Statistical Analysis
Claire A. McLean
Divergent male and female mate preferences do not explain incipient speciation between lizard lineages
Claire A. McLean 1, 2, Richard A. Bartle 1, Caroline M. Dong 1, 2, Katrina J. Rankin 1 & Devi Stuart-Fox 1
1 The University of Melbourne, 2 Museums Victoria
Female-male behavioural trials
The dataset consists of 147 behavioural trials involving 44 female and 42 male tawny dragons (Ctenophorus decresii).
Model 1: Number of copulation attempts
Generalised linear mixed model with female lineage, male lineage, female lineage * male lineage as fixed effects and female ID, male ID and pairing number (female’s first or second trial) as random effects.
lmer.copulation.attempts.model= lmer(cop_attempts~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.copulation.attempts.model)
qqnorm(resid(lmer.copulation.attempts.model))
qqline(resid(lmer.copulation.attempts.model))
shapiro.test(resid(lmer.copulation.attempts.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.copulation.attempts.model)
## W = 0.73671, p-value = 6.251e-15log transform the data to meet model assumptions of normality
log.lmer.copulation.attempts.model= lmer(log1p(cop_attempts)~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))
summary(log.lmer.copulation.attempts.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula:
## log1p(cop_attempts) ~ female_lineage + male_lineage + female_lineage *
## male_lineage + (1 | female_ID) + (1 | male_ID) + (1 | pairing_number)
## Data: female_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 340.5 364.4 -162.3 324.5 139
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.2511 -0.7551 -0.4082 0.6581 3.0484
##
## Random effects:
## Groups Name Variance Std.Dev.
## female_ID (Intercept) 0.034799 0.18654
## male_ID (Intercept) 0.004685 0.06845
## pairing_number (Intercept) 0.002057 0.04536
## Residual 0.494035 0.70288
## Number of obs: 147, groups: female_ID, 44; male_ID, 42; pairing_number, 2
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.58656 0.07329 2.61781 8.003 0.00656
## female_lineage1 -0.06679 0.06509 41.50078 -1.026 0.31078
## male_lineage1 -0.01673 0.05921 30.52861 -0.282 0.77950
## female_lineage1:male_lineage1 0.14887 0.05826 103.21037 2.555 0.01207
##
## (Intercept) **
## female_lineage1
## male_lineage1
## female_lineage1:male_lineage1 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fml_l1 ml_ln1
## female_lng1 0.005
## male_lineg1 -0.006 -0.006
## fml_lng1:_1 -0.005 -0.005 0.007anova(log.lmer.copulation.attempts.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## female_lineage 0.5202 0.5202 1 41.501 1.0529 0.31078
## male_lineage 0.0394 0.0394 1 30.529 0.0798 0.77950
## female_lineage:male_lineage 3.2259 3.2259 1 103.210 6.5297 0.01207 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(log.lmer.copulation.attempts.model)## 2.5 % 97.5 %
## .sig01 0.00000000 0.38077128
## .sig02 0.00000000 0.30633379
## .sig03 0.00000000 0.38869990
## .sigma 0.60724512 0.81335180
## (Intercept) 0.35422579 0.82038591
## female_lineage1 -0.19795413 0.06430442
## male_lineage1 -0.13853953 0.10194896
## female_lineage1:male_lineage1 0.03337237 0.26435283lsmeansLT(log.lmer.copulation.attempts.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower
## female_lineageN 0.519773 0.098260 7.4 5.2897 0.289929
## female_lineageS 0.653344 0.097783 7.2 6.6816 0.423725
## male_lineageN 0.569833 0.093965 6.8 6.0643 0.346073
## male_lineageS 0.603283 0.094483 6.9 6.3851 0.379292
## female_lineageN:male_lineageN 0.651921 0.128185 20.2 5.0858 0.384737
## female_lineageS:male_lineageN 0.487746 0.128127 20.4 3.8067 0.220782
## female_lineageN:male_lineageS 0.387625 0.129517 21.6 2.9928 0.118746
## female_lineageS:male_lineageS 0.818942 0.128109 20.4 6.3926 0.552078
## upper Pr(>|t|)
## female_lineageN 0.749617 0.0009512 ***
## female_lineageS 0.882963 0.0002420 ***
## male_lineageN 0.793594 0.0005799 ***
## male_lineageS 0.827275 0.0003924 ***
## female_lineageN:male_lineageN 0.919104 5.448e-05 ***
## female_lineageS:male_lineageN 0.754710 0.0010767 **
## female_lineageN:male_lineageS 0.656504 0.0067899 **
## female_lineageS:male_lineageS 1.085806 2.789e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(log.lmer.copulation.attempts.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate
## female_lineageN - female_lineageS -0.13357133
## male_lineageN - male_lineageS -0.03345004
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.16417426
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.26429555
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -0.16702137
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.10012129
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.33119563
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -0.43131692
## Std. Error df
## female_lineageN - female_lineageS 0.13017276 41.5
## male_lineageN - male_lineageS 0.11842558 30.5
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.17429394 105.5
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.16670947 65.8
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.17548859 66.6
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.17647347 70.8
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.16556146 63.9
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.17511404 107.8
## t value
## female_lineageN - female_lineageS -1.0261
## male_lineageN - male_lineageS -0.2825
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.9419
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 1.5854
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -0.9518
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.5673
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -2.0004
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -2.4631
## lower
## female_lineageN - female_lineageS -0.39636424
## male_lineageN - male_lineageS -0.27513185
## female_lineageN:male_lineageN - female_lineageS:male_lineageN -0.18139767
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -0.06857140
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -0.51734143
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -0.25177223
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.66195363
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -0.77843052
## upper
## female_lineageN - female_lineageS 0.12922159
## male_lineageN - male_lineageS 0.20823177
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.50974620
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.59716250
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.18329870
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.45201480
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.00043763
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -0.08420331
## Pr(>|t|)
## female_lineageN - female_lineageS 0.31078
## male_lineageN - male_lineageS 0.77950
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.34837
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.11768
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.34467
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.57227
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.04971 *
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.01536 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(log.lmer.copulation.attempts.model)## R2m R2c
## [1,] 0.04799139 0.1218333
Model 2: Number of male head-bobs
Generalised linear mixed model with female lineage, male lineage, female lineage * male lineage as fixed effects and female ID, male ID and pairing number (female’s first or second trial) as random effects.
lmer.male.headbob.model= lmer(male_headbob~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.male.headbob.model)
qqnorm(resid(lmer.male.headbob.model))
qqline(resid(lmer.male.headbob.model))
shapiro.test(resid(lmer.male.headbob.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.male.headbob.model)
## W = 0.87894, p-value = 1.33e-09log transform the data to meet model assumptions of normality
log.lmer.male.headbob.model= lmer(log1p(male_headbob)~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))
summary(log.lmer.male.headbob.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula:
## log1p(male_headbob) ~ female_lineage + male_lineage + female_lineage *
## male_lineage + (1 | female_ID) + (1 | male_ID) + (1 | pairing_number)
## Data: female_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 544.1 568.1 -264.1 528.1 139
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1270 -0.7184 0.1460 0.7270 2.2249
##
## Random effects:
## Groups Name Variance Std.Dev.
## female_ID (Intercept) 0.20587 0.4537
## male_ID (Intercept) 0.07737 0.2782
## pairing_number (Intercept) 0.08626 0.2937
## Residual 1.83442 1.3544
## Number of obs: 147, groups: female_ID, 44; male_ID, 42; pairing_number, 2
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.77509 0.25066 2.35011 11.071 0.00443 **
## female_lineage1 -0.27192 0.13389 31.87373 -2.031 0.05068 .
## male_lineage1 -0.03033 0.12165 26.77984 -0.249 0.80502
## female_lineage1:male_lineage1 0.29270 0.11386 91.19778 2.571 0.01177 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fml_l1 ml_ln1
## female_lng1 0.002
## male_lineg1 -0.003 -0.004
## fml_lng1:_1 -0.002 0.000 0.006anova(log.lmer.male.headbob.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## female_lineage 7.5662 7.5662 1 31.874 4.1245 0.05068 .
## male_lineage 0.1140 0.1140 1 26.780 0.0622 0.80502
## female_lineage:male_lineage 12.1234 12.1234 1 91.198 6.6088 0.01177 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(log.lmer.male.headbob.model)## 2.5 % 97.5 %
## .sig01 0.00000000 0.868374190
## .sig02 0.00000000 0.726058795
## .sig03 0.00000000 1.401635426
## .sigma 1.14706171 1.602266951
## (Intercept) 1.95426198 3.567107442
## female_lineage1 -0.54003188 0.006138033
## male_lineage1 -0.27271255 0.224586355
## female_lineage1:male_lineage1 0.06584042 0.518881123lsmeansLT(log.lmer.male.headbob.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower upper
## female_lineageN 2.50317 0.28446 3.8 8.7997 1.69632 3.31003
## female_lineageS 3.04701 0.28389 3.8 10.7332 2.23869 3.85532
## male_lineageN 2.74476 0.27824 3.5 9.8647 1.92484 3.56469
## male_lineageS 2.80542 0.27899 3.5 10.0555 1.98687 3.62396
## female_lineageN:male_lineageN 2.76554 0.32918 6.6 8.4013 1.97872 3.55236
## female_lineageS:male_lineageN 2.72398 0.32904 6.6 8.2787 1.93704 3.51093
## female_lineageN:male_lineageS 2.24081 0.33061 6.8 6.7777 1.45459 3.02703
## female_lineageS:male_lineageS 3.37003 0.32884 6.6 10.2482 2.58370 4.15636
## Pr(>|t|)
## female_lineageN 0.0011638 **
## female_lineageS 0.0005877 ***
## male_lineageN 0.0011479 **
## male_lineageS 0.0010295 **
## female_lineageN:male_lineageN 8.888e-05 ***
## female_lineageS:male_lineageN 9.876e-05 ***
## female_lineageN:male_lineageS 0.0002919 ***
## female_lineageS:male_lineageS 2.614e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(log.lmer.male.headbob.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate
## female_lineageN - female_lineageS -0.5438330
## male_lineageN - male_lineageS -0.0606573
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.0415602
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.5247359
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -0.6044903
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.4831757
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.6460506
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -1.1292263
## Std. Error df
## female_lineageN - female_lineageS 0.2677795 31.9
## male_lineageN - male_lineageS 0.2432973 26.8
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.3515412 89.1
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.3341510 60.6
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.3610366 56.0
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.3625624 57.4
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.3323188 57.5
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.3514769 91.3
## t value
## female_lineageN - female_lineageS -2.0309
## male_lineageN - male_lineageS -0.2493
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.1182
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 1.5704
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -1.6743
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 1.3327
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -1.9441
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -3.2128
## lower
## female_lineageN - female_lineageS -1.0893668
## male_lineageN - male_lineageS -0.5600543
## female_lineageN:male_lineageN - female_lineageS:male_lineageN -0.6569298
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -0.1435365
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -1.3277302
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -0.2427317
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -1.3113764
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -1.8273629
## upper
## female_lineageN - female_lineageS 0.0017008
## male_lineageN - male_lineageS 0.4387396
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.7400503
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 1.1930084
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.1187496
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 1.2090831
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.0192752
## female_lineageN:male_lineageS - female_lineageS:male_lineageS -0.4310896
## Pr(>|t|)
## female_lineageN - female_lineageS 0.050676 .
## male_lineageN - male_lineageS 0.805021
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.906157
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.121542
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.099644 .
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.187906
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.056784 .
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.001817 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(log.lmer.male.headbob.model)## R2m R2c
## [1,] 0.06798395 0.2242402
Model 3: Number of female head-bobs
Generalised linear mixed model with female lineage, male lineage, female lineage * male lineage as fixed effects and female ID, male ID and pairing number (female’s first or second trial) as random effects.
lmer.female.headbob.model= lmer(female_headbob~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.female.headbob.model)
qqnorm(resid(lmer.female.headbob.model))
qqline(resid(lmer.female.headbob.model))
shapiro.test(resid(lmer.female.headbob.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.female.headbob.model)
## W = 0.44471, p-value < 2.2e-16log transform the data to meet model assumptions of normality
log.lmer.female.headbob.model= lmer(log1p(female_headbob)~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))
summary(log.lmer.female.headbob.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula:
## log1p(female_headbob) ~ female_lineage + male_lineage + female_lineage *
## male_lineage + (1 | female_ID) + (1 | male_ID) + (1 | pairing_number)
## Data: female_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 444.9 468.8 -214.4 428.9 139
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8634 -0.7911 -0.1397 0.7080 2.8354
##
## Random effects:
## Groups Name Variance Std.Dev.
## female_ID (Intercept) 0.264675 0.51447
## male_ID (Intercept) 0.000000 0.00000
## pairing_number (Intercept) 0.008862 0.09414
## Residual 0.876505 0.93622
## Number of obs: 147, groups: female_ID, 44; male_ID, 42; pairing_number, 2
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.21190 0.12914 4.27059 9.384 0.000523
## female_lineage1 0.18876 0.11067 41.08576 1.706 0.095629
## male_lineage1 -0.08673 0.07735 101.25582 -1.121 0.264848
## female_lineage1:male_lineage1 0.01795 0.07726 100.56916 0.232 0.816769
##
## (Intercept) ***
## female_lineage1 .
## male_lineage1
## female_lineage1:male_lineage1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fml_l1 ml_ln1
## female_lng1 0.003
## male_lineg1 -0.004 -0.005
## fml_lng1:_1 -0.004 -0.005 0.008
## convergence code: 0
## boundary (singular) fit: see ?isSingularanova(log.lmer.female.headbob.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## female_lineage 2.5499 2.5499 1 41.086 2.9091 0.09563 .
## male_lineage 1.1019 1.1019 1 101.256 1.2571 0.26485
## female_lineage:male_lineage 0.0473 0.0473 1 100.569 0.0540 0.81677
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(log.lmer.female.headbob.model)## 2.5 % 97.5 %
## .sig01 0.25933800 0.76355045
## .sig02 0.00000000 0.33690374
## .sig03 0.00000000 0.60974542
## .sigma 0.82026431 1.08240897
## (Intercept) 0.83862880 1.58320059
## female_lineage1 -0.03251174 0.41168824
## male_lineage1 -0.24030362 0.06699339
## female_lineage1:male_lineage1 -0.13473916 0.17111456lsmeansLT(log.lmer.female.headbob.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower upper
## female_lineageN 1.40066 0.17032 10.8 8.2237 1.02482 1.77650
## female_lineageS 1.02314 0.16983 10.6 6.0244 0.64782 1.39846
## male_lineageN 1.12517 0.15025 7.9 7.4885 0.77773 1.47261
## male_lineageS 1.29863 0.15082 8.0 8.6102 0.95088 1.64638
## female_lineageN:male_lineageN 1.33188 0.20175 21.4 6.6015 0.91273 1.75102
## female_lineageS:male_lineageN 0.91846 0.20175 21.4 4.5524 0.49931 1.33761
## female_lineageN:male_lineageS 1.46944 0.20348 22.1 7.2216 1.04757 1.89130
## female_lineageS:male_lineageS 1.12782 0.20175 21.4 5.5901 0.70867 1.54696
## Pr(>|t|)
## female_lineageN 5.747e-06 ***
## female_lineageS 9.875e-05 ***
## male_lineageN 7.600e-05 ***
## male_lineageS 2.551e-05 ***
## female_lineageN:male_lineageN 1.422e-06 ***
## female_lineageS:male_lineageN 0.0001672 ***
## female_lineageN:male_lineageS 2.999e-07 ***
## female_lineageS:male_lineageS 1.422e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(log.lmer.female.headbob.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate
## female_lineageN - female_lineageS 0.377519
## male_lineageN - male_lineageS -0.173460
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.413417
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -0.137562
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.204058
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -0.550979
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.209359
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.341620
## Std. Error df
## female_lineageN - female_lineageS 0.221338 41.1
## male_lineageN - male_lineageS 0.154707 101.3
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.269286 83.7
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.219504 101.1
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.269409 83.8
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.270682 84.9
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.217820 100.8
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.270601 84.8
## t value lower
## female_lineageN - female_lineageS 1.7056 -0.069454
## male_lineageN - male_lineageS -1.1212 -0.480349
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 1.5352 -0.122115
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -0.6267 -0.572995
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.7574 -0.331710
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -2.0355 -1.089176
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.9612 -0.641468
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 1.2624 -0.196423
## upper
## female_lineageN - female_lineageS 0.824491
## male_lineageN - male_lineageS 0.133428
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.948950
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.297872
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.739827
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -0.012782
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.222749
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.879663
## Pr(>|t|)
## female_lineageN - female_lineageS 0.09563 .
## male_lineageN - male_lineageS 0.26485
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.12850
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.53227
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.45092
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.04492 *
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.33877
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.21025
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(log.lmer.female.headbob.model)## R2m R2c
## [1,] 0.03653702 0.2656959
Model 4: Number of female rejection behaviours
Generalised linear mixed model with female lineage, male lineage, female lineage * male lineage as fixed effects and female ID, male ID and pairing number (female’s first or second trial) as random effects.
lmer.female.rejection.model= lmer(female_reject~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.female.rejection.model)
qqnorm(resid(lmer.female.rejection.model))
qqline(resid(lmer.female.rejection.model))
shapiro.test(resid(lmer.female.rejection.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.female.rejection.model)
## W = 0.84186, p-value = 2.757e-11log transform the data to meet model assumptions of normality
log.lmer.female.rejection.model= lmer(log1p(female_reject)~female_lineage+male_lineage+female_lineage*male_lineage+(1|female_ID)+(1|male_ID)+(1|pairing_number),data=female_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))
summary(log.lmer.female.rejection.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula:
## log1p(female_reject) ~ female_lineage + male_lineage + female_lineage *
## male_lineage + (1 | female_ID) + (1 | male_ID) + (1 | pairing_number)
## Data: female_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 420.5 444.4 -202.2 404.5 139
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.73515 -0.80009 0.00939 0.69348 2.34509
##
## Random effects:
## Groups Name Variance Std.Dev.
## female_ID (Intercept) 0.03378 0.1838
## male_ID (Intercept) 0.07612 0.2759
## pairing_number (Intercept) 0.00000 0.0000
## Residual 0.81796 0.9044
## Number of obs: 147, groups: female_ID, 44; male_ID, 42; pairing_number, 2
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.21754 0.09252 31.04325 13.160 3.07e-14
## female_lineage1 0.17756 0.08245 40.24909 2.154 0.03732
## male_lineage1 -0.27907 0.08800 38.88284 -3.171 0.00296
## female_lineage1:male_lineage1 -0.07403 0.07730 103.86495 -0.958 0.34042
##
## (Intercept) ***
## female_lineage1 *
## male_lineage1 **
## female_lineage1:male_lineage1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fml_l1 ml_ln1
## female_lng1 0.004
## male_lineg1 -0.007 -0.003
## fml_lng1:_1 -0.003 0.006 0.004
## convergence code: 0
## boundary (singular) fit: see ?isSingularanova(log.lmer.female.rejection.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## female_lineage 3.7935 3.7935 1 40.249 4.6377 0.037320 *
## male_lineage 8.2270 8.2270 1 38.883 10.0580 0.002958 **
## female_lineage:male_lineage 0.7503 0.7503 1 103.865 0.9173 0.340419
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1confint(log.lmer.female.rejection.model)## 2.5 % 97.5 %
## .sig01 0.000000000 0.46238223
## .sig02 0.000000000 0.50324677
## .sig03 0.000000000 0.39417572
## .sigma 0.781920000 1.05017578
## (Intercept) 0.964994649 1.46652546
## female_lineage1 0.008675924 0.34096119
## male_lineage1 -0.457218093 -0.10340036
## female_lineage1:male_lineage1 -0.226866905 0.07946624lsmeansLT(log.lmer.female.rejection.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower upper
## female_lineageN 1.39510 0.12414 40.9 11.2377 1.14437 1.64583
## female_lineageS 1.03998 0.12371 39.7 8.4066 0.78989 1.29007
## male_lineageN 0.93847 0.12721 42.4 7.3775 0.68182 1.19512
## male_lineageS 1.49662 0.12816 41.7 11.6776 1.23793 1.75530
## female_lineageN:male_lineageN 1.04200 0.17042 77.2 6.1143 0.70266 1.38133
## female_lineageS:male_lineageN 0.83494 0.17033 74.4 4.9018 0.49557 1.17431
## female_lineageN:male_lineageS 1.74821 0.17125 81.1 10.2088 1.40749 2.08892
## female_lineageS:male_lineageS 1.24503 0.17007 76.8 7.3206 0.90636 1.58369
## Pr(>|t|)
## female_lineageN 4.419e-14 ***
## female_lineageS 2.381e-10 ***
## male_lineageN 4.013e-09 ***
## male_lineageS 9.854e-15 ***
## female_lineageN:male_lineageN 3.705e-08 ***
## female_lineageS:male_lineageN 5.417e-06 ***
## female_lineageN:male_lineageS 3.252e-16 ***
## female_lineageS:male_lineageS 2.066e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(log.lmer.female.rejection.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate
## female_lineageN - female_lineageS 0.355119
## male_lineageN - male_lineageS -0.558149
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.207056
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -0.706211
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -0.203030
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -0.913267
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -0.410086
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.503181
## Std. Error df
## female_lineageN - female_lineageS 0.164900 40.2
## male_lineageN - male_lineageS 0.175992 38.9
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.226685 110.4
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.234707 74.0
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.240772 76.9
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.241578 77.3
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.233793 70.8
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.225384 109.3
## t value lower
## female_lineageN - female_lineageS 2.1535 0.021907
## male_lineageN - male_lineageS -3.1714 -0.914161
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.9134 -0.242162
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -3.0089 -1.173870
## female_lineageN:male_lineageN - female_lineageS:male_lineageS -0.8432 -0.682473
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -3.7804 -1.394283
## female_lineageS:male_lineageN - female_lineageS:male_lineageS -1.7541 -0.876278
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 2.2326 0.056493
## upper
## female_lineageN - female_lineageS 0.688330
## male_lineageN - male_lineageS -0.202136
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.656275
## female_lineageN:male_lineageN - female_lineageN:male_lineageS -0.238552
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.276413
## female_lineageS:male_lineageN - female_lineageN:male_lineageS -0.432252
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.056105
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.949868
## Pr(>|t|)
## female_lineageN - female_lineageS 0.0373204 *
## male_lineageN - male_lineageS 0.0029579 **
## female_lineageN:male_lineageN - female_lineageS:male_lineageN 0.3630172
## female_lineageN:male_lineageN - female_lineageN:male_lineageS 0.0035819 **
## female_lineageN:male_lineageN - female_lineageS:male_lineageS 0.4017038
## female_lineageS:male_lineageN - female_lineageN:male_lineageS 0.0003065 ***
## female_lineageS:male_lineageN - female_lineageS:male_lineageS 0.0837469 .
## female_lineageN:male_lineageS - female_lineageS:male_lineageS 0.0276161 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(log.lmer.female.rejection.model)## R2m R2c
## [1,] 0.1098666 0.2152939
Male-male behavioural trials
The dataset consists of 94 behavioural trials involving 26 male tawny dragons (Ctenophorus decresii).
Model 1: Focal male latency to emerge
Generalised linear mixed model with focal male behavioural group, opponent male behavioural group, focal male behavioural group * opponent male behavioural group, focal male condition and opponent male condition as fixed effects and focal male ID and focal male trial number as random effects.
lmer.latency.model= lmer(latency_min~fm_behav+om_behav+fm_behav*om_behav+fm_condition+om_condition+(1|fm_ID)+(1|fm_order),data=male_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.latency.model)
qqnorm(resid(lmer.latency.model))
qqline(resid(lmer.latency.model))
shapiro.test(resid(lmer.latency.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.latency.model)
## W = 0.98229, p-value = 0.234summary(lmer.latency.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula:
## latency_min ~ fm_behav + om_behav + fm_behav * om_behav + fm_condition +
## om_condition + (1 | fm_ID) + (1 | fm_order)
## Data: male_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## 641.2 676.9 -306.6 613.2 80
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.01708 -0.52266 -0.07469 0.55408 2.67168
##
## Random effects:
## Groups Name Variance Std.Dev.
## fm_ID (Intercept) 31.74 5.634
## fm_order (Intercept) 4.72 2.173
## Residual 19.16 4.378
## Number of obs: 94, groups: fm_ID, 38; fm_order, 8
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 11.7390 1.4282 26.0003 8.220 1.06e-08 ***
## fm_behav1 -2.9951 1.4599 41.2135 -2.052 0.0466 *
## fm_behav2 4.4984 1.6655 40.4616 2.701 0.0101 *
## om_behav1 -1.5561 0.8554 59.0914 -1.819 0.0740 .
## om_behav2 -0.9446 0.9577 57.0955 -0.986 0.3282
## fm_condition -0.7128 0.3641 91.1959 -1.958 0.0533 .
## om_condition -0.5836 0.3209 75.7467 -1.819 0.0729 .
## fm_behav1:om_behav1 0.6200 0.9247 55.5989 0.670 0.5053
## fm_behav2:om_behav1 -1.3355 1.0946 55.3981 -1.220 0.2276
## fm_behav1:om_behav2 -0.6648 1.0903 58.6057 -0.610 0.5444
## fm_behav2:om_behav2 -0.5345 1.2851 58.0010 -0.416 0.6790
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fm_bh1 fm_bh2 om_bh1 om_bh2 fm_cnd om_cnd f_1:_1 f_2:_1
## fm_behav1 -0.328
## fm_behav2 0.052 -0.347
## om_behav1 -0.121 0.084 -0.004
## om_behav2 0.165 -0.146 -0.038 -0.632
## fm_conditin -0.024 0.265 -0.167 0.061 -0.064
## om_conditin -0.197 0.047 -0.010 0.397 -0.241 -0.121
## fm_bhv1:m_1 0.048 -0.111 0.029 -0.515 0.375 -0.131 -0.080
## fm_bhv2:m_1 -0.026 0.037 -0.094 0.026 0.053 0.094 0.155 -0.202
## fm_bhv1:m_2 -0.090 0.154 0.022 0.376 -0.579 0.151 0.018 -0.564 0.014
## fm_bhv2:m_2 -0.061 0.008 0.130 0.118 -0.068 -0.084 0.088 -0.001 -0.530
## f_1:_2
## fm_behav1
## fm_behav2
## om_behav1
## om_behav2
## fm_conditin
## om_conditin
## fm_bhv1:m_1
## fm_bhv2:m_1
## fm_bhv1:m_2
## fm_bhv2:m_2 -0.151anova(lmer.latency.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## fm_behav 166.817 83.408 2 41.525 4.3526 0.019226 *
## om_behav 208.998 104.499 2 58.131 5.4531 0.006753 **
## fm_condition 73.444 73.444 1 91.196 3.8326 0.053322 .
## om_condition 63.388 63.388 1 75.747 3.3078 0.072903 .
## fm_behav:om_behav 72.992 18.248 4 57.236 0.9523 0.440729
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeansLT(lmer.latency.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower upper Pr(>|t|)
## fm_behavB 8.6555 1.6466 31.3 5.2566 5.2984 12.0125 1.004e-05
## fm_behavC 16.1489 2.2495 41.4 7.1790 11.6075 20.6904 8.688e-09
## fm_behavO 10.1472 2.5178 46.5 4.0301 5.0806 15.2138 0.0002048
## om_behavB 10.0944 1.5870 39.8 6.3605 6.8863 13.3025 1.507e-07
## om_behavC 10.7059 1.8198 57.6 5.8832 7.0627 14.3492 2.168e-07
## om_behavO 14.1513 1.5561 36.0 9.0943 10.9955 17.3071 7.343e-11
## fm_behavB:om_behavB 7.7193 1.8195 46.7 4.2426 4.0584 11.3802 0.0001037
## fm_behavC:om_behavB 13.2573 2.5348 65.8 5.2302 8.1962 18.3185 1.889e-06
## fm_behavO:om_behavB 9.3066 2.9265 72.9 3.1801 3.4740 15.1392 0.0021618
## fm_behavB:om_behavC 7.0461 1.9453 54.6 3.6221 3.1469 10.9452 0.0006414
## fm_behavC:om_behavC 14.6699 2.8498 79.8 5.1476 8.9983 20.3414 1.853e-06
## fm_behavO:om_behavC 10.4019 3.6899 93.3 2.8190 3.0748 17.7290 0.0058826
## fm_behavB:om_behavO 11.2010 1.8897 52.5 5.9275 7.4101 14.9920 2.426e-07
## fm_behavC:om_behavO 20.5197 2.6901 67.7 7.6278 15.1512 25.8881 1.067e-10
## fm_behavO:om_behavO 10.7332 2.6787 59.6 4.0069 5.3743 16.0921 0.0001734
##
## fm_behavB ***
## fm_behavC ***
## fm_behavO ***
## om_behavB ***
## om_behavC ***
## om_behavO ***
## fm_behavB:om_behavB ***
## fm_behavC:om_behavB ***
## fm_behavO:om_behavB **
## fm_behavB:om_behavC ***
## fm_behavC:om_behavC ***
## fm_behavO:om_behavC **
## fm_behavB:om_behavO ***
## fm_behavC:om_behavO ***
## fm_behavO:om_behavO ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(lmer.latency.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value
## fm_behavB - fm_behavC -7.49347 2.56787 39.5 -2.9182
## fm_behavB - fm_behavO -1.49176 2.81453 43.3 -0.5300
## fm_behavC - fm_behavO 6.00171 3.13843 42.2 1.9123
## om_behavB - om_behavC -0.61152 1.63850 58.0 -0.3732
## om_behavB - om_behavO -4.05687 1.33160 59.1 -3.0466
## om_behavC - om_behavO -3.44535 1.52630 56.9 -2.2573
## fm_behavB:om_behavB - fm_behavC:om_behavB -5.53801 2.86507 60.5 -1.9329
## fm_behavB:om_behavB - fm_behavO:om_behavB -1.58731 3.25532 68.7 -0.4876
## fm_behavB:om_behavB - fm_behavB:om_behavC 0.67324 1.57345 52.8 0.4279
## fm_behavB:om_behavB - fm_behavC:om_behavC -6.95055 3.24523 74.9 -2.1418
## fm_behavB:om_behavB - fm_behavO:om_behavC -2.68258 4.01457 88.4 -0.6682
## fm_behavB:om_behavB - fm_behavB:om_behavO -3.48173 1.53963 52.9 -2.2614
## fm_behavB:om_behavB - fm_behavC:om_behavO -12.80033 3.07610 67.9 -4.1612
## fm_behavB:om_behavB - fm_behavO:om_behavO -3.01388 3.06667 60.0 -0.9828
## fm_behavC:om_behavB - fm_behavO:om_behavB 3.95070 3.66413 67.8 1.0782
## fm_behavC:om_behavB - fm_behavB:om_behavC 6.21125 3.01711 68.0 2.0587
## fm_behavC:om_behavB - fm_behavC:om_behavC -1.41254 2.55667 56.2 -0.5525
## fm_behavC:om_behavB - fm_behavO:om_behavC 2.85543 4.36284 87.0 0.6545
## fm_behavC:om_behavB - fm_behavB:om_behavO 2.05628 2.98203 67.2 0.6896
## fm_behavC:om_behavB - fm_behavC:om_behavO -7.26233 2.44954 59.8 -2.9648
## fm_behavC:om_behavB - fm_behavO:om_behavO 2.52413 3.49686 61.6 0.7218
## fm_behavO:om_behavB - fm_behavB:om_behavC 2.26055 3.32590 71.8 0.6797
## fm_behavO:om_behavB - fm_behavC:om_behavC -5.36324 3.88177 74.5 -1.3816
## fm_behavO:om_behavB - fm_behavO:om_behavC -1.09527 3.63676 60.2 -0.3012
## fm_behavO:om_behavB - fm_behavB:om_behavO -1.89442 3.31489 71.9 -0.5715
## fm_behavO:om_behavB - fm_behavC:om_behavO -11.21302 3.80227 72.8 -2.9490
## fm_behavO:om_behavB - fm_behavO:om_behavO -1.42657 2.55791 57.1 -0.5577
## fm_behavB:om_behavC - fm_behavC:om_behavC -7.62378 3.28583 76.4 -2.3202
## fm_behavB:om_behavC - fm_behavO:om_behavC -3.35582 4.02775 88.5 -0.8332
## fm_behavB:om_behavC - fm_behavB:om_behavO -4.15496 1.65812 55.7 -2.5058
## fm_behavB:om_behavC - fm_behavC:om_behavO -13.47357 3.09075 68.9 -4.3593
## fm_behavB:om_behavC - fm_behavO:om_behavO -3.68712 3.14150 63.9 -1.1737
## fm_behavC:om_behavC - fm_behavO:om_behavC 4.26797 4.44304 88.6 0.9606
## fm_behavC:om_behavC - fm_behavB:om_behavO 3.46882 3.26154 76.8 1.0636
## fm_behavC:om_behavC - fm_behavC:om_behavO -5.84979 2.69667 60.7 -2.1693
## fm_behavC:om_behavC - fm_behavO:om_behavO 3.93667 3.70954 69.7 1.0612
## fm_behavO:om_behavC - fm_behavB:om_behavO -0.79915 3.99347 88.3 -0.2001
## fm_behavO:om_behavC - fm_behavC:om_behavO -10.11775 4.34194 87.4 -2.3302
## fm_behavO:om_behavC - fm_behavO:om_behavO -0.33130 3.35281 57.4 -0.0988
## fm_behavB:om_behavO - fm_behavC:om_behavO -9.31861 3.09272 69.8 -3.0131
## fm_behavB:om_behavO - fm_behavO:om_behavO 0.46785 3.11319 63.0 0.1503
## fm_behavC:om_behavO - fm_behavO:om_behavO 9.78645 3.59163 65.2 2.7248
## lower upper Pr(>|t|)
## fm_behavB - fm_behavC -12.68517 -2.30176 0.005782 **
## fm_behavB - fm_behavO -7.16657 4.18305 0.598803
## fm_behavC - fm_behavO -0.33091 12.33432 0.062634 .
## om_behavB - om_behavC -3.89128 2.66823 0.710343
## om_behavB - om_behavO -6.72128 -1.39247 0.003455 **
## om_behavC - om_behavO -6.50183 -0.38887 0.027844 *
## fm_behavB:om_behavB - fm_behavC:om_behavB -11.26799 0.19198 0.057926 .
## fm_behavB:om_behavB - fm_behavO:om_behavB -8.08201 4.90739 0.627382
## fm_behavB:om_behavB - fm_behavB:om_behavC -2.48305 3.82952 0.670484
## fm_behavB:om_behavB - fm_behavC:om_behavC -13.41551 -0.48558 0.035463 *
## fm_behavB:om_behavB - fm_behavO:om_behavC -10.66024 5.29508 0.505741
## fm_behavB:om_behavB - fm_behavB:om_behavO -6.57001 -0.39344 0.027873 *
## fm_behavB:om_behavB - fm_behavC:om_behavO -18.93872 -6.66194 9.109e-05 ***
## fm_behavB:om_behavB - fm_behavO:om_behavO -9.14820 3.12045 0.329662
## fm_behavC:om_behavB - fm_behavO:om_behavB -3.36135 11.26274 0.284762
## fm_behavC:om_behavB - fm_behavB:om_behavC 0.19066 12.23183 0.043361 *
## fm_behavC:om_behavB - fm_behavC:om_behavC -6.53375 3.70867 0.582802
## fm_behavC:om_behavB - fm_behavO:om_behavC -5.81622 11.52708 0.514524
## fm_behavC:om_behavB - fm_behavB:om_behavO -3.89562 8.00818 0.492849
## fm_behavC:om_behavB - fm_behavC:om_behavO -12.16242 -2.36223 0.004345 **
## fm_behavC:om_behavB - fm_behavO:om_behavO -4.46690 9.51515 0.473132
## fm_behavO:om_behavB - fm_behavB:om_behavC -4.36979 8.89089 0.498891
## fm_behavO:om_behavB - fm_behavC:om_behavC -13.09693 2.37046 0.171208
## fm_behavO:om_behavB - fm_behavO:om_behavC -8.36949 6.17895 0.764327
## fm_behavO:om_behavB - fm_behavB:om_behavO -8.50265 4.71382 0.569452
## fm_behavO:om_behavB - fm_behavC:om_behavO -18.79125 -3.63479 0.004283 **
## fm_behavO:om_behavB - fm_behavO:om_behavO -6.54843 3.69529 0.579223
## fm_behavB:om_behavC - fm_behavC:om_behavC -14.16758 -1.07999 0.023003 *
## fm_behavB:om_behavC - fm_behavO:om_behavC -11.35956 4.64792 0.406991
## fm_behavB:om_behavC - fm_behavB:om_behavO -7.47698 -0.83295 0.015166 *
## fm_behavB:om_behavC - fm_behavC:om_behavO -19.63957 -7.30757 4.460e-05 ***
## fm_behavB:om_behavC - fm_behavO:om_behavO -9.96316 2.58892 0.244878
## fm_behavC:om_behavC - fm_behavO:om_behavC -4.56082 13.09675 0.339369
## fm_behavC:om_behavC - fm_behavB:om_behavO -3.02602 9.96366 0.290864
## fm_behavC:om_behavC - fm_behavC:om_behavO -11.24272 -0.45685 0.033991 *
## fm_behavC:om_behavC - fm_behavO:om_behavO -3.46242 11.33576 0.292252
## fm_behavO:om_behavC - fm_behavB:om_behavO -8.73489 7.13660 0.841852
## fm_behavO:om_behavC - fm_behavC:om_behavO -18.74725 -1.48825 0.022097 *
## fm_behavO:om_behavC - fm_behavO:om_behavO -7.04427 6.38167 0.921632
## fm_behavB:om_behavO - fm_behavC:om_behavO -15.48716 -3.15005 0.003602 **
## fm_behavB:om_behavO - fm_behavO:om_behavO -5.75343 6.68913 0.881025
## fm_behavC:om_behavO - fm_behavO:om_behavO 2.61397 16.95894 0.008250 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(lmer.latency.model)## R2m R2c
## [1,] 0.2244903 0.7328283
Model 2: Focal male display behaviour
Generalised linear mixed model with focal male behavioural group, opponent male behavioural group, focal male behavioural group * opponent male behavioural group, focal male condition and opponent male condition as fixed effects and focal male ID and focal male trial number as random effects.
lmer.display.model= lmer(display_num_prop~fm_behav+om_behav+fm_behav*om_behav+fm_condition+om_condition+(1|fm_ID)+(1|fm_order),data=male_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.display.model)
qqnorm(resid(lmer.display.model))
qqline(resid(lmer.display.model))
shapiro.test(resid(lmer.display.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.display.model)
## W = 0.82174, p-value = 2.753e-09log transform the data to meet model assumptions of normality
log.lmer.display.model= lmer(log1p(display_num_prop)~fm_behav+om_behav+fm_behav*om_behav+fm_condition+om_condition+(1|fm_ID)+(1|fm_order),data=male_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))
summary(log.lmer.display.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: log1p(display_num_prop) ~ fm_behav + om_behav + fm_behav * om_behav +
## fm_condition + om_condition + (1 | fm_ID) + (1 | fm_order)
## Data: male_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -625.3 -589.7 326.6 -653.3 80
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.3986 -0.6161 -0.1585 0.2039 3.8821
##
## Random effects:
## Groups Name Variance Std.Dev.
## fm_ID (Intercept) 7.078e-06 0.002660
## fm_order (Intercept) 6.128e-06 0.002475
## Residual 4.603e-05 0.006785
## Number of obs: 94, groups: fm_ID, 38; fm_order, 8
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.0045086 0.0013857 9.5752594 3.254 0.00916 **
## fm_behav1 -0.0010435 0.0012311 30.2734546 -0.848 0.40332
## fm_behav2 -0.0009652 0.0014107 31.8092131 -0.684 0.49883
## om_behav1 0.0011457 0.0012456 58.1439208 0.920 0.36147
## om_behav2 -0.0015463 0.0013865 61.2795448 -1.115 0.26910
## fm_condition 0.0001413 0.0003885 65.6317843 0.364 0.71718
## om_condition 0.0004348 0.0004170 92.6297087 1.043 0.29980
## fm_behav1:om_behav1 0.0026244 0.0013766 51.3026433 1.906 0.06220 .
## fm_behav2:om_behav1 0.0026595 0.0016287 51.1611190 1.633 0.10863
## fm_behav1:om_behav2 -0.0010421 0.0015757 61.3862358 -0.661 0.51087
## fm_behav2:om_behav2 -0.0010708 0.0018711 59.9078653 -0.572 0.56926
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fm_bh1 fm_bh2 om_bh1 om_bh2 fm_cnd om_cnd f_1:_1 f_2:_1
## fm_behav1 -0.310
## fm_behav2 0.017 -0.298
## om_behav1 -0.153 0.094 0.023
## om_behav2 0.217 -0.196 -0.085 -0.626
## fm_conditin 0.056 0.283 -0.197 -0.048 0.018
## om_conditin -0.252 0.020 0.053 0.361 -0.254 -0.336
## fm_bhv1:m_1 0.054 -0.142 0.029 -0.490 0.348 -0.058 -0.061
## fm_bhv2:m_1 -0.017 0.041 -0.141 0.028 0.038 0.074 0.081 -0.238
## fm_bhv1:m_2 -0.117 0.206 0.050 0.358 -0.552 0.077 0.036 -0.562 0.055
## fm_bhv2:m_2 -0.088 0.018 0.203 0.100 -0.068 -0.121 0.120 0.038 -0.544
## f_1:_2
## fm_behav1
## fm_behav2
## om_behav1
## om_behav2
## fm_conditin
## om_conditin
## fm_bhv1:m_1
## fm_bhv2:m_1
## fm_bhv1:m_2
## fm_bhv2:m_2 -0.171anova(log.lmer.display.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## fm_behav 0.00007737 3.8684e-05 2 32.533 0.8403 0.44072
## om_behav 0.00006098 3.0488e-05 2 58.511 0.6623 0.51949
## fm_condition 0.00000609 6.0920e-06 1 65.632 0.1323 0.71718
## om_condition 0.00005005 5.0049e-05 1 92.630 1.0872 0.29980
## fm_behav:om_behav 0.00043918 1.0980e-04 4 56.237 2.3851 0.06196 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1lsmeansLT(log.lmer.display.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower
## fm_behavB 0.00362278 0.00149439 11.2 2.4243 0.00034253
## fm_behavC 0.00370110 0.00199194 23.2 1.8580 -0.00041800
## fm_behavO 0.00667490 0.00229581 33.4 2.9074 0.00200622
## om_behavB 0.00581194 0.00174028 24.0 3.3397 0.00222040
## om_behavC 0.00311994 0.00211030 44.4 1.4784 -0.00113191
## om_behavO 0.00506691 0.00167270 20.8 3.0292 0.00158648
## fm_behavB:om_behavB 0.00739285 0.00190875 32.0 3.8731 0.00350490
## fm_behavC:om_behavB 0.00750632 0.00270451 70.8 2.7755 0.00211336
## fm_behavO:om_behavB 0.00253666 0.00318584 81.5 0.7962 -0.00380160
## fm_behavB:om_behavC 0.00103438 0.00213235 40.1 0.4851 -0.00327505
## fm_behavC:om_behavC 0.00108395 0.00318556 85.9 0.3403 -0.00524885
## fm_behavO:om_behavC 0.00724150 0.00443353 92.5 1.6333 -0.00156326
## fm_behavB:om_behavO 0.00244112 0.00204024 38.3 1.1965 -0.00168823
## fm_behavC:om_behavO 0.00251305 0.00289414 65.4 0.8683 -0.00326624
## fm_behavO:om_behavO 0.01024655 0.00277785 70.9 3.6887 0.00470749
## upper Pr(>|t|)
## fm_behavB 0.00690304 0.0333014 *
## fm_behavC 0.00782020 0.0759236 .
## fm_behavO 0.01134359 0.0064294 **
## om_behavB 0.00940349 0.0027307 **
## om_behavC 0.00737179 0.1463453
## om_behavO 0.00854733 0.0064237 **
## fm_behavB:om_behavB 0.01128080 0.0004993 ***
## fm_behavC:om_behavB 0.01289927 0.0070464 **
## fm_behavO:om_behavB 0.00887492 0.4282116
## fm_behavB:om_behavC 0.00534380 0.6302567
## fm_behavC:om_behavC 0.00741675 0.7344847
## fm_behavO:om_behavC 0.01604626 0.1057959
## fm_behavB:om_behavO 0.00657047 0.2388696
## fm_behavC:om_behavO 0.00829234 0.3883911
## fm_behavO:om_behavO 0.01578561 0.0004386 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(log.lmer.display.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value
## fm_behavB - fm_behavC -7.8322e-05 2.1307e-03 27.9 -0.0368
## fm_behavB - fm_behavO -3.0521e-03 2.4464e-03 36.2 -1.2476
## fm_behavC - fm_behavO -2.9738e-03 2.7218e-03 36.5 -1.0926
## om_behavB - om_behavC 2.6920e-03 2.3740e-03 60.6 1.1339
## om_behavB - om_behavO 7.4504e-04 1.9503e-03 55.6 0.3820
## om_behavC - om_behavO -1.9470e-03 2.2175e-03 60.0 -0.8780
## fm_behavB:om_behavB - fm_behavC:om_behavB -1.1346e-04 2.9579e-03 83.9 -0.0384
## fm_behavB:om_behavB - fm_behavO:om_behavB 4.8562e-03 3.4723e-03 89.3 1.3986
## fm_behavB:om_behavB - fm_behavB:om_behavC 6.3585e-03 2.3726e-03 48.1 2.6799
## fm_behavB:om_behavB - fm_behavC:om_behavC 6.3089e-03 3.5342e-03 87.5 1.7851
## fm_behavB:om_behavB - fm_behavO:om_behavC 1.5135e-04 4.7342e-03 89.8 0.0320
## fm_behavB:om_behavB - fm_behavB:om_behavO 4.9517e-03 2.3079e-03 50.9 2.1456
## fm_behavB:om_behavB - fm_behavC:om_behavO 4.8798e-03 3.2349e-03 86.9 1.5085
## fm_behavB:om_behavB - fm_behavO:om_behavO -2.8537e-03 3.1484e-03 88.1 -0.9064
## fm_behavC:om_behavB - fm_behavO:om_behavB 4.9697e-03 3.9062e-03 87.5 1.2722
## fm_behavC:om_behavB - fm_behavB:om_behavC 6.4719e-03 3.2215e-03 86.3 2.0090
## fm_behavC:om_behavB - fm_behavC:om_behavC 6.4224e-03 3.7724e-03 53.6 1.7025
## fm_behavC:om_behavB - fm_behavO:om_behavC 2.6482e-04 5.1328e-03 89.1 0.0516
## fm_behavC:om_behavB - fm_behavB:om_behavO 5.0652e-03 3.1672e-03 87.9 1.5993
## fm_behavC:om_behavB - fm_behavC:om_behavO 4.9933e-03 3.5576e-03 56.7 1.4035
## fm_behavC:om_behavB - fm_behavO:om_behavO -2.7402e-03 3.6389e-03 86.9 -0.7530
## fm_behavO:om_behavB - fm_behavB:om_behavC 1.5023e-03 3.6055e-03 89.4 0.4167
## fm_behavO:om_behavB - fm_behavC:om_behavC 1.4527e-03 4.2669e-03 87.1 0.3405
## fm_behavO:om_behavB - fm_behavO:om_behavC -4.7048e-03 5.2027e-03 66.9 -0.9043
## fm_behavO:om_behavB - fm_behavB:om_behavO 9.5543e-05 3.5849e-03 91.0 0.0267
## fm_behavO:om_behavB - fm_behavC:om_behavO 2.3612e-05 4.1192e-03 92.2 0.0057
## fm_behavO:om_behavB - fm_behavO:om_behavO -7.7099e-03 3.7988e-03 51.8 -2.0295
## fm_behavB:om_behavC - fm_behavC:om_behavC -4.9570e-05 3.6193e-03 87.5 -0.0137
## fm_behavB:om_behavC - fm_behavO:om_behavC -6.2071e-03 4.7209e-03 91.0 -1.3148
## fm_behavB:om_behavC - fm_behavB:om_behavO -1.4067e-03 2.4504e-03 55.8 -0.5741
## fm_behavB:om_behavC - fm_behavC:om_behavO -1.4787e-03 3.2836e-03 87.6 -0.4503
## fm_behavB:om_behavC - fm_behavO:om_behavO -9.2122e-03 3.2898e-03 90.1 -2.8002
## fm_behavC:om_behavC - fm_behavO:om_behavC -6.1576e-03 5.2523e-03 89.9 -1.1724
## fm_behavC:om_behavC - fm_behavB:om_behavO -1.3572e-03 3.5878e-03 89.3 -0.3783
## fm_behavC:om_behavC - fm_behavC:om_behavO -1.4291e-03 3.8622e-03 64.2 -0.3700
## fm_behavC:om_behavC - fm_behavO:om_behavO -9.1626e-03 4.0051e-03 88.5 -2.2878
## fm_behavO:om_behavC - fm_behavB:om_behavO 4.8004e-03 4.7000e-03 90.4 1.0214
## fm_behavO:om_behavC - fm_behavC:om_behavO 4.7284e-03 5.0647e-03 91.5 0.9336
## fm_behavO:om_behavC - fm_behavO:om_behavO -3.0050e-03 4.8611e-03 60.7 -0.6182
## fm_behavB:om_behavO - fm_behavC:om_behavO -7.1930e-05 3.2796e-03 88.6 -0.0219
## fm_behavB:om_behavO - fm_behavO:om_behavO -7.8054e-03 3.2433e-03 90.1 -2.4067
## fm_behavC:om_behavO - fm_behavO:om_behavO -7.7335e-03 3.7828e-03 90.0 -2.0444
## lower upper Pr(>|t|)
## fm_behavB - fm_behavC -4.4435e-03 4.2869e-03 0.970939
## fm_behavB - fm_behavO -8.0125e-03 1.9083e-03 0.220177
## fm_behavC - fm_behavO -8.4915e-03 2.5439e-03 0.281748
## om_behavB - om_behavC -2.0558e-03 7.4398e-03 0.261287
## om_behavB - om_behavO -3.1626e-03 4.6526e-03 0.703916
## om_behavC - om_behavO -6.3825e-03 2.4886e-03 0.383436
## fm_behavB:om_behavB - fm_behavC:om_behavB -5.9956e-03 5.7687e-03 0.969492
## fm_behavB:om_behavB - fm_behavO:om_behavB -2.0429e-03 1.1755e-02 0.165412
## fm_behavB:om_behavB - fm_behavB:om_behavC 1.5882e-03 1.1129e-02 0.010054 *
## fm_behavB:om_behavB - fm_behavC:om_behavC -7.1517e-04 1.3333e-02 0.077712 .
## fm_behavB:om_behavB - fm_behavO:om_behavC -9.2543e-03 9.5570e-03 0.974567
## fm_behavB:om_behavB - fm_behavB:om_behavO 3.1835e-04 9.5851e-03 0.036695 *
## fm_behavB:om_behavB - fm_behavC:om_behavO -1.5500e-03 1.1310e-02 0.135057
## fm_behavB:om_behavB - fm_behavO:om_behavO -9.1103e-03 3.4029e-03 0.367192
## fm_behavC:om_behavB - fm_behavO:om_behavB -2.7938e-03 1.2733e-02 0.206661
## fm_behavC:om_behavB - fm_behavB:om_behavC 6.8014e-05 1.2876e-02 0.047668 *
## fm_behavC:om_behavB - fm_behavC:om_behavC -1.1422e-03 1.3987e-02 0.094464 .
## fm_behavC:om_behavB - fm_behavO:om_behavC -9.9338e-03 1.0463e-02 0.958968
## fm_behavC:om_behavB - fm_behavB:om_behavO -1.2290e-03 1.1359e-02 0.113348
## fm_behavC:om_behavB - fm_behavC:om_behavO -2.1314e-03 1.2118e-02 0.165904
## fm_behavC:om_behavB - fm_behavO:om_behavO -9.9730e-03 4.4926e-03 0.453462
## fm_behavO:om_behavB - fm_behavB:om_behavC -5.6613e-03 8.6659e-03 0.677922
## fm_behavO:om_behavB - fm_behavC:om_behavC -7.0282e-03 9.9337e-03 0.734331
## fm_behavO:om_behavB - fm_behavO:om_behavC -1.5090e-02 5.6799e-03 0.369073
## fm_behavO:om_behavB - fm_behavB:om_behavO -7.0254e-03 7.2165e-03 0.978796
## fm_behavO:om_behavB - fm_behavC:om_behavO -8.1573e-03 8.2046e-03 0.995439
## fm_behavO:om_behavB - fm_behavO:om_behavO -1.5334e-02 -8.6122e-05 0.047559 *
## fm_behavB:om_behavC - fm_behavC:om_behavC -7.2427e-03 7.1436e-03 0.989104
## fm_behavB:om_behavC - fm_behavO:om_behavC -1.5585e-02 3.1704e-03 0.191878
## fm_behavB:om_behavC - fm_behavB:om_behavO -6.3157e-03 3.5023e-03 0.568208
## fm_behavB:om_behavC - fm_behavC:om_behavO -8.0046e-03 5.0472e-03 0.653592
## fm_behavB:om_behavC - fm_behavO:om_behavO -1.5748e-02 -2.6765e-03 0.006249 **
## fm_behavC:om_behavC - fm_behavO:om_behavC -1.6592e-02 4.2771e-03 0.244148
## fm_behavC:om_behavC - fm_behavB:om_behavO -8.4856e-03 5.7712e-03 0.706120
## fm_behavC:om_behavC - fm_behavC:om_behavO -9.1441e-03 6.2859e-03 0.712579
## fm_behavC:om_behavC - fm_behavO:om_behavO -1.7121e-02 -1.2040e-03 0.024535 *
## fm_behavO:om_behavC - fm_behavB:om_behavO -4.5364e-03 1.4137e-02 0.309808
## fm_behavO:om_behavC - fm_behavC:om_behavO -5.3313e-03 1.4788e-02 0.352968
## fm_behavO:om_behavC - fm_behavO:om_behavO -1.2726e-02 6.7163e-03 0.538770
## fm_behavB:om_behavO - fm_behavC:om_behavO -6.5887e-03 6.4449e-03 0.982551
## fm_behavB:om_behavO - fm_behavO:om_behavO -1.4249e-02 -1.3622e-03 0.018141 *
## fm_behavC:om_behavO - fm_behavO:om_behavO -1.5249e-02 -2.1836e-04 0.043836 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(log.lmer.display.model)## R2m R2c
## [1,] 0.1436591 0.3345564
Model 3: Focal male physical aggression
Generalised linear mixed model with focal male behavioural group, opponent male behavioural group, focal male behavioural group * opponent male behavioural group, focal male condition and opponent male condition as fixed effects and focal male ID and focal male trial number as random effects.
lmer.aggression.model= lmer(agg_dur_prop~fm_behav+om_behav+fm_behav*om_behav+fm_condition+om_condition+(1|fm_ID)+(1|fm_order),data=male_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))Check the normality of the residuals
plot(lmer.aggression.model)
qqnorm(resid(lmer.aggression.model))
qqline(resid(lmer.aggression.model))
shapiro.test(resid(lmer.aggression.model))##
## Shapiro-Wilk normality test
##
## data: resid(lmer.aggression.model)
## W = 0.70014, p-value = 1.466e-12log transform the data to meet model assumptions of normality
log.lmer.aggression.model= lmer(log1p(agg_dur_prop)~fm_behav+om_behav+fm_behav*om_behav+fm_condition+om_condition+(1|fm_ID)+(1|fm_order),data=male_male_data, REML = FALSE, control = lmerControl(optimizer ="Nelder_Mead"))
summary(log.lmer.aggression.model)## Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's
## method [lmerModLmerTest]
## Formula: log1p(agg_dur_prop) ~ fm_behav + om_behav + fm_behav * om_behav +
## fm_condition + om_condition + (1 | fm_ID) + (1 | fm_order)
## Data: male_male_data
## Control: lmerControl(optimizer = "Nelder_Mead")
##
## AIC BIC logLik deviance df.resid
## -60.7 -25.1 44.4 -88.7 80
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.9538 -0.5032 -0.3237 -0.0215 3.6407
##
## Random effects:
## Groups Name Variance Std.Dev.
## fm_ID (Intercept) 0.0000000 0.0000
## fm_order (Intercept) 0.0002433 0.0156
## Residual 0.0225604 0.1502
## Number of obs: 94, groups: fm_ID, 38; fm_order, 8
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 0.0665931 0.0202257 13.0780379 3.292 0.00579 **
## fm_behav1 0.0264974 0.0229171 93.4932373 1.156 0.25053
## fm_behav2 -0.0386606 0.0265934 92.7382952 -1.454 0.14939
## om_behav1 0.0323745 0.0264743 93.9748288 1.223 0.22444
## om_behav2 -0.0098936 0.0296112 91.8519361 -0.334 0.73905
## fm_condition 0.0087941 0.0076204 92.6134690 1.154 0.25146
## om_condition 0.0001505 0.0084482 93.9958067 0.018 0.98583
## fm_behav1:om_behav1 0.0201236 0.0296437 93.4900891 0.679 0.49891
## fm_behav2:om_behav1 -0.0077706 0.0352285 91.9399609 -0.221 0.82591
## fm_behav1:om_behav2 -0.0086570 0.0335078 93.4131840 -0.258 0.79670
## fm_behav2:om_behav2 -0.0025688 0.0399245 92.3053730 -0.064 0.94884
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fm_bh1 fm_bh2 om_bh1 om_bh2 fm_cnd om_cnd f_1:_1 f_2:_1
## fm_behav1 -0.434
## fm_behav2 -0.013 -0.289
## om_behav1 -0.218 0.096 0.029
## om_behav2 0.309 -0.209 -0.088 -0.625
## fm_conditin 0.072 0.270 -0.214 -0.065 0.032
## om_conditin -0.303 0.021 0.104 0.348 -0.268 -0.384
## fm_bhv1:m_1 0.080 -0.146 0.032 -0.469 0.333 -0.047 -0.049
## fm_bhv2:m_1 -0.016 0.052 -0.143 0.036 0.026 0.071 0.054 -0.267
## fm_bhv1:m_2 -0.194 0.227 0.038 0.341 -0.537 0.063 0.055 -0.561 0.083
## fm_bhv2:m_2 -0.101 0.022 0.231 0.081 -0.065 -0.119 0.113 0.070 -0.550
## f_1:_2
## fm_behav1
## fm_behav2
## om_behav1
## om_behav2
## fm_conditin
## om_conditin
## fm_bhv1:m_1
## fm_bhv2:m_1
## fm_bhv1:m_2
## fm_bhv2:m_2 -0.187
## convergence code: 0
## boundary (singular) fit: see ?isSingularanova(log.lmer.aggression.model, type = 3)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## fm_behav 0.061008 0.0305040 2 93.450 1.3521 0.2637
## om_behav 0.040583 0.0202917 2 93.594 0.8994 0.4103
## fm_condition 0.030045 0.0300449 1 92.613 1.3318 0.2515
## om_condition 0.000007 0.0000072 1 93.996 0.0003 0.9858
## fm_behav:om_behav 0.011274 0.0028185 4 92.836 0.1249 0.9731lsmeansLT(log.lmer.aggression.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value lower upper
## fm_behavB 0.0910859 0.0220234 15.5 4.1359 0.0442772 0.1378947
## fm_behavC 0.0259279 0.0333869 53.2 0.7766 -0.0410334 0.0928891
## fm_behavO 0.0767518 0.0406695 78.1 1.8872 -0.0042127 0.1577163
## om_behavB 0.0969630 0.0303688 38.8 3.1928 0.0355262 0.1583998
## om_behavC 0.0546950 0.0395658 78.4 1.3824 -0.0240682 0.1334581
## om_behavO 0.0421076 0.0287988 38.9 1.4621 -0.0161467 0.1003618
## fm_behavB:om_behavB 0.1435840 0.0343320 59.8 4.1822 0.0749060 0.2122619
## fm_behavC:om_behavB 0.0505317 0.0521442 86.6 0.9691 -0.0531172 0.1541807
## fm_behavO:om_behavB 0.0967733 0.0621590 88.1 1.5569 -0.0267534 0.2203001
## fm_behavB:om_behavC 0.0725354 0.0391826 65.3 1.8512 -0.0057106 0.1507813
## fm_behavC:om_behavC 0.0134655 0.0630828 93.9 0.2135 -0.1117884 0.1387193
## fm_behavO:om_behavC 0.0780841 0.0895081 94.0 0.8724 -0.0996368 0.2558050
## fm_behavB:om_behavO 0.0571384 0.0372979 67.3 1.5319 -0.0173020 0.1315788
## fm_behavC:om_behavO 0.0137864 0.0547624 74.3 0.2517 -0.0953228 0.1228957
## fm_behavO:om_behavO 0.0553979 0.0536675 89.0 1.0322 -0.0512377 0.1620335
## Pr(>|t|)
## fm_behavB 0.0008246 ***
## fm_behavC 0.4408446
## fm_behavO 0.0628461 .
## om_behavB 0.0027932 **
## om_behavC 0.1707807
## om_behavO 0.1517313
## fm_behavB:om_behavB 9.572e-05 ***
## fm_behavC:om_behavB 0.3352055
## fm_behavO:om_behavB 0.1230887
## fm_behavB:om_behavC 0.0686609 .
## fm_behavC:om_behavC 0.8314331
## fm_behavO:om_behavC 0.3852306
## fm_behavB:om_behavO 0.1302217
## fm_behavC:om_behavO 0.8019299
## fm_behavO:om_behavO 0.3047541
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaitedifflsmeans(log.lmer.aggression.model, test.effs = NULL)## Least Squares Means table:
##
## Estimate Std. Error df t value
## fm_behavB - fm_behavC 0.06515804 0.03981121 91.8 1.6367
## fm_behavB - fm_behavO 0.01433414 0.04585767 94.0 0.3126
## fm_behavC - fm_behavO -0.05082390 0.05146815 93.8 -0.9875
## om_behavB - om_behavC 0.04226806 0.05057166 93.3 0.8358
## om_behavB - om_behavO 0.05485546 0.04148257 93.7 1.3224
## om_behavC - om_behavO 0.01258740 0.04741957 92.0 0.2654
## fm_behavB:om_behavB - fm_behavC:om_behavB 0.09305225 0.06051337 90.9 1.5377
## fm_behavB:om_behavB - fm_behavO:om_behavB 0.04681064 0.07035369 93.9 0.6654
## fm_behavB:om_behavB - fm_behavB:om_behavC 0.07104863 0.05177370 89.5 1.3723
## fm_behavB:om_behavB - fm_behavC:om_behavC 0.13011852 0.07229060 90.6 1.7999
## fm_behavB:om_behavB - fm_behavO:om_behavC 0.06549993 0.09720178 92.9 0.6739
## fm_behavB:om_behavB - fm_behavB:om_behavO 0.08644561 0.05000493 91.1 1.7287
## fm_behavB:om_behavB - fm_behavC:om_behavO 0.12979759 0.06507050 94.0 1.9947
## fm_behavB:om_behavB - fm_behavO:om_behavO 0.08818608 0.06338088 94.0 1.3914
## fm_behavC:om_behavB - fm_behavO:om_behavB -0.04624161 0.07982745 91.9 -0.5793
## fm_behavC:om_behavB - fm_behavB:om_behavC -0.02200362 0.06602823 91.1 -0.3332
## fm_behavC:om_behavB - fm_behavC:om_behavC 0.03706627 0.08141729 91.5 0.4553
## fm_behavC:om_behavB - fm_behavO:om_behavC -0.02755232 0.10550498 93.4 -0.2611
## fm_behavC:om_behavB - fm_behavB:om_behavO -0.00660664 0.06424138 93.6 -0.1028
## fm_behavC:om_behavB - fm_behavC:om_behavO 0.03674534 0.07585614 94.0 0.4844
## fm_behavC:om_behavB - fm_behavO:om_behavO -0.00486618 0.07415054 92.9 -0.0656
## fm_behavO:om_behavB - fm_behavB:om_behavC 0.02423799 0.07349141 93.4 0.3298
## fm_behavO:om_behavB - fm_behavC:om_behavC 0.08330788 0.08762469 92.0 0.9507
## fm_behavO:om_behavB - fm_behavO:om_behavC 0.01868928 0.10926129 94.0 0.1711
## fm_behavO:om_behavB - fm_behavB:om_behavO 0.03963497 0.07238213 94.0 0.5476
## fm_behavO:om_behavB - fm_behavC:om_behavO 0.08298694 0.08246187 91.7 1.0064
## fm_behavO:om_behavB - fm_behavO:om_behavO 0.04137543 0.08153084 93.9 0.5075
## fm_behavB:om_behavC - fm_behavC:om_behavC 0.05906989 0.07437974 90.1 0.7942
## fm_behavB:om_behavC - fm_behavO:om_behavC -0.00554870 0.09637118 93.6 -0.0576
## fm_behavB:om_behavC - fm_behavB:om_behavO 0.01539698 0.05262141 91.8 0.2926
## fm_behavB:om_behavC - fm_behavC:om_behavO 0.05874896 0.06651214 93.7 0.8833
## fm_behavB:om_behavC - fm_behavO:om_behavO 0.01713745 0.06628274 94.0 0.2586
## fm_behavC:om_behavC - fm_behavO:om_behavC -0.06461859 0.10802971 92.6 -0.5982
## fm_behavC:om_behavC - fm_behavB:om_behavO -0.04367291 0.07336785 91.0 -0.5953
## fm_behavC:om_behavC - fm_behavC:om_behavO -0.00032093 0.08171312 93.7 -0.0039
## fm_behavC:om_behavC - fm_behavO:om_behavO -0.04193244 0.08199255 91.9 -0.5114
## fm_behavO:om_behavC - fm_behavB:om_behavO 0.02094568 0.09633958 92.8 0.2174
## fm_behavO:om_behavC - fm_behavC:om_behavO 0.06429766 0.10309416 94.0 0.6237
## fm_behavO:om_behavC - fm_behavO:om_behavO 0.02268615 0.10390148 91.7 0.2183
## fm_behavB:om_behavO - fm_behavC:om_behavO 0.04335198 0.06577745 94.0 0.6591
## fm_behavB:om_behavO - fm_behavO:om_behavO 0.00174047 0.06511481 94.0 0.0267
## fm_behavC:om_behavO - fm_behavO:om_behavO -0.04161151 0.07602531 93.6 -0.5473
## lower upper Pr(>|t|)
## fm_behavB - fm_behavC -0.01391231 0.14422839 0.10512
## fm_behavB - fm_behavO -0.07671736 0.10538563 0.75529
## fm_behavC - fm_behavO -0.15301806 0.05137025 0.32595
## om_behavB - om_behavC -0.05815273 0.14268885 0.40540
## om_behavB - om_behavO -0.02751306 0.13722398 0.18926
## om_behavC - om_behavO -0.08159219 0.10676698 0.79126
## fm_behavB:om_behavB - fm_behavC:om_behavB -0.02715156 0.21325606 0.12759
## fm_behavB:om_behavB - fm_behavO:om_behavB -0.09288107 0.18650236 0.50745
## fm_behavB:om_behavB - fm_behavB:om_behavC -0.03181673 0.17391399 0.17340
## fm_behavB:om_behavB - fm_behavC:om_behavC -0.01348735 0.27372440 0.07520 .
## fm_behavB:om_behavB - fm_behavO:om_behavC -0.12752593 0.25852579 0.50208
## fm_behavB:om_behavB - fm_behavB:om_behavO -0.01288125 0.18577246 0.08724 .
## fm_behavB:om_behavB - fm_behavC:om_behavO 0.00059859 0.25899659 0.04897 *
## fm_behavB:om_behavB - fm_behavO:om_behavO -0.03765884 0.21403100 0.16740
## fm_behavC:om_behavB - fm_behavO:om_behavB -0.20478821 0.11230500 0.56382
## fm_behavC:om_behavB - fm_behavB:om_behavC -0.15315823 0.10915098 0.73971
## fm_behavC:om_behavB - fm_behavC:om_behavC -0.12464624 0.19877878 0.65000
## fm_behavC:om_behavB - fm_behavO:om_behavC -0.23705306 0.18194841 0.79455
## fm_behavC:om_behavB - fm_behavB:om_behavO -0.13416657 0.12095329 0.91831
## fm_behavC:om_behavB - fm_behavC:om_behavO -0.11386895 0.18735962 0.62922
## fm_behavC:om_behavB - fm_behavO:om_behavO -0.15211682 0.14238447 0.94782
## fm_behavO:om_behavB - fm_behavB:om_behavC -0.12169382 0.17016979 0.74228
## fm_behavO:om_behavB - fm_behavC:om_behavC -0.09072307 0.25733883 0.34423
## fm_behavO:om_behavB - fm_behavO:om_behavC -0.19825158 0.23563015 0.86455
## fm_behavO:om_behavB - fm_behavB:om_behavO -0.10408166 0.18335159 0.58528
## fm_behavO:om_behavB - fm_behavC:om_behavO -0.08079769 0.24677158 0.31689
## fm_behavO:om_behavB - fm_behavO:om_behavO -0.12050932 0.20326018 0.61301
## fm_behavB:om_behavC - fm_behavC:om_behavC -0.08869717 0.20683695 0.42919
## fm_behavB:om_behavC - fm_behavO:om_behavC -0.19690715 0.18580974 0.95421
## fm_behavB:om_behavC - fm_behavB:om_behavO -0.08911621 0.11991017 0.77049
## fm_behavB:om_behavC - fm_behavC:om_behavO -0.07331783 0.19081575 0.37934
## fm_behavB:om_behavC - fm_behavO:om_behavO -0.11446851 0.14874341 0.79655
## fm_behavC:om_behavC - fm_behavO:om_behavC -0.27915608 0.14991889 0.55120
## fm_behavC:om_behavC - fm_behavB:om_behavO -0.18940983 0.10206401 0.55315
## fm_behavC:om_behavC - fm_behavC:om_behavO -0.16257118 0.16192932 0.99687
## fm_behavC:om_behavC - fm_behavO:om_behavO -0.20477844 0.12091355 0.61028
## fm_behavO:om_behavC - fm_behavB:om_behavO -0.17037014 0.21226150 0.82836
## fm_behavO:om_behavC - fm_behavC:om_behavO -0.14039823 0.26899355 0.53435
## fm_behavO:om_behavC - fm_behavO:om_behavO -0.18368029 0.22905259 0.82765
## fm_behavB:om_behavO - fm_behavC:om_behavO -0.08725093 0.17395489 0.51146
## fm_behavB:om_behavO - fm_behavO:om_behavO -0.12754661 0.13102755 0.97873
## fm_behavC:om_behavO - fm_behavO:om_behavO -0.19257101 0.10934799 0.58545
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Confidence level: 95%
## Degrees of freedom method: Satterthwaiter.squaredGLMM(log.lmer.aggression.model)## R2m R2c
## [1,] 0.07592327 0.08578127