=1.85), LOO=-2.20 [SE=1.49], WAIC=-1.73 [SE=0.89], KFOLD=0.55 [SE=2.12]
- comparison ‘null’ vs ‘ASPM’: [B= L< W<(15%:85%) K=]: anecdotal evidence for null against ASPM (BF=1.85), LOO=-2.20 [SE=1.49], WAIC=-1.73 [SE=0.89], KFOLD=0.55 [SE=2.12]
MCPH1 only:
- β = -1.5, 89%HDI = [-3.58, 0.81]
- posterior probability p(β<0) = 0.87 (evidence ratio = 7), p(β=0) = 0.59 (evidence ratio = 1.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 6.7%; p_ROPE = 0.06
- comparison ‘null’ vs ‘MCPH1’: [B= L<< W<<(7%:93%) K<]: anecdotal evidence for null against MCPH1 (BF=1.44), LOO=-3.54 [SE=1.49], WAIC=-2.57 [SE=0.77], KFOLD=-2.53 [SE=1.67]
- comparison ‘null’ vs ‘MCPH1’: [B= L<< W<<(7%:93%) K<]: anecdotal evidence for null against MCPH1 (BF=1.44), LOO=-3.54 [SE=1.49], WAIC=-2.57 [SE=0.77], KFOLD=-2.53 [SE=1.67]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L<< W<<(1%:99%) K=]: moderate evidence for null against both (BF=3.18), LOO=-4.04 [SE=1.54], WAIC=-4.41 [SE=1.11], KFOLD=-1.87 [SE=2.04]
- interaction:
  - posterior probability p(=0) = 0.64 (evidence ratio = 1.7)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 8.6%; p_ROPE = 0.076
  - comparison ‘no interaction’ vs ‘with interaction’: [B= L< W<<(21%:79%) K>]: anecdotal evidence for no interaction against with interaction (BF=1.25), LOO=-1.44 [SE=0.86], WAIC=-1.30 [SE=0.47], KFOLD=1.08 [SE=1.05]
- ASPM (partial):
  - β = -1.02, 89%HDI = [-3.30, 1.32]
  - posterior probability p(β<0) = 0.77 (evidence ratio = 3.3), p(β=0) = 0.7 (evidence ratio = 2.3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 11.1%; p_ROPE = 0.098
- MCPH1 (partial):
  - β = -1.53, 89%HDI = [-3.91, 0.86]
  - posterior probability p(β<0) = 0.86 (evidence ratio = 6.4), p(β=0) = 0.6 (evidence ratio = 1.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 7.2%; p_ROPE = 0.064

Figure 181. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 182. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 183. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 184. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.63 (0.37, 0.78), p=0, decomposed into:
average direct effect (ADE): 0.44 (0.15, 0.67), p=0, and
average indirect effect (ACME) mediated by ASPM-D: 0.19 (0.07, 0.34), p=0, mediating 30.0% (9.7%, 62.3%), p=0 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.17 ±0.25, p=6.3e-06, and
- effect of ASPM-D on tone: -1.02 ±0.30, p=0.00057.

For MCPH1-D:

TE: 0.64 (0.40, 0.79), p=0, decomposed into:
ADE: 0.71 (0.38, 0.86), p=0, and
ACME: -0.07 (-0.22, 0.22), p=0.37, mediating -12.3% (-51.6%, 35.7%), p=0.37 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.45 ±0.15, p=8.9e-32, and
- effect of MCPH1-D on tone: 0.40 ±0.44, p=0.37.

Restricted sampling

Figure 185. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM-D and MCPH1-D; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (solid), 0.05 (dashed) and 0.10 (dotted).

For ASPM-D:

TE: mean = 0.2, median = 0.15; 0.0% significant at α-level 0.05 and 10.4% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 59.0, p = 0;
ADE: mean = 0.15, median = 0.11; 0.0% significant at α-level 0.05 and 2.6% significant at α-level 0.10; 98.8% > 0.0; one-sample one-sided t-test vs 0: t(999) = 42.9, p = 5.1e-229;
ACME: mean = 0.057, median = 0.056; 0.0% significant at α-level 0.05 and 2.4% significant at α-level 0.10; 99.9% > 0.0; one-sample one-sided t-test vs 0: t(999) = 86.9, p = 0;
β(Africa → allele): mean = -0.63, median = -0.67; 5.0% significant at α-level 0.05 and 38.4% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -123.7, p = 0;
β(allele → tone | Africa): mean = -0.81, median = -0.8; 8.1% significant at α-level 0.05 and 31.0% significant at α-level 0.10; 99.9% < 0.0; one-sample one-sided t-test vs 0: t(999) = -100.0, p = 0.

For MCPH1-D:

TE: mean = 0.2, median = 0.15; 0.0% significant at α-level 0.05 and 10.4% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 57.6, p = 3.9e-320;
ADE: mean = 0.22, median = 0.2; 0.1% significant at α-level 0.05 and 2.1% significant at α-level 0.10; 98.9% > 0.0; one-sample one-sided t-test vs 0: t(999) = 58.3, p = 0;
ACME: mean = -0.017, median = -0.04; 0.0% significant at α-level 0.05 and 0.5% significant at α-level 0.10; 34.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = -4.9, p = 1;
β(Africa → allele): mean = -2.5, median = -2.5; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -487.0, p = 0;
β(allele → tone | Africa): mean = 0.37, median = 0.39; 0.0% significant at α-level 0.05 and 0.4% significant at α-level 0.10; 26.3% < 0.0; one-sample one-sided t-test vs 0: t(999) = 21.3, p = 1.

Given the low sample size N = 30 unique families, relatively few effect sizes are big enough to be significant for each individual analysis; however, there are many more significant ACMEs for ASPM-D than for MCPH1-D: 8.1% vs 0.0% (Inf times) for α-level 0.05, and 31.0% vs 0.4% (77.5 times) for α-level 0.10.

`brms`

Figure 186. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 187. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 188. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

All data

With Africa and tone1 coded numerically, the model fit is: χ²(1)=0.03, p=0.86; CFI=1.00, TLI=1.03, NNFI=1.03 and RFI=1.00:

Figure 189. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as numeric binary (tone_bin_num with Yes=1 and Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Likewise, with Africa and tone1 coded as ordered binary factors, the model fit is: χ²(1)=0.08, p=0.78; CFI=1.00, TLI=1.21, NNFI=1.21 and RFI=0.99:

Figure 190. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as ordered binary factors (tone_bin_ord with No < Yes, and Africa_ord with outside Africa < in Africa); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Restricted sampling

Figure 191. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

models fits:
- 80.7% of the p-values are not significant
- mean(CFI) = 0.98, median(CFI) = 0.99, sd(CFI) = 0.03, IQR(CFI) = 0.04
- mean(TLI) = 0.9, median(TLI) = 0.96, sd(TLI) = 0.2, IQR(TLI) = 0.27
- mean(NNFI) = 0.9, median(NNFI) = 0.96, sd(NNFI) = 0.2, IQR(NNFI) = 0.27
- mean(RFI) = 0.81, median(RFI) = 0.86, sd(RFI) = 0.17, IQR(RFI) = 0.24
Africa → ASPM-D: mean = -0.62, median = -0.66, sd = 0.16, IQR = 0.21, 100.0% < 0; 79.4% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -1.2e+02, p = 0;
Africa → MCPH1-D: mean = -2.5, median = -2.5, sd = 0.16, IQR = 0.23, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -5.1e+02, p = 0;
Africa → tone1: mean = 0.49, median = 0.53, sd = 0.36, IQR = 0.52, 88.1% > 0; 20.3% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 43, p = 4.3e-232;
ASPM-D → tone1: mean = -0.16, median = -0.16, sd = 0.051, IQR = 0.069, 99.9% < 0; 52.2% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -1e+02, p = 0;
MCPH1-D → tone1: mean = 0.0056, median = 0.02, as = 0.12, IQR = 0.17, 43.1% < 0; 1.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 1.4, p = 0.92.

tone2

The resulting dataset has 121 observations, distributed among 83 unique Glottolg codes in 30 families (ranging from a minimum of 1 language per family to a maximum of 36, with a mean 4 and median 1.5 languages per family) and 4 macroareas.

There are 121:95:83 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
No	8	82	9	4	103
Yes	6	11	1	0	18
Sum	14	93	10	4	121

Figure 192. Distribution of tone2.

Figure 193. Map of tone2.

Figure 194. Relationship between tone2, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 97.3%
macroarea: p_{macroarea/null} = 0.58
ASPM:
- by itself: R² = 0.7%, β = -0.89 ± 1.03, p_ASPM/null = 0.37
- quadratic: R² = 51.9%, β_ASPM2 = -10.31 ± 6.43, p_ASPM2/ASPM = 0.0089
- with macroarea: R² = 11.3%, p_{macroarea/ASPM} = 0.74, p_{ASPM/macroarea} = 0.78
MCPH1:
- by itself: R² = 1.2%, β = -1.18 ± 0.90, p_MCPH1/null = 0.15
- quadratic: R² = 2.2%, β_MCPH12 = -1.38 ± 0.90, p_MCPH12/MCPH1 = 0.31
- with macroarea: R² = 8.7%, p_{macroarea/MCPH1} = 0.94, p_{MCPH1/macroarea} = 0.47
both alleles (no macroarea):
- ASPM + MCPH1: R² = 1.5%, β_ASPM = -0.42 ± 1.20, p_ASPM/MCPH1 = 0.73, β_MCPH1 = -1.05 ± 0.96, p_MCPH1/ASPM = 0.24, p_{ASPM+MCPH1/null} = 0.33,
- interaction: R² = 2.2%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.68

Randomization

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	6%	5%	7%	6%	0%
unrestricted	none	alleles-together	42%	11%	10%	25%	10%	6%
unrestricted	none	alleles-independent	42%	9%	9%	28%	7%	4%
unrestricted	fixef	tone	0%	6%	5%	13%	6%	1%
unrestricted	fixef	alleles-together	81%	10%	10%	30%	10%	8%
unrestricted	fixef	alleles-independent	80%	11%	8%	27%	11%	9%
macroareas	none	tone	0%	43%	2%	7%	52%	0%
macroareas	none	alleles-together	46%	8%	7%	41%	8%	28%
macroareas	none	alleles-independent	46%	6%	7%	41%	7%	28%
macroareas	fixef	tone	0%	6%	5%	15%	5%	1%
macroareas	fixef	alleles-together	79%	9%	7%	37%	9%	21%
macroareas	fixef	alleles-independent	79%	10%	10%	35%	9%	21%
families	none	tone	82%	9%	5%	44%	10%	24%
families	none	alleles-together	49%	6%	6%	42%	6%	16%
families	none	alleles-independent	52%	7%	7%	48%	6%	20%
families	fixef	tone	87%	6%	7%	53%	5%	25%
families	fixef	alleles-together	87%	12%	7%	38%	13%	18%
families	fixef	alleles-independent	88%	13%	9%	42%	12%	21%

Restricted sampling

Figure 195. Results for 1000 restricted samplings. For ASPM-D (left): 99.7% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -76.7, mean = -0.49, p = 0), 99.8%, when controlling for the macroarea (t(999) = -76.3, mean = -0.77, p = 0), and 99.7% when controlling for both macroarea and MCPH1 (t(999) = -73.9, mean = -0.90, p = 0). For MCPH1-D (right): 73.3% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -29.3, mean = -0.24, p = 7.1e-137), 18.8% when controlling for the macroarea (t(999) = 28.6, mean = 0.91, p = 1), and 14.9% when controlling for both macroarea and ASPM (t(999) = 31.5, mean = 1.19, p = 1).

`brms`

ASPM only:
- β = -1.54, 89%HDI = [-4.00, 0.73]
- posterior probability p(β<0) = 0.87 (evidence ratio = 6.6), p(β=0) = 0.59 (evidence ratio = 1.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 7.4%; p_ROPE = 0.066
- comparison ‘null’ vs ‘ASPM’: [B= L= W<(27%:73%) K=]: anecdotal evidence for null against ASPM (BF=1.04), LOO=-0.73 [SE=0.83], WAIC=-0.98 [SE=0.61], KFOLD=0.18 [SE=1.19]
- comparison ‘null’ vs ‘ASPM’: [B= L= W<(27%:73%) K=]: anecdotal evidence for null against ASPM (BF=1.04), LOO=-0.73 [SE=0.83], WAIC=-0.98 [SE=0.61], KFOLD=0.18 [SE=1.19]
MCPH1 only:
- β = -1.14, 89%HDI = [-2.96, 0.90]
- posterior probability p(β<0) = 0.84 (evidence ratio = 5.4), p(β=0) = 0.64 (evidence ratio = 1.8)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 8.3%; p_ROPE = 0.074
- comparison ‘null’ vs ‘MCPH1’: [B= L< W<(30%:70%) K<]: anecdotal evidence for null against MCPH1 (BF=1.47), LOO=-1.02 [SE=0.99], WAIC=-0.86 [SE=0.58], KFOLD=-2.71 [SE=1.77]
- comparison ‘null’ vs ‘MCPH1’: [B= L< W<(30%:70%) K<]: anecdotal evidence for null against MCPH1 (BF=1.47), LOO=-1.02 [SE=0.99], WAIC=-0.86 [SE=0.58], KFOLD=-2.71 [SE=1.77]
both alleles:
- comparison ‘null’ vs ‘both’: [B= L< W<<(11%:89%) K<]: anecdotal evidence for null against both (BF=2.2), LOO=-1.21 [SE=0.96], WAIC=-2.12 [SE=0.73], KFOLD=-2.65 [SE=1.67]
- interaction:
  - posterior probability p(=0) = 0.68 (evidence ratio = 2.1)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 10.1%; p_ROPE = 0.09
  - comparison ‘no interaction’ vs ‘with interaction’: [B= L= W<(41%:59%) K=]: anecdotal evidence for no interaction against with interaction (BF=1.83), LOO=-0.03 [SE=0.55], WAIC=-0.34 [SE=0.23], KFOLD=0.69 [SE=0.86]
- ASPM (partial):
  - β = -1.32, 89%HDI = [-3.80, 1.15]
  - posterior probability p(β<0) = 0.81 (evidence ratio = 4.3), p(β=0) = 0.62 (evidence ratio = 1.6)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 7.6%; p_ROPE = 0.068
- MCPH1 (partial):
  - β = -0.96, 89%HDI = [-2.92, 1.13]
  - posterior probability p(β<0) = 0.79 (evidence ratio = 3.7), p(β=0) = 0.68 (evidence ratio = 2.1)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 10.6%; p_ROPE = 0.094

Figure 196. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 197. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 198. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 199. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Mediation and path analysis

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 0.32 (0.09, 0.57), p=0.004, decomposed into:
average direct effect (ADE): 0.14 (-0.07, 0.40), p=0.23, and
average indirect effect (ACME) mediated by ASPM-D: 0.19 (0.03, 0.37), p=0.004, mediating 58.1% (12.2%, 158.4%), p=0.008 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.34 ±0.26, p=8.8e-07, and
- effect of ASPM-D on tone: -0.92 ±0.38, p=0.016.

For MCPH1-D:

TE: 0.32 (0.09, 0.57), p=0, decomposed into:
ADE: 0.36 (-0.11, 0.70), p=0.13, and
ACME: -0.04 (-0.32, 0.36), p=0.74, mediating -21.2% (-179.3%, 161.8%), p=0.74 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.56 ±0.16, p=7e-31, and
- effect of MCPH1-D on tone: 0.22 ±0.53, p=0.68.

Restricted sampling

Figure 200. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM-D and MCPH1-D; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (solid), 0.05 (dashed) and 0.10 (dotted).

For ASPM-D:

TE: mean = 0.22, median = 0.23; 2.9% significant at α-level 0.05 and 15.2% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 61.3, p = 0;
ADE: mean = 0.17, median = 0.18; 0.1% significant at α-level 0.05 and 3.7% significant at α-level 0.10; 95.8% > 0.0; one-sample one-sided t-test vs 0: t(999) = 52.2, p = 9e-288;
ACME: mean = 0.043, median = 0.042; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 99.8% > 0.0; one-sample one-sided t-test vs 0: t(999) = 72.0, p = 0;
β(Africa → allele): mean = -0.74, median = -0.74; 9.7% significant at α-level 0.05 and 65.4% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -319.7, p = 0;
β(allele → tone | Africa): mean = -0.35, median = -0.35; 0.0% significant at α-level 0.05 and 0.0% significant at α-level 0.10; 99.6% < 0.0; one-sample one-sided t-test vs 0: t(999) = -81.0, p = 0.

For MCPH1-D:

TE: mean = 0.22, median = 0.23; 2.8% significant at α-level 0.05 and 14.9% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 61.3, p = 0;
ADE: mean = 0.33, median = 0.34; 0.0% significant at α-level 0.05 and 2.5% significant at α-level 0.10; 99.3% > 0.0; one-sample one-sided t-test vs 0: t(999) = 82.5, p = 0;
ACME: mean = -0.11, median = -0.12; 0.0% significant at α-level 0.05 and 0.9% significant at α-level 0.10; 19.1% > 0.0; one-sample one-sided t-test vs 0: t(999) = -28.4, p = 1;
β(Africa → allele): mean = -2.6, median = -2.6; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -725.0, p = 0;
β(allele → tone | Africa): mean = 0.7, median = 0.66; 0.0% significant at α-level 0.05 and 0.6% significant at α-level 0.10; 10.7% < 0.0; one-sample one-sided t-test vs 0: t(999) = 37.7, p = 1.

Given the low sample size N = 30 unique families, relatively few effect sizes are big enough to be significant for each individual analysis; however, there are many more significant ACMEs for ASPM-D than for MCPH1-D: 0.0% vs 0.0% (NaN times) for α-level 0.05, and 0.0% vs 0.6% (0.0 times) for α-level 0.10.

`brms`

Figure 201. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 202. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 203. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

All data

With Africa and tone1 coded numerically, the model fit is: χ²(1)=0.14, p=0.71; CFI=1.00, TLI=1.03, NNFI=1.03 and RFI=1.00:

Figure 204. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as numeric binary (tone_complex_num with Yes=1 and Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Likewise, with Africa and tone1 coded as ordered binary factors, the model fit is: χ²(1)=0.43, p=0.51; CFI=1.00, TLI=1.69, NNFI=1.69 and RFI=0.77:

Figure 205. Path analysis model with standardised coefficients and significance stars. tone1 and macroarea (Africa vs non-Africa) are coded as ordered binary factors (tone_complex_ord with No < Yes, and Africa_ord with outside Africa < in Africa); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D.

Restricted sampling

Figure 206. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

models fits:
- 84.6% of the p-values are not significant
- mean(CFI) = 0.98, median(CFI) = 0.99, sd(CFI) = 0.03, IQR(CFI) = 0.03
- mean(TLI) = 0.9, median(TLI) = 0.94, sd(TLI) = 0.2, IQR(TLI) = 0.27
- mean(NNFI) = 0.9, median(NNFI) = 0.94, sd(NNFI) = 0.2, IQR(NNFI) = 0.27
- mean(RFI) = 0.81, median(RFI) = 0.84, sd(RFI) = 0.17, IQR(RFI) = 0.22
Africa → ASPM-D: mean = -0.73, median = -0.74, sd = 0.072, IQR = 0.096, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -3.2e+02, p = 0;
Africa → MCPH1-D: mean = -2.6, median = -2.6, sd = 0.11, IQR = 0.16, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -7.3e+02, p = 0;
Africa → tone1: mean = 0.36, median = 0.37, sd = 0.22, IQR = 0.29, 95.1% > 0; 3.7% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 53, p = 1.7e-293;
ASPM-D → tone1: mean = -0.041, median = -0.04, sd = 0.027, IQR = 0.036, 93.9% < 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -49, p = 6.9e-266;
MCPH1-D → tone1: mean = 0.067, median = 0.073, as = 0.079, IQR = 0.093, 18.4% < 0; 0.1% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 27, p = 1.

Tone counts

There are 121:95:83 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
0	2	77	4	4	87
1	2	4	5	0	11
2	9	3	0	0	12
3	1	2	0	0	3
4	0	4	1	0	5
5	0	2	0	0	2
6	0	1	0	0	1
Sum	14	93	10	4	121

Figure 207. Distribution of tone counts.

Figure 208. Distribution of tone counts across the world.

Figure 209. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 100.0%
the Poisson model is not overdispersed: χ²(119) = 60.4, p = 1
macroarea: p_{macroarea/null} = 0.037
ASPM:
- by itself: R² = 4.5%, β = -0.33 ± 0.29, p_ASPM/null = 0.28
- quadratic: R² = 34.1%, β_ASPM2 = -0.72 ± 0.41, p_ASPM2/ASPM = 0.086
- with macroarea: R² = 82.1%, p_{macroarea/ASPM} = 0.061, p_{ASPM/macroarea} = 0.82
MCPH1:
- by itself: R² = 5.1%, β = -0.37 ± 0.24, p_MCPH1/null = 0.12
- quadratic: R² = 6.0%, β_MCPH12 = -0.37 ± 0.24, p_MCPH12/MCPH1 = 0.38
- with macroarea: R² = 81.4%, p_{macroarea/MCPH1} = 0.11, p_{MCPH1/macroarea} = 0.92
both alleles (no macroarea):
- ASPM + MCPH1: R² = 8.6%, β_ASPM = -0.24 ± 0.31, p_ASPM/MCPH1 = 0.43, β_MCPH1 = -0.32 ± 0.24, p_MCPH1/ASPM = 0.17, p_{ASPM+MCPH1/null} = 0.22,
- interaction: R² = 8.5%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.94

Randomization

We performed 1000 independent replications:

Regressions with randomizations for tone *counts*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	22%	18%	15%	15%	7%
unrestricted	none	alleles-together	27%	6%	6%	6%	6%	2%
unrestricted	none	alleles-independent	26%	6%	6%	5%	7%	0%
unrestricted	fixef	tone	0%	28%	20%	34%	19%	46%
unrestricted	fixef	alleles-together	98%	8%	6%	30%	7%	37%
unrestricted	fixef	alleles-independent	98%	8%	6%	30%	8%	39%
macroareas	none	tone	0%	41%	22%	25%	30%	25%
macroareas	none	alleles-together	50%	18%	13%	26%	12%	28%
macroareas	none	alleles-independent	53%	17%	12%	26%	16%	31%
macroareas	fixef	tone	0%	35%	25%	39%	24%	42%
macroareas	fixef	alleles-together	98%	11%	11%	34%	8%	45%
macroareas	fixef	alleles-independent	98%	9%	11%	39%	8%	45%
families	none	tone	89%	34%	23%	62%	17%	41%
families	none	alleles-together	50%	22%	20%	54%	5%	19%
families	none	alleles-independent	58%	27%	28%	62%	10%	25%
families	fixef	tone	86%	11%	16%	70%	2%	48%
families	fixef	alleles-together	99%	11%	15%	65%	3%	37%
families	fixef	alleles-independent	97%	10%	14%	63%	5%	45%

Restricted sampling

Figure 210. Results for 1000 restricted samplings. For ASPM-D (left): 100% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -141.3, mean = -0.40, p = 0), 99.2%, when controlling for the macroarea (t(999) = -65.0, mean = -0.48, p = 0), and 99.3% when controlling for both macroarea and MCPH1 (t(999) = -62.1, mean = -0.61, p = 0). For MCPH1-D (right): 94.4% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -52.3, mean = -0.14, p = 1.8e-288), 1.7% when controlling for the macroarea (t(999) = 60.7, mean = 0.95, p = 1), and 1.3% when controlling for both macroarea and ASPM (t(999) = 54.3, mean = 1.19, p = 1).

`brms`

ASPM only:
- β = -0.36, 89%HDI = [-1.06, 0.33]
- posterior probability p(β<0) = 0.8 (evidence ratio = 3.9), p(β=0) = 0.84 (evidence ratio = 5.3)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 14.1%; p_ROPE = 0.126
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(64%:36%) K=]: moderate evidence for null against ASPM (BF=7.92), LOO=0.10 [SE=0.91], WAIC=0.59 [SE=0.62], KFOLD=0.09 [SE=1.48]
MCPH1 only:
- β = -0.12, 89%HDI = [-0.81, 0.56]
- posterior probability p(β<0) = 0.63 (evidence ratio = 1.7), p(β=0) = 0.88 (evidence ratio = 7.2)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 19%; p_ROPE = 0.169
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(55%:45%) K=]: moderate evidence for null against MCPH1 (BF=7.2), LOO=0.43 [SE=0.49], WAIC=0.20 [SE=0.31], KFOLD=0.28 [SE=1.64]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W>(77%:23%) K=]: very strong evidence for null against both (BF=35.1), LOO=1.24 [SE=0.86], WAIC=1.22 [SE=0.72], KFOLD=0.58 [SE=1.48]
- interaction:
  - posterior probability p(=0) = 0.86 (evidence ratio = 6.3)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 16.2%; p_ROPE = 0.144
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L<< W<<(32%:68%) K=]: moderate evidence for no interaction against with interaction (BF=7.21), LOO=-1.01 [SE=0.46], WAIC=-0.77 [SE=0.26], KFOLD=0.66 [SE=0.89]
- ASPM (partial):
  - β = -0.3, 89%HDI = [-1.01, 0.40]
  - posterior probability p(β<0) = 0.76 (evidence ratio = 3.2), p(β=0) = 0.86 (evidence ratio = 6.1)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 16.5%; p_ROPE = 0.147
- MCPH1 (partial):
  - β = -0.07, 89%HDI = [-0.73, 0.60]
  - posterior probability p(β<0) = 0.6 (evidence ratio = 1.5), p(β=0) = 0.88 (evidence ratio = 7.4)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 20%; p_ROPE = 0.178

Figure 211. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 212. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 213. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Mediation analysis

`(g)lm`

All data

For ASPM-D:

total effect (TE) of being in Africa on tone: 1.63 (0.64, 3.36), p=0, decomposed into:
average direct effect (ADE): 0.43 (-0.21, 1.26), p=0.19, and
average indirect effect (ACME) mediated by ASPM-D: 1.20 (0.47, 2.56), p=0, mediating 73.4% (44.5%, 123.6%), p=0 of the effect, resulting from:
- effect of being in Africa on ASPM-D: -1.34 ±0.26, p=8.8e-07, and
- effect of ASPM-D on tone: -0.75 ±0.16, p=2e-06.

For MCPH1-D:

TE: 1.19 (0.53, 2.06), p=0, decomposed into:
ADE: 3.69 (0.97, 9.95), p=0, and
ACME: -2.50 (-8.35, -0.01), p=0.05, mediating -165.7% (-811.6%, -0.5%), p=0.05 of the effect, resulting from:
- effect of being in Africa on MCPH1-D: -2.56 ±0.16, p=7e-31, and
- effect of MCPH1-D on tone: 0.43 ±0.24, p=0.081.

Restricted sampling

Figure 214. Mediation analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost panels show the distribution of point estimates of the Total Effect (TE), the Direct Effect (ADE) and the Indirect Effect (ACME) for ASPM and MCPH1; the middle panels show the distribution of the p-values for the same effects, while the rightmost panels show the distribution of the regression slopes (β) for the two alleles, top: for the regression of the allele frequency on within vs outside Africa, and bottom: for the regression of tone on the allele while controlling for within vs outside Africa. The black vertical lines show: 0.0 (dotted), 0.05 (solid) and 0.10 (dashed).

For ASPM-D:

TE: mean = 1.2, median = 1.3; 44.2% significant at α-level 0.05 and 67.0% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 116.8, p = 0;
ADE: mean = 0.89, median = 0.9; 14.8% significant at α-level 0.05 and 32.0% significant at α-level 0.10; 99.8% > 0.0; one-sample one-sided t-test vs 0: t(999) = 86.8, p = 0;
ACME: mean = 0.35, median = 0.34; 0.0% significant at α-level 0.05 and 1.2% significant at α-level 0.10; 99.7% > 0.0; one-sample one-sided t-test vs 0: t(999) = 72.3, p = 0;
β(Africa → allele): mean = -0.73, median = -0.73; 10.3% significant at α-level 0.05 and 64.3% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -310.5, p = 0;
β(allele → tone | Africa): mean = -0.29, median = -0.3; 2.8% significant at α-level 0.05 and 10.2% significant at α-level 0.10; 99.8% < 0.0; one-sample one-sided t-test vs 0: t(999) = -93.0, p = 0.

For MCPH1-D:

TE: mean = 1.3, median = 1.3; 37.1% significant at α-level 0.05 and 61.0% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 101.0, p = 0;
ADE: mean = 43, median = 22; 73.6% significant at α-level 0.05 and 87.0% significant at α-level 0.10; 100.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = 23.8, p = 8.4e-100;
ACME: mean = -42, median = -21; 50.6% significant at α-level 0.05 and 66.2% significant at α-level 0.10; 0.0% > 0.0; one-sample one-sided t-test vs 0: t(999) = -23.1, p = 1;
β(Africa → allele): mean = -2.6, median = -2.6; 100.0% significant at α-level 0.05 and 100.0% significant at α-level 0.10; 100.0% < 0.0; one-sample one-sided t-test vs 0: t(999) = -720.1, p = 0;
β(allele → tone | Africa): mean = 0.88, median = 0.87; 50.8% significant at α-level 0.05 and 67.8% significant at α-level 0.10; 0.2% < 0.0; one-sample one-sided t-test vs 0: t(999) = 78.3, p = 1.

Given the low sample size N = 35 unique families, relatively few effect sizes are big enough to be significant; however, there are many more significant indirect effects (ACME) for ASPM-D than for MCPH1-D: 2.8% vs 50.8% (0.1 times) for α-level 0.05, and 10.2% vs 67.8% (0.2 times) for α-level 0.10.

`brms`

Figure 215. Graphical representation of the Bayesian mediation analysis for ASPM-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 216. Graphical representation of the Bayesian mediation analysis for MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Figure 217. Graphical representation of the Bayesian mediation analysis for both ASPM-D and MCPH1-D showing the means of the effects and the actual partial regression coefficients, with their 89% HDIs and p-ROPEs. The colors reflect the sign of the mean estimate (blue=negative, red=positive, gray=(p-ROPE >= 0.05)); solid=(0 not in the HDI), dashed=(0 is in the HDI).

Path analysis

Please note that path analysis uses a linear model (so not a Poisson one) for the tone counts; also I only use the numeric coding for Africa.

All data

Coding Africa numerically, the model fits the data very well (χ²(1)=0.14, p=0.71; CFI=1.00, TLI=1.03, NNFI=1.03 and RFI=1.00):

Figure 218. Path analysis model with standardised coefficients and significance stars. Here, macroarea (Africa vs non-Africa) is coded as numeric binary (Africa_num with in Africa=1); ASPM_z is ASPM-D and MCPH1_z is MCPH1-D..

Restricted sampling

Figure 219. Path analysis for 1000 restricted samples (i.e., picking one random language per family). The leftmost row of two plots shows the coefficient estimates and the p-values, respectively, for the five paths in the model (see the path plots above). The rightmost plot shows the various fit indices. The black horiontal lines show: 0.0 (solid), 0.05 (dashed) and 1.0 (dotted).

It can be seen that:

the models fits:
- 85.3% of the p-values are not significant
- mean(CFI) = 0.98, median(CFI) = 0.99, sd(CFI) = 0.03, IQR(CFI) = 0.04
- mean(TLI) = 0.91, median(TLI) = 0.93, sd(TLI) = 0.19, IQR(TLI) = 0.28
- mean(NNFI) = 0.91, median(NNFI) = 0.93, sd(NNFI) = 0.19, IQR(NNFI) = 0.28
- mean(RFI) = 0.81, median(RFI) = 0.84, sd(RFI) = 0.16, IQR(RFI) = 0.23
Africa → ASPM-D: mean = -0.73, median = -0.73, sd = 0.07, IQR = 0.095, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -3.3e+02, p = 0
Africa → MCPH1-D: mean = -2.6, median = -2.6, sd = 0.12, IQR = 0.15, 100.0% < 0; 100.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -7.1e+02, p = 0
Africa → tone counts: mean = 2.7, median = 2.7, sd = 0.84, IQR = 1.3, 100.0% > 0; 65.4% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 1e+02, p = 0
ASPM-D → tone counts: mean = -0.17, median = -0.17, sd = 0.12, IQR = 0.16, 92.2% < 0; 0.0% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = -46, p = 2.5e-251
MCPH1-D → tone counts: mean = 0.68, median = 0.68, as = 0.28, IQR = 0.38, 0.8% < 0; 36.1% significant at α-level 0.05; one-sample one-sided t-test vs 0: t(999) = 76, p = 1

Appendix V: Alternative agreement coding of tone

The explicit hierarchy of the sources for tone as used in the paper is:

for binary and 3-way: LAPSyD > WALS > DL2007 > WPHON > PHOIBLE, and
for counts: LAPSyD > WPHON > PHOIBLE

but there can be other justified choices; among these choices, I test here the alternative hierarchy:

for binary and 3-way: WALS > WPHON > LAPSyD > DL2007 > PHOIBLE, and
for counts: WPHON > LaPSyD > PHOIBLE.

The “corrected” counts are computed as LAPSyD_corr = 0.074 +1.256LAPSyD -0.11LAPSyD², and PHOIBLE_corr = 0.415 +0.815PHOIBLE -0.049PHOIBLE², respectively.

Relationship between alternative and main agreement codings

Binary classification

	No	Yes
No	2527	14
Yes	13	1244

Figure 220. Relationship between the agreement and the `alternative’ agreement codings for the binary classification.

Pearson’s Chi-squared test with Yates’ continuity correction: `cooc_tab`
Test statistic	df	P value
3673	1	0 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
3677	NA	9.999e-05 * * *

The disagreements are:

The 27 languages for which the original and the alternative binary codings disagree
glottocode	PHOIBLE	WALS	LAPSyD	LAPSyD (#)	DL2007	WPHON	agreement (orig)	decision (orig)	agreement (alt)	decision (alt)
amah1246	0	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
beja1238	0	Simple	None	0	NA	1	No	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	Yes	WALS
broo1239	NA	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
chua1250	0	NA	None	0	NA	3	No	LAPSyD	Yes	WPHON
cofa1242	0	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
fuln1247	0	Simple	None	0	NA	0	No	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	Yes	WALS
gras1249	0	Simple	None	0	NA	1	No	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	Yes	WALS
hopi1249	0	Simple	None	0	NA	1	No	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	Yes	WALS
mand1446	NA	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
meri1244	NA	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
naas1242	0	NA	None	0	No	1	No	LAPSyD + Dediu & Ladd, Dediu & Ladd winns except when LAPSyD says Moderately complex or Complex	Yes	WPHON
sapu1248	NA	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
sout2982	0	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
wano1243	NA	NA	None	0	NA	1	No	LAPSyD	Yes	WPHON
bora1263	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
brib1243	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
buru1296	2	None	NA	NA	Yes	0	Yes	WALS + Dediu & Ladd, Dediu & Ladd winns except when WALS says Complex	No	WALS
chim1309	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
darf1239	0	None	Simple	1	NA	2	Yes	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	No	WALS
lepc1244	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
lith1251	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
mund1330	1	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
scot1245	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON
sene1264	0	None	Simple	1	NA	1	Yes	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	No	WALS
shek1245	NA	NA	Complex	8	NA	0	Yes	LAPSyD	No	WPHON
wich1260	0	None	Simple	1	NA	1	Yes	LAPSyD + WALS, LAPSyD winns except when WALS says Complex	No	WALS
yuru1263	0	NA	Simple	1	NA	0	Yes	LAPSyD	No	WPHON

3-way classification

	None	Simple	Complex
None	2523	14	1
Simple	11	922	3
Complex	1	21	289

Figure 221. Relationship between the agreement and the `alternative’ agreement codings for the 3-way classification.

Pearson’s Chi-squared test: `cooc_tab`
Test statistic	df	P value
7027	4	0 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
7027	NA	9.999e-05 * * *

The disagreements are:

The 51 languages for which the original and the alternative 3-way codings disagree
glottocode	PHOIBLE	WALS	LAPSyD	LAPSyD (#)	DL2007	WPHON	agreement (orig)	decision (orig)	agreement (alt)	decision (alt)
amah1246	0	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
beja1238	0	Simple	None	0	NA	1	None	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
broo1239	NA	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
chua1250	0	NA	None	0	NA	3	None	LAPSyD	Simple	WPHON
cofa1242	0	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
fuln1247	0	Simple	None	0	NA	0	None	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
gras1249	0	Simple	None	0	NA	1	None	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
hopi1249	0	Simple	None	0	NA	1	None	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
mand1446	NA	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
meri1244	NA	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
naas1242	0	NA	None	0	No	1	None	LAPSyD wins	Simple	WPHON
sapu1248	NA	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
sout2982	0	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
wano1243	NA	NA	None	0	NA	1	None	LAPSyD	Simple	WPHON
ndut1239	0	Complex	None	0	NA	0	None	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Complex	WALS
bora1263	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
brib1243	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
chim1309	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
darf1239	0	None	Simple	1	NA	2	Simple	LAPSyD + WALS, LAPSyD winns except for Moderately complex	None	WALS
lepc1244	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
lith1251	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
mund1330	1	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
scot1245	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
sene1264	0	None	Simple	1	NA	1	Simple	LAPSyD + WALS, LAPSyD winns except for Moderately complex	None	WALS
wich1260	0	None	Simple	1	NA	1	Simple	LAPSyD + WALS, LAPSyD winns except for Moderately complex	None	WALS
yuru1263	0	NA	Simple	1	NA	0	Simple	LAPSyD	None	WPHON
east2652	1	Complex	Simple	1	NA	1	Simple	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Complex	WALS
nort2740	0	NA	Simple	1	NA	4	Simple	LAPSyD	Complex	WPHON
vani1248	0	Complex	Simple	1	NA	2	Simple	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Complex	WALS
shek1245	NA	NA	Complex	8	NA	0	Complex	LAPSyD	None	WPHON
abun1252	NA	NA	Moderately complex	2	NA	1	Complex	LAPSyD	Simple	WPHON
bamu1253	0	NA	NA	NA	Yes	3	Complex	From n_tones	Simple	WPHON
bass1258	NA	NA	Moderately complex	3	NA	2	Complex	LAPSyD	Simple	WPHON
cacu1241	0	Simple	Complex	3	NA	3	Complex	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
cent2144	2	NA	Complex	3	NA	2	Complex	LAPSyD	Simple	WPHON
diga1241	NA	NA	Complex	3	NA	3	Complex	LAPSyD	Simple	WPHON
gaam1241	2	Simple	Complex	3	NA	1	Complex	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
hlai1239	NA	NA	Moderately complex	2	NA	3	Complex	LAPSyD	Simple	WPHON
jeme1245	0	NA	Moderately complex	2	NA	3	Complex	LAPSyD	Simple	WPHON
jica1244	2	NA	Moderately complex	2	NA	1	Complex	LAPSyD	Simple	WPHON
kala1373	NA	Simple	Complex	4	NA	1	Complex	LAPSyD + WALS, LAPSyD winns except for Moderately complex	Simple	WALS
kris1246	3	NA	Complex	3	NA	3	Complex	LAPSyD	Simple	WPHON
lele1276	2	NA	Moderately complex	2	NA	2	Complex	LAPSyD	Simple	WPHON
madi1260	3	NA	Moderately complex	2	Yes	2	Complex	LAPSyD wins	Simple	WPHON
nort2732	NA	NA	NA	NA	Yes	3	Complex	From n_tones	Simple	WPHON
nucl1620	0	NA	Moderately complex	2	NA	2	Complex	LAPSyD	Simple	WPHON
puin1248	0	NA	Complex	3	NA	1	Complex	LAPSyD	Simple	WPHON
sand1273	4	Simple	Complex	3	Yes	2	Complex	LAPSyD wins	Simple	WALS
xhos1239	1	NA	NA	NA	Yes	2	Complex	From n_tones	Simple	WPHON
yaka1272	NA	NA	NA	NA	Yes	2	Complex	From n_tones	Simple	WPHON
yuhu1238	0	NA	Complex	3	NA	1	Complex	LAPSyD	Simple	WPHON

Counts

Figure 222. Relationship between the agreement and the `alternative’ agreement codings for the counts.

Pearson’s product-moment correlation: `agreement` and `agreement_alt`
Test statistic	df	P value	Alternative hypothesis	cor
164.8	3783	0 * * *	two.sided	0.9369

Spearman’s rank correlation rho: `agreement` and `agreement_alt`
Test statistic	P value	Alternative hypothesis	rho
193189299	0 * * *	two.sided	0.9786

Look at the serious disagreements (i.e., more than 1):

The 59 languages for which the original and the alternative count codings disagree, ordered by their absolute difference
glottocode	PHOIBLE	WALS	LAPSyD	LAPSyD (#)	DL2007	WPHON	agreement (orig)	agreement (alt)	difference (abs)
achu1247	0	Simple	Simple	1	NA	3	1	3	2
anga1290	0	Simple	Moderately complex	2	NA	0	2	0	2
awng1244	6	Simple	Simple	1	NA	3	1	3	2
cent2050	3	Simple	Simple	1	NA	3	1	3	2
efik1245	0	Simple	Moderately complex	2	NA	4	2	4	2
gaam1241	2	Simple	Complex	3	NA	1	3	1	2
gads1258	3	Complex	Complex	3	NA	1	3	1	2
hmon1333	NA	NA	NA	NA	NA	7	5	7	2
iumi1238	3	Complex	NA	NA	NA	7	5	7	2
kera1255	0	Complex	Moderately complex	2	NA	0	2	0	2
komc1235	6	NA	NA	NA	NA	7	5	7	2
koro1298	NA	None	None	0	NA	2	0	2	2
koyr1240	5	None	None	0	NA	2	0	2	2
kuta1241	NA	NA	NA	NA	NA	6	4	6	2
lamn1239	6	NA	NA	NA	NA	7	5	7	2
larg1235	NA	NA	NA	NA	NA	6	4	6	2
mind1253	0	Complex	NA	NA	NA	7	5	7	2
mruu1242	NA	NA	NA	NA	NA	7	5	7	2
murl1244	0	Simple	Simple	2	NA	4	2	4	2
nama1264	0	Complex	Complex	5	Yes	3	5	3	2
ncan1245	5	NA	NA	NA	NA	6	4	6	2
ngba1285	0	NA	NA	NA	NA	6	4	6	2
nort2747	NA	NA	NA	NA	NA	7	5	7	2
nort2819	2	Complex	NA	NA	NA	6	4	6	2
nucl1649	0	None	None	0	NA	2	0	2	2
nucl1770	NA	NA	NA	NA	NA	7	5	7	2
nung1283	0	Complex	Complex	5	NA	3	5	3	2
pira1253	0	Simple	Simple	1	NA	3	1	3	2
puin1248	0	NA	Complex	3	NA	1	3	1	2
puxi1243	NA	NA	NA	NA	NA	6	4	6	2
pwon1235	4	Complex	Complex	3	NA	5	3	5	2
smal1236	NA	NA	NA	NA	NA	7	5	7	2
sout2741	NA	NA	NA	NA	NA	6	4	6	2
sout2754	NA	NA	NA	NA	NA	7	5	7	2
sout2844	0	NA	NA	NA	NA	6	4	6	2
tain1252	0	NA	NA	NA	Yes	6	4	6	2
thak1245	0	NA	Simple	1	NA	3	1	3	2
timn1235	3	Simple	Simple	1	NA	3	1	3	2
veng1238	8	NA	NA	NA	NA	7	5	7	2
yako1252	NA	NA	NA	NA	NA	6	4	6	2
youn1235	NA	NA	NA	NA	NA	7	5	7	2
yuhu1238	0	NA	Complex	3	NA	1	3	1	2
bero1242	0	Complex	Complex	6	NA	3	6	3	3
chua1250	0	NA	None	0	NA	3	0	3	3
kala1373	NA	Simple	Complex	4	NA	1	4	1	3
lada1244	0	None	None	0	NA	3	0	3	3
mmen1238	4	NA	NA	NA	NA	8	5	8	3
nige1255	1	Complex	NA	NA	NA	8	5	8	3
nort2740	0	NA	Simple	1	NA	4	1	4	3
ticu1245	8	Complex	Complex	4	NA	7	4	7	3
aghe1239	1	Simple	Simple	1	NA	5	1	5	4
cent1394	NA	NA	Complex	3	NA	7	3	7	4
ejag1239	4	Complex	Complex	5	NA	1	5	1	4
monz1249	NA	NA	NA	NA	NA	9	5	9	4
gban1258	NA	NA	NA	NA	NA	10	5	10	5
vute1244	4	NA	NA	NA	NA	10	5	10	5
niel1243	2	Complex	NA	NA	NA	11	5	11	6
mali1285	NA	NA	Complex	10	NA	NA	10	2	8
shek1245	NA	NA	Complex	8	NA	0	8	0	8

Conclusion

So, the “original” and the “alternative” codings agree rather well…

Stats

Here, I re-do that stats using the “alternative” coding.

tone1

There are 181 observations, distributed among 119 unique Glottolg codes in 35 families (ranging from a minimum of 1 language per family to a maximum of 48, with a mean 5.2 and median 2 languages per family) and 4 macroareas.

There are 161:126:119 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
No	9	101	4	6	120
Yes	27	25	6	3	61
Sum	36	126	10	9	181

Figure 223. Distribution of tone1.

Figure 224. Map of tone1.

Figure 225. Relationship between tone1, ASPM-D and MCPH1-D.

The agreement with the original tone1 coding is extremely high:

	No	Yes
No	119	1
Yes	1	60

Figure 226. Relationship between the agreement and the `alternative’ agreement codings for tone1.

Pearson’s Chi-squared test with Yates’ continuity correction: `cooc_tab`
Test statistic	df	P value
167.8	1	2.212e-38 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
172.2	NA	9.999e-05 * * *

The disagreements are:

The 2 languages for which the original and the alternative *tone1* disagree
glottocode	Pop_ID	metapopulation	family	macroarea	original	alternative
naas1242	SA002261L	Melanesian_Nasioi	South Bougainville	Papunesia	No	Yes
buru1296	SA001482P	Burusho	Burushaski	Eurasia	Yes	No

so I expect the results of the analysis to be virtually identical…

tone2

The resulting dataset has 180 observations, distributed among 118 unique Glottolg codes in 35 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 5.1 and median 2 languages per family) and 4 macroareas.

There are 156:121:118 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
No	31	106	9	9	155
Yes	6	17	1	1	25
Sum	37	123	10	10	180

Figure 227. Distribution of tone2.

Figure 228. Map of tone2.

Figure 229. Relationship between tone2, ASPM-D and MCPH1-D.

The agreement with the original tone2 coding is extremely high:

	No	Yes
No	151	0
Yes	4	25

Figure 230. Relationship between the agreement and the `alternative’ agreement codings for tone2.

Pearson’s Chi-squared test with Yates’ continuity correction: `cooc_tab`
Test statistic	df	P value
144	1	3.472e-33 * * *

Pearson’s Chi-squared test with simulated p-value (based on 10000 replicates): `cooc_tab`
Test statistic	df	P value
151.2	NA	9.999e-05 * * *

The disagreements are:

The 4 languages for which the original and the alternative *tone2* disagree
glottocode	Pop_ID	metapopulation	family	macroarea	original	alternative
bamu1253	MB2005_Bamoun	Bamoun	Atlantic-Congo	Africa	Yes	No
sand1273	SA004366T	Sandawe	Sandawe	Africa	Yes	No
nort2732	SA001484R	Tujia	Sino-Tibetan	Eurasia	Yes	No
yaka1272	SA002256P	Biaka	Atlantic-Congo	Africa	Yes	No

so I expect the results of the analysis to be very similar…

Tone counts

The resulting dataset has 183 observations, distributed among 120 unique Glottolg codes in 35 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 5.2 and median 2 languages per family) and 4 macroareas.

There are 156:121:120 unique samples:(meta)populations:languages retained.

	Africa	Eurasia	America	Papunesia	Sum
0	9	97	4	6	116
1	9	7	5	2	23
2	15	1	0	1	17
3	4	5	0	1	10
4	1	3	0	0	4
5	0	8	0	0	8
6	0	3	0	0	3
7	0	1	1	0	2
Sum	38	125	10	10	183

Figure 231. Distribution of tone counts.

Figure 232. Distribution of tone counts across the world.

Figure 233. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

The original and alternative tone counts are very similar:

Figure 234. Relationship between the agreement and the `alternative’ agreement for tone counts.

Pearson’s product-moment correlation: `n_tones_orig` and `n_tones_alt`
Test statistic	df	P value	Alternative hypothesis	cor
38.96	181	6.161e-90 * * *	two.sided	0.9452

Spearman’s rank correlation rho: `n_tones_orig` and `n_tones_alt`
Test statistic	P value	Alternative hypothesis	rho
17364	3.499e-135 * * *	two.sided	0.983

Look at the serious disagreements (i.e., more than 1):

The 6 languages for which the original and the alternative tone *counts* disagree by more than 1
glottocode	Pop_ID	metapopulation	family	macroarea	original	alternative	difference
awng1244	SA004368V	Jews_Ethiopian	Afro-Asiatic	Africa	1	3	2
nama1264	SA001469U	San	Khoe-Kwadi	Africa	5	3	2
tain1252	SA001493R	Dai	Tai-Kadai	Eurasia	4	6	2
tain1252	SA004238R	Dai	Tai-Kadai	Eurasia	4	6	2
ticu1245	SA004389Y	Ticuna	Ticuna-Yuri	America	4	7	3
cent1394	SA001486T	Miao	Hmong-Mien	Eurasia	3	7	4

so I expect the results of the analysis to be very similar…

Appendix IV: Macroareas as units of analysis

Excluding Africa

Here I exclude from the analysis all the African data points.

tone1

There are 145 observations, distributed among 89 unique Glottolg codes in 28 families (ranging from a minimum of 1 language per family to a maximum of 48, with a mean 5.2 and median 2 languages per family) and 3 macroareas.

There are 134:102:89 unique samples:(meta)populations:languages retained.

	America	Eurasia	Papunesia	Sum
No	4	100	7	111
Yes	6	26	2	34
Sum	10	126	9	145

Figure 235. Distribution of tone1.

Figure 236. Map of tone1.

Figure 237. Relationship between tone1, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 85.6%
macroarea: p_{macroarea/null} = 0.2
ASPM:
- by itself: R² = 0.3%, β = -0.23 ± 0.52, p_ASPM/null = 0.67
- quadratic: R² = 1.6%, β_ASPM2 = -0.14 ± 0.72, p_ASPM2/ASPM = 0.28
- with macroarea: R² = 9.2%, p_{macroarea/ASPM} = 0.2, p_{ASPM/macroarea} = 0.71
MCPH1:
- by itself: R² = 0.0%, β = 0.11 ± 0.42, p_MCPH1/null = 0.8
- quadratic: R² = 0.7%, β_MCPH12 = 0.07 ± 0.48, p_MCPH12/MCPH1 = 0.18
- with macroarea: R² = 9.3%, p_{macroarea/MCPH1} = 0.2, p_{MCPH1/macroarea} = 0.91
both alleles (no macroarea):
- ASPM + MCPH1: R² = 0.7%, β_ASPM = -0.30 ± 0.54, p_ASPM/MCPH1 = 0.59, β_MCPH1 = 0.17 ± 0.41, p_MCPH1/ASPM = 0.67, p_{ASPM+MCPH1/null} = 0.83,
- interaction: R² = 2.1%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.27

Randomization

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	4%	4%	6%	5%	79%
unrestricted	none	alleles-together	85%	7%	7%	22%	8%	64%
unrestricted	none	alleles-independent	84%	7%	7%	22%	6%	64%
unrestricted	fixef	tone	0%	5%	4%	84%	5%	45%
unrestricted	fixef	alleles-together	93%	9%	9%	66%	7%	46%
unrestricted	fixef	alleles-independent	94%	6%	6%	70%	6%	46%
macroareas	none	tone	0%	19%	15%	33%	13%	47%
macroareas	none	alleles-together	87%	7%	7%	36%	7%	52%
macroareas	none	alleles-independent	87%	8%	7%	36%	9%	51%
macroareas	fixef	tone	0%	5%	6%	82%	6%	47%
macroareas	fixef	alleles-together	94%	7%	7%	65%	6%	46%
macroareas	fixef	alleles-independent	93%	7%	7%	69%	6%	48%
families	none	tone	88%	6%	7%	49%	3%	53%
families	none	alleles-together	91%	9%	10%	62%	5%	44%
families	none	alleles-independent	90%	9%	10%	57%	6%	55%
families	fixef	tone	81%	5%	5%	73%	2%	38%
families	fixef	alleles-together	93%	6%	7%	78%	3%	37%
families	fixef	alleles-independent	92%	5%	6%	75%	5%	47%

Restricted sampling

Figure 238. Results for 1000 restricted samplings. For ASPM-D (left): 99.9% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -66.0, mean = -0.71, p = 0), 95.2%, when controlling for the macroarea (t(999) = -42.2, mean = -0.65, p = 1.2e-224), and 95.5% when controlling for both macroarea and MCPH1 (t(999) = -33.2, mean = -0.89, p = 8.2e-164). For MCPH1-D (right): 32.1% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = 15.3, mean = 0.13, p = 1), 87.6% when controlling for the macroarea (t(999) = -35.5, mean = -0.50, p = 1.2e-179), and 86.9% when controlling for both macroarea and ASPM (t(999) = -30.3, mean = -0.80, p = 6e-144).

`brms`

ASPM only:
- β = -0.19, 89%HDI = [-1.54, 1.17]
- posterior probability p(β<0) = 0.6 (evidence ratio = 1.5), p(β=0) = 0.8 (evidence ratio = 4.1)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 19.9%; p_ROPE = 0.177
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(43%:57%) K=]: moderate evidence for null against ASPM (BF=3.3), LOO=0.23 [SE=0.70], WAIC=-0.29 [SE=0.32], KFOLD=0.74 [SE=0.91]
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(43%:57%) K=]: moderate evidence for null against ASPM (BF=3.3), LOO=0.23 [SE=0.70], WAIC=-0.29 [SE=0.32], KFOLD=0.74 [SE=0.91]
MCPH1 only:
- β = 0.32, 89%HDI = [-0.76, 1.62]
- posterior probability p(β<0) = 0.35 (evidence ratio = 0.54), p(β=0) = 0.81 (evidence ratio = 4.2)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 21.5%; p_ROPE = 0.191
- comparison ‘null’ vs ‘MCPH1’: [B> L= W<(33%:67%) K>]: moderate evidence for null against MCPH1 (BF=3.79), LOO=-0.58 [SE=0.74], WAIC=-0.69 [SE=0.36], KFOLD=2.03 [SE=1.93]
- comparison ‘null’ vs ‘MCPH1’: [B> L= W<(33%:67%) K>]: moderate evidence for null against MCPH1 (BF=3.79), LOO=-0.58 [SE=0.74], WAIC=-0.69 [SE=0.36], KFOLD=2.03 [SE=1.93]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W=(37%:63%) K=]: strong evidence for null against both (BF=10.8), LOO=1.02 [SE=0.89], WAIC=-0.53 [SE=0.56], KFOLD=-0.24 [SE=3.20]
- interaction:
  - posterior probability p(=0) = 0.77 (evidence ratio = 3.3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 16%; p_ROPE = 0.142
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L< W<(27%:73%) K>>]: moderate evidence for no interaction against with interaction (BF=4.09), LOO=-1.73 [SE=0.94], WAIC=-0.98 [SE=0.65], KFOLD=9.48 [SE=3.05]
- ASPM (partial):
  - β = -0.16, 89%HDI = [-1.54, 1.43]
  - posterior probability p(β<0) = 0.58 (evidence ratio = 1.4), p(β=0) = 0.79 (evidence ratio = 3.7)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 18.9%; p_ROPE = 0.168
- MCPH1 (partial):
  - β = 0.37, 89%HDI = [-0.90, 1.61]
  - posterior probability p(β<0) = 0.33 (evidence ratio = 0.48), p(β=0) = 0.8 (evidence ratio = 4.1)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 20.7%; p_ROPE = 0.184

Figure 239. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 240. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 241. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 242. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

tone2

The resulting dataset has 143 observations, distributed among 87 unique Glottolg codes in 28 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 5.1 and median 2 languages per family) and 3 macroareas.

There are 131:99:87 unique samples:(meta)populations:languages retained.

	America	Eurasia	Papunesia	Sum
No	9	105	9	123
Yes	1	18	1	20
Sum	10	123	10	143

Figure 243. Distribution of tone2.

Figure 244. Map of tone2.

Figure 245. Relationship between tone2, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 98.3%
macroarea: p_{macroarea/null} = 0.97
ASPM:
- by itself: R² = 0.1%, β = 0.35 ± 1.11, p_ASPM/null = 0.75
- quadratic: R² = 37.2%, β_ASPM2 = -8.33 ± 6.96, p_ASPM2/ASPM = 0.028
- with macroarea: R² = 0.1%, p_{macroarea/ASPM} = 0.93, p_{ASPM/macroarea} = 0.67
MCPH1:
- by itself: R² = 0.0%, β = 0.20 ± 0.96, p_MCPH1/null = 0.83
- quadratic: R² = 1.0%, β_MCPH12 = 0.07 ± 1.26, p_MCPH12/MCPH1 = 0.15
- with macroarea: R² = 0.1%, p_{macroarea/MCPH1} = 0.98, p_{MCPH1/macroarea} = 0.87
both alleles (no macroarea):
- ASPM + MCPH1: R² = 0.1%, β_ASPM = 0.32 ± 1.12, p_ASPM/MCPH1 = 0.77, β_MCPH1 = 0.17 ± 1.01, p_MCPH1/ASPM = 0.86, p_{ASPM+MCPH1/null} = 0.94,
- interaction: R² = 0.2%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.53

Randomization

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	6%	6%	87%	6%	72%
unrestricted	none	alleles-together	94%	8%	8%	65%	8%	60%
unrestricted	none	alleles-independent	95%	8%	8%	65%	7%	58%
unrestricted	fixef	tone	0%	6%	5%	96%	6%	56%
unrestricted	fixef	alleles-together	94%	8%	8%	74%	8%	54%
unrestricted	fixef	alleles-independent	94%	10%	8%	74%	9%	54%
macroareas	none	tone	0%	3%	4%	87%	5%	74%
macroareas	none	alleles-together	95%	9%	8%	70%	8%	54%
macroareas	none	alleles-independent	95%	10%	10%	68%	9%	58%
macroareas	fixef	tone	0%	6%	6%	95%	6%	53%
macroareas	fixef	alleles-together	93%	12%	10%	74%	11%	52%
macroareas	fixef	alleles-independent	92%	12%	10%	74%	10%	51%
families	none	tone	63%	8%	7%	77%	4%	45%
families	none	alleles-together	90%	6%	5%	75%	3%	45%
families	none	alleles-independent	89%	7%	7%	74%	6%	54%
families	fixef	tone	63%	8%	8%	82%	4%	34%
families	fixef	alleles-together	86%	6%	5%	76%	4%	40%
families	fixef	alleles-independent	89%	7%	9%	78%	7%	48%

Restricted sampling

Figure 246. Results for 1000 restricted samplings. For ASPM-D (left): 100% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -98.2, mean = -0.74, p = 0), 100%, when controlling for the macroarea (t(999) = -77.7, mean = -1.35, p = 0), and 100% when controlling for both macroarea and MCPH1 (t(999) = -68.8, mean = -1.58, p = 0). For MCPH1-D (right): 62.1% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -9.5, mean = -0.10, p = 5.2e-21), 65.7% when controlling for the macroarea (t(999) = -12.0, mean = -0.21, p = 1.5e-31), and 68.7% when controlling for both macroarea and ASPM (t(999) = -14.4, mean = -0.42, p = 5.7e-43).

`brms`

ASPM only:
- β = -0.68, 89%HDI = [-2.49, 1.31]
- posterior probability p(β<0) = 0.72 (evidence ratio = 2.6), p(β=0) = 0.72 (evidence ratio = 2.6)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 11.5%; p_ROPE = 0.102
- comparison ‘null’ vs ‘ASPM’: [B> L> W>(65%:35%) K>]: moderate evidence for null against ASPM (BF=3.61), LOO=1.75 [SE=1.00], WAIC=0.60 [SE=0.48], KFOLD=0.72 [SE=0.65]
- comparison ‘null’ vs ‘ASPM’: [B> L> W>(65%:35%) K>]: moderate evidence for null against ASPM (BF=3.61), LOO=1.75 [SE=1.00], WAIC=0.60 [SE=0.48], KFOLD=0.72 [SE=0.65]
MCPH1 only:
- β = 0.13, 89%HDI = [-1.41, 1.84]
- posterior probability p(β<0) = 0.46 (evidence ratio = 0.84), p(β=0) = 0.78 (evidence ratio = 3.6)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 17.9%; p_ROPE = 0.16
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(51%:49%) K<]: moderate evidence for null against MCPH1 (BF=3.36), LOO=-0.12 [SE=0.43], WAIC=0.03 [SE=0.31], KFOLD=-0.96 [SE=0.51]
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(51%:49%) K<]: moderate evidence for null against MCPH1 (BF=3.36), LOO=-0.12 [SE=0.43], WAIC=0.03 [SE=0.31], KFOLD=-0.96 [SE=0.51]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L= W=(52%:48%) K>>]: moderate evidence for null against both (BF=7.53), LOO=0.20 [SE=0.62], WAIC=0.06 [SE=0.56], KFOLD=8.34 [SE=4.00]
- interaction:
  - posterior probability p(=0) = 0.7 (evidence ratio = 2.4)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 10.5%; p_ROPE = 0.094
  - comparison ‘no interaction’ vs ‘with interaction’: [B= L< W<(33%:67%) K<]: anecdotal evidence for no interaction against with interaction (BF=2.84), LOO=-0.76 [SE=0.51], WAIC=-0.69 [SE=0.35], KFOLD=-5.06 [SE=4.57]
- ASPM (partial):
  - β = -0.68, 89%HDI = [-2.85, 1.40]
  - posterior probability p(β<0) = 0.71 (evidence ratio = 2.4), p(β=0) = 0.71 (evidence ratio = 2.4)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 11.5%; p_ROPE = 0.102
- MCPH1 (partial):
  - β = 0.15, 89%HDI = [-1.44, 1.90]
  - posterior probability p(β<0) = 0.46 (evidence ratio = 0.84), p(β=0) = 0.78 (evidence ratio = 3.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 17%; p_ROPE = 0.152

Figure 247. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 248. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 249. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 250. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Tone counts

The resulting dataset has 146 observations, distributed among 89 unique Glottolg codes in 28 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 5.2 and median 2 languages per family) and 3 macroareas.

There are 131:99:89 unique samples:(meta)populations:languages retained.

	America	Eurasia	Papunesia	Sum
0	4	98	7	109
1	5	6	1	12
2	0	3	2	5
3	0	5	0	5
4	1	8	0	9
5	0	4	0	4
6	0	2	0	2
Sum	10	126	10	146

Figure 251. Distribution of tone counts.

Figure 252. Distribution of tone counts across the world.

Figure 253. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 100.0%
the Poisson model is not overdispersed: χ²(144) = 78.8, p = 1
macroarea: p_{macroarea/null} = 0.6
ASPM:
- by itself: R² = 0.0%, β = 0.00 ± 0.25, p_ASPM/null = 1
- quadratic: R² = 8.5%, β_ASPM2 = -0.33 ± 0.33, p_ASPM2/ASPM = 0.073
- with macroarea: R² = 2.3%, p_{macroarea/ASPM} = 0.58, p_{ASPM/macroarea} = 0.79
MCPH1:
- by itself: R² = 0.2%, β = -0.08 ± 0.17, p_MCPH1/null = 0.63
- quadratic: R² = 2.0%, β_MCPH12 = -0.04 ± 0.18, p_MCPH12/MCPH1 = 0.16
- with macroarea: R² = 2.7%, p_{macroarea/MCPH1} = 0.53, p_{MCPH1/macroarea} = 0.5
both alleles (no macroarea):
- ASPM + MCPH1: R² = 0.2%, β_ASPM = -0.01 ± 0.25, p_ASPM/MCPH1 = 0.96, β_MCPH1 = -0.08 ± 0.17, p_MCPH1/ASPM = 0.63, p_{ASPM+MCPH1/null} = 0.89,
- interaction: R² = 0.3%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.76

Randomization

We performed 1000 independent replications:

Regressions with randomizations for tone *counts*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	35%	24%	40%	25%	35%
unrestricted	none	alleles-together	89%	3%	3%	43%	4%	24%
unrestricted	none	alleles-independent	88%	3%	4%	44%	4%	22%
unrestricted	fixef	tone	0%	36%	25%	56%	24%	28%
unrestricted	fixef	alleles-together	78%	4%	4%	68%	3%	15%
unrestricted	fixef	alleles-independent	74%	2%	3%	71%	3%	12%
macroareas	none	tone	0%	33%	20%	50%	24%	28%
macroareas	none	alleles-together	88%	3%	3%	54%	4%	17%
macroareas	none	alleles-independent	88%	3%	4%	55%	4%	17%
macroareas	fixef	tone	0%	35%	24%	54%	25%	28%
macroareas	fixef	alleles-together	77%	3%	4%	69%	3%	15%
macroareas	fixef	alleles-independent	76%	3%	4%	68%	4%	18%
families	none	tone	69%	5%	11%	79%	1%	33%
families	none	alleles-together	90%	6%	10%	80%	0%	23%
families	none	alleles-independent	88%	6%	13%	80%	1%	23%
families	fixef	tone	67%	5%	10%	84%	1%	23%
families	fixef	alleles-together	77%	7%	10%	86%	1%	22%
families	fixef	alleles-independent	77%	6%	11%	86%	1%	19%

Restricted sampling

Figure 254. Results for 1000 restricted samplings. For ASPM-D (left): 99.9% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -74.5, mean = -0.43, p = 0), 98.2%, when controlling for the macroarea (t(999) = -59.5, mean = -0.60, p = 0), and 98.4% when controlling for both macroarea and MCPH1 (t(999) = -61.1, mean = -0.67, p = 0). For MCPH1-D (right): 35.2% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = 15.6, mean = 0.13, p = 1), 43.2% when controlling for the macroarea (t(999) = 8.4, mean = 0.11, p = 1), and 45.2% when controlling for both macroarea and ASPM (t(999) = 8.2, mean = 0.15, p = 1).

`brms`

ASPM only:
- β = -0.12, 89%HDI = [-0.64, 0.40]
- posterior probability p(β<0) = 0.64 (evidence ratio = 1.8), p(β=0) = 0.91 (evidence ratio = 9.9)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 26.2%; p_ROPE = 0.233
- comparison ‘null’ vs ‘ASPM’: [B>> L>> W>>(67%:33%) K=]: strong evidence for null against ASPM (BF=11.8), LOO=1.40 [SE=0.57], WAIC=0.71 [SE=0.33], KFOLD=-0.27 [SE=2.39]
MCPH1 only:
- β = 0.01, 89%HDI = [-0.33, 0.34]
- posterior probability p(β<0) = 0.48 (evidence ratio = 0.92), p(β=0) = 0.94 (evidence ratio = 16)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 42.3%; p_ROPE = 0.376
- comparison ‘null’ vs ‘MCPH1’: [B>> L= W=(57%:43%) K=]: strong evidence for null against MCPH1 (BF=12.8), LOO=0.01 [SE=0.58], WAIC=0.28 [SE=0.29], KFOLD=-1.27 [SE=2.61]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L>> W>>(77%:23%) K=]: very strong evidence for null against both (BF=80.5), LOO=1.83 [SE=0.81], WAIC=1.20 [SE=0.49], KFOLD=1.19 [SE=2.51]
- interaction:
  - posterior probability p(=0) = 0.92 (evidence ratio = 11)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 28.7%; p_ROPE = 0.255
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L= W=(45%:55%) K=]: moderate evidence for no interaction against with interaction (BF=8.41), LOO=-0.69 [SE=0.85], WAIC=-0.21 [SE=0.30], KFOLD=-0.59 [SE=1.39]
- ASPM (partial):
  - β = -0.13, 89%HDI = [-0.67, 0.40]
  - posterior probability p(β<0) = 0.66 (evidence ratio = 1.9), p(β=0) = 0.91 (evidence ratio = 9.9)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 25.9%; p_ROPE = 0.231
- MCPH1 (partial):
  - β = 0, 89%HDI = [-0.34, 0.34]
  - posterior probability p(β<0) = 0.5 (evidence ratio = 0.98), p(β=0) = 0.94 (evidence ratio = 15)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 40%; p_ROPE = 0.356

Figure 255. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 256. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 257. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Only Africa

Here I use only the African data points.

tone1

There are 36 observations, distributed among 30 unique Glottolg codes in 8 families (ranging from a minimum of 1 language per family to a maximum of 16, with a mean 4.5 and median 1.5 languages per family) and 1 macroareas.

There are 27:24:30 unique samples:(meta)populations:languages retained.

	Africa	Sum
No	9	9
Yes	27	27
Sum	36	36

Figure 258. Distribution of tone1.

Figure 259. Map of tone1.

Figure 260. Relationship between tone1, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

trying to fit a random effects structure with language family as the random effects results in convergence problems (boundary (singular) fit: see ?isSingular) and the random effects seems to not matter at all (Can't compute random effect variances. Some variance components equal zero. Your model may suffer from singulariy. Solution: Respecify random structure!), so that I reverted to a “flat” model without random effects (using glm() instead of glmer()). As expected, the anova() comparisons produce the same p-values for this glm “flat” approach as for the glmer with family as random effects, but without the convergence issues…

null model: R² = 0.0%
ASPM:
- by itself: R² = 3.6%, β = -0.38 ± 0.36, p_ASPM/null = 0.29
- quadratic: R² = 9.2%, β_ASPM2 = 0.74 ± 0.94, p_ASPM2/ASPM = 0.18
MCPH1:
- by itself: R² = 2.9%, β = -0.36 ± 0.38, p_MCPH1/null = 0.34
- quadratic: R² = 7.7%, β_MCPH12 = 0.15 ± 0.57, p_MCPH12/MCPH1 = 0.23
both alleles (no macroarea):
- ASPM + MCPH1: R² = 3.9%, β_ASPM = -0.28 ± 0.53, p_ASPM/MCPH1 = 0.6, β_MCPH1 = -0.14 ± 0.55, p_MCPH1/ASPM = 0.8, p_{ASPM+MCPH1/null} = 0.56,
- interaction: R² = 12.1%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.085

Randomization

1000 independent replications.

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	64%	6%	7%	31%	8%	38%
unrestricted	none	alleles-together	61%	7%	8%	28%	7%	40%
unrestricted	none	alleles-independent	61%	8%	8%	22%	6%	32%
families	none	tone	55%	5%	3%	10%	5%	60%
families	none	alleles-together	51%	5%	4%	10%	4%	59%
families	none	alleles-independent	55%	5%	5%	19%	6%	51%

Restricted sampling

Figure 261. Results for 1000 restricted samplings. For ASPM-D (left): 33.7% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = 23.4, mean = 24.18, p = 1), and 34.1% when controlling for MCPH1 (t(999) = 5.6, mean = 58.21, p = 1). For MCPH1-D (right): 34.3% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = 10.0, mean = 11.26, p = 1), and 43.6% when controlling for ASPM (t(999) = -2.8, mean = -8.39, p = 0.003).

`brms`

ASPM only:
- β = -0.64, 89%HDI = [-1.50, 0.35]
- posterior probability p(β<0) = 0.88 (evidence ratio = 7.1), p(β=0) = 0.78 (evidence ratio = 3.6)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 17.5%; p_ROPE = 0.156
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(57%:43%) K=]: moderate evidence for null against ASPM (BF=3.4), LOO=0.43 [SE=1.11], WAIC=0.27 [SE=1.10], KFOLD=0.58 [SE=1.46]
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(57%:43%) K=]: moderate evidence for null against ASPM (BF=3.4), LOO=0.43 [SE=1.11], WAIC=0.27 [SE=1.10], KFOLD=0.58 [SE=1.46]
MCPH1 only:
- β = -0.49, 89%HDI = [-1.30, 0.34]
- posterior probability p(β<0) = 0.83 (evidence ratio = 5.1), p(β=0) = 0.82 (evidence ratio = 4.5)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 21.7%; p_ROPE = 0.194
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(68%:32%) K>]: moderate evidence for null against MCPH1 (BF=4.01), LOO=0.81 [SE=0.95], WAIC=0.75 [SE=0.95], KFOLD=1.98 [SE=1.30]
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(68%:32%) K>]: moderate evidence for null against MCPH1 (BF=4.01), LOO=0.81 [SE=0.95], WAIC=0.75 [SE=0.95], KFOLD=1.98 [SE=1.30]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W>(78%:22%) K>]: strong evidence for null against both (BF=14.4), LOO=1.65 [SE=1.24], WAIC=1.25 [SE=1.23], KFOLD=2.22 [SE=1.46]
- interaction:
  - posterior probability p(=0) = 0.55 (evidence ratio = 1.2)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 2%; p_ROPE = 0.049
  - comparison ‘no interaction’ vs ‘with interaction’: [B= L= W=(37%:63%) K=]: anecdotal evidence for no interaction against with interaction (BF=1.01), LOO=-0.18 [SE=1.85], WAIC=-0.51 [SE=1.70], KFOLD=-0.79 [SE=2.41]
- ASPM (partial):
  - β = -0.62, 89%HDI = [-1.95, 0.72]
  - posterior probability p(β<0) = 0.77 (evidence ratio = 3.3), p(β=0) = 0.78 (evidence ratio = 3.6)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 17.7%; p_ROPE = 0.158
- MCPH1 (partial):
  - β = -0.11, 89%HDI = [-1.39, 1.03]
  - posterior probability p(β<0) = 0.56 (evidence ratio = 1.3), p(β=0) = 0.81 (evidence ratio = 4.3)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 21%; p_ROPE = 0.187

Figure 262. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 263. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 264. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 265. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

tone2

The resulting dataset has 37 observations, distributed among 31 unique Glottolg codes in 8 families (ranging from a minimum of 1 language per family to a maximum of 18, with a mean 4.6 and median 2 languages per family) and 1 macroareas.

There are 25:22:31 unique samples:(meta)populations:languages retained.

	Africa	Sum
No	28	28
Yes	9	9
Sum	37	37

Figure 266. Distribution of tone2.

Figure 267. Map of tone2.

Figure 268. Relationship between tone2, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 3.1%
ASPM:
- by itself: R² = 1.6%, β = -0.23 ± 0.47, p_ASPM/null = 0.6
- quadratic: R² = 5.8%, β_ASPM2 = 0.30 ± 0.94, p_ASPM2/ASPM = 0.5
MCPH1:
- by itself: R² = 0.1%, β = -0.06 ± 0.43, p_MCPH1/null = 0.89
- quadratic: R² = 5.3%, β_MCPH12 = 0.19 ± 0.56, p_MCPH12/MCPH1 = 0.39
both alleles (no macroarea):
- ASPM + MCPH1: R² = 1.9%, β_ASPM = -0.31 ± 0.56, p_ASPM/MCPH1 = 0.58, β_MCPH1 = 0.14 ± 0.57, p_MCPH1/ASPM = 0.81, p_{ASPM+MCPH1/null} = 0.85,
- interaction: R² = 1.9%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.98

Randomization

Regressions with randomizations for *tone2*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	86%	7%	8%	34%	5%	61%
unrestricted	none	alleles-together	88%	9%	9%	40%	6%	60%
unrestricted	none	alleles-independent	87%	8%	7%	32%	7%	60%
families	none	tone	90%	7%	10%	55%	6%	39%
families	none	alleles-together	92%	7%	10%	54%	5%	43%
families	none	alleles-independent	87%	9%	11%	43%	6%	50%

Restricted sampling

Figure 269. Results for 1000 restricted samplings. For ASPM-D (left): 29.6% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = 7.8, mean = 1.59, p = 1) and 45.1% when controlling for MCPH1 (t(999) = 9.3, mean = 2.47, p = 1). For MCPH1-D (right): 27% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = 9.5, mean = 11.06, p = 1) and 32.6% when controlling for ASPM (t(999) = 8.5, mean = 2.40, p = 1).

`brms`

ASPM only:
- β = -0.37, 89%HDI = [-1.88, 0.99]
- posterior probability p(β<0) = 0.68 (evidence ratio = 2.1), p(β=0) = 0.79 (evidence ratio = 3.7)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 18.4%; p_ROPE = 0.164
- comparison ‘null’ vs ‘ASPM’: [B> L> W=(61%:39%) K>>]: moderate evidence for null against ASPM (BF=3.68), LOO=0.85 [SE=0.79], WAIC=0.45 [SE=0.59], KFOLD=2.38 [SE=1.05]
- comparison ‘null’ vs ‘ASPM’: [B> L> W=(61%:39%) K>>]: moderate evidence for null against ASPM (BF=3.68), LOO=0.85 [SE=0.79], WAIC=0.45 [SE=0.59], KFOLD=2.38 [SE=1.05]
MCPH1 only:
- β = -0.3, 89%HDI = [-1.61, 0.97]
- posterior probability p(β<0) = 0.65 (evidence ratio = 1.8), p(β=0) = 0.81 (evidence ratio = 4.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 21%; p_ROPE = 0.187
- comparison ‘null’ vs ‘MCPH1’: [B> L>> W=(57%:43%) K=]: moderate evidence for null against MCPH1 (BF=4.69), LOO=1.13 [SE=0.45], WAIC=0.29 [SE=0.38], KFOLD=-0.04 [SE=0.93]
- comparison ‘null’ vs ‘MCPH1’: [B> L>> W=(57%:43%) K=]: moderate evidence for null against MCPH1 (BF=4.69), LOO=1.13 [SE=0.45], WAIC=0.29 [SE=0.38], KFOLD=-0.04 [SE=0.93]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L> W=(58%:42%) K>>]: strong evidence for null against both (BF=14), LOO=1.57 [SE=0.80], WAIC=0.34 [SE=0.61], KFOLD=7.10 [SE=2.10]
- interaction:
  - posterior probability p(=0) = 0.79 (evidence ratio = 3.7)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 18.1%; p_ROPE = 0.161
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L= W=(43%:57%) K<<]: moderate evidence for no interaction against with interaction (BF=3.54), LOO=0.27 [SE=0.81], WAIC=-0.28 [SE=0.34], KFOLD=-4.42 [SE=2.17]
- ASPM (partial):
  - β = -0.2, 89%HDI = [-2.07, 1.53]
  - posterior probability p(β<0) = 0.58 (evidence ratio = 1.4), p(β=0) = 0.76 (evidence ratio = 3.1)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 15.5%; p_ROPE = 0.138
- MCPH1 (partial):
  - β = -0.24, 89%HDI = [-1.83, 1.37]
  - posterior probability p(β<0) = 0.57 (evidence ratio = 1.3), p(β=0) = 0.78 (evidence ratio = 3.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 17.9%; p_ROPE = 0.159

Figure 270. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 271. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 272. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 273. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Tone counts

The resulting dataset has 38 observations, distributed among 32 unique Glottolg codes in 8 families (ranging from a minimum of 1 language per family to a maximum of 19, with a mean 4.8 and median 2 languages per family) and 1 macroareas.

There are 25:22:32 unique samples:(meta)populations:languages retained.

	Africa	Sum
0	9	9
1	10	10
2	16	16
3	2	2
5	1	1
Sum	38	38

Figure 274. Distribution of tone counts.

Figure 275. Distribution of tone counts across the world.

Figure 276. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

Regressions

`glmer`

All data

null model:
ASPM:
- by itself: , β = -0.07 ± 0.15, p_ASPM/null = 0.64
- quadratic: , β_ASPM2 = 0.02 ± 0.32, p_ASPM2/ASPM = 0.75
MCPH1:
- by itself: , β = -0.06 ± 0.14, p_MCPH1/null = 0.66
- quadratic: , β_MCPH12 = -0.03 ± 0.17, p_MCPH12/MCPH1 = 0.7
both alleles (no macroarea):
- ASPM + MCPH1: , β_ASPM = -0.05 ± 0.18, p_ASPM/MCPH1 = 0.79, β_MCPH1 = -0.04 ± 0.17, p_MCPH1/ASPM = 0.82, p_{ASPM+MCPH1/null} = 0.88,
- interaction: , p_{ASPM:MCPH1/ASPM+MCPH1} = 0.53

Randomization

We performed 1000 independent replications:

Regressions with randomizations for tone *counts*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	87%	2%	3%	41%	3%	40%
unrestricted	none	alleles-together	87%	4%	4%	42%	2%	42%
unrestricted	none	alleles-independent	86%	3%	4%	36%	2%	39%
families	none	tone	96%	1%	0%	33%	2%	76%
families	none	alleles-together	80%	0%	0%	36%	2%	74%
families	none	alleles-independent	86%	1%	0%	52%	3%	74%

Restricted sampling

Figure 277. Results for 1000 restricted samplings. For ASPM-D (left): 39.3% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = 9.9, mean = 0.07, p = 1) and 29.7% when controlling for MCPH1 (t(999) = 15.4, mean = 0.10, p = 1). For MCPH1-D (right): 47.5% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = 5.2, mean = 0.04, p = 1) and 56.2% when controlling for ASPM (t(999) = -3.1, mean = -0.02, p = 0.00086).

`brms`

ASPM only:
- β = -0.1, 89%HDI = [-0.38, 0.17]
- posterior probability p(β<0) = 0.7 (evidence ratio = 2.4), p(β=0) = 0.94 (evidence ratio = 17)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 44.6%; p_ROPE = 0.397
- comparison ‘null’ vs ‘ASPM’: [B>> L> W>(71%:29%) K=]: strong evidence for null against ASPM (BF=16.5), LOO=1.00 [SE=0.58], WAIC=0.89 [SE=0.53], KFOLD=-0.93 [SE=1.69]
- comparison ‘null’ vs ‘ASPM’: [B>> L> W>(71%:29%) K=]: strong evidence for null against ASPM (BF=16.5), LOO=1.00 [SE=0.58], WAIC=0.89 [SE=0.53], KFOLD=-0.93 [SE=1.69]
MCPH1 only:
- β = -0.05, 89%HDI = [-0.31, 0.20]
- posterior probability p(β<0) = 0.62 (evidence ratio = 1.6), p(β=0) = 0.95 (evidence ratio = 20)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 50.4%; p_ROPE = 0.448
- comparison ‘null’ vs ‘MCPH1’: [B>> L>> W>>(73%:27%) K<]: strong evidence for null against MCPH1 (BF=19.3), LOO=0.97 [SE=0.35], WAIC=0.99 [SE=0.31], KFOLD=-1.71 [SE=1.51]
- comparison ‘null’ vs ‘MCPH1’: [B>> L>> W>>(73%:27%) K<]: strong evidence for null against MCPH1 (BF=19.3), LOO=0.97 [SE=0.35], WAIC=0.99 [SE=0.31], KFOLD=-1.71 [SE=1.51]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L>> W>>(85%:15%) K>>]: extreme evidence for null against both (BF=280), LOO=1.89 [SE=0.63], WAIC=1.74 [SE=0.59], KFOLD=1.47 [SE=0.69]
- interaction:
  - posterior probability p(=0) = 0.95 (evidence ratio = 20)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 49.6%; p_ROPE = 0.441
  - comparison ‘no interaction’ vs ‘with interaction’: [B>> L> W>(70%:30%) K=]: strong evidence for no interaction against with interaction (BF=17.6), LOO=1.04 [SE=0.85], WAIC=0.86 [SE=0.74], KFOLD=0.67 [SE=1.07]
- ASPM (partial):
  - β = -0.1, 89%HDI = [-0.42, 0.25]
  - posterior probability p(β<0) = 0.68 (evidence ratio = 2.1), p(β=0) = 0.93 (evidence ratio = 14)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 38.3%; p_ROPE = 0.341
- MCPH1 (partial):
  - β = 0, 89%HDI = [-0.31, 0.33]
  - posterior probability p(β<0) = 0.5 (evidence ratio = 0.99), p(β=0) = 0.94 (evidence ratio = 16)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 43.6%; p_ROPE = 0.388

Figure 278. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 279. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 280. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Only Eurasia

Here I use only the Eurasian data points.

tone1

There are 126 observations, distributed among 74 unique Glottolg codes in 19 families (ranging from a minimum of 1 language per family to a maximum of 48, with a mean 6.6 and median 3 languages per family) and 1 macroareas.

There are 118:89:74 unique samples:(meta)populations:languages retained.

	Eurasia	Sum
No	100	100
Yes	26	26
Sum	126	126

Figure 281. Distribution of tone1.

Figure 282. Map of tone1.

Figure 283. Relationship between tone1, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 99.0%
ASPM:
- by itself: R² = 0.0%, β = 0.10 ± 0.56, p_ASPM/null = 0.86
- quadratic: R² = 0.6%, β_ASPM2 = 0.37 ± 0.86, p_ASPM2/ASPM = 0.057
MCPH1:
- by itself: R² = 0.0%, β = -0.07 ± 0.41, p_MCPH1/null = 0.87
- quadratic: R² = 0.6%, β_MCPH12 = -0.15 ± 0.48, p_MCPH12/MCPH1 = 0.06
both alleles (no macroarea):
- ASPM + MCPH1: R² = 0.0%, β_ASPM = 0.16 ± 0.60, p_ASPM/MCPH1 = 0.79, β_MCPH1 = -0.12 ± 0.45, p_MCPH1/ASPM = 0.8, p_{ASPM+MCPH1/null} = 0.95,
- interaction: R² = 0.0%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.64

Randomization

1000 independent replications.

Regressions on 1000 permuted data. The first 3 columns show the permutation constraints (if any), how the *macroarea* is considered (if at all), and what is permuted. The next columns show the percent of the permutations that, in order, have a better AIC compared to the original fit, are significantly better than the null model (thus testing the effect of both alleles simultaneously), have a significant effect of *ASPM*-D, have a smaller effect (β) of *ASPM*-D than the original fit, and the same for *MCPH1*-D.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	4%	5%	74%	6%	28%
unrestricted	none	alleles-together	95%	4%	6%	60%	4%	34%
unrestricted	none	alleles-independent	96%	5%	6%	62%	4%	35%
families	none	tone	74%	4%	5%	66%	3%	30%
families	none	alleles-together	96%	5%	4%	66%	4%	31%
families	none	alleles-independent	97%	6%	5%	68%	6%	37%

Restricted sampling

Figure 284. Results for 1000 restricted samplings. For ASPM-D (left): 99.9% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -86.0, mean = -0.93, p = 0), and 99.9% when controlling for MCPH1 (t(999) = -4.2, mean = -7.89, p = 1.4e-05). For MCPH1-D (right): 98.9% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -58.5, mean = -1.18, p = 0), and 98.5% when controlling for ASPM (t(999) = -3.5, mean = -11.46, p = 0.00025).

`brms`

ASPM only:
- β = -0.14, 89%HDI = [-1.48, 1.34]
- posterior probability p(β<0) = 0.57 (evidence ratio = 1.3), p(β=0) = 0.8 (evidence ratio = 3.9)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 19.2%; p_ROPE = 0.171
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(54%:46%) K=]: moderate evidence for null against ASPM (BF=3.77), LOO=0.25 [SE=0.63], WAIC=0.14 [SE=0.32], KFOLD=2.38 [SE=3.34]
- comparison ‘null’ vs ‘ASPM’: [B> L= W=(54%:46%) K=]: moderate evidence for null against ASPM (BF=3.77), LOO=0.25 [SE=0.63], WAIC=0.14 [SE=0.32], KFOLD=2.38 [SE=3.34]
MCPH1 only:
- β = -0.04, 89%HDI = [-1.16, 1.19]
- posterior probability p(β<0) = 0.55 (evidence ratio = 1.2), p(β=0) = 0.83 (evidence ratio = 4.8)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 24%; p_ROPE = 0.214
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(51%:49%) K=]: moderate evidence for null against MCPH1 (BF=4.7), LOO=0.22 [SE=0.55], WAIC=0.06 [SE=0.28], KFOLD=-1.06 [SE=2.93]
- comparison ‘null’ vs ‘MCPH1’: [B> L= W=(51%:49%) K=]: moderate evidence for null against MCPH1 (BF=4.7), LOO=0.22 [SE=0.55], WAIC=0.06 [SE=0.28], KFOLD=-1.06 [SE=2.93]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L= W=(50%:50%) K=]: strong evidence for null against both (BF=18.5), LOO=0.90 [SE=0.93], WAIC=0.00 [SE=0.43], KFOLD=-1.63 [SE=1.82]
- interaction:
  - posterior probability p(=0) = 0.8 (evidence ratio = 3.9)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 18.6%; p_ROPE = 0.166
  - comparison ‘no interaction’ vs ‘with interaction’: [B> L= W=(48%:52%) K>]: moderate evidence for no interaction against with interaction (BF=3.76), LOO=0.55 [SE=0.60], WAIC=-0.07 [SE=0.38], KFOLD=4.85 [SE=2.79]
- ASPM (partial):
  - β = -0.11, 89%HDI = [-1.68, 1.37]
  - posterior probability p(β<0) = 0.54 (evidence ratio = 1.2), p(β=0) = 0.78 (evidence ratio = 3.6)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 18.3%; p_ROPE = 0.163
- MCPH1 (partial):
  - β = -0.06, 89%HDI = [-1.28, 1.29]
  - posterior probability p(β<0) = 0.54 (evidence ratio = 1.2), p(β=0) = 0.82 (evidence ratio = 4.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 22.6%; p_ROPE = 0.202

Figure 285. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 286. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 287. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 288. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

tone2

The resulting dataset has 123 observations, distributed among 71 unique Glottolg codes in 19 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 6.5 and median 3 languages per family) and 1 macroareas.

There are 115:86:71 unique samples:(meta)populations:languages retained.

	Eurasia	Sum
No	105	105
Yes	18	18
Sum	123	123

Figure 289. Distribution of tone2.

Figure 290. Map of tone2.

Figure 291. Relationship between tone2, ASPM-D and MCPH1-D.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 98.7%
ASPM:
- by itself: R² = 0.0%, β = 0.03 ± 1.46, p_ASPM/null = 1
- quadratic: R² = 81.7%, β_ASPM2 = -191.71 ± 77.88, p_ASPM2/ASPM = 4e-05
MCPH1:
- by itself: R² = 0.1%, β = -0.63 ± 1.12, p_MCPH1/null = 0.6
- quadratic: R² = 0.4%, β_MCPH12 = -0.42 ± 1.31, p_MCPH12/MCPH1 = 0.25
both alleles (no macroarea):
- ASPM + MCPH1: R² = 0.2%, β_ASPM = -0.02 ± 1.39, p_ASPM/MCPH1 = 1, β_MCPH1 = -0.63 ± 1.11, p_MCPH1/ASPM = 0.6, p_{ASPM+MCPH1/null} = 0.87,
- interaction: R² = 0.3%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.72

Randomization

Regressions with randomizations for *tone2*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	5%	6%	44%	5%	0%
unrestricted	none	alleles-together	90%	12%	12%	48%	10%	27%
unrestricted	none	alleles-independent	88%	12%	12%	49%	10%	28%
families	none	tone	49%	9%	10%	62%	4%	19%
families	none	alleles-together	80%	8%	10%	60%	4%	16%
families	none	alleles-independent	84%	10%	12%	68%	6%	19%

Restricted sampling

Figure 292. Results for 1000 restricted samplings. For ASPM-D (left): 99.9% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -72.3, mean = -1.10, p = 0) and 99.8% when controlling for MCPH1 (t(999) = -65.0, mean = -1.31, p = 0). For MCPH1-D (right): 75.3% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -20.5, mean = -0.38, p = 9.5e-79) and 76.2% when controlling for ASPM (t(999) = -21.1, mean = -0.64, p = 2.1e-82).

`brms`

ASPM only:
- β = -1.44, 89%HDI = [-3.63, 1.13]
- posterior probability p(β<0) = 0.84 (evidence ratio = 5.4), p(β=0) = 0.58 (evidence ratio = 1.4)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 6.9%; p_ROPE = 0.062
- comparison ‘null’ vs ‘ASPM’: [B= L= W=(47%:53%) K>]: anecdotal evidence for null against ASPM (BF=1.49), LOO=-0.11 [SE=0.84], WAIC=-0.13 [SE=0.66], KFOLD=2.88 [SE=2.04]
- comparison ‘null’ vs ‘ASPM’: [B= L= W=(47%:53%) K>]: anecdotal evidence for null against ASPM (BF=1.49), LOO=-0.11 [SE=0.84], WAIC=-0.13 [SE=0.66], KFOLD=2.88 [SE=2.04]
MCPH1 only:
- β = -0.42, 89%HDI = [-2.51, 1.61]
- posterior probability p(β<0) = 0.64 (evidence ratio = 1.8), p(β=0) = 0.72 (evidence ratio = 2.5)
- ROPE = [-0.18, 0.18], % HDI inside ROPE = 12.8%; p_ROPE = 0.114
- comparison ‘null’ vs ‘MCPH1’: [B= L= W<(45%:55%) K=]: anecdotal evidence for null against MCPH1 (BF=2.44), LOO=0.09 [SE=0.28], WAIC=-0.21 [SE=0.19], KFOLD=0.33 [SE=0.47]
- comparison ‘null’ vs ‘MCPH1’: [B= L= W<(45%:55%) K=]: anecdotal evidence for null against MCPH1 (BF=2.44), LOO=0.09 [SE=0.28], WAIC=-0.21 [SE=0.19], KFOLD=0.33 [SE=0.47]
both alleles:
- comparison ‘null’ vs ‘both’: [B> L< W<(31%:69%) K>]: moderate evidence for null against both (BF=3.62), LOO=-0.77 [SE=0.75], WAIC=-0.78 [SE=0.67], KFOLD=5.80 [SE=3.74]
- interaction:
  - posterior probability p(=0) = 0.71 (evidence ratio = 2.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 11.8%; p_ROPE = 0.105
  - comparison ‘no interaction’ vs ‘with interaction’: [B= L>> W<(47%:53%) K<]: anecdotal evidence for no interaction against with interaction (BF=2.31), LOO=0.47 [SE=0.24], WAIC=-0.12 [SE=0.09], KFOLD=-5.61 [SE=3.74]
- ASPM (partial):
  - β = -1.44, 89%HDI = [-4.09, 1.20]
  - posterior probability p(β<0) = 0.82 (evidence ratio = 4.6), p(β=0) = 0.59 (evidence ratio = 1.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 6.8%; p_ROPE = 0.06
- MCPH1 (partial):
  - β = -0.52, 89%HDI = [-2.53, 1.68]
  - posterior probability p(β<0) = 0.66 (evidence ratio = 2), p(β=0) = 0.72 (evidence ratio = 2.5)
  - ROPE = [-0.18, 0.18], % HDI inside ROPE = 12.3%; p_ROPE = 0.11

Figure 293. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 294. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 295. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Figure 296. Confusion matrices for ASPM-D (left) and MCPH1-D (right).

Tone counts

The resulting dataset has 126 observations, distributed among 73 unique Glottolg codes in 19 families (ranging from a minimum of 1 language per family to a maximum of 47, with a mean 6.6 and median 3 languages per family) and 1 macroareas.

There are 115:86:73 unique samples:(meta)populations:languages retained.

	Eurasia	Sum
0	98	98
1	6	6
2	3	3
3	5	5
4	8	8
5	4	4
6	2	2
Sum	126	126

Figure 297. Distribution of tone counts.

Figure 298. Distribution of tone counts across the world.

Figure 299. Relationship between tone counts (colors) and the two alleles (frequency) by macroarea.

Regressions

`glmer`

All data

null model: R² = 0.0%, ICC = 100.0%
the Poisson model is not overdispersed: χ²(124) = 64.3, p = 1
ASPM:
- by itself: R² = 0.0%, β = 0.05 ± 0.27, p_ASPM/null = 0.84
- quadratic: R² = 27.2%, β_ASPM2 = -1.02 ± 0.60, p_ASPM2/ASPM = 0.013
MCPH1:
- by itself: R² = 0.4%, β = -0.20 ± 0.17, p_MCPH1/null = 0.26
- quadratic: R² = 0.8%, β_MCPH12 = -0.15 ± 0.18, p_MCPH12/MCPH1 = 0.15
both alleles (no macroarea):
- ASPM + MCPH1: R² = 0.4%, β_ASPM = 0.00 ± 0.26, p_ASPM/MCPH1 = 0.99, β_MCPH1 = -0.20 ± 0.17, p_MCPH1/ASPM = 0.27, p_{ASPM+MCPH1/null} = 0.53,
- interaction: R² = 0.5%, p_{ASPM:MCPH1/ASPM+MCPH1} = 0.64

Randomization

We performed 1000 independent replications:

Regressions with randomizations for tone *counts*.
Permute within	Macroarea	Permute	AIC	Signif.	p_ASPM-D	β_ASPM-D	p_MCPH1-D	β_MCPH1-D
unrestricted	none	tone	0%	37%	25%	47%	26%	16%
unrestricted	none	alleles-together	46%	3%	3%	50%	3%	4%
unrestricted	none	alleles-independent	48%	2%	3%	52%	3%	4%
families	none	tone	47%	5%	11%	74%	1%	10%
families	none	alleles-together	49%	5%	10%	74%	1%	9%
families	none	alleles-independent	47%	4%	8%	70%	1%	7%

Restricted sampling

Figure 300. Results for 1000 restricted samplings. For ASPM-D (left): 99.9% of βs are negative when regressing tone on ASPM alone (one-sided t-test < 0: t(999) = -86.3, mean = -0.69, p = 0) and 99.9% when controlling for MCPH1 (t(999) = -88.2, mean = -0.76, p = 0). For MCPH1-D (right): 62.9% of βs are negative when regressing tone on MCPH1 alone (one-sided t-test < 0: t(999) = -9.3, mean = -0.11, p = 4.3e-20) and 63.7% when controlling for ASPM (t(999) = -7.7, mean = -0.13, p = 1.7e-14).

`brms`

ASPM only:
- β = -0.19, 89%HDI = [-0.77, 0.37]
- posterior probability p(β<0) = 0.7 (evidence ratio = 2.4), p(β=0) = 0.89 (evidence ratio = 8.2)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 20.9%; p_ROPE = 0.186
- comparison ‘null’ vs ‘ASPM’: [B> L>> W>>(75%:25%) K=]: moderate evidence for null against ASPM (BF=9.85), LOO=1.67 [SE=0.55], WAIC=1.09 [SE=0.41], KFOLD=0.57 [SE=1.33]
- comparison ‘null’ vs ‘ASPM’: [B> L>> W>>(75%:25%) K=]: moderate evidence for null against ASPM (BF=9.85), LOO=1.67 [SE=0.55], WAIC=1.09 [SE=0.41], KFOLD=0.57 [SE=1.33]
MCPH1 only:
- β = -0.1, 89%HDI = [-0.44, 0.23]
- posterior probability p(β<0) = 0.69 (evidence ratio = 2.2), p(β=0) = 0.93 (evidence ratio = 13)
- ROPE = [-0.10, 0.10], % HDI inside ROPE = 37%; p_ROPE = 0.329
- comparison ‘null’ vs ‘MCPH1’: [B>> L>> W>>(79%:21%) K=]: strong evidence for null against MCPH1 (BF=16.8), LOO=1.75 [SE=0.48], WAIC=1.30 [SE=0.38], KFOLD=-0.32 [SE=1.41]
- comparison ‘null’ vs ‘MCPH1’: [B>> L>> W>>(79%:21%) K=]: strong evidence for null against MCPH1 (BF=16.8), LOO=1.75 [SE=0.48], WAIC=1.30 [SE=0.38], KFOLD=-0.32 [SE=1.41]
both alleles:
- comparison ‘null’ vs ‘both’: [B>> L>> W>>(85%:15%) K=]: very strong evidence for null against both (BF=92.8), LOO=2.74 [SE=0.92], WAIC=1.75 [SE=0.66], KFOLD=-0.19 [SE=1.57]
- interaction:
  - posterior probability p(=0) = 0.9 (evidence ratio = 9.3)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 24.8%; p_ROPE = 0.221
  - comparison ‘no interaction’ vs ‘with interaction’: [B>> L= W=(52%:48%) K>>]: strong evidence for no interaction against with interaction (BF=10.4), LOO=-0.14 [SE=0.62], WAIC=0.09 [SE=0.31], KFOLD=3.56 [SE=1.62]
- ASPM (partial):
  - β = -0.21, 89%HDI = [-0.79, 0.36]
  - posterior probability p(β<0) = 0.72 (evidence ratio = 2.5), p(β=0) = 0.89 (evidence ratio = 8)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 21.6%; p_ROPE = 0.192
- MCPH1 (partial):
  - β = -0.12, 89%HDI = [-0.49, 0.19]
  - posterior probability p(β<0) = 0.71 (evidence ratio = 2.5), p(β=0) = 0.93 (evidence ratio = 13)
  - ROPE = [-0.10, 0.10], % HDI inside ROPE = 34.4%; p_ROPE = 0.306

Figure 301. Posterior distributions (with 50% probability mass highlighted) versus 0.0 (the vertical line) for ASPM-D (left) and MCPH1-D (right).

Figure 302. Conditional effects of ASPM-D (left) and MCPH1-D (right).

Figure 303. Posterior predictive checks for ASPM-D (left) and MCPH1-D (right).

Only America

Too little data…

Only Papunesia

Too little data…

Appendix VII: Draw diagrams for paper

Generic mediation model with a single mediator

Generic mediation model with a two mediators or a path analysis

tone1: simultaneous mediation through both alleles

tone1: path analysis (numeric coding)

tone1: path analysis (restricted sampling)

tone2: simultaneous mediation through both alleles

tone2: path analysis (numeric coding)

tone2: path analysis (restricted sampling)

Tone counts: simultaneous mediation through both alleles

Tone counts: path analysis

Tone counts: path analysis (restricted sampling)

Session information

CPU: AMD Ryzen 7 3700X 8-Core Processor (16 threads)

RAM (memory): 67.5 GB

R version 4.0.5 (2021-03-31)

Platform: x86_64-pc-linux-gnu (64-bit)

locale: LC_CTYPE=en_US.UTF-8, LC_NUMERIC=C, LC_TIME=en_US.UTF-8, LC_COLLATE=en_US.UTF-8, LC_MONETARY=en_US.UTF-8, LC_MESSAGES=en_US.UTF-8, LC_PAPER=en_US.UTF-8, LC_NAME=C, LC_ADDRESS=C, LC_TELEPHONE=C, LC_MEASUREMENT=en_US.UTF-8 and LC_IDENTIFICATION=C

attached base packages: grid, stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: benchmarkme(v.1.0.7), magick(v.2.7.2), pdftools(v.3.0.1), rsvg(v.2.1.2), DiagrammeRsvg(v.0.1), simr(v.1.0.5), phytools(v.0.7-70), ape(v.5.5), tidybayes(v.2.3.1), bayestestR(v.0.9.0), brms(v.2.15.0), Rcpp(v.1.0.6), dagitty(v.0.3-1), e1071(v.1.7-6), cowplot(v.1.1.1), maps(v.3.3.0), lavaanPlot(v.0.5.1), lavaan(v.0.6-8), randomForest(v.4.6-14), caret(v.6.0-86), lattice(v.0.20-44), partykit(v.1.2-13), libcoin(v.1.0-8), rsample(v.0.1.0), mediation(v.4.5.0), sandwich(v.3.0-0), mvtnorm(v.1.1-1), MASS(v.7.3-54), DiagrammeR(v.1.0.6.1), pbapply(v.1.4-3), sjPlot(v.2.8.7), ggnewscale(v.0.4.5), glmmTMB(v.1.0.2.1), data.table(v.1.14.0), reshape2(v.1.4.4), dplyr(v.1.0.6), lmerTest(v.3.1-3), lme4(v.1.1-26), Matrix(v.1.3-3), performance(v.0.7.1), png(v.0.1-7), jpeg(v.0.1-8.1), tiff(v.0.1-8), gridExtra(v.2.3), ggplot2(v.3.3.3), stringr(v.1.4.0), pander(v.0.6.3), knitr(v.1.33) and RhpcBLASctl(v.0.20-137)

loaded via a namespace (and not attached): estimability(v.1.3), ModelMetrics(v.1.2.2.2), coda(v.0.19-4), tidyr(v.1.1.3), clusterGeneration(v.1.3.7), dygraphs(v.1.1.1.6), rpart(v.4.1-15), inline(v.0.3.17), doParallel(v.1.0.16), generics(v.0.1.0), callr(v.3.7.0), combinat(v.0.0-8), proxy(v.0.4-25), future(v.1.21.0), RLRsim(v.3.1-6), lubridate(v.1.7.10), httpuv(v.1.6.1), StanHeaders(v.2.21.0-7), assertthat(v.0.2.1), gower(v.0.2.2), xfun(v.0.22), hms(v.1.0.0), ggdist(v.2.4.0), jquerylib(v.0.1.4), bayesplot(v.1.8.0), evaluate(v.0.14), promises(v.1.2.0.1), fansi(v.0.4.2), readxl(v.1.3.1), igraph(v.1.2.6), DBI(v.1.1.1), tmvnsim(v.1.0-2), htmlwidgets(v.1.5.3), stats4(v.4.0.5), benchmarkmeData(v.1.0.4), purrr(v.0.3.4), ellipsis(v.0.3.2), crosstalk(v.1.1.1), backports(v.1.2.1), binom(v.1.1-1), V8(v.3.4.2), pbivnorm(v.0.6.0), insight(v.0.14.0), markdown(v.1.1), RcppParallel(v.5.1.4), vctrs(v.0.3.8), sjlabelled(v.1.1.8), abind(v.1.4-5), withr(v.2.4.2), checkmate(v.2.0.0), emmeans(v.1.6.0), xts(v.0.12.1), prettyunits(v.1.1.1), mnormt(v.2.0.2), cluster(v.2.1.2), crayon(v.1.4.1), recipes(v.0.1.16), pkgconfig(v.2.0.3), nlme(v.3.1-152), nnet(v.7.3-16), rlang(v.0.4.11), globals(v.0.14.0), lifecycle(v.1.0.0), miniUI(v.0.1.1.1), colourpicker(v.1.1.0), modelr(v.0.1.8), cellranger(v.1.1.0), distributional(v.0.2.2), matrixStats(v.0.58.0), phangorn(v.2.7.0), loo(v.2.4.1), carData(v.3.0-4), boot(v.1.3-28), zoo(v.1.8-9), base64enc(v.0.1-3), gamm4(v.0.2-6), ggridges(v.0.5.3), processx(v.3.5.2), parameters(v.0.13.0), visNetwork(v.2.0.9), pROC(v.1.17.0.1), parallelly(v.1.25.0), qpdf(v.1.1), shinystan(v.2.5.0), ggeffects(v.1.1.0), scales(v.1.1.1), lpSolve(v.5.6.15), magrittr(v.2.0.1), plyr(v.1.8.6), threejs(v.0.3.3), compiler(v.4.0.5), rstantools(v.2.1.1), RColorBrewer(v.1.1-2), plotrix(v.3.8-1), cli(v.2.5.0), listenv(v.0.8.0), ps(v.1.6.0), TMB(v.1.7.20), Brobdingnag(v.1.2-6), htmlTable(v.2.1.0), Formula(v.1.2-4), mgcv(v.1.8-35), tidyselect(v.1.1.1), stringi(v.1.6.1), forcats(v.0.5.1), projpred(v.2.0.2), yaml(v.2.2.1), askpass(v.1.1), svUnit(v.1.0.6), latticeExtra(v.0.6-29), bridgesampling(v.1.1-2), sass(v.0.4.0), fastmatch(v.1.1-0), tools(v.4.0.5), rio(v.0.5.26), parallel(v.4.0.5), rstudioapi(v.0.13), foreach(v.1.5.1), foreign(v.0.8-81), inum(v.1.0-4), prodlim(v.2019.11.13), scatterplot3d(v.0.3-41), farver(v.2.1.0), digest(v.0.6.27), shiny(v.1.6.0), lava(v.1.6.9), quadprog(v.1.5-8), car(v.3.0-10), broom(v.0.7.6), later(v.1.2.0), httr(v.1.4.2), rsconnect(v.0.8.17), effectsize(v.0.4.4-1), sjstats(v.0.18.1), colorspace(v.2.0-1), splines(v.4.0.5), statmod(v.1.4.36), expm(v.0.999-6), shinythemes(v.1.2.0), xtable(v.1.8-4), jsonlite(v.1.7.2), nloptr(v.1.2.2.2), timeDate(v.3043.102), rstan(v.2.21.2), ipred(v.0.9-11), R6(v.2.5.0), Hmisc(v.4.5-0), pillar(v.1.6.0), htmltools(v.0.5.1.1), mime(v.0.10), glue(v.1.4.2), fastmap(v.1.1.0), minqa(v.1.2.4), DT(v.0.18), class(v.7.3-19), codetools(v.0.2-18), pkgbuild(v.1.2.0), furrr(v.0.2.2), utf8(v.1.2.1), bslib(v.0.2.5), tibble(v.3.1.1), pbkrtest(v.0.5.1), numDeriv(v.2016.8-1.1), arrayhelpers(v.1.1-0), curl(v.4.3.1), gtools(v.3.8.2), zip(v.2.1.1), openxlsx(v.4.2.3), shinyjs(v.2.0.0), survival(v.3.2-11), rmarkdown(v.2.8), munsell(v.0.5.0), iterators(v.1.0.13), haven(v.2.4.1), sjmisc(v.2.8.7) and gtable(v.0.3.0)

References

Dediu, D., & Ladd, D. R. (2007). Linguistic tone is related to the population frequency of the adaptive haplogroups of two brain size genes, ASPM and Microcephalin. Proc Natl Acad Sci U S A, 104(26), 10944–10949. https://doi.org/10.1073/pnas.0610848104

Evans, P. D., Gilbert, S. L., Mekel-Bobrov, N., Vallender, E. J., Anderson, J. R., Vaez-Azizi, L. M., … Lahn, B. T. (2005). Microcephalin, a gene regulating brain size, continues to evolve adaptively in humans. Science, 309(5741), 1717–1720. https://doi.org/10.1126/science.1113722

McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and Stan (2nd ed.). CRC Press LLC.

Mekel-Bobrov, N., Gilbert, S. L., Evans, P. D., Vallender, E. J., Anderson, J. R., Hudson, R. R., … Lahn, B. T. (2005). Ongoing adaptive evolution of ASPM, a brain size determinant in Homo sapiens. Science, 309(5741), 1720–1722. https://doi.org/10.1126/science.1116815

Wong, Patrick C. M., Chandrasekaran, B., & Zheng, J. (2012). The Derived Allele of ASPM Is Associated with Lexical Tone Perception. PLoS One, 7(4), e34243. https://doi.org/10.1371/journal.pone.0034243

Wong, Patrick C. M., Kang, X., Wong, K. H. Y., So, H.-C., Choy, K. W., & Geng, X. (2020). ASPM-lexical tone association in speakers of a tone language: Direct evidence for the genetic-biasing hypothesis of language evolution. Science Advances, 6(22), eaba5090. https://doi.org/10.1126/sciadv.aba5090

For mixed-effects models, this is Nakagawa’s R² estimate, where the marginal estimate considers only the fixed effects, while the conditional also considers the random effects as well. Here, we show only the marginal ICC, as we are interested in the fixed effects. See ?performance::r2 for more details.↩︎
ICC represents the proportion of the variance explained by the grouping due to the random effects, and varies between 0% (the grouping contains no info) to 100% (basically all individual observations in a given group are identical); the adjusted ICC only considers the random effect, while the conditional ICC also considers the fixed effects as well; they are equal when there are no fixed effects (i.e., for the null models). Here, we show only the adjusted ICC, as we are interested in the random effects. See ?performance::icc for more details.↩︎
Here I use model comparisons to estimate the p-value of adding (or removing) a predictor, v, by comparing the model without the predictor (m) with the model with the predictor (m_v), anova(m, m_v) and report the p-value denoted as p_v/m to make clear what predictor is added to which model.↩︎
The ROPE (region of practical equivalence) is a small interval around 0.0 (usually, [-0.1, 0.1] but can vary depending on the particular model). Can be used either to estimate the percent of the HDI that falls within this interval, or the proportion of the whole posterior distribution that does so. It can be used in a manner similar to that of frequentist p-values to judge if 0.0 can be ruled out as a probable value of the parameter of interest.↩︎
This compares two brms models, m1 and m2, using Bayes Factors (BF), LOO, WAIC and KFOLD. For the latter three, I show the difference between m1 and m2 (in this order), and the SE of this difference; if the difference is negative (<0) then m1 is worse, while if it is positive (>0) m1 is better, but the “significance” of this difference can be interpreted only in the context of the SE. These results are summarized using the [B? L? W?(x%:y%) K?] notation, where the symbol * can be “=” when the models are pretty much equivalent, “<” if m1 is worse than m2 (and “<<” if this difference is really big), or “>” if m1 is better than m2 (and “>>” if this difference is really big); for WAIC (“W”) I also give the relative weights of the two models as (x%:y%).↩︎
Please note that for path analyses/SEM models, we want the goodness-of-fit χ² test to be non-significant, meaning that there is no reason to reject the hypothesis that the model fits the data. On the other hand, there is a plethora of goodness of fit indices (we show a few) where the idea is that the closer they are to 1.00 the better the model fits to the data.↩︎

	None	Marginal	Simple	Moderately complex	Complex
0	314	6	57	13	15
1	1	0	0	0	0
2	2	1	13	0	1
3	0	0	3	9	3
4	0	0	2	4	2
5	0	0	1	3	6
6	1	0	1	3	0
7	0	0	1	0	1
8	0	0	0	0	1
9	0	0	0	0	2
10	0	0	0	0	1

	None	Simple	Complex
0	270	9	3
1	0	0	0
2	13	73	9
3	6	24	18
4	1	11	20
5	0	2	10
6	0	1	8
7	0	0	2
8	0	0	3
9	0	0	1
10	0	0	0
11	0	0	0
12	0	0	1

	None	Marginal	Simple	Moderately complex	Complex
0	334	1	11	2	1
1	0	0	1	0	0
2	19	6	49	6	6
3	3	0	11	20	6
4	2	0	6	6	9
5	0	0	2	1	7
6	0	0	1	0	4
7	0	0	0	0	1
8	0	0	0	0	3
9	0	0	0	0	0
10	0	0	0	0	0
11	0	0	0	0	0
12	0	0	0	0	0

	0	1	2	3	4	5	6	7	8	9	10
0	918	1	8	6	8	3	1	0	0	0	0
1	3	0	0	0	0	0	0	0	0	0	0
2	131	0	27	21	16	7	2	1	1	0	0
3	48	0	17	37	6	5	6	2	1	0	0
4	43	0	14	4	13	6	7	2	1	0	0
5	9	0	2	5	4	7	1	0	0	1	1
6	5	0	1	4	1	2	2	1	0	1	0
7	3	0	0	1	0	1	1	0	0	0	0
8	2	0	0	0	1	0	0	2	0	2	0
9	0	0	1	0	0	1	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	1	0	0	0	0	0
12	0	0	0	1	0	0	0	0	0	0	0

	None	Marginal	Simple	Moderately complex	Complex
0	314	6	57	13	15
1	1	0	0	0	0
2	2	1	13	0	1
3	0	0	3	9	3
4	0	0	2	4	2
5	0	0	1	3	6
6	1	0	1	3	0
7	0	0	1	0	1
8	0	0	0	0	1
9	0	0	0	0	2
10	0	0	0	0	1

	None	Simple	Complex
0	270	9	3
1	0	0	0
2	13	73	9
3	6	24	18
4	1	11	20
5	0	2	10
6	0	1	8
7	0	0	2
8	0	0	3
9	0	0	1
10	0	0	0
11	0	0	0
12	0	0	1

	None	Marginal	Simple	Moderately complex	Complex
0	334	1	11	2	1
1	0	0	1	0	0
2	19	6	49	6	6
3	3	0	11	20	6
4	2	0	6	6	9
5	0	0	2	1	7
6	0	0	1	0	4
7	0	0	0	0	1
8	0	0	0	0	3
9	0	0	0	0	0
10	0	0	0	0	0
11	0	0	0	0	0
12	0	0	0	0	0

	0	1	2	3	4	5	6	7	8	9	10
0	918	1	8	6	8	3	1	0	0	0	0
1	3	0	0	0	0	0	0	0	0	0	0
2	131	0	27	21	16	7	2	1	1	0	0
3	48	0	17	37	6	5	6	2	1	0	0
4	43	0	14	4	13	6	7	2	1	0	0
5	9	0	2	5	4	7	1	0	0	1	1
6	5	0	1	4	1	2	2	1	0	1	0
7	3	0	0	1	0	1	1	0	0	0	0
8	2	0	0	0	1	0	0	2	0	2	0
9	0	0	1	0	0	1	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	1	0	0	0	0	0
12	0	0	0	1	0	0	0	0	0	0	0

Tone and genes: new cross-linguistic data and methods support the weak negative effect of the “derived” allele of ASPM on tone, but not of Microcephalin

Full analysis report

Dan Dediu (dan.dediu@univ-lyon2.fr)

Sun May 16 13:38:58 2021

Introduction

Data

Tone

The data sources

WALS

LAPSyD

Dediu & Ladd (2007)

PHOIBLE

WPHON

Relationships between data sources

WALS - LAPSyD

WALS - Dediu & Ladd (2007)

LAPSyD - Dediu & Ladd (2007)

PHOIBLE - WALS

PHOIBLE - LAPSyD

PHOIBLE - Dediu & Ladd (2007)

WPHON - WALS

WPHON - LAPSyD

WPHON - Dediu & Ladd (2007)

WPHON - PHOIBLE

Reconciliating the sources

Collapse LAPSyD 4-way

The content of the sources

The reconciliation rules

The “agreement” classifications

Distributions

Binary classification

3-way classification

Counts

Relationships with original sources

With WALS

Binary classification

3-way classification

With LAPSyD

Binary classification

3-way classification

Counts

With Dediu & Ladd (2007)

Binary classification

3-way classification

With PHOIBLE

Counts

With WPHON

Counts

Conclusions about tone

Distribution of retained tone data

Binary

3-way

Counts

Counts (unrounded)

Intersection

ASPM-D and MCPH1-D population frequencies

ASPM-D

All SNPs

Excluding “proxy” SNPs

New samples

MCPH1-D

All SNPs

Excluding “proxy” SNPs

New samples

The original Dediu & Ladd (2007) samples

Putting tone and genes together

Stats

tone1 (is there tone?)

Regressions

glmer

All data

Alleles on macroarea

Randomization

Restricted sampling

brms

Mediation and path analysis

Mediation analysis

(g)lm

All data

Restricted sampling

`glmer`

`brms`

`(g)lm`

`brms`

`glmer`

`brms`

`(g)lm`

`brms`

`glmer`

`brms`

`(g)lm`

`brms`

	None	Marginal	Simple	Moderately complex	Complex
0	314	6	57	13	15
1	1	0	0	0	0
2	2	1	13	0	1
3	0	0	3	9	3
4	0	0	2	4	2
5	0	0	1	3	6
6	1	0	1	3	0
7	0	0	1	0	1
8	0	0	0	0	1
9	0	0	0	0	2
10	0	0	0	0	1

	None	Simple	Complex
0	270	9	3
1	0	0	0
2	13	73	9
3	6	24	18
4	1	11	20
5	0	2	10
6	0	1	8
7	0	0	2
8	0	0	3
9	0	0	1
10	0	0	0
11	0	0	0
12	0	0	1

	None	Marginal	Simple	Moderately complex	Complex
0	334	1	11	2	1
1	0	0	1	0	0
2	19	6	49	6	6
3	3	0	11	20	6
4	2	0	6	6	9
5	0	0	2	1	7
6	0	0	1	0	4
7	0	0	0	0	1
8	0	0	0	0	3
9	0	0	0	0	0
10	0	0	0	0	0
11	0	0	0	0	0
12	0	0	0	0	0

	0	1	2	3	4	5	6	7	8	9	10
0	918	1	8	6	8	3	1	0	0	0	0
1	3	0	0	0	0	0	0	0	0	0	0
2	131	0	27	21	16	7	2	1	1	0	0
3	48	0	17	37	6	5	6	2	1	0	0
4	43	0	14	4	13	6	7	2	1	0	0
5	9	0	2	5	4	7	1	0	0	1	1
6	5	0	1	4	1	2	2	1	0	1	0
7	3	0	0	1	0	1	1	0	0	0	0
8	2	0	0	0	1	0	0	2	0	2	0
9	0	0	1	0	0	1	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	1	0	0	0	0	0
12	0	0	0	1	0	0	0	0	0	0	0