Load packages

pacman::p_load(tidyverse, kableExtra, DataExplorer, viridis, cowplot, maps, rotl,
    ape, metafor, patchwork, orchaRd, car, MuMIn, GGally)

Data processing and exploration

Load the raw data set

d.raw: raw data set

d.raw <- read_csv("data/Raw_data.csv")

Calculate effect sizes

The sampling variance of ARRD (effect size) was calculated based on the adjusted sample size (the sample size was divided by two when experimental groups were involved in multiple comparisons)

  • ARR_f: Acclimation response ratio of females
  • ARR_m: Acclimation response ratio of males
  • ARRD: Difference in acclimation response ratios between females and males (i.e. effect size in this study)
  • Var_ARRD: Sampling variance of ARRD; calculated with adjusted sample sizes (i.e. sample size divided by half when experimental groups were involved in multiple comparisons)
  • precision: Inverse of the squared sampling variance of ARRD
  • The latitude was also converted to absolute values, abs_latitude
d.raw <- d.raw %>%
    mutate(abs_latitude = abs(latitude)) %>%
    mutate(abs_longitude = abs(longitude)) %>%
    mutate(ARR_f = ((mean_high_f - mean_low_f)/(acc_temp_high - acc_temp_low))) %>%
    mutate(ARR_m = ((mean_high_m - mean_low_m)/(acc_temp_high - acc_temp_low))) %>%
    mutate(ARRD = ARR_f - ARR_m) %>%
    mutate(Var_ARRD = ((1/(acc_temp_high - acc_temp_low))^2 * (sd_low_f^2/n_low_f_adj +
        sd_high_f^2/n_high_f_adj + sd_low_m^2/n_low_m_adj + sd_high_m^2/n_high_m_adj))) %>%
    mutate(precision = (1/sqrt(Var_ARRD)))

Check and reformat variables

The categorical variables were converted to factors

d.raw$es_ID = as.factor(d.raw$es_ID)
d.raw$species_ID = as.factor(d.raw$species_ID)
d.raw$study_ID = as.factor(d.raw$study_ID)
d.raw$shared_trt_ID = as.factor(d.raw$shared_trt_ID)
d.raw$shared_measurement_ID = as.factor(d.raw$shared_measurement_ID)
d.raw$data_type = as.factor(d.raw$data_type)
d.raw$peer_reviewed = as.factor(d.raw$peer_reviewed)
d.raw$ref = as.factor(d.raw$ref)
d.raw$class = as.factor(d.raw$class)
d.raw$order = as.factor(d.raw$order)
d.raw$genus_species = as.factor(d.raw$genus_species)
d.raw$habitat = as.factor(d.raw$habitat)
d.raw$taxonomic_group = as.factor(d.raw$taxonomic_group)
d.raw$taxonomic_group_sub = as.factor(d.raw$taxonomic_group_sub)
d.raw$origin = as.factor(d.raw$origin)
d.raw$outcome = as.factor(d.raw$outcome)

Inspection of the summary of the data set

  • We can see that the sample size for PBT data is small (n=14). It is probably best not to run the analyses of the interaction between our predictor variables and the outcome (PBT, UTL or LTL) because it could result in type I and type II errors due to low sample size.

  • We also have a better coverage for the body mass dimorphism index MDI compared to the size dimorphism index SDI. Hence, we would use the former variable to investigate the influence of sexual size dimorphism on sex differences in acclimation capacity.

  • The minimum and maximum values of ARRD, ARR_f and ARR_m are quite extreme. However, these values seem plausible and may not need to be removed just based on their values.

kable(summary(d.raw), "html") %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")
es_ID species_ID study_ID shared_trt_ID shared_measurement_ID fig_ID fig_file_name data_type peer_reviewed data_file_name ref title pub_year authors journal doi language phylum class order family genus species genus_species variety habitat taxonomic_group taxonomic_group_sub life_stage origin n_generations_lab population latitude longitude elevation season year body_length_f.cm body_length_m.cm diff_body_length SDI source_body_length body_mass_f.g body_mass_m.g diff_body_mass MDI source_body_mass age incubation_temp outcome method endpoint acc_temp_low acc_temp_high acc_duration ramping.deg.min measurement_rate.h exp_duration.h n_observations gradient_type gradient_range humidity.percent oxygen.mg.L salinity.ppt pH photoperiod.light gravidity major_concern minor_concern notes_moderators mean_low_f sd_low_f n_low_f n_low_f_adj mean_high_f sd_high_f n_high_f n_high_f_adj mean_low_m sd_low_m n_low_m n_low_m_adj mean_high_m sd_high_m n_high_m n_high_m_adj exp_group_discarded notes_outcome abs_latitude abs_longitude ARR_f ARR_m ARRD Var_ARRD precision
es1 : 1 sp8 : 30 st6 : 30 t94 : 14 m173 : 5 Min. : 1.0 Length:240 published :109 not peer-reviewed: 49 Length:240 Watson and McMahon 2008 : 30 Length:240 Min. :1994 Length:240 Length:240 Length:240 Length:240 Length:240 Insecta :76 Cyprinodontiformes:54 Length:240 Length:240 Length:240 Gambusia affinis : 30 Length:240 aquatic :137 invertebrate:129 Aquatic Invertebrates :53 Length:240 lab : 71 Min. : 1.000 Length:240 Min. :-46.90 Min. :-155.0535 Min. : 0.0 Length:240 Min. :1975 Min. : 0.094 Min. : 0.0800 Min. :-1.00000 Min. :-0.70714 Length:240 Min. : 0.0002 Min. : 0.0002 Min. :-14.38400 Min. :-2.8694 Length:240 Min. : 7.00 Min. :14.00 LTL:103 Length:240 Length:240 Min. : 2.30 Min. : 7.2 Min. : 1.00 Min. :0.0001 Min. : 0.4286 Min. : 2.000 Min. : 1.00 Length:240 Min. :20.09 Min. : 43.00 Min. :6.000 Min. : 1.00 Min. :7.100 Min. :10.00 Length:240 Length:240 Length:240 Length:240 Min. :-18.430 Min. :0.1329 Min. : 2.00 Min. : 1.00 Min. :-19.530 Min. :0.06788 Min. : 2 Min. : 1.00 Min. :-18.710 Min. :0.1414 Min. : 2.00 Min. : 1.000 Min. :-19.510 Min. :0.1269 Min. : 2.00 Min. : 1.000 Length:240 Length:240 Min. :10.43 Min. : 0.7994 Min. :-0.57119 Min. :-0.50843 Min. :-0.765818 Min. :0.0001011 Min. : 0.9275
es10 : 1 sp1 : 20 st1 : 20 t119 : 6 m172 : 4 1st Qu.: 4.0 Class :character unpublished:131 peer-reviewed :191 Class :character Allen et al. 2012 : 20 Class :character 1st Qu.:2008 Class :character Class :character Class :character Class :character Class :character Actinopterygii:62 Coleoptera :38 Class :character Class :character Class :character Tenebrio molitor : 20 Class :character terrestrial:103 vertebrate :111 Fishes :66 Class :character wild:165 1st Qu.: 1.000 Class :character 1st Qu.:-33.87 1st Qu.: -81.0000 1st Qu.: 0.0 Class :character 1st Qu.:2007 1st Qu.: 0.554 1st Qu.: 0.6248 1st Qu.: 0.00334 1st Qu.: 0.01348 Class :character 1st Qu.: 0.0643 1st Qu.: 0.0683 1st Qu.: -0.01274 1st Qu.:-0.1368 Class :character 1st Qu.:10.00 1st Qu.:25.00 PBT: 14 Class :character Class :character 1st Qu.:10.80 1st Qu.:20.0 1st Qu.: 6.00 1st Qu.:0.2000 1st Qu.: 1.3333 1st Qu.: 2.750 1st Qu.: 11.00 Class :character 1st Qu.:27.62 1st Qu.: 69.00 1st Qu.:6.000 1st Qu.:20.00 1st Qu.:7.100 1st Qu.:12.00 Class :character Class :character Class :character Class :character 1st Qu.: 3.773 1st Qu.:0.4205 1st Qu.: 4.00 1st Qu.: 4.00 1st Qu.: 6.165 1st Qu.:0.37000 1st Qu.: 4 1st Qu.: 3.50 1st Qu.: 3.946 1st Qu.:0.4548 1st Qu.: 5.00 1st Qu.: 4.000 1st Qu.: 6.071 1st Qu.:0.4401 1st Qu.: 5.00 1st Qu.: 4.000 Class :character Class :character 1st Qu.:30.49 1st Qu.: 18.6240 1st Qu.: 0.04937 1st Qu.: 0.04281 1st Qu.:-0.052371 1st Qu.:0.0017246 1st Qu.: 6.5039
es100 : 1 sp21 : 18 st5 : 20 t118 : 5 m123 : 2 Median :14.0 Mode :character NA NA Mode :character Lyons et al. 2012 : 20 Mode :character Median :2012 Mode :character Mode :character Mode :character Mode :character Mode :character Malacostraca :49 Diptera :31 Mode :character Mode :character Mode :character Hyperolius marmoratus: 18 Mode :character NA NA Reptiles and Amphibians :45 Mode :character NA’s: 4 Median : 4.000 Mode :character Median : 30.15 Median : -0.7994 Median : 7.0 Mode :character Median :2008 Median : 3.742 Median : 2.9081 Median : 0.22600 Median : 0.12337 Mode :character Median : 0.3018 Median : 0.1554 Median : 0.01090 Median : 0.1300 Mode :character Median :15.00 Median :25.00 UTL:123 Mode :character Mode :character Median :15.00 Median :25.0 Median : 14.00 Median :0.3000 Median : 6.0000 Median : 7.625 Median : 27.00 Mode :character Median :29.00 Median : 80.00 Median :6.750 Median :20.00 Median :7.150 Median :12.00 Mode :character Mode :character Mode :character Mode :character Median : 27.708 Median :0.7262 Median : 8.00 Median : 6.00 Median : 27.797 Median :0.70242 Median : 8 Median : 6.00 Median : 28.146 Median :0.7128 Median : 8.00 Median : 5.000 Median : 28.762 Median :0.6873 Median : 8.00 Median : 5.000 Mode :character Mode :character Median :33.91 Median : 32.7831 Median : 0.14848 Median : 0.14778 Median :-0.003267 Median :0.0058757 Median :13.0458
es101 : 1 sp23 : 17 st18 : 18 t116 : 3 m124 : 2 Mean :12.4 NA NA NA NA Davies et al. 2015 : 18 NA Mean :2011 NA NA NA NA NA Reptilia :23 Amphipoda :23 NA NA NA Fundulus heteroclitus: 17 NA NA NA Terrestrial Invertebrates:76 NA NA Mean : 5.955 NA Mean : 11.19 Mean : -20.7520 Mean : 146.6 NA Mean :2007 Mean : 5.015 Mean : 4.2045 Mean : 0.83650 Mean : 0.16469 NA Mean : 24.6402 Mean : 19.9282 Mean : 4.82695 Mean : 0.1305 NA Mean :15.18 Mean :24.38 NA NA NA Mean :15.26 Mean :24.6 Mean : 16.69 Mean :0.4333 Mean : 5.0068 Mean :15.071 Mean : 84.21 NA Mean :30.83 Mean : 75.69 Mean :6.709 Mean :24.81 Mean :7.221 Mean :12.33 NA NA NA NA Mean : 22.280 Mean :0.9383 Mean : 13.88 Mean : 12.43 Mean : 23.781 Mean :0.92771 Mean : 14 Mean : 12.59 Mean : 22.287 Mean :0.9957 Mean : 10.45 Mean : 8.967 Mean : 23.756 Mean :0.9281 Mean : 11.05 Mean : 9.575 NA NA Mean :35.35 Mean : 48.6475 Mean : 0.16955 Mean : 0.16480 Mean : 0.004756 Mean :0.0481600 Mean :20.3597
es102 : 1 sp20 : 16 st20 : 17 t117 : 3 m125 : 2 3rd Qu.:18.0 NA NA NA NA Fangue et al. 2006 : 17 NA 3rd Qu.:2014 NA NA NA NA NA Amphibia :22 Anura :20 NA NA NA Enochrus politus : 16 NA NA NA NA NA NA 3rd Qu.:10.500 NA 3rd Qu.: 38.17 3rd Qu.: 18.7850 3rd Qu.: 187.0 NA 3rd Qu.:2011 3rd Qu.: 6.177 3rd Qu.: 5.9264 3rd Qu.: 1.01219 3rd Qu.: 0.33158 NA 3rd Qu.: 1.7000 3rd Qu.: 1.4000 3rd Qu.: 0.16425 3rd Qu.: 0.5451 NA 3rd Qu.:20.00 3rd Qu.:25.00 NA NA NA 3rd Qu.:20.00 3rd Qu.:30.0 3rd Qu.: 21.00 3rd Qu.:0.5000 3rd Qu.: 6.0000 3rd Qu.:24.000 3rd Qu.:144.00 NA 3rd Qu.:38.00 3rd Qu.: 80.00 3rd Qu.:6.750 3rd Qu.:32.00 3rd Qu.:7.150 3rd Qu.:12.00 NA NA NA NA 3rd Qu.: 39.281 3rd Qu.:1.1248 3rd Qu.: 12.00 3rd Qu.: 8.00 3rd Qu.: 40.430 3rd Qu.:1.13383 3rd Qu.: 12 3rd Qu.: 8.00 3rd Qu.: 38.883 3rd Qu.:1.1676 3rd Qu.: 11.00 3rd Qu.: 9.000 3rd Qu.: 39.980 3rd Qu.:1.0768 3rd Qu.: 10.00 3rd Qu.: 8.000 NA NA 3rd Qu.:43.03 3rd Qu.: 81.7522 3rd Qu.: 0.29331 3rd Qu.: 0.29161 3rd Qu.: 0.060442 3rd Qu.:0.0236410 3rd Qu.:24.0809
es103 : 1 sp18 : 14 st17 : 16 t164 : 3 m126 : 2 Max. :25.0 NA NA NA NA Botella-Cruz et al. 2016: 16 NA Max. :2020 NA NA NA NA NA Chondrichthyes: 4 Squamata :19 NA NA NA Crangon crangon : 14 NA NA NA NA NA NA Max. :20.000 NA Max. : 61.20 Max. : 147.2667 Max. :2975.7 NA Max. :2019 Max. :26.877 Max. :24.9357 Max. : 7.75000 Max. : 1.00000 NA Max. :907.2000 Max. :724.9500 Max. :283.61750 Max. : 2.1083 NA Max. :30.00 Max. :27.00 NA NA NA Max. :32.10 Max. :35.1 Max. :126.00 Max. :1.0000 Max. :12.0000 Max. :48.000 Max. :288.00 NA Max. :43.00 Max. :100.00 Max. :9.300 Max. :60.00 Max. :7.750 Max. :24.00 NA NA NA NA Max. : 53.853 Max. :5.4300 Max. :181.00 Max. :181.00 Max. : 54.417 Max. :8.29597 Max. :263 Max. :263.00 Max. : 54.333 Max. :7.5728 Max. :142.00 Max. :142.000 Max. : 54.333 Max. :7.5728 Max. :261.00 Max. :261.000 NA NA Max. :61.20 Max. :155.0535 Max. : 1.82289 Max. : 1.30526 Max. : 0.860000 Max. :1.1623167 Max. :99.4402
(Other):234 (Other):125 (Other):119 (Other):206 (Other):223 NA’s :167 NA NA NA NA (Other) :119 NA NA NA NA NA NA NA (Other) : 4 (Other) :55 NA NA NA (Other) :125 NA NA NA NA NA NA NA’s :218 NA NA’s :16 NA’s :16 NA’s :16 NA NA’s :62 NA’s :77 NA’s :77 NA’s :82 NA’s :82 NA NA’s :30 NA’s :30 NA’s :35 NA’s :35 NA NA’s :218 NA’s :184 NA NA NA NA NA NA’s :7 NA’s :18 NA’s :226 NA’s :226 NA’s :226 NA NA’s :226 NA’s :167 NA’s :229 NA’s :173 NA’s :228 NA’s :49 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA’s :16 NA’s :16 NA NA NA NA NA

Check for extreme values

Here, we checked the mean, minimum, and maximum values of ARRD, ARR_f and ARR_m for each study to see if the extreme values are particularly condensed in certain studies.

We also plotted the distribution of ARRD to see if the response variable is skewed.

kable(d.raw %>%
    group_by(ref) %>%
    summarise(mean_ARRD = mean(ARRD), var_ARRD = mean(Var_ARRD), prec = mean(precision),
        max_ARRD = max(ARRD), min_ARRD = min(ARRD), mean_ARRf = mean(ARR_f), sd_ARRf = sd(ARR_f),
        max_ARRf = max(ARR_f), min_ARRf = min(ARR_f), mean_ARRm = mean(ARR_m), sd_ARRm = sd(ARR_m),
        max_ARRm = max(ARR_m), min_ARRm = min(ARR_m), n = n())) %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")
ref mean_ARRD var_ARRD prec max_ARRD min_ARRD mean_ARRf sd_ARRf max_ARRf min_ARRf mean_ARRm sd_ARRm max_ARRm min_ARRm n
Allen et al. 2012 -0.0010898 0.0001854 76.118554 0.0198699 -0.0437768 0.0900550 0.0262627 0.1330775 0.0474964 0.0911448 0.0227055 0.1427266 0.0635193 20
Alveal et al. 2019 0.0750000 0.2389012 2.045930 0.0750000 0.0750000 -0.2110000 NA -0.2110000 -0.2110000 -0.2860000 NA -0.2860000 -0.2860000 1
Anthony 2019 0.0647176 0.0023154 22.981454 0.1423122 -0.0128770 -0.0149012 0.0466632 0.0180947 -0.0478970 -0.0796188 0.0630722 -0.0350200 -0.1242175 2
Artacho et al. 2017 -0.0787933 0.0429659 5.051649 0.1086033 -0.2661900 -0.3060744 0.2002479 -0.1644778 -0.4476711 -0.2272811 0.0647710 -0.1814811 -0.2730811 2
Basson and Clusella-Trullas 2016 -0.0258621 0.2252742 2.106902 -0.0258621 -0.0258621 0.3103448 NA 0.3103448 0.3103448 0.3362069 NA 0.3362069 0.3362069 1
Botella-Cruz et al. 2016 -0.0305815 0.1395659 4.070788 0.3758334 -0.6000000 -0.0958541 0.2284568 0.3233334 -0.5388888 -0.0652726 0.2000951 0.2700000 -0.4187302 16
Chung 2001 -0.0072222 0.0183211 7.717205 0.1366667 -0.2100000 0.1433333 0.0872799 0.2533333 0.0533333 0.1505556 0.0752896 0.2800000 0.0633333 6
Cortemeglia and Beitinger 2006 0.0600000 0.0089853 10.549564 0.0600000 0.0600000 0.1600000 NA 0.1600000 0.1600000 0.1000000 NA 0.1000000 0.1000000 1
Darnell et al. 2015 -0.0350741 0.0014731 26.286444 -0.0222222 -0.0479259 0.2584444 0.0095328 0.2651852 0.2517037 0.2935185 0.0086424 0.2996296 0.2874074 2
Davies et al. 2015 0.0621892 0.2774309 2.713077 0.8600000 -0.4349333 0.2738981 0.3586072 0.9550000 -0.5060000 0.2117089 0.2865826 1.1000000 -0.1860000 18
Do Amaral et al. 2002 0.0233750 0.0053409 14.095050 0.2565000 -0.1480000 -0.0463750 0.1175850 0.1235000 -0.1470000 -0.0697500 0.1057083 0.0740000 -0.1630000 4
Fangue and Bennett 2003 0.0129279 0.0038762 17.613402 0.0575342 -0.0259941 0.3750718 0.0571309 0.4100457 0.2897260 0.3621439 0.0886229 0.4234168 0.2321918 4
Fangue et al. 2006 0.0133863 0.0437233 8.098033 0.5176274 -0.2381579 0.4721978 0.4414369 1.8228905 -0.2330826 0.4588115 0.3779378 1.3052632 -0.3552632 17
Faulkner et al. 2014 0.0547020 0.0146890 14.088149 0.4196429 -0.1181976 0.1172211 0.1640725 0.4887440 -0.1130952 0.0625191 0.1600301 0.4577381 -0.1864587 15
Fries and Gibson 2010 -0.0813467 0.0121751 13.140742 -0.0099767 -0.1527167 0.5411111 0.3549000 0.7920633 0.2901589 0.6224578 0.4558325 0.9447800 0.3001356 2
Gvozdik et al. 2007 0.0095413 0.1375387 9.960750 0.0818333 -0.0627508 -0.2114262 0.5087769 0.1483333 -0.5711858 -0.2209675 0.4065404 0.0665000 -0.5084350 2
Haggerty 2016 0.0388430 0.0009023 33.291546 0.0388430 0.0388430 0.1024793 NA 0.1024793 0.1024793 0.0636364 NA 0.0636364 0.0636364 1
Hernandez et al. 2002 -0.7658183 0.0058803 13.040714 -0.7658183 -0.7658183 0.0307503 NA 0.0307503 0.0307503 0.7965686 NA 0.7965686 0.7965686 1
Huang et al. 2020 0.6750000 0.0481458 4.557437 0.6750000 0.6750000 0.3500000 NA 0.3500000 0.3500000 -0.3250000 NA -0.3250000 -0.3250000 1
Kelley et al. 2011 0.0409459 0.0224700 10.824818 0.2347282 -0.1528365 0.2242297 0.0960638 0.2921571 0.1563024 0.1832838 0.1779858 0.3091388 0.0574288 2
Kolbe et al. 2014 0.0223692 0.0050395 14.842259 0.0884110 -0.0769756 0.1941600 0.0573785 0.2535842 0.0855095 0.1717908 0.0410203 0.2607527 0.1158901 9
Krstevska and Hoffman 1994 -0.0166754 0.0200704 7.139264 0.0000000 -0.0333509 0.0166754 0.0136531 0.0263296 0.0070212 0.0333509 0.0099295 0.0403721 0.0263296 2
Kubisch et al. 2016 0.0800385 0.0406666 11.871210 0.1144873 0.0455897 0.0459173 0.0419845 0.0756048 0.0162298 -0.0341212 0.0067335 -0.0293599 -0.0388825 2
Lin et al. 2019 -0.3091675 0.0561906 4.303574 -0.1791675 -0.4391675 -0.1404175 0.1573313 -0.0291675 -0.2516675 0.1687500 0.0265165 0.1875000 0.1500000 2
Llewelyn et al. 2017 -0.0111117 0.0023512 20.630710 0.0370367 -0.0592600 0.0657406 0.0327367 0.0888889 0.0425922 0.0768522 0.0353553 0.1018522 0.0518522 2
Lyons et al. 2012 0.0157399 0.0078726 14.009763 0.1677102 -0.1868132 0.1123225 0.1102609 0.3890710 -0.0535519 0.0965826 0.0865081 0.3118397 -0.0338798 20
Massamba-N’Siala et al. 2012 -0.0010000 0.0098027 11.888592 0.1380000 -0.1400000 0.0866667 0.0292271 0.1073333 0.0660000 0.0876667 0.2258028 0.2473333 -0.0720000 2
Mesher 2009 -0.0204702 0.0173181 8.784751 0.2928330 -0.3175000 0.1028159 0.1821068 0.3577770 -0.3500000 0.1232861 0.1667344 0.4733330 -0.1966670 16
Morey et al. 2012 -0.1164444 0.4264452 1.643966 -0.0660000 -0.1500000 -0.2633333 0.2676440 -0.0200000 -0.5500000 -0.1468889 0.2290175 0.0460000 -0.4000000 3
Pallares et al. 2020 0.1502860 0.0018708 23.119944 0.1502860 0.1502860 0.0692860 NA 0.0692860 0.0692860 -0.0810000 NA -0.0810000 -0.0810000 1
Piyaphongkul et al. 2014 0.0333333 0.0021000 36.292079 0.0533333 0.0133333 0.2850000 0.1956849 0.5533333 0.0866667 0.2516667 0.1852626 0.5066667 0.0733333 4
Ransberry et al. 2011 0.0123239 0.0002870 64.338580 0.0560363 -0.0290551 0.2842276 0.0754234 0.3538644 0.2041132 0.2719037 0.1179443 0.3829195 0.1480769 3
Reiser et al. 2014 0.0228571 0.0054276 14.624523 0.2080000 -0.0760000 0.3451429 0.0908616 0.4800000 0.2000000 0.3222857 0.0605099 0.3780000 0.2420000 14
Shinner et al. 2020 0.1300000 0.0445090 4.739975 0.1300000 0.1300000 -0.2400000 NA -0.2400000 -0.2400000 -0.3700000 NA -0.3700000 -0.3700000 1
Spinks et al. 2019 0.0164600 0.0022729 20.975537 0.0164600 0.0164600 0.0007550 NA 0.0007550 0.0007550 -0.0157050 NA -0.0157050 -0.0157050 1
Watson and McMahon 2008 -0.0183474 0.0019498 30.079119 0.0768548 -0.2663270 0.2857171 0.0608625 0.3991853 0.1715628 0.3040645 0.0861690 0.5366670 0.1474783 30
Worthen and Haney 1999 0.0014000 0.0067280 15.414114 0.0334000 -0.0250000 0.0354167 0.0569830 0.1268000 -0.0400000 0.0340167 0.0528858 0.1300000 -0.0150000 6
Xia et al. 2019 -0.0206388 0.0003303 57.059923 0.0566820 -0.0963359 0.3431493 0.1234410 0.4457143 0.1945245 0.3637881 0.0593536 0.4302857 0.2908604 4
ggplot(d.raw, aes(ARRD)) + geom_histogram(fill = "darkcyan", col = "black", binwidth = 0.05) +
    theme_classic()

Data exploration with DataExplorer

The package DataExplorer provides useful functions for data exploration

Missing data

  • Again, we can see that the coverage of MDI is much higher than SDI so we would rather use MDI for the analyses of sexual size dimorphism.

  • Besides the variables we extracted to answer our a priori hypotheses, we can see that we obtained a relatively good data coverage for longitude, elevation, season, year, method and endpoint

plot_missing(d.raw)

Frequency of each categorical variable

  • The outcome data is quite heterogenous. We obtained very few data on PBT (n=14)
plot_bar(d.raw)

Frequency of each continuous variable

We observe no major concerns visually

plot_histogram(d.raw)

Check for strong effect sizes outliers

We plotted the response variables against all the tested moderators

  • The number of effect sizes for PBT is quite low. We can see that the minimum ARRD value for PBT is outside the range of the other values and has a strong precision. This observation (from Hernandez et al. 2002) will likely bias our estimate of PBT and it is probably better to exclude it for further analyses.

  • The impact of the exclusion of this data point will be tested in SENSITIVITY ANALYSES. Because the sample size of PBT data is very low (n=14), the likelihood of obtaining type II errors when testing whether ARRD vary between outcome variables is also important. Therefore, in SENSITIVITY ANALYSES, we will perform analyses without the entire PBT subset, and determine whether removing the data point from Hernandez et al. 2002 qualitatively modifies the results, relative to removing the entire PBT subset, and the entire data set.

Biological factors

ARRD_outcome<-ggplot(data=d.raw, aes(y=ARRD, x=outcome, col=outcome,size=precision))+
                     geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+ # line for y = 0 (no difference between males and females)
                     geom_jitter(alpha=0.5)+ # display data points with a jitter, so they don't overlap
                     scale_size_continuous(range = c(1, 7))+ # change scaling of data points
                     labs(x="Type of outcome variable",y="ARRD") + # rename axis labels
                     theme_classic() # classic theme

ARRD_habitat<-ggplot(data=d.raw, aes(y=ARRD, x=habitat, col=habitat,size=precision))+
                     geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+
                     geom_jitter(alpha=0.5)+ 
                     scale_size_continuous(range = c(1, 7))+
                     labs(x="Species habitat",y="ARRD") +
                     theme_classic()

ARRD_taxa<-ggplot(data=d.raw, aes(y=ARRD, x=taxonomic_group, col=taxonomic_group,size=precision))+
                  geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+
                  geom_jitter(alpha=0.5)+ 
                  scale_size_continuous(range = c(1, 7))+
                  labs(x="Taxonomic group",y="ARRD",color = "taxon") +
                  theme_classic()

ARRD_origin<-ggplot(data=d.raw, aes(y=ARRD, x=origin, col=origin,size=precision))+
                    geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+
                    geom_jitter(alpha=0.5)+ 
                    scale_size_continuous(range = c(1, 7))+
                    labs(x="Animals origin",y="ARRD")+
                    theme_classic()

plot_grid(ARRD_outcome, ARRD_habitat, ARRD_taxa, ARRD_origin, nrow = 2,ncol=2, labels = "auto", rel_heights = c(1, 1, 1,1))

Geographical coordinates

ARRD_latitude <- ggplot(data = d.raw, aes(y = ARRD, x = abs_latitude, size = precision)) +
    geom_hline(yintercept = 0, linetype = 2, colour = "black", alpha = 0.5) + geom_point(col = "darkcyan",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + labs(x = "Absolute latitude",
    y = "ARRD") + theme_classic()

ARRD_longitude <- ggplot(data = d.raw, aes(y = ARRD, x = abs_longitude, size = precision)) +
    geom_hline(yintercept = 0, linetype = 2, colour = "black", alpha = 0.5) + geom_point(col = "darkcyan",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + labs(x = "Absolute Longitude",
    y = "ARRD") + theme_classic()

ARRD_elevation <- ggplot(data = d.raw, aes(y = ARRD, x = elevation, size = precision)) +
    geom_hline(yintercept = 0, linetype = 2, colour = "black", alpha = 0.5) + geom_point(col = "darkcyan",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + labs(x = "Elevation",
    y = "ARRD") + theme_classic()

plot_grid(ARRD_latitude, ARRD_longitude, ARRD_elevation, nrow = 2, labels = "auto",
    rel_heights = c(1, 1, 1, 1, 1))

Sexual size and body mass dimorphism

ARRD_SDI <- ggplot(data = d.raw, aes(y = ARRD, x = SDI, size = precision)) + geom_hline(yintercept = 0,
    linetype = 2, colour = "black", alpha = 0.5) + geom_vline(xintercept = 0, linetype = 2,
    colour = "black", alpha = 0.5) + geom_point(col = "darkcyan", alpha = 0.5) +
    scale_size_continuous(range = c(1, 9)) + labs(x = "Size dimorphism index", y = "ARRD") +
    theme_classic()

ARRD_MDI <- ggplot(data = d.raw, aes(y = ARRD, x = MDI, size = precision)) + geom_hline(yintercept = 0,
    linetype = 2, colour = "black", alpha = 0.5) + geom_vline(xintercept = 0, linetype = 2,
    colour = "black", alpha = 0.5) + geom_point(col = "darkcyan", alpha = 0.5) +
    scale_size_continuous(range = c(1, 9)) + labs(x = "Mass dimorphism index", y = "ARRD") +
    theme_classic()

plot_grid(ARRD_SDI, ARRD_MDI, nrow = 1, ncol = 2, labels = "auto", rel_heights = c(1,
    1, 1, 1, 1))

Methodological factors

ARRD_duration <- ggplot(data = d.raw, aes(y = ARRD, x = acc_duration, size = precision)) +
    geom_hline(yintercept = 0, linetype = 2, colour = "black", alpha = 0.5) + geom_point(col = "darkcyan",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + labs(x = "Duration of acclimation",
    y = "ARRD") + theme_classic()

ARRD_ramping <- ggplot(data = d.raw, aes(y = ARRD, x = ramping.deg.min, size = precision)) +
    geom_hline(yintercept = 0, linetype = 2, colour = "black", alpha = 0.5) + geom_point(col = "darkcyan",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + labs(x = "Ramping rate",
    y = "ARRD") + theme_classic()

plot_grid(ARRD_duration, ARRD_ramping, nrow = 1, ncol = 2, labels = "auto", rel_heights = c(1,
    1, 1, 1, 1))

Sociological factors

ARRD_pub_year <- ggplot(data = d.raw, aes(y = ARRD, x = pub_year, col = pub_year,
    size = precision)) + geom_hline(yintercept = 0, linetype = 2, colour = "black",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + geom_point(col = "darkcyan",
    alpha = 0.5) + scale_size_continuous(range = c(1, 9)) + labs(x = "Publication year",
    y = "ARRD") + theme_classic()

ARRD_data_type <- ggplot(data = d.raw, aes(y = ARRD, x = data_type, col = data_type,
    size = precision)) + geom_hline(yintercept = 0, linetype = 2, colour = "black",
    alpha = 0.5) + scale_size_continuous(range = c(1, 7)) + geom_jitter(alpha = 0.5) +
    labs(x = "Data type", y = "ARRD") + theme_classic()

ARRD_peer <- ggplot(data = d.raw, aes(y = ARRD, x = peer_reviewed, col = peer_reviewed,
    size = precision)) + geom_hline(yintercept = 0, linetype = 2, colour = "black",
    alpha = 0.5) + scale_size_continuous(range = c(1, 7)) + geom_jitter(alpha = 0.5) +
    labs(x = "Peer-review", y = "ARRD") + theme_classic()


plot_grid(ARRD_pub_year, ARRD_data_type, ARRD_peer, nrow = 2, ncol = 2, labels = "auto",
    rel_heights = c(1, 1, 1, 1, 1))

Geographical coverage

Overall, the geographical coverage is very sparse

# Distribution of the data points

WorldData <- map_data("world")

ggplot(d.raw, aes(x = longitude, y = latitude, size = precision, col = taxonomic_group_sub)) +
    geom_map(data = WorldData, map = WorldData, aes(x = long, y = lat, group = group,
        map_id = region), fill = "white", colour = "#7f7f7f", size = 0.5) + geom_point(alpha = 0.6) +
    scale_colour_viridis(discrete = T) + xlim(min(WorldData$long), max(WorldData$long)) +
    ylim(min(WorldData$lat), max(WorldData$lat)) + theme_minimal() + labs(x = "Longitude",
    y = "Latitude") + scale_size_continuous(range = c(2, 8))

Create a data subset without the influential effect size from Hernandez et al. 2002

Sample size prior to subsetting data

Here we calculated the number of studies, species and effect sizes for the main categorical moderators. These sample sizes are different from the ones presented in Figure S5 as they have been calculated prior to the exclusion of the study from Hernandez et al. (2002).

d.raw %>%
  summarise(
    `Studies` = n_distinct(study_ID),
    `Species` = n_distinct(species_ID),
    `Levels (shared treatment)` = n_distinct(shared_trt_ID),
    `Levels (shared measurement)` = n_distinct(shared_measurement_ID),
    `Effect sizes` = n_distinct(es_ID),
    
    `Effect sizes (LTL)` = n_distinct(es_ID[outcome=="LTL"]),
    `Studies (LTL)` = n_distinct(study_ID[outcome=="LTL"]),
    `Species (LTL)` = n_distinct(species_ID[outcome=="LTL"]),

    `Effect sizes (UTL)` = n_distinct(es_ID[outcome=="UTL"]),
    `Studies (UTL)` = n_distinct(study_ID[outcome=="UTL"]),
    `Species (UTL)` = n_distinct(species_ID[outcome=="UTL"]),

    `Effect sizes (PBT)` = n_distinct(es_ID[outcome=="PBT"]),
    `Studies (PBT)` = n_distinct(study_ID[outcome=="PBT"]),
    `Species (PBT)` = n_distinct(species_ID[outcome=="PBT"]),
    
    `Effect sizes (invertebrates)` = n_distinct(es_ID[taxonomic_group=="invertebrate"]),
    `Studies (invertebrates)` = n_distinct(study_ID[taxonomic_group=="invertebrate"]),
    `Effect sizes (vertebrates)` = n_distinct(es_ID[taxonomic_group=="vertebrate"]),
    `Studies (vertebrates)` = n_distinct(study_ID[taxonomic_group=="vertebrate"]),
    
    `Effect sizes (Fishes)` = n_distinct(es_ID[taxonomic_group_sub=="Fishes"]),
    `Studies (Fishes)` = n_distinct(study_ID[taxonomic_group_sub=="Fishes"]),
    `Effect sizes (Reptiles and Amphibians)` = n_distinct(es_ID[taxonomic_group_sub=="Reptiles and Amphibians"]),
    `Studies (Reptiles and Amphibians)` = n_distinct(study_ID[taxonomic_group_sub=="Reptiles and Amphibians"]),
    `Effect sizes (Aquatic Invertebrates)` = n_distinct(es_ID[taxonomic_group_sub=="Aquatic Invertebrates"]),
    `Studies (Aquatic Invertebrates)` = n_distinct(study_ID[taxonomic_group_sub=="Aquatic Invertebrates"]),
    `Effect sizes (Terrestrial Invertebrates)` = n_distinct(es_ID[taxonomic_group_sub=="Terrestrial Invertebrates"]),
    `Studies (Terrestrial Invertebrates)` = n_distinct(study_ID[taxonomic_group_sub=="Terrestrial Invertebrates"]),
    
    `Effect sizes (aquatic)` = n_distinct(es_ID[habitat=="aquatic"]),
    `Studies (aquatic)` = n_distinct(study_ID[habitat=="aquatic"]),
    `Effect sizes (terrestrial)` = n_distinct(es_ID[habitat=="terrestrial"]),
    `Studies (terrestrial)` = n_distinct(study_ID[habitat=="terrestrial"]),
    
    `Effect sizes (wild)` = n_distinct(es_ID[origin=="wild"]),
    `Studies (wild)` = n_distinct(study_ID[origin=="wild"]),
    `Effect sizes (lab)` = n_distinct(es_ID[origin=="lab"]),
    `Studies (lab)` = n_distinct(study_ID[origin=="lab"]),
    
    `Effect sizes (published)` = n_distinct(es_ID[data_type=="published"]),
    `Studies (published)` = n_distinct(study_ID[data_type=="published"]),
    `Effect sizes (unpublished)` = n_distinct(es_ID[data_type=="unpublished"]),
    `Studies (unpublished)` = n_distinct(study_ID[data_type=="unpublished"]),
    
    `origin`=n_distinct(study_ID[origin=="lab"])
    
          ) -> table_sample_sizes.raw

table_sample_sizes.raw<-t(table_sample_sizes.raw)
colnames(table_sample_sizes.raw)<-"n (sample size)"
kable(table_sample_sizes.raw) %>% kable_styling("striped", position="left") 
n (sample size)
Studies 38
Species 45
Levels (shared treatment) 185
Levels (shared measurement) 216
Effect sizes 240
Effect sizes (LTL) 103
Studies (LTL) 21
Species (LTL) 21
Effect sizes (UTL) 123
Studies (UTL) 21
Species (UTL) 29
Effect sizes (PBT) 14
Studies (PBT) 9
Species (PBT) 10
Effect sizes (invertebrates) 129
Studies (invertebrates) 17
Effect sizes (vertebrates) 111
Studies (vertebrates) 21
Effect sizes (Fishes) 66
Studies (Fishes) 9
Effect sizes (Reptiles and Amphibians) 45
Studies (Reptiles and Amphibians) 12
Effect sizes (Aquatic Invertebrates) 53
Studies (Aquatic Invertebrates) 7
Effect sizes (Terrestrial Invertebrates) 76
Studies (Terrestrial Invertebrates) 10
Effect sizes (aquatic) 137
Studies (aquatic) 19
Effect sizes (terrestrial) 103
Studies (terrestrial) 19
Effect sizes (wild) 166
Studies (wild) 24
Effect sizes (lab) 72
Studies (lab) 15
Effect sizes (published) 109
Studies (published) 18
Effect sizes (unpublished) 131
Studies (unpublished) 21
origin 15
d <- subset(d.raw, ref != "Hernandez et al. 2002")

Load and reformat processed data

Export processed data

d <- as_tibble(d)
write.csv(d, file = "data/data_processed.csv")

Load the processed data set and reformat variables

The data set that will be used for the rest of the analyses was named d

d <- read_csv("data/data_processed.csv")
d$es_ID = as.factor(d$es_ID)
d$species_ID = as.factor(d$species_ID)
d$study_ID = as.factor(d$study_ID)
d$shared_trt_ID = as.factor(d$shared_trt_ID)
d$shared_measurement_ID = as.factor(d$shared_measurement_ID)
d$data_type = as.factor(d$data_type)
d$peer_reviewed = as.factor(d$peer_reviewed)
d$class = as.factor(d$class)
d$order = as.factor(d$order)
d$genus_species = as.factor(d$genus_species)
d$habitat = as.factor(d$habitat)
d$taxonomic_group = as.factor(d$taxonomic_group)
d$taxonomic_group_sub = as.factor(d$taxonomic_group_sub)
d$life_stage = as.factor(d$life_stage)
d$origin = as.factor(d$origin)
d$season = as.factor(d$season)
d$outcome = as.factor(d$outcome)
d$method = as.factor(d$method)
d$endpoint = as.factor(d$endpoint)
d$gravidity = as.factor(d$gravidity)

Data transformation

Standardize the continuous variables

scale: z-transformation (i.e. mean=0, standard deviation=1). We standardized all continuous moderators we tested to facilitate the interpretation of the coefficients.

d$z_abs_latitude <- scale(d$abs_latitude)
d$z_acc_duration <- scale(d$acc_duration)
d$z_ramping.deg.min <- scale(d$ramping.deg.min)
d$z_pub_year <- scale(d$pub_year)

Sample sizes

  • Because there is a strong overlap between the number of studies (study_ID, n=37) and the number of species (species_ID, n=44), we cannot include both variables as random effects in the models. Therefore, we decided to keep species_ID because it has more levels.

  • Because there is a strong overlap between shared measurement ID (shared_measurement_ID, n=214) and effect size ID (es_ID, n=238), we cannot include both variables as random effects in the model. Therefore, we will only account for the non-independence of traits measured on the same cohorts by using a variance-covariance matrix (see calculations of VCV_ARRD in the next section) and use es_ID as a random term in the models.

  • Because we can only include one variance-covariance matrix in the models, we accounted for non-independence of comparisons involving the same experimental groups (shared_trt_ID) by dividing the sample size of these groups by half. This adjustment was made directly in the spreadsheet.

  • Because we removed the observation from Hernandez et al. 2002, the sample size presented here is different from the one presented in the PRISMA diagram (which presents all effects sizes prior to the data attrition). The distribution of sample sizes is also presented in a readable format in Figure S5.

d %>%
  summarise( # Calculate the number of effect sizes, studies and species for the main categorical variables
    `Studies` = n_distinct(study_ID),
    `Species` = n_distinct(species_ID),
    `Levels (shared treatment)` = n_distinct(shared_trt_ID),
    `Levels (shared measurement)` = n_distinct(shared_measurement_ID),
    `Effect sizes` = n_distinct(es_ID),
    
    `Effect sizes (LTL)` = n_distinct(es_ID[outcome=="LTL"]),
    `Studies (LTL)` = n_distinct(study_ID[outcome=="LTL"]),
    `Species (LTL)` = n_distinct(species_ID[outcome=="LTL"]),

    `Effect sizes (UTL)` = n_distinct(es_ID[outcome=="UTL"]),
    `Studies (UTL)` = n_distinct(study_ID[outcome=="UTL"]),
    `Species (UTL)` = n_distinct(species_ID[outcome=="UTL"]),

    `Effect sizes (PBT)` = n_distinct(es_ID[outcome=="PBT"]),
    `Studies (PBT)` = n_distinct(study_ID[outcome=="PBT"]),
    `Species (PBT)` = n_distinct(species_ID[outcome=="PBT"]),
    
    `Effect sizes (invertebrates)` = n_distinct(es_ID[taxonomic_group=="invertebrate"]),
    `Studies (invertebrates)` = n_distinct(study_ID[taxonomic_group=="invertebrate"]),
    `Effect sizes (vertebrates)` = n_distinct(es_ID[taxonomic_group=="vertebrate"]),
    `Studies (vertebrates)` = n_distinct(study_ID[taxonomic_group=="vertebrate"]),
    
    `Effect sizes (Fishes)` = n_distinct(es_ID[taxonomic_group_sub=="Fishes"]),
    `Studies (Fishes)` = n_distinct(study_ID[taxonomic_group_sub=="Fishes"]),
    `Effect sizes (Reptiles and Amphibians)` = n_distinct(es_ID[taxonomic_group_sub=="Reptiles and Amphibians"]),
    `Studies (Reptiles and Amphibians)` = n_distinct(study_ID[taxonomic_group_sub=="Reptiles and Amphibians"]),
    `Effect sizes (Aquatic Invertebrates)` = n_distinct(es_ID[taxonomic_group_sub=="Aquatic Invertebrates"]),
    `Studies (Aquatic Invertebrates)` = n_distinct(study_ID[taxonomic_group_sub=="Aquatic Invertebrates"]),
    `Effect sizes (Terrestrial Invertebrates)` = n_distinct(es_ID[taxonomic_group_sub=="Terrestrial Invertebrates"]),
    `Studies (Terrestrial Invertebrates)` = n_distinct(study_ID[taxonomic_group_sub=="Terrestrial Invertebrates"]),
    
    `Effect sizes (aquatic)` = n_distinct(es_ID[habitat=="aquatic"]),
    `Studies (aquatic)` = n_distinct(study_ID[habitat=="aquatic"]),
    `Effect sizes (terrestrial)` = n_distinct(es_ID[habitat=="terrestrial"]),
    `Studies (terrestrial)` = n_distinct(study_ID[habitat=="terrestrial"]),
    
    `Effect sizes (wild)` = n_distinct(es_ID[origin=="wild"]),
    `Studies (wild)` = n_distinct(study_ID[origin=="wild"]),
    `Effect sizes (lab)` = n_distinct(es_ID[origin=="lab"]),
    `Studies (lab)` = n_distinct(study_ID[origin=="lab"]),
    
    `Effect sizes (published)` = n_distinct(es_ID[data_type=="published"]),
    `Studies (published)` = n_distinct(study_ID[data_type=="published"]),
    `Effect sizes (unpublished)` = n_distinct(es_ID[data_type=="unpublished"]),
    `Studies (unpublished)` = n_distinct(study_ID[data_type=="unpublished"]),
    
          ) -> table_sample_sizes

table_sample_sizes<-t(table_sample_sizes)
colnames(table_sample_sizes)<-"n (sample size)"
kable(table_sample_sizes) %>% kable_styling("striped", position="left")
n (sample size)
Studies 37
Species 44
Levels (shared treatment) 184
Levels (shared measurement) 215
Effect sizes 239
Effect sizes (LTL) 103
Studies (LTL) 21
Species (LTL) 21
Effect sizes (UTL) 123
Studies (UTL) 21
Species (UTL) 29
Effect sizes (PBT) 13
Studies (PBT) 8
Species (PBT) 9
Effect sizes (invertebrates) 129
Studies (invertebrates) 17
Effect sizes (vertebrates) 110
Studies (vertebrates) 20
Effect sizes (Fishes) 65
Studies (Fishes) 8
Effect sizes (Reptiles and Amphibians) 45
Studies (Reptiles and Amphibians) 12
Effect sizes (Aquatic Invertebrates) 53
Studies (Aquatic Invertebrates) 7
Effect sizes (Terrestrial Invertebrates) 76
Studies (Terrestrial Invertebrates) 10
Effect sizes (aquatic) 136
Studies (aquatic) 18
Effect sizes (terrestrial) 103
Studies (terrestrial) 19
Effect sizes (wild) 165
Studies (wild) 23
Effect sizes (lab) 72
Studies (lab) 15
Effect sizes (published) 108
Studies (published) 17
Effect sizes (unpublished) 131
Studies (unpublished) 21

Phylogenetic tree and variance-covariance matrices

Phylogenetic variance-covariance matrix

Build the phylogenetic tree

We first matched the species names genus_species with the Open Tree Taxonomy

  • Gammarus marinus was assumed to be synonym to Marinogammarus marinus
  • Hyale hirtipalma was assumed to be synonym to Apohyale hirtipalma
  • Uca panacea was assumed to be synonym to Leptuca panacea
taxa <- tnrs_match_names(names = levels(d$genus_species), context_name = "Animals")
kable(taxa) %>%
    kable_styling("striped", position = "left")  # Check if all species names match with the Open Tree Taxonomy
search_string unique_name approximate_match ott_id is_synonym flags number_matches
acanthochromis polyacanthus Acanthochromis polyacanthus FALSE 100410 FALSE incertae_sedis_inherited 1
anolis sagrei Anolis sagrei FALSE 970153 FALSE 1
anopheles arabiensis Anopheles arabiensis FALSE 218728 FALSE 2
anopheles funestus Anopheles funestus FALSE 286257 FALSE 1
carcinus maenas Carcinus maenas FALSE 1089892 FALSE 1
cordylus oelofseni Cordylus oelofseni FALSE 487423 FALSE 1
corophium volutator Corophium volutator FALSE 1054530 FALSE 1
crangon crangon Crangon crangon FALSE 497498 FALSE sibling_higher 1
danio rerio Danio rerio FALSE 1005914 FALSE 1
dasyatis sabina Dasyatis sabina FALSE 351766 FALSE sibling_higher 1
dionda diaboli Dionda diaboli FALSE 222446 FALSE 1
drosophila falleni Drosophila falleni FALSE 86637 FALSE 1
drosophila melanogaster Drosophila melanogaster FALSE 505714 FALSE 1
drosophila putrida Drosophila putrida FALSE 871280 FALSE 1
drosophila simulans Drosophila simulans FALSE 660828 FALSE 1
drosophila tripunctata Drosophila tripunctata FALSE 940413 FALSE 1
eleutherodactylus coqui Eleutherodactylus coqui FALSE 1085754 FALSE 1
enochrus politus Enochrus politus FALSE 3341759 FALSE 1
eutropis longicaudata Eutropis longicaudata FALSE 391880 FALSE 1
eutropis multifasciata Eutropis multifasciata FALSE 621434 FALSE 1
exosphaeroma gigas Exosphaeroma gigas FALSE 2995748 FALSE 1
exosphaeroma laeviusculum Exosphaeroma laeviusculum FALSE 2995772 FALSE 1
fundulus heteroclitus Fundulus heteroclitus FALSE 583633 FALSE 1
gambusia affinis Gambusia affinis FALSE 617445 FALSE 1
gammarus chevreuxi Gammarus chevreuxi FALSE 343320 FALSE 1
gammarus marinus Marinogammarus marinus FALSE 5809983 TRUE 1
harmonia axyridis Harmonia axyridis FALSE 258281 FALSE 1
helicoverpa zea Helicoverpa zea FALSE 167928 FALSE 1
hyale grandicornis Hyale grandicornis FALSE 2983574 FALSE 2
hyale hirtipalma Apohyale hirtipalma FALSE 2983536 TRUE 1
hydroporus sabaudus Hydroporus sabaudus FALSE 1024850 FALSE 1
hyperolius marmoratus Hyperolius marmoratus FALSE 441372 FALSE 1
lampropholis coggeri Lampropholis coggeri FALSE 1073190 FALSE 1
liolaemus pictus Liolaemus pictus FALSE 665055 FALSE 1
nilaparvata lugens Nilaparvata lugens FALSE 876508 FALSE 1
ophryotrocha labronica Ophryotrocha labronica FALSE 864359 FALSE 1
pardosa furcifera Pardosa furcifera FALSE 339957 FALSE 1
pleurodema thaul Pleurodema thaul FALSE 67848 FALSE sibling_higher 1
poecilia reticulata Poecilia reticulata FALSE 312452 FALSE 1
tenebrio molitor Tenebrio molitor FALSE 1093470 FALSE 1
terrapene carolina Terrapene carolina FALSE 848786 FALSE 1
terrapene ornata Terrapene ornata FALSE 1013359 FALSE 1
triturus dobrogicus Triturus dobrogicus FALSE 1041781 FALSE 1
uca panacea Leptuca panacea FALSE 813090 TRUE 1
d$genus_species <- str_replace(d$genus_species, "Gammarus marinus", "Marinogammarus marinus")  # Replace names to match with Open Tree Taxonomy
d$genus_species <- str_replace(d$genus_species, "Hyale hirtipalma", "Apohyale hirtipalma")  # Replace names to match with Open Tree Taxonomy
d$genus_species <- str_replace(d$genus_species, "Uca panacea", "Leptuca panacea")  # Replace names to match with Open Tree Taxonomy

phylo_tree <- tol_induced_subtree(ott_ids = taxa$ott_id, label_format = "name")  # Generate the phylogenetic tree

Make the tree binary

We had a polytomy between the amphipods taxa (Gammaridae, Hyalidae and Corophiidae). We resolved the polytomy as random.

is.binary(phylo_tree)  # Check if the tree is binary (= are there some polytomies?)
## [1] FALSE
plot(phylo_tree)  # check for polytomies visually

set.seed(1234)
binary_tree <- multi2di(phylo_tree, random = TRUE)  # resolve polytomy at random with a set seed

is.binary(binary_tree)  # the tree is now binary
## [1] TRUE

Plot of the phylogenetic tree

set.seed(1234)
binary_tree <- multi2di(phylo_tree, random = TRUE)  # This part need to be run once again to generate the same tree in a different code chunk

png("output/phylogeny.png", bg = "transparent", height = 15, width = 8, units = "in",
    res = 1200)
plot(binary_tree)
dev.off()
## png 
##   2

Compute branch lengths and variance-covariance matrix

phylo_matrix : variance-covariance matrix of the phylogenetic correlation between the species

d$genus_species <- as.factor(d$genus_species)  # convert genus_species (species name) as a factor 
binary_tree$tip.label <- as.factor(binary_tree$tip.label)  # convert the species names in the tree as a factor

levels(binary_tree$tip.label) <- levels(d$genus_species)  # make sure names match
binary_tree$tip.label <- as.character(binary_tree$tip.label)  # convert names back to characters

# Compute branch length
phylo_branch <- compute.brlen(binary_tree, method = "Grafen", power = 1)

is.ultrametric(phylo_branch)  # check if tree is ultrametric
## [1] TRUE
# Create a phylogenetic matrix

phylo_matrix <- vcv(phylo_branch, cor = T)  # the vcv function returns a variance-covariance matrix

kable(phylo_matrix, "html") %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")
Terrapene ornata Terrapene carolina Anolis sagrei Leptuca panacea Eutropis multifasciata Eutropis longicaudata Hyperolius marmoratus Cordylus oelofseni Marinogammarus marinus Pleurodema thaul Eleutherodactylus coqui Triturus dobrogicus Dionda diaboli Danio rerio Acanthochromis polyacanthus Poecilia reticulata Gambusia affinis Fundulus heteroclitus Dasyatis sabina Ophryotrocha labronica Helicoverpa zea Drosophila putrida Drosophila falleni Drosophila tripunctata Drosophila melanogaster Drosophila simulans Anopheles funestus Anopheles arabiensis Tenebrio molitor Harmonia axyridis Enochrus politus Hydroporus sabaudus Nilaparvata lugens Exosphaeroma gigas Exosphaeroma laeviusculum Corophium volutator Apohyale hirtipalma Hyale grandicornis Gammarus chevreuxi Liolaemus pictus Crangon crangon Lampropholis coggeri Carcinus maenas Pardosa furcifera
Terrapene ornata 1.0000000 0.9767442 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Terrapene carolina 0.9767442 1.0000000 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Anolis sagrei 0.8372093 0.8372093 1.0000000 0.9767442 0.8837209 0.8837209 0.8837209 0.8837209 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Leptuca panacea 0.8372093 0.8372093 0.9767442 1.0000000 0.8837209 0.8837209 0.8837209 0.8837209 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Eutropis multifasciata 0.8372093 0.8372093 0.8837209 0.8837209 1.0000000 0.9767442 0.9534884 0.9302326 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Eutropis longicaudata 0.8372093 0.8372093 0.8837209 0.8837209 0.9767442 1.0000000 0.9534884 0.9302326 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Hyperolius marmoratus 0.8372093 0.8372093 0.8837209 0.8837209 0.9534884 0.9534884 1.0000000 0.9302326 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Cordylus oelofseni 0.8372093 0.8372093 0.8837209 0.8837209 0.9302326 0.9302326 0.9302326 1.0000000 0.7441860 0.7441860 0.7441860 0.7441860 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Marinogammarus marinus 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 1.0000000 0.9534884 0.9534884 0.9302326 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Pleurodema thaul 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.9534884 1.0000000 0.9767442 0.9302326 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Eleutherodactylus coqui 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.9534884 0.9767442 1.0000000 0.9302326 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Triturus dobrogicus 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.9302326 0.9302326 0.9302326 1.0000000 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Dionda diaboli 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 1.0000000 0.9767442 0.8837209 0.8837209 0.8837209 0.8837209 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Danio rerio 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.9767442 1.0000000 0.8837209 0.8837209 0.8837209 0.8837209 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Acanthochromis polyacanthus 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.8837209 0.8837209 1.0000000 0.9302326 0.9302326 0.9302326 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Poecilia reticulata 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.8837209 0.8837209 0.9302326 1.0000000 0.9767442 0.9534884 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Gambusia affinis 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.8837209 0.8837209 0.9302326 0.9767442 1.0000000 0.9534884 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Fundulus heteroclitus 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.6046512 0.8837209 0.8837209 0.9302326 0.9534884 0.9534884 1.0000000 0.5813953 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Dasyatis sabina 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 0.5813953 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
Ophryotrocha labronica 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605 0.4418605
Helicoverpa zea 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 1.0000000 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.8372093 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Drosophila putrida 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 1.0000000 0.9767442 0.9534884 0.9069767 0.9069767 0.8604651 0.8604651 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Drosophila falleni 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 0.9767442 1.0000000 0.9534884 0.9069767 0.9069767 0.8604651 0.8604651 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Drosophila tripunctata 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 0.9534884 0.9534884 1.0000000 0.9069767 0.9069767 0.8604651 0.8604651 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Drosophila melanogaster 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 0.9069767 0.9069767 0.9069767 1.0000000 0.9767442 0.8604651 0.8604651 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Drosophila simulans 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 0.9069767 0.9069767 0.9069767 0.9767442 1.0000000 0.8604651 0.8604651 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Anopheles funestus 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 0.8604651 0.8604651 0.8604651 0.8604651 0.8604651 1.0000000 0.9767442 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Anopheles arabiensis 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.8372093 0.8604651 0.8604651 0.8604651 0.8604651 0.8604651 0.9767442 1.0000000 0.7441860 0.7441860 0.7441860 0.7441860 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Tenebrio molitor 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 1.0000000 0.9767442 0.9534884 0.9302326 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Harmonia axyridis 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.9767442 1.0000000 0.9534884 0.9302326 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Enochrus politus 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.9534884 0.9534884 1.0000000 0.9302326 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Hydroporus sabaudus 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.7441860 0.9302326 0.9302326 0.9302326 1.0000000 0.7209302 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Nilaparvata lugens 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 0.7209302 1.0000000 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4651163
Exosphaeroma gigas 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 1.0000000 0.9767442 0.8604651 0.8604651 0.8604651 0.8604651 0.8604651 0.7906977 0.7906977 0.7906977 0.4651163
Exosphaeroma laeviusculum 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.9767442 1.0000000 0.8604651 0.8604651 0.8604651 0.8604651 0.8604651 0.7906977 0.7906977 0.7906977 0.4651163
Corophium volutator 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.8604651 0.8604651 1.0000000 0.9069767 0.9069767 0.9069767 0.9069767 0.7906977 0.7906977 0.7906977 0.4651163
Apohyale hirtipalma 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.8604651 0.8604651 0.9069767 1.0000000 0.9767442 0.9302326 0.9302326 0.7906977 0.7906977 0.7906977 0.4651163
Hyale grandicornis 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.8604651 0.8604651 0.9069767 0.9767442 1.0000000 0.9302326 0.9302326 0.7906977 0.7906977 0.7906977 0.4651163
Gammarus chevreuxi 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.8604651 0.8604651 0.9069767 0.9302326 0.9302326 1.0000000 0.9767442 0.7906977 0.7906977 0.7906977 0.4651163
Liolaemus pictus 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.8604651 0.8604651 0.9069767 0.9302326 0.9302326 0.9767442 1.0000000 0.7906977 0.7906977 0.7906977 0.4651163
Crangon crangon 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 1.0000000 0.9534884 0.9534884 0.4651163
Lampropholis coggeri 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.9534884 1.0000000 0.9767442 0.4651163
Carcinus maenas 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.4883721 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.7906977 0.9534884 0.9767442 1.0000000 0.4651163
Pardosa furcifera 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.4418605 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 0.4651163 1.0000000

Generate variance-covariance matrices to account for non-independence

Function to create a variance-covariance matrix with a r = 0.5 correlation between sampling variances

Taken from metaAidR - https://github.com/daniel1noble/metaAidR/blob/master/R/make_VCV_matrix.R

Using this function is akin to the formula we presented in the manuscript, with the correlation between sampling variances taken to be r = 0.5.

#' @title Covariance and correlation matrix function basing on shared level ID
#' @description Function for generating simple covariance and correlation matrices 
#' @param data Dataframe object containing effect sizes, their variance, unique IDs and clustering variable
#' @param V Name of the variable (as a string – e.g, 'V1') containing effect size variances variances
#' @param cluster Name of the variable (as a string – e.g, 'V1') indicating which effects belong to the same cluster. Same value of 'cluster' are assumed to be nonindependent (correlated).
#' @param obs Name of the variable (as a string – e.g, 'V1') containing individual IDs for each value in the V (Vector of variances). If this parameter is missing, label will be labelled with consecutive integers starting from 1.
#' @param rho Known or assumed correlation value among effect sizes sharing same 'cluster' value. Default value is 0.5.
#' @param type Optional logical parameter indicating whether a full variance-covariance matrix (default or 'vcv') is needed or a correlation matrix ('cor') for the non-independent blocks of variance values.
#' @export

make_VCV_matrix <- function(data, V, cluster, obs, type = c("vcv", "cor"), rho = 0.5) {
    type <- match.arg(type)
    if (missing(data)) {
        stop("Must specify dataframe via 'data' argument.")
    }
    if (missing(V)) {
        stop("Must specify name of the variance variable via 'V' argument.")
    }
    if (missing(cluster)) {
        stop("Must specify name of the clustering variable via 'cluster' argument.")
    }
    if (missing(obs)) {
        obs <- 1:length(V)
    }
    if (missing(type)) {
        type <- "vcv"
    }

    new_matrix <- matrix(0, nrow = dim(data)[1], ncol = dim(data)[1])  #make empty matrix of the same size as data length
    rownames(new_matrix) <- data[, obs]
    colnames(new_matrix) <- data[, obs]
    # find start and end coordinates for the subsets
    shared_coord <- which(data[, cluster] %in% data[duplicated(data[, cluster]),
        cluster] == TRUE)
    # matrix of combinations of coordinates for each experiment with shared
    # control
    combinations <- do.call("rbind", tapply(shared_coord, data[shared_coord, cluster],
        function(x) t(utils::combn(x, 2))))

    if (type == "vcv") {
        # calculate covariance values between values at the positions in
        # shared_list and place them on the matrix
        for (i in 1:dim(combinations)[1]) {
            p1 <- combinations[i, 1]
            p2 <- combinations[i, 2]
            p1_p2_cov <- rho * sqrt(data[p1, V]) * sqrt(data[p2, V])
            new_matrix[p1, p2] <- p1_p2_cov
            new_matrix[p2, p1] <- p1_p2_cov
        }
        diag(new_matrix) <- data[, V]  #add the diagonal
    }

    if (type == "cor") {
        # calculate covariance values between values at the positions in
        # shared_list and place them on the matrix
        for (i in 1:dim(combinations)[1]) {
            p1 <- combinations[i, 1]
            p2 <- combinations[i, 2]
            p1_p2_cov <- rho
            new_matrix[p1, p2] <- p1_p2_cov
            new_matrix[p2, p1] <- p1_p2_cov
        }
        diag(new_matrix) <- 1  #add the diagonal of 1
    }

    return(new_matrix)
}

Generate variance-covariance matrices for shared_measurement_ID (traits measured on the same animals): VCV_ARRD

names(d) <- make.names(names(d))  # Need to run the code

d <- as.data.frame(d)  # Convert the data set to a data frame (it does not work with tibbles)

VCV_ARRD <- make_VCV_matrix(d, V = "Var_ARRD", cluster = "shared_measurement_ID",
    obs = "es_ID")  # calculate the variance covariance matrix

kable(VCV_ARRD, "html") %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")  # display the matrix
es1 es2 es3 es4 es5 es6 es7 es8 es9 es10 es11 es12 es13 es14 es15 es16 es17 es18 es19 es20 es21 es22 es24 es25 es26 es27 es28 es29 es30 es31 es32 es33 es34 es35 es36 es37 es38 es39 es40 es41 es42 es43 es44 es45 es46 es47 es48 es49 es50 es51 es52 es53 es54 es55 es56 es57 es58 es59 es60 es61 es62 es63 es64 es65 es66 es67 es68 es69 es70 es71 es72 es73 es74 es75 es76 es77 es78 es79 es80 es81 es82 es83 es84 es85 es86 es87 es88 es89 es90 es91 es92 es93 es94 es95 es96 es97 es98 es99 es100 es101 es102 es103 es104 es105 es106 es107 es108 es109 es110 es111 es112 es113 es114 es115 es116 es117 es118 es119 es120 es121 es122 es123 es124 es125 es126 es127 es128 es129 es130 es131 es132 es133 es134 es135 es136 es137 es138 es139 es140 es141 es142 es143 es144 es145 es146 es147 es148 es149 es150 es151 es152 es153 es154 es155 es156 es157 es158 es159 es160 es161 es162 es163 es164 es165 es166 es167 es168 es169 es170 es171 es172 es173 es174 es175 es176 es177 es178 es179 es180 es181 es182 es183 es184 es185 es186 es187 es188 es189 es190 es191 es192 es193 es194 es195 es196 es197 es198 es199 es200 es201 es202 es203 es204 es205 es206 es207 es208 es209 es210 es211 es212 es213 es214 es215 es216 es217 es218 es219 es220 es221 es222 es223 es224 es225 es226 es227 es228 es229 es230 es231 es232 es233 es234 es235 es236 es237 es238 es239 es240
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Intercept meta-analytical model

How much variance is to be explained?

var(d$ARRD)
## [1] 0.02374816

Meta-analytical model with all effect sizes and random effects discussed earlier (see Sample sizes)

We used the rma.mv function from the package metafor to run all meta-analytic models and meta-regressions. This function allows to incorporate variance-covariance matrices in the V term.

genus_species (phylogenetic correlation between species) does not account for any variance in the model. We originally decided to remove this random effect from the analyses but we were advised, during the peer-review process, to keep it to account for statistical non-independence due to shared evolutionary history.

meta_ana_model<-rma.mv(yi=ARRD~1, V=VCV_ARRD,  # Intercept model 
                   method="REML", # Restricted maximum likelihood
                   random=list(~1|species_ID,
                               ~1|genus_species,
                               ~1|es_ID), # all possible random effects
                   R = list(genus_species = phylo_matrix), # Assign the genus_species term to the phylogenetic correlation matrix created earlier
                   data=d)

summary(meta_ana_model) # Results of the model
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  208.4347  -416.8695  -408.8695  -394.9804  -408.6978   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0076     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0083     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0278    239     no          es_ID   no 
## 
## Test for Heterogeneity:
## Q(df = 238) = 383.0201, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0056  0.0069  0.8186  0.4130  -0.0079  0.0192    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total heterogeneity and heterogeneity explained by species_ID and es_ID

The i2_ml function in the package orchaRd allows a simple calculation of heterogeneity

# To install the orchaRd package:
# devtools::install_github('itchyshin/orchard_plot', subdir = 'orchaRd', force
# = TRUE, build_vignettes = TRUE)

i2_ml(meta_ana_model)
##         I2_total    I2_species_ID I2_genus_species         I2_es_ID 
##       0.43862487       0.02798587       0.03343257       0.37720643

Plot the results

If ARRD is positive, females are more plastic. If ARRD is negative, males are more plastic

orchard_plot(meta_ana_model,mod="Int",xlab="ARRD")+ # core of the function
        annotate(geom = "text", x = -0.5, y = 1.5, label = paste0("italic(I)^{2} == ", round(i2_ml(meta_ana_model)[1] * 100, 2)), color = "black", parse = TRUE, size = 5) + # display heterogeneity
        geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6)+  # change the thickness of prediction intervals
        geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.04, show.legend = FALSE, size = 1)+ # change the thickness of confidence intervals
        annotate(geom = "text", x = -0.32, y = 1.49, label = "%", color = "black", parse = FALSE, size = 5) + 
        geom_point(aes(fill = name), size = 4, shape = 21)+ # change mean estimate point size 
        scale_colour_manual(values = "darkcyan")+ # change colour of data points
        scale_fill_manual(values="gold") +  # change colour of the mean estimate
        scale_y_discrete(labels = "Overall mean")+ # rename y label
        scale_size_continuous(range = c(1, 9)) + # change scaling of data points
        theme(text = element_text(size = 20, colour = "black", hjust = 0.5),
              axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
              legend.title = element_text(size=16))

Create a function to run the models with the same structure

To avoid repeating the same lines of codes, we created a function run.model to run the models wit the same random effect structure. Because some models will be performed on subsets of data, we also generate a new variance covariance matrix for the specific data set that will be used in the model.

run.model<-function(data,formula){
  data<-as.data.frame(data) # convert data set into a data frame to calculate VCV matrix 
  VCV<-make_VCV_matrix(data, V="Var_ARRD", cluster="shared_measurement_ID", obs="es_ID") # create VCV matrix for the specified data
  
  rma.mv(yi=ARRD, V=VCV, # run the model, as described earlier
        method="REML",
        mods= formula,
        random=list(~1|species_ID,
                    ~1|genus_species,
                    ~1|es_ID), # all possible random effects
        R = list(genus_species = phylo_matrix),
        data=data)
}

Functions to run orchard plots with either two levels of a categorical moderator

Because most of the moderators we tested have only two levels, we created a function plot.two.levels to create orchard plots with two levels of a categorical moderator.

plot.two.levels<-function(data,formula,moderator){
    model<-run.model(data,formula) # Run the model that will be used for the plot (must be a model without intercept) using the function we just created
    orchard_plot(model, mod=moderator,xlab="ARRD")+ # Create an orchard plot
    geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6)+  #prediction intervals
    geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.06, show.legend = FALSE, size = 1)+ # confidence intervals
    geom_point(aes(fill = name), size = 4, shape = 21)+# size of the mean estimate
    scale_size_continuous(range = c(1, 8))+ # size of the bubble points
    scale_colour_manual(values = c("purple","seagreen3"))+ #colors
    scale_fill_manual(values=c("purple","seagreen3"))+ #colors
    theme(text = element_text(size = 20, colour = "black", hjust = 0.5), #font sizes
           axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
           legend.title = element_text(size=16))
}

Meta-regressions with single moderators

For all subsequent models, we also tested whether the variance of residuals was homogeneous, which is one of the assumption of the models.

Categorical predictors

Outcome

Type of outcome: LTL (lower thermal limit), UTL (upper thermal limit), PBT (preferred body temperature)

As mentioned earlier, the sample size of PBT data is rather low relative to the other groups. Therefore, interpretations of these results must be careful.

outcome_model<-run.model(d,~outcome-1) # use the `run.model` function we just created 
summary(outcome_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  205.6350  -411.2699  -399.2699  -378.4869  -398.9031   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0086     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0079     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0280    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 236) = 379.3625, p-val < .0001
## 
## Test of Moderators (coefficients 1:3):
## QM(df = 3) = 1.1463, p-val = 0.7659
## 
## Model Results:
## 
##             estimate      se     zval    pval    ci.lb   ci.ub 
## outcomeLTL    0.0082  0.0080   1.0208  0.3073  -0.0075  0.0238    
## outcomePBT   -0.0094  0.0387  -0.2428  0.8081  -0.0852  0.0665    
## outcomeUTL    0.0046  0.0079   0.5801  0.5619  -0.0108  0.0199    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
orchard_plot(outcome_model,mod="outcome",xlab="ARRD")+ # plot the results
        geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.5)+ 
        geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.06, show.legend = FALSE, size = 1.1)+
        geom_point(aes(fill = name), size = 4, shape = 21)+
        scale_size_continuous(range = c(1, 8))+
        scale_colour_manual(values = c("#00BDD0","#CF78FF","coral2"))+
        scale_fill_manual(values=c("#00BDD0","#CF78FF","coral2"))+
        theme(text = element_text(size = 20, colour = "black", hjust = 0.5),
              axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
              legend.title = element_text(size=16))

qplot(y = sqrt(residuals(outcome_model)^2), x = fitted(outcome_model)) + # plot sqrt(residuals^2) against fitted values
      geom_point() +
      geom_smooth(method = "lm") + # method ="lm" to generate a straight line 
      geom_hline(yintercept = 0, colour="red") # assumption of homogeneity of variance seem satisfied

Habitat

Habitat: aquatic or terrestrial

habitat_model <- run.model(d, ~habitat - 1)
summary(habitat_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  207.2876  -414.5753  -404.5753  -387.2350  -404.3155   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0115     44     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0277    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 379.8879, p-val < .0001
## 
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 2.9737, p-val = 0.2261
## 
## Model Results:
## 
##                     estimate      se    zval    pval    ci.lb   ci.ub 
## habitataquatic        0.0017  0.0073  0.2353  0.8140  -0.0125  0.0159    
## habitatterrestrial    0.0134  0.0078  1.7083  0.0876  -0.0020  0.0287  . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot.two.levels(d, ~habitat - 1, "habitat")  # We used the plot.two.levels function created earlier 

qplot(y = sqrt(residuals(habitat_model)^2), x = fitted(habitat_model)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem satisfied

Taxonomic group

Taxonomic group: vertebrate or invertebrate

taxon_model <- run.model(d, ~taxonomic_group - 1)
summary(taxon_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  207.2765  -414.5530  -404.5530  -387.2127  -404.2933   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0087     44     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0281    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 378.4899, p-val < .0001
## 
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 2.7623, p-val = 0.2513
## 
## Model Results:
## 
##                              estimate      se     zval    pval    ci.lb   ci.ub 
## taxonomic_groupinvertebrate    0.0104  0.0063   1.6533  0.0983  -0.0019  0.0228 
## taxonomic_groupvertebrate     -0.0013  0.0079  -0.1698  0.8652  -0.0167  0.0141 
##  
## taxonomic_groupinvertebrate  . 
## taxonomic_groupvertebrate 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot.two.levels(d, ~taxonomic_group - 1, "taxonomic_group")

qplot(y = sqrt(residuals(taxon_model)^2), x = fitted(taxon_model)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem satisfied

Taxonomic group subdivided (bonus analysis)

Taxonomic group subdivided: Fishes, Reptiles and Amphibians, Terrestrial Invertebrates or Aquatic Invertebrates

Similar categories have been used in Morley et al. (2019) Global Ecology and Biogeography

  • Fishes: 65 effect sizes from 8 studies
  • Reptiles and Amphibians: 45 effect sizes from 12 studies
  • Terrestrial Invertebrate: 76 effect sizes from 10 studies
  • Aquatic Invertebrates: 51 effect sizes from 6 studies

Here, we provide an finer analysis between taxonomic groups. It seems like we have enough sample size to subdivide vertebrates and invertebrates into these new categories, but probably not enough to subset these categories for each outcome variable. Hence, we will stick to the original categories of taxonomic_group: vertebrates and invertebrates

n.taxa<-d %>% summarise(
                        `Fishes`=n_distinct(ref[taxonomic_group_sub=="Fishes"]),
                        `Reptiles and Amphibians`=n_distinct(ref[taxonomic_group_sub=="Reptiles and Amphibians"]),
                        `Terrestrial Invertebrates`=n_distinct(ref[taxonomic_group_sub=="Terrestrial Invertebrates"]),
                        `Aquatic Invertebrates`=n_distinct(ref[taxonomic_group_sub=="Aquatic Invertebrates"])) %>%  # Calculate the number of distinct studies for each taxonomic group
                                                                                                                  kable()

taxon_model.sub<-run.model(d,~taxonomic_group_sub-1)
summary(taxon_model.sub)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  205.4974  -410.9947  -396.9947  -372.7776  -396.5013   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0071     44     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0279    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 235) = 372.4469, p-val < .0001
## 
## Test of Moderators (coefficients 1:4):
## QM(df = 4) = 5.3967, p-val = 0.2490
## 
## Model Results:
## 
##                                               estimate      se     zval    pval 
## taxonomic_group_subAquatic Invertebrates        0.0100  0.0110   0.9090  0.3633 
## taxonomic_group_subFishes                      -0.0080  0.0082  -0.9740  0.3300 
## taxonomic_group_subReptiles and Amphibians      0.0235  0.0175   1.3414  0.1798 
## taxonomic_group_subTerrestrial Invertebrates    0.0096  0.0071   1.3500  0.1770 
##                                                 ci.lb   ci.ub 
## taxonomic_group_subAquatic Invertebrates      -0.0115  0.0315    
## taxonomic_group_subFishes                     -0.0240  0.0081    
## taxonomic_group_subReptiles and Amphibians    -0.0108  0.0578    
## taxonomic_group_subTerrestrial Invertebrates  -0.0044  0.0236    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
orchard_plot((run.model(d,~taxonomic_group_sub-1)), mod="taxonomic_group_sub", xlab="Taxonomic group")+ 
    geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6)+ 
    geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.06, show.legend = FALSE, size = 1.1)+
        geom_point(aes(fill = name), size = 4, shape = 21)+
        scale_colour_manual(values = c("green4","dodgerblue2","darkcyan","darkgoldenrod3"))+
        scale_fill_manual(values=c("green4","dodgerblue2","darkcyan","darkgoldenrod3"))+ 
        scale_size_continuous(range = c(1, 9))+
        theme(text = element_text(size = 20, colour = "black", hjust = 0.5),
              axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
              legend.title = element_text(size=16))

Origin

Origin: wild or lab

Homogeneity of residual variance seem violated between lab and wild animals. We used the robust.rma.mv to correct the estimates, as part of a sensitivity analyses.

origin_model <- run.model(d, ~origin - 1)
summary(origin_model)
## 
## Multivariate Meta-Analysis Model (k = 235; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  207.2416  -414.4832  -404.4832  -387.2280  -404.2188   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0034     42     no     species_ID   no 
## sigma^2.2  0.0003  0.0171     42     no  genus_species  yes 
## sigma^2.3  0.0007  0.0259    235     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 233) = 368.8768, p-val < .0001
## 
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 2.9892, p-val = 0.2243
## 
## Model Results:
## 
##             estimate      se     zval    pval    ci.lb   ci.ub 
## originlab    -0.0044  0.0130  -0.3401  0.7338  -0.0299  0.0210    
## originwild    0.0147  0.0122   1.2097  0.2264  -0.0091  0.0385    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot.two.levels(d, ~origin - 1, "origin")

qplot(y = sqrt(residuals(origin_model)^2), x = fitted(origin_model)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem violated. 

robust.rma.mv(origin_model, cluster = d$species_ID)  # robust.rma.mv uses robust sandwich-type estimators to correct for problems such as the heteroscedasticity of residuals
## 
## Number of outcomes:   235
## Number of clusters:   42
## Outcomes per cluster: 1-30 (mean: 5.60, median: 3)
## 
## Test of Moderators (coefficients 1:2):
## F(df1 = 2, df2 = 40) = 0.9223, p-val = 0.4059
## 
## Model Results:
## 
##             estimate      se     tval    pval    ci.lb   ci.ub 
## originlab    -0.0044  0.0066  -0.6661  0.5092  -0.0178  0.0090    
## originwild    0.0147  0.0114   1.2894  0.2046  -0.0083  0.0377    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Because the variance of wild animals appear to be much greater than the variance of lab animals, we decided to run a post-hoc F-test to test for differences in variances between wild and lab animals.

var.test(d$ARRD[d$origin == "wild"], d$ARRD[d$origin == "lab"])  # F-test
## 
##  F test to compare two variances
## 
## data:  d$ARRD[d$origin == "wild"] and d$ARRD[d$origin == "lab"]
## F = 8.0113, num df = 163, denom df = 70, p-value < 2.2e-16
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##   5.291705 11.745802
## sample estimates:
## ratio of variances 
##           8.011254
leveneTest(d$ARRD ~ d$origin)  # alternative Levene's Test give similar results
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   1  21.207 6.781e-06 ***
##       233                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Continuous predictors

Function to plot continuous variables with the same structure

plot_continuous<-function(data, model, moderator, xlab){

pred<-predict.rma(model)

data %>% mutate(fit=pred$pred, 
               ci.lb=pred$ci.lb,
               ci.ub=pred$ci.ub,
               pr.lb=pred$cr.lb,
               pr.ub=pred$cr.ub) %>% 
ggplot(aes(x = moderator, y = ARRD)) +
     geom_ribbon(aes(ymin = pr.lb, ymax = pr.ub, color = NULL), alpha = .1) +
     geom_ribbon(aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_point(aes(size=(1/sqrt(Var_ARRD))), shape=21, alpha=0.7, fill="sienna1", col="gray25",stroke=1) +
     geom_line(aes(y = fit), size = 1.5)+  
  labs(x = xlab, y = "ARRD", size = "Precison (1/SE)") +
  theme_bw() +
  scale_size_continuous(range=c(1,12))+
  geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+   # horizontal line at lnRR = 0
  theme(text = element_text(size = 18, colour = "black", hjust = 0.5), # change font sizes and legend position
          legend.text=element_text(size=14),
          legend.position=c(0,0), 
          legend.justification = c(0,0),
          legend.background = element_blank(), 
          legend.direction="horizontal",
          legend.title = element_text(size=15), 
          panel.border=element_rect(colour="black", fill=NA, size=1.2))
}

Absolute latitude (lab + wild)

We obtained latitude data for some lab animals. This latitude data corresponds to the latitude at which the animals were collected in the wild prior to be reared in the laboratory.

I plotted the prediction from the model along with confidence intervals (dark grey shading) and prediction intervals (light gray shading)

latitude_model <- run.model(d, ~z_abs_latitude)
summary(latitude_model)
## 
## Multivariate Meta-Analysis Model (k = 223; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  197.0710  -394.1421  -384.1421  -367.1513  -383.8630   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0132     39     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     39     no  genus_species  yes 
## sigma^2.3  0.0003  0.0184    223     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 221) = 317.2441, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 0.3790, p-val = 0.5381
## 
## Model Results:
## 
##                 estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt           0.0100  0.0056  1.7823  0.0747  -0.0010  0.0210  . 
## z_abs_latitude    0.0034  0.0056  0.6157  0.5381  -0.0075  0.0143    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(latitude_model)^2), x = fitted(latitude_model)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem satisfied

# Generate predictions and plot the results

d.lat <- filter(d, z_abs_latitude != "NA")
plot_continuous(d.lat, latitude_model, d.lat$abs_latitude, "Absolute latitude")

Absolute latitude (wild only)

Because the influence of latitude on ARRD is mostly relevant in wild animals, I created a data subset without lab animals: d.wild

d.wild <- subset(d, origin == "wild")
latitude_model_wild <- run.model(d.wild, ~z_abs_latitude)

summary(latitude_model_wild)
## 
## Multivariate Meta-Analysis Model (k = 164; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  101.9557  -203.9114  -193.9114  -178.4734  -193.5268   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0145     26     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     26     no  genus_species  yes 
## sigma^2.3  0.0017  0.0413    164     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 162) = 246.7804, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 0.3532, p-val = 0.5523
## 
## Model Results:
## 
##                 estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt           0.0102  0.0092  1.1147  0.2650  -0.0077  0.0282    
## z_abs_latitude    0.0049  0.0082  0.5943  0.5523  -0.0112  0.0210    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(latitude_model_wild)^2), x = fitted(latitude_model_wild)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem satisfied

# Generate predictions and plot the results

d.lat.wild <- filter(d.wild, z_abs_latitude != "NA")
plot_continuous(d.lat.wild, latitude_model_wild, d.lat.wild$abs_latitude, "Absolute latitude (wild animals)")

Sexual size dimorphism

The sexual size dimorphism index used was MDI: the body mass dimorphism index

The body mass dimorphism index was calculated according to Lovich and Gibbons (1992)

MDI_model <- run.model(d, ~MDI)
summary(MDI_model)
## 
## Multivariate Meta-Analysis Model (k = 205; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  191.4154  -382.8308  -372.8308  -356.2648  -372.5262   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0000     40     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     40     no  genus_species  yes 
## sigma^2.3  0.0007  0.0269    205     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 203) = 334.1057, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 4.1861, p-val = 0.0408
## 
## Model Results:
## 
##          estimate      se     zval    pval    ci.lb    ci.ub 
## intrcpt    0.0053  0.0045   1.1846  0.2362  -0.0035   0.0141    
## MDI       -0.0123  0.0060  -2.0460  0.0408  -0.0240  -0.0005  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(MDI_model)^2), x = fitted(MDI_model)) + geom_point() + geom_smooth(method = "lm") +
    geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem satisfied

robust.MDI <- robust.rma.mv(MDI_model, cluster = d$species_ID)  # robust estimates
summary(robust.MDI)
## 
## Number of outcomes:   205
## Number of clusters:   40
## Outcomes per cluster: 1-30 (mean: 5.12, median: 2.5)
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 38) = 15.2500, p-val = 0.0004
## 
## Model Results:
## 
##          estimate      se     tval    pval    ci.lb    ci.ub 
## intrcpt    0.0053  0.0038   1.3763  0.1768  -0.0025   0.0131      
## MDI       -0.0123  0.0031  -3.9051  0.0004  -0.0186  -0.0059  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Generate predictions and plot the results

d.MDI <- filter(d, MDI != "NA")
plot_continuous(d.MDI, MDI_model, d.MDI$MDI, "Body mass dimorphism index") + geom_vline(xintercept = 0,
    linetype = 2, alpha = 0.5)

Duration of acclimation

duration_model <- run.model(d, ~z_acc_duration)
summary(duration_model)
## 
## Multivariate Meta-Analysis Model (k = 232; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  201.0273  -402.0546  -392.0546  -374.8642  -391.7867   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0127     42     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     42     no  genus_species  yes 
## sigma^2.3  0.0008  0.0286    232     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 230) = 378.2431, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 1.9889, p-val = 0.1585
## 
## Model Results:
## 
##                 estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt           0.0066  0.0057   1.1561  0.2476  -0.0046  0.0177    
## z_acc_duration   -0.0068  0.0048  -1.4103  0.1585  -0.0162  0.0026    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(duration_model)^2), x = fitted(duration_model)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem violated

robust.duration <- robust.rma.mv(duration_model, cluster = d$species_ID)  # robust estimates
summary(robust.duration)
## 
## Number of outcomes:   232
## Number of clusters:   42
## Outcomes per cluster: 1-30 (mean: 5.52, median: 2)
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 40) = 3.3401, p-val = 0.0751
## 
## Model Results:
## 
##                 estimate      se     tval    pval    ci.lb   ci.ub 
## intrcpt           0.0066  0.0055   1.1849  0.2431  -0.0046  0.0177    
## z_acc_duration   -0.0068  0.0037  -1.8276  0.0751  -0.0143  0.0007  . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Generate predictions and plot the results

d.duration <- filter(d, acc_duration != "NA")
plot_continuous(d.duration, duration_model, d.duration$acc_duration, "Duration of acclimation (days)")

Ramping rate

ramping_model <- run.model(d, ~z_ramping.deg.min)
summary(ramping_model)
## 
## Multivariate Meta-Analysis Model (k = 222; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  199.3774  -398.7548  -388.7548  -371.7867  -388.4745   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0000     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0070     36     no  genus_species  yes 
## sigma^2.3  0.0007  0.0260    222     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 220) = 342.2747, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 2.1739, p-val = 0.1404
## 
## Model Results:
## 
##                    estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt              0.0059  0.0064  0.9173  0.3590  -0.0067  0.0185    
## z_ramping.deg.min    0.0093  0.0063  1.4744  0.1404  -0.0031  0.0218    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(ramping_model)^2), x = fitted(ramping_model)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # assumption of homogeneity of variance seem violated

robust.ramp <- robust.rma.mv(ramping_model, cluster = d$species_ID)  # robusts estimates
summary(robust.ramp)
## 
## Number of outcomes:   222
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.17, median: 3.5)
## 
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 34) = 1.4545, p-val = 0.2361
## 
## Model Results:
## 
##                    estimate      se    tval    pval    ci.lb   ci.ub 
## intrcpt              0.0059  0.0057  1.0439  0.3039  -0.0056  0.0174    
## z_ramping.deg.min    0.0093  0.0077  1.2060  0.2361  -0.0064  0.0251    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Generate predictions and plot the results

d.ramping <- filter(d, ramping.deg.min != "NA")
plot_continuous(d.ramping, ramping_model, d.ramping$ramping.deg.min, "Ramping rate (°C/min)")

Interaction between the moderator variables and the type of outcome variable

In this section, we aim to answer whether the moderator variables we tested affected differently upper and lower thermal limits (UTL and LTL).

We did not include PBT data in this section because the low sample size (n=13) could increase the chance of type II errors.

Create a data subset without PBT data, d.TL

d.TL <- subset(d, outcome != "PBT")

Create a function to make orchard plots with four categorical levels (2 levels of a moderator x 2 outcome levels), plot.four.levels

plot.four.levels<-function(data,formula,moderator){
  model<-run.model(data,formula) # Run the model that will be used for the plot (must be a model without intercept)
  orchard_plot(model, mod=moderator,xlab="ARRD")+ # Create an orchard plot
        geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6)+ 
        geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.1, show.legend = FALSE, size = 1)+
        geom_point(aes(fill = name), size = 4.3, shape = 21)+ # mean estimates
        scale_size_continuous(range = c(1, 7))+ # data point scaling
        scale_colour_manual(values = c("#00BFC4","#00BBD8","coral1","coral2"))+ # colour of the data points
        scale_fill_manual(values=c("#00BFC4","#00BBD8","coral1","coral2"))+ # colour of the mean estimates
        theme(text = element_text(size = 20, colour = "black", hjust = 0.5),
              axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
              legend.title = element_text(size=16))
}

Categorical predictors

Habitat x Outcome

habitat_model.outcome <- run.model(d.TL, ~outcome:habitat - 1)
summary(habitat_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  201.9271  -403.8541  -389.8541  -366.0354  -389.3308   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0107     38     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     38     no  genus_species  yes 
## sigma^2.3  0.0008  0.0279    226     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 222) = 357.9273, p-val < .0001
## 
## Test of Moderators (coefficients 1:4):
## QM(df = 4) = 5.3133, p-val = 0.2566
## 
## Model Results:
## 
##                                estimate      se     zval    pval    ci.lb 
## outcomeLTL:habitataquatic       -0.0041  0.0099  -0.4166  0.6770  -0.0234 
## outcomeUTL:habitataquatic        0.0048  0.0085   0.5611  0.5747  -0.0119 
## outcomeLTL:habitatterrestrial    0.0199  0.0092   2.1610  0.0307   0.0019 
## outcomeUTL:habitatterrestrial    0.0059  0.0101   0.5847  0.5588  -0.0138 
##                                 ci.ub 
## outcomeLTL:habitataquatic      0.0152    
## outcomeUTL:habitataquatic      0.0215    
## outcomeLTL:habitatterrestrial  0.0379  * 
## outcomeUTL:habitatterrestrial  0.0256    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
int.habitat_outcome <- interaction(d.TL$outcome:d.TL$habitat)  # create the interaction term manually. If we don't do this step, the labels on the y axis are not displayed correctly
plot.four.levels(d.TL, ~int.habitat_outcome - 1, "int.habitat_outcome")  # use the plot.four.levels function we just created

qplot(y = sqrt(residuals(habitat_model.outcome)^2), x = fitted(habitat_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of residual variance seem satisfied

Taxonomic group x Outcome

taxon_model.outcome <- run.model(d.TL, ~outcome:taxonomic_group - 1)
summary(taxon_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  201.1863  -402.3725  -388.3725  -364.5538  -387.8491   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0085     38     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     38     no  genus_species  yes 
## sigma^2.3  0.0008  0.0282    226     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 222) = 357.1589, p-val < .0001
## 
## Test of Moderators (coefficients 1:4):
## QM(df = 4) = 3.5720, p-val = 0.4670
## 
## Model Results:
## 
##                                         estimate      se     zval    pval 
## outcomeLTL:taxonomic_groupinvertebrate    0.0148  0.0082   1.8167  0.0693 
## outcomeUTL:taxonomic_groupinvertebrate    0.0060  0.0080   0.7398  0.4594 
## outcomeLTL:taxonomic_groupvertebrate     -0.0034  0.0104  -0.3321  0.7398 
## outcomeUTL:taxonomic_groupvertebrate      0.0005  0.0100   0.0498  0.9603 
##                                           ci.lb   ci.ub 
## outcomeLTL:taxonomic_groupinvertebrate  -0.0012  0.0309  . 
## outcomeUTL:taxonomic_groupinvertebrate  -0.0098  0.0217    
## outcomeLTL:taxonomic_groupvertebrate    -0.0238  0.0169    
## outcomeUTL:taxonomic_groupvertebrate    -0.0190  0.0200    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
int.taxon_outcome <- interaction(d.TL$outcome:d.TL$taxonomic_group)
plot.four.levels(d.TL, ~int.taxon_outcome - 1, "int.taxon_outcome")

qplot(y = sqrt(residuals(taxon_model.outcome)^2), x = fitted(taxon_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem ok

Origin x Outcome

origin_model.outcome <- run.model(d.TL, ~outcome:origin - 1)
summary(origin_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  203.9031  -407.8062  -393.8062  -369.9875  -393.2828   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0055     38     no     species_ID   no 
## sigma^2.2  0.0003  0.0159     38     no  genus_species  yes 
## sigma^2.3  0.0006  0.0242    226     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 222) = 351.1403, p-val < .0001
## 
## Test of Moderators (coefficients 1:4):
## QM(df = 4) = 8.4451, p-val = 0.0766
## 
## Model Results:
## 
##                        estimate      se     zval    pval    ci.lb   ci.ub 
## outcomeLTL:originlab     0.0054  0.0133   0.4078  0.6834  -0.0207  0.0316    
## outcomeUTL:originlab    -0.0131  0.0133  -0.9834  0.3254  -0.0391  0.0130    
## outcomeLTL:originwild    0.0068  0.0132   0.5204  0.6028  -0.0189  0.0326    
## outcomeUTL:originwild    0.0216  0.0128   1.6926  0.0905  -0.0034  0.0466  . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
int.origin_outcome <- interaction(d.TL$outcome:d.TL$origin)
plot.four.levels(d.TL, ~int.origin_outcome - 1, "int.origin_outcome")

qplot(y = sqrt(residuals(origin_model.outcome)^2), x = fitted(origin_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem violated

robust.rma.mv(origin_model.outcome, cluster = d.TL$species_ID)  # robust estimates
## 
## Number of outcomes:   226
## Number of clusters:   38
## Outcomes per cluster: 1-30 (mean: 5.95, median: 3)
## 
## Test of Moderators (coefficients 1:4):
## F(df1 = 4, df2 = 34) = 2.7611, p-val = 0.0433
## 
## Model Results:
## 
##                        estimate      se     tval    pval    ci.lb   ci.ub 
## outcomeLTL:originlab     0.0054  0.0064   0.8444  0.4043  -0.0077  0.0185    
## outcomeUTL:originlab    -0.0131  0.0121  -1.0807  0.2874  -0.0376  0.0115    
## outcomeLTL:originwild    0.0068  0.0170   0.4017  0.6904  -0.0278  0.0415    
## outcomeUTL:originwild    0.0216  0.0089   2.4203  0.0210   0.0035  0.0397  * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Here, we also tested whether the variance in ARRD varied between wild and lab animals, as a function of the type of outcome variable using a F-test

var.test(d$ARRD[d.TL$origin == "wild" & d.TL$outcome == "UTL"], d$ARRD[d.TL$origin ==
    "lab" & d.TL$outcome == "UTL"])  # F-test for UTL
## 
##  F test to compare two variances
## 
## data:  d$ARRD[d.TL$origin == "wild" & d.TL$outcome == "UTL"] and d$ARRD[d.TL$origin == "lab" & d.TL$outcome == "UTL"]
## F = 2.1647, num df = 87, denom df = 44, p-value = 0.005684
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  1.260911 3.554507
## sample estimates:
## ratio of variances 
##           2.164662
var.test(d$ARRD[d.TL$origin == "wild" & d.TL$outcome == "LTL"], d$ARRD[d.TL$origin ==
    "lab" & d.TL$outcome == "LTL"])  # F-test for LTL
## 
##  F test to compare two variances
## 
## data:  d$ARRD[d.TL$origin == "wild" & d.TL$outcome == "LTL"] and d$ARRD[d.TL$origin == "lab" & d.TL$outcome == "LTL"]
## F = 6.7417, num df = 69, denom df = 35, p-value = 2.553e-08
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##   3.659897 11.742324
## sample estimates:
## ratio of variances 
##           6.741679
leveneTest(ARRD ~ origin:outcome, data = d.TL)  # alternative Levene's Test give similar results
## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value    Pr(>F)    
## group   3  6.9301 0.0001765 ***
##       222                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Continuous predictors

Create data subsets for LTL and PBT to generate prediction lines for each outcome variable

d.LTL <- subset(d.TL, outcome == "LTL")  # data subset on lower thermal limits
d.UTL <- subset(d.TL, outcome == "UTL")  # data subset on upper thermal limits

Absolute latitude (wild + lab) x Outcome

Here, latitude data on wild and laboratory animals are included.

latitude_model.outcome <- run.model(d.TL, ~outcome:z_abs_latitude)
summary(latitude_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 214; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  194.3090  -388.6180  -376.6180  -356.5068  -376.2062   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0151     35     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     35     no  genus_species  yes 
## sigma^2.3  0.0003  0.0174    214     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 211) = 311.3158, p-val < .0001
## 
## Test of Moderators (coefficients 2:3):
## QM(df = 2) = 1.9114, p-val = 0.3845
## 
## Model Results:
## 
##                            estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                      0.0105  0.0059   1.7752  0.0759  -0.0011  0.0222 
## outcomeLTL:z_abs_latitude    0.0089  0.0074   1.2070  0.2274  -0.0055  0.0233 
## outcomeUTL:z_abs_latitude   -0.0048  0.0083  -0.5761  0.5646  -0.0211  0.0115 
##  
## intrcpt                    . 
## outcomeLTL:z_abs_latitude 
## outcomeUTL:z_abs_latitude 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(latitude_model.outcome)^2), x = fitted(latitude_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem ok

Plot Absolute latitude (wild + lab) x Outcome

We only represented the confidence intervals (and not the prediction intervals) because the figure becomes unreadable with both intervals.

d.lat.UTL<-subset(d.UTL,abs_latitude!="NA") # create a data subset without NA values on which to add prediction values
d.lat.LTL<-subset(d.LTL,abs_latitude!="NA")# create a data subset without NA values on which to add prediction values

## Prediction: Outcome = UTL

lat_model.UTL<-run.model(d.lat.UTL,~z_abs_latitude) # fit model

pred_lat_model.UTL<- predict.rma(lat_model.UTL) # predict values

d.lat.UTL <- mutate(d.lat.UTL,
                    ci.lb = pred_lat_model.UTL$ci.lb, # lower bound of the confidence interval for UTL
                    ci.ub = pred_lat_model.UTL$ci.ub, # upper bound of the confidence interval for UTL
                    fit = pred_lat_model.UTL$pred) # regression line for UTL

## Prediction: Outcome = LTL
    
lat_model.LTL<-run.model(d.lat.LTL,~z_abs_latitude)
pred_lat_model.LTL<- predict.rma(lat_model.LTL)

d.lat.LTL <- mutate(d.lat.LTL, 
                        ci.lb = pred_lat_model.LTL$ci.lb, # lower bound of the confidence interval for LTL
                        ci.ub = pred_lat_model.LTL$ci.ub, # upper bound of the confidence interval for LTL
                        fit = pred_lat_model.LTL$pred) # regression line for LTL
    

## Plot   

ggplot(d.TL,aes(x = abs_latitude, y = ARRD, fill=outcome)) +
  
     geom_ribbon(data=d.lat.LTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data=d.lat.LTL,aes(y = fit), size = 1.5, col="#00BFC4")+  
  
     geom_ribbon(data=d.lat.UTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data=d.lat.UTL,aes(y = fit), size = 1.5, col="coral2")+  
  
     geom_point(aes(size=(1/sqrt(Var_ARRD)), fill=outcome), shape=21, alpha=0.7, col="gray25",stroke=1) +
     scale_fill_manual(values=c("#00BFC4", "coral2"))+
  labs(x = "Absolute latitude", y = "ARRD", size = "Precison (1/SE)") +
  theme_bw() +
  scale_size_continuous(range=c(1,12))+
  geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+   
  theme(text = element_text(size = 18, colour = "black", hjust = 0.5), 
          legend.text=element_text(size=14),
          legend.position=c(0,0), 
          legend.justification = c(0,0),
          legend.background = element_blank(), 
          legend.direction="horizontal",
          legend.title = element_text(size=15), 
          panel.border=element_rect(colour="black", fill=NA, size=1.2))

Absolute latitude (wild only) x Outcome

d.TL.wild <- subset(d.TL, origin == "wild")

latitude_model.outcome.wild <- run.model(d.TL.wild, ~outcome:z_abs_latitude)
summary(latitude_model.outcome.wild)
## 
## Multivariate Meta-Analysis Model (k = 158; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  103.3704  -206.7409  -194.7409  -176.4803  -194.1733   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0008  0.0281     24     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     24     no  genus_species  yes 
## sigma^2.3  0.0011  0.0333    158     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 155) = 236.4041, p-val < .0001
## 
## Test of Moderators (coefficients 2:3):
## QM(df = 2) = 5.6548, p-val = 0.0592
## 
## Model Results:
## 
##                            estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                      0.0193  0.0112   1.7244  0.0846  -0.0026  0.0411 
## outcomeLTL:z_abs_latitude    0.0208  0.0123   1.6812  0.0927  -0.0034  0.0450 
## outcomeUTL:z_abs_latitude   -0.0178  0.0125  -1.4307  0.1525  -0.0423  0.0066 
##  
## intrcpt                    . 
## outcomeLTL:z_abs_latitude  . 
## outcomeUTL:z_abs_latitude 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(latitude_model.outcome.wild)^2), x = fitted(latitude_model.outcome.wild)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem ok

Plot Absolute latitude (wild only) x Outcome

MDI x Outcome

MDI_model.outcome <- run.model(d.TL, ~outcome:MDI)
summary(MDI_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 192; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  187.1087  -374.2175  -362.2175  -342.7670  -361.7559   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0038     34     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     34     no  genus_species  yes 
## sigma^2.3  0.0007  0.0262    192     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 189) = 315.9016, p-val < .0001
## 
## Test of Moderators (coefficients 2:3):
## QM(df = 2) = 4.4347, p-val = 0.1089
## 
## Model Results:
## 
##                 estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt           0.0065  0.0048   1.3640  0.1726  -0.0029  0.0159    
## outcomeLTL:MDI   -0.0166  0.0088  -1.8849  0.0594  -0.0339  0.0007  . 
## outcomeUTL:MDI   -0.0096  0.0077  -1.2553  0.2094  -0.0246  0.0054    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(MDI_model.outcome)^2), x = fitted(MDI_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem violated

robust.rma.mv(MDI_model.outcome, cluster = d.TL$species_ID)  # robust estimates
## 
## Number of outcomes:   192
## Number of clusters:   34
## Outcomes per cluster: 1-30 (mean: 5.65, median: 3)
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 31) = 6.3970, p-val = 0.0047
## 
## Model Results:
## 
##                 estimate      se     tval    pval    ci.lb   ci.ub 
## intrcpt           0.0065  0.0045   1.4544  0.1559  -0.0026  0.0157    
## outcomeLTL:MDI   -0.0166  0.0091  -1.8249  0.0777  -0.0352  0.0020  . 
## outcomeUTL:MDI   -0.0096  0.0062  -1.5476  0.1319  -0.0223  0.0031    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot MDI x Outcome

d.MDI.UTL<-subset(d.UTL,MDI!="NA")
d.MDI.LTL<-subset(d.LTL,MDI!="NA")

## Prediction: Outcome = UTL

MDI_model.UTL<-run.model(d.MDI.UTL,~MDI)
pred_MDI_model.UTL<- predict.rma(MDI_model.UTL)

    d.MDI.UTL <- mutate(d.MDI.UTL,
                        ci.lb = pred_MDI_model.UTL$ci.lb, 
                        ci.ub = pred_MDI_model.UTL$ci.ub, 
                        fit = pred_MDI_model.UTL$pred)

## Prediction: Outcome = LTL
    
MDI_model.LTL<-run.model(d.MDI.LTL,~MDI)
pred_MDI_model.LTL<-  predict.rma(MDI_model.LTL)

    d.MDI.LTL <- mutate(d.MDI.LTL,
                        ci.lb = pred_MDI_model.LTL$ci.lb, 
                        ci.ub = pred_MDI_model.LTL$ci.ub, 
                        fit = pred_MDI_model.LTL$pred)

## Plot   
ggplot(d.TL,aes(x = MDI, y = ARRD, fill=outcome)) +
  
     geom_ribbon(data=d.MDI.LTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data=d.MDI.LTL,aes(y = fit), size = 1.5, col="#00BFC4")+  
  
     geom_ribbon(data=d.MDI.UTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data=d.MDI.UTL,aes(y = fit), size = 1.5, col="coral2")+  
  
     geom_point(aes(size=(1/sqrt(Var_ARRD)), fill=outcome), shape=21, alpha=0.7, col="gray25",stroke=1) +
     scale_fill_manual(values=c("#00BFC4", "coral2"))+
  labs(x = "Body mass dimorphism index", y = "ARRD", size = "Precison (1/SE)") +
  theme_bw() +
  scale_size_continuous(range=c(1,12))+
  geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+   
  geom_vline(xintercept = 0,linetype = 2, colour = "black",alpha=0.5)+
  theme(text = element_text(size = 18, colour = "black", hjust = 0.5), # change font sizes and legend position
          legend.text=element_text(size=14),
          legend.position=c(0,0), 
          legend.justification = c(0,0),
          legend.background = element_blank(), 
          legend.direction="horizontal",
          legend.title = element_text(size=15), 
          panel.border=element_rect(colour="black", fill=NA, size=1.2))

Duration of acclimation x Outcome

duration_model.outcome <- run.model(d.TL, ~outcome:z_acc_duration)
summary(duration_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 219; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  197.7036  -395.4072  -383.4072  -363.1555  -383.0053   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0133     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0022     36     no  genus_species  yes 
## sigma^2.3  0.0007  0.0271    219     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 216) = 353.8016, p-val < .0001
## 
## Test of Moderators (coefficients 2:3):
## QM(df = 2) = 4.6523, p-val = 0.0977
## 
## Model Results:
## 
##                            estimate      se     zval    pval    ci.lb    ci.ub 
## intrcpt                      0.0073  0.0059   1.2343  0.2171  -0.0043   0.0189 
## outcomeLTL:z_acc_duration   -0.0117  0.0056  -2.0652  0.0389  -0.0227  -0.0006 
## outcomeUTL:z_acc_duration    0.0026  0.0076   0.3380  0.7354  -0.0123   0.0174 
##  
## intrcpt 
## outcomeLTL:z_acc_duration  * 
## outcomeUTL:z_acc_duration 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(duration_model.outcome)^2), x = fitted(duration_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem violated

robust.rma.mv(duration_model.outcome, cluster = d.TL$species_ID)  # robust estimates
## 
## Number of outcomes:   219
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.08, median: 3)
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 8.0054, p-val = 0.0015
## 
## Model Results:
## 
##                            estimate      se     tval    pval    ci.lb    ci.ub 
## intrcpt                      0.0073  0.0058   1.2678  0.2137  -0.0044   0.0190 
## outcomeLTL:z_acc_duration   -0.0117  0.0030  -3.8987  0.0004  -0.0177  -0.0056 
## outcomeUTL:z_acc_duration    0.0026  0.0048   0.5290  0.6003  -0.0073   0.0124 
##  
## intrcpt 
## outcomeLTL:z_acc_duration  *** 
## outcomeUTL:z_acc_duration 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot Duration of accclimation x Outcome

d.acc.UTL<-subset(d.UTL,acc_duration!="NA")
d.acc.LTL<-subset(d.LTL,acc_duration!="NA")

## Prediction: Outcome = UTL
acc_model.UTL<-run.model(d.acc.UTL,~z_acc_duration)
pred_acc_model.UTL<- predict.rma(acc_model.UTL)

    d.acc.UTL <- mutate(d.acc.UTL,
                        ci.lb = pred_acc_model.UTL$ci.lb, 
                        ci.ub = pred_acc_model.UTL$ci.ub, 
                        fit = pred_acc_model.UTL$pred)

## Prediction: Outcome = LTL
acc_model.LTL<-run.model(d.acc.LTL,~z_acc_duration)
pred_acc_model.LTL<- predict.rma(acc_model.LTL)

    d.acc.LTL <- mutate(d.acc.LTL, 
                        ci.lb = pred_acc_model.LTL$ci.lb, 
                        ci.ub = pred_acc_model.LTL$ci.ub, 
                        fit = pred_acc_model.LTL$pred)

## Plot   
ggplot(d.TL,aes(x = acc_duration, y = ARRD, fill=outcome)) +
  
     geom_ribbon(data= d.acc.LTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data= d.acc.LTL,aes(y = fit), size = 1.5, col="#00BFC4")+  
  
     geom_ribbon(data=d.acc.UTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data=d.acc.UTL,aes(y = fit), size = 1.5, col="coral2")+  
  
     geom_point(aes(size=(1/sqrt(Var_ARRD)), fill=outcome), shape=21, alpha=0.7, col="gray25",stroke=1) +
     scale_fill_manual(values=c("#00BFC4", "coral2"))+
  labs(x = "Duration of acclimation (days)", y = "ARRD", size = "Precison (1/SE)") +
  theme_bw() +
  scale_size_continuous(range=c(1,12))+
  geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+   # horizontal line at lnRR = 0
  theme(text = element_text(size = 18, colour = "black", hjust = 0.5), # change font sizes and legend position
          legend.text=element_text(size=14),
          legend.position=c(0,0), 
          legend.justification = c(0,0),
          legend.background = element_blank(), 
          legend.direction="horizontal",
          legend.title = element_text(size=15), 
          panel.border=element_rect(colour="black", fill=NA, size=1.2))

Ramping rate x Outcome

ramping_model.outcome <- run.model(d.TL, ~outcome:z_ramping.deg.min)
summary(ramping_model.outcome)
## 
## Multivariate Meta-Analysis Model (k = 222; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  197.8458  -395.6916  -383.6916  -363.3572  -383.2954   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0000     36     no     species_ID   no 
## sigma^2.2  0.0001  0.0072     36     no  genus_species  yes 
## sigma^2.3  0.0007  0.0263    222     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 219) = 342.2022, p-val < .0001
## 
## Test of Moderators (coefficients 2:3):
## QM(df = 2) = 2.3673, p-val = 0.3062
## 
## Model Results:
## 
##                               estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt                         0.0062  0.0065  0.9531  0.3405  -0.0066  0.0190 
## outcomeLTL:z_ramping.deg.min    0.0127  0.0094  1.3433  0.1792  -0.0058  0.0311 
## outcomeUTL:z_ramping.deg.min    0.0075  0.0073  1.0362  0.3001  -0.0067  0.0218 
##  
## intrcpt 
## outcomeLTL:z_ramping.deg.min 
## outcomeUTL:z_ramping.deg.min 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(ramping_model.outcome)^2), x = fitted(ramping_model.outcome)) +
    geom_point() + geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # homogeneity of variance seem violated

robust.rma.mv(ramping_model.outcome, cluster = d.TL$species_ID)  # robust estimates
## 
## Number of outcomes:   222
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.17, median: 3.5)
## 
## Test of Moderators (coefficients 2:3):
## F(df1 = 2, df2 = 33) = 0.7110, p-val = 0.4985
## 
## Model Results:
## 
##                               estimate      se    tval    pval    ci.lb   ci.ub 
## intrcpt                         0.0062  0.0058  1.0772  0.2892  -0.0055  0.0180 
## outcomeLTL:z_ramping.deg.min    0.0127  0.0136  0.9286  0.3599  -0.0151  0.0404 
## outcomeUTL:z_ramping.deg.min    0.0075  0.0085  0.8888  0.3805  -0.0097  0.0248 
##  
## intrcpt 
## outcomeLTL:z_ramping.deg.min 
## outcomeUTL:z_ramping.deg.min 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot Ramping x Outcome

d.ramp.UTL<-subset(d.UTL,ramping.deg.min!="NA")
d.ramp.LTL<-subset(d.LTL,ramping.deg.min!="NA")

## Prediction: Outcome = UTL

ramp_model.UTL<-run.model(d.ramp.UTL,~z_ramping.deg.min)
pred_ramp_model.UTL<- predict.rma(ramp_model.UTL)

    d.ramp.UTL <- mutate(d.ramp.UTL,
                         ci.lb = pred_ramp_model.UTL$ci.lb, 
                         ci.ub = pred_ramp_model.UTL$ci.ub, 
                         fit = pred_ramp_model.UTL$pred)

## Prediction: Outcome = LTL
    
ramp_model.LTL<-run.model(d.ramp.LTL,~z_ramping.deg.min)
pred_ramp_model.LTL<- predict.rma(ramp_model.LTL)

    d.ramp.LTL <- mutate(d.ramp.LTL, 
                         ci.lb = pred_ramp_model.LTL$ci.lb, 
                         ci.ub = pred_ramp_model.LTL$ci.ub, 
                         fit = pred_ramp_model.LTL$pred)

## Plot   
ggplot(d.TL,aes(x = ramping.deg.min, y = ARRD, fill=outcome)) +
  
     geom_ribbon(data= d.ramp.LTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data= d.ramp.LTL,aes(y = fit), size = 1.5, col="#00BFC4")+  
  
     geom_ribbon(data=d.ramp.UTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL), alpha = .3) +
     geom_line(data=d.ramp.UTL,aes(y = fit), size = 1.5, col="coral2")+  
  
     geom_point(aes(size=(1/sqrt(Var_ARRD)), fill=outcome), shape=21, alpha=0.7, col="gray25",stroke=1) +
     scale_fill_manual(values=c("#00BFC4", "coral2"))+
  labs(x = "Ramping rate (°C/min)", y = "ARRD", size = "Precison (1/SE)") +
  theme_bw() +
  scale_size_continuous(range=c(1,12))+
  geom_hline(yintercept = 0,linetype = 2, colour = "black",alpha=0.5)+   # horizontal line at lnRR = 0
  theme(text = element_text(size = 18, colour = "black", hjust = 0.5), # change font sizes and legend position
          legend.text=element_text(size=14),
          legend.position=c(0,0), 
          legend.justification = c(0,0),
          legend.background = element_blank(), 
          legend.direction="horizontal",
          legend.title = element_text(size=15), 
          panel.border=element_rect(colour="black", fill=NA, size=1.2))

Full models

Assess the multicollinearity between predictor variables

The package GGally provides the ggpairs function to test for the correlation between variables

None of the variables tested seem highly collinear (i.e., r > 0.7) but we do have a correlation between MDI and ramping.deg.min of 0.4

d %>% 
  select(outcome, habitat, taxonomic_group, origin, abs_latitude, MDI, acc_duration, ramping.deg.min) %>% # Correlation between moderators
  ggpairs() 

Full model with all moderator variables, without interactions

In the following “full” models, I removed z_ramping.deg.min from the full model because this variable was not significant or marginally significant in any of the models we fitted.

Fit the model, assess collinearity and sample sizes

Here, the analysis is on 35 species and 189 effect sizes. We lose a substantial amount of data by incorporating latitude and MDI (see Data Exploration for missing data patterns).

full_model.all.mod <- run.model(d, ~outcome + habitat + taxonomic_group + origin +
    z_abs_latitude + MDI + z_acc_duration)
summary(full_model.all.mod)  # very reduced sample size
## 
## Multivariate Meta-Analysis Model (k = 189; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  175.1638  -350.3277  -326.3277  -288.0122  -324.4594   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0140     35     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     35     no  genus_species  yes 
## sigma^2.3  0.0002  0.0153    189     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 180) = 258.8681, p-val = 0.0001
## 
## Test of Moderators (coefficients 2:9):
## QM(df = 8) = 11.3072, p-val = 0.1849
## 
## Model Results:
## 
##                            estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                     -0.0350  0.0230  -1.5251  0.1272  -0.0800  0.0100 
## outcomePBT                  -0.0566  0.0714  -0.7928  0.4279  -0.1965  0.0833 
## outcomeUTL                   0.0012  0.0068   0.1830  0.8548  -0.0121  0.0146 
## habitatterrestrial           0.0389  0.0208   1.8688  0.0617  -0.0019  0.0798 
## taxonomic_groupvertebrate    0.0343  0.0212   1.6149  0.1063  -0.0073  0.0759 
## originwild                   0.0262  0.0241   1.0839  0.2784  -0.0211  0.0735 
## z_abs_latitude               0.0066  0.0079   0.8377  0.4022  -0.0089  0.0221 
## MDI                         -0.0171  0.0091  -1.8887  0.0589  -0.0349  0.0006 
## z_acc_duration              -0.0104  0.0054  -1.9297  0.0536  -0.0209  0.0002 
##  
## intrcpt 
## outcomePBT 
## outcomeUTL 
## habitatterrestrial         . 
## taxonomic_groupvertebrate 
## originwild 
## z_abs_latitude 
## MDI                        . 
## z_acc_duration             . 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
vif.rma(full_model.all.mod)  # No major problems of collinearity (VIF <4)
##                outcomePBT                outcomeUTL        habitatterrestrial 
##                    1.0161                    1.0643                    3.0413 
## taxonomic_groupvertebrate                originwild            z_abs_latitude 
##                    2.9468                    3.9797                    1.8368 
##                       MDI            z_acc_duration 
##                    1.4099                    1.4307

Full model with a more representative data set, without interactions

6.7% of the latitude data and 14.5% of the MDI data was missing. Therefore, the inclusion of those terms significantly reduces the number of effect sizes analysed, which could generate conflicts with the results of our previous models. All other variables included have <3% of missing data (see Data Exploration for missing data patterns)

Therefore, we fitted a full model without MDI and latitude to make the full model more comparable with our univariate analyses.

This data subset was comprised of 228 effect sizes across 40 species, which is much more inclusive

full_model.red <- run.model(d, ~outcome + taxonomic_group + habitat + origin + z_acc_duration)
summary(full_model.red)
## 
## Multivariate Meta-Analysis Model (k = 228; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  196.6509  -393.3018  -373.3018  -339.3202  -372.2542   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0138     40     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     40     no  genus_species  yes 
## sigma^2.3  0.0007  0.0261    228     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 221) = 347.4344, p-val < .0001
## 
## Test of Moderators (coefficients 2:7):
## QM(df = 6) = 9.4208, p-val = 0.1513
## 
## Model Results:
## 
##                            estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                     -0.0286  0.0181  -1.5779  0.1146  -0.0641  0.0069 
## outcomePBT                  -0.0575  0.0719  -0.7994  0.4240  -0.1983  0.0834 
## outcomeUTL                  -0.0027  0.0080  -0.3386  0.7349  -0.0183  0.0129 
## taxonomic_groupvertebrate    0.0051  0.0144   0.3534  0.7238  -0.0232  0.0334 
## habitatterrestrial           0.0354  0.0170   2.0912  0.0365   0.0022  0.0687 
## originwild                   0.0385  0.0156   2.4724  0.0134   0.0080  0.0690 
## z_acc_duration              -0.0082  0.0054  -1.5357  0.1246  -0.0187  0.0023 
##  
## intrcpt 
## outcomePBT 
## outcomeUTL 
## taxonomic_groupvertebrate 
## habitatterrestrial         * 
## originwild                 * 
## z_acc_duration 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
vif.rma(full_model.red)  # No collinearity
##                outcomePBT                outcomeUTL taxonomic_groupvertebrate 
##                    1.0129                    1.0283                    1.4894 
##        habitatterrestrial                originwild            z_acc_duration 
##                    2.1043                    1.8081                    1.2733
robust.rma.mv(full_model.red, cluster = d$species_ID)
## 
## Number of outcomes:   228
## Number of clusters:   40
## Outcomes per cluster: 1-30 (mean: 5.70, median: 2.5)
## 
## Test of Moderators (coefficients 2:7):
## F(df1 = 6, df2 = 33) = 1.6952, p-val = 0.1533
## 
## Model Results:
## 
##                            estimate      se     tval    pval    ci.lb   ci.ub 
## intrcpt                     -0.0286  0.0172  -1.6648  0.1054  -0.0636  0.0064 
## outcomePBT                  -0.0575  0.0462  -1.2449  0.2219  -0.1514  0.0364 
## outcomeUTL                  -0.0027  0.0129  -0.2092  0.8356  -0.0289  0.0235 
## taxonomic_groupvertebrate    0.0051  0.0156   0.3280  0.7450  -0.0266  0.0368 
## habitatterrestrial           0.0354  0.0154   2.3046  0.0276   0.0042  0.0667 
## originwild                   0.0385  0.0140   2.7406  0.0098   0.0099  0.0670 
## z_acc_duration              -0.0082  0.0071  -1.1537  0.2569  -0.0227  0.0063 
##  
## intrcpt 
## outcomePBT 
## outcomeUTL 
## taxonomic_groupvertebrate 
## habitatterrestrial          * 
## originwild                 ** 
## z_acc_duration 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Full model with interactions

Here, we used the same moderator structure as above, where we did not include latitude and MDI because of the extent of missing data in these variables (>5%). We also excluded used the d.TL data set because of the presence of interactions with outcome and the limited sample size of PBT.

This data subset was comprised of 219 effect sizes across 36 studies

full_model.int <- run.model(d.TL, ~outcome + taxonomic_group + habitat + origin +
    z_acc_duration + outcome:habitat + outcome:origin + outcome:taxonomic_group +
    outcome:z_acc_duration)
summary(full_model.int)
## 
## Multivariate Meta-Analysis Model (k = 219; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  194.9474  -389.8948  -363.8948  -320.4444  -362.0281   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0004  0.0209     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     36     no  genus_species  yes 
## sigma^2.3  0.0003  0.0176    219     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 209) = 317.2567, p-val < .0001
## 
## Test of Moderators (coefficients 2:10):
## QM(df = 9) = 28.5616, p-val = 0.0008
## 
## Model Results:
## 
##                                       estimate      se     zval    pval 
## intrcpt                                -0.0310  0.0232  -1.3373  0.1811 
## outcomeUTL                             -0.0508  0.0309  -1.6452  0.0999 
## taxonomic_groupvertebrate               0.0245  0.0220   1.1122  0.2660 
## habitatterrestrial                      0.0394  0.0219   1.7997  0.0719 
## originwild                              0.0215  0.0209   1.0273  0.3043 
## z_acc_duration                         -0.0148  0.0062  -2.3712  0.0177 
## outcomeUTL:habitatterrestrial           0.0575  0.0313   1.8406  0.0657 
## outcomeUTL:originwild                   0.0782  0.0237   3.2926  0.0010 
## outcomeUTL:taxonomic_groupvertebrate   -0.0151  0.0263  -0.5741  0.5659 
## outcomeUTL:z_acc_duration               0.0259  0.0117   2.2173  0.0266 
##                                         ci.lb    ci.ub 
## intrcpt                               -0.0764   0.0144      
## outcomeUTL                            -0.1114   0.0097    . 
## taxonomic_groupvertebrate             -0.0186   0.0676      
## habitatterrestrial                    -0.0035   0.0824    . 
## originwild                            -0.0195   0.0625      
## z_acc_duration                        -0.0270  -0.0026    * 
## outcomeUTL:habitatterrestrial         -0.0037   0.1188    . 
## outcomeUTL:originwild                  0.0316   0.1247  *** 
## outcomeUTL:taxonomic_groupvertebrate  -0.0667   0.0365      
## outcomeUTL:z_acc_duration              0.0030   0.0487    * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
robust.rma.mv(full_model.int, cluster = d.TL$species_ID)
## 
## Number of outcomes:   219
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.08, median: 3)
## 
## Test of Moderators (coefficients 2:10):
## F(df1 = 9, df2 = 26) = 12.9164, p-val < .0001
## 
## Model Results:
## 
##                                       estimate      se     tval    pval 
## intrcpt                                -0.0310  0.0308  -1.0052  0.3241 
## outcomeUTL                             -0.0508  0.0432  -1.1776  0.2496 
## taxonomic_groupvertebrate               0.0245  0.0290   0.8442  0.4062 
## habitatterrestrial                      0.0394  0.0304   1.2989  0.2054 
## originwild                              0.0215  0.0342   0.6288  0.5350 
## z_acc_duration                         -0.0148  0.0035  -4.2050  0.0003 
## outcomeUTL:habitatterrestrial           0.0575  0.0436   1.3208  0.1981 
## outcomeUTL:originwild                   0.0782  0.0455   1.7171  0.0979 
## outcomeUTL:taxonomic_groupvertebrate   -0.0151  0.0307  -0.4921  0.6268 
## outcomeUTL:z_acc_duration               0.0259  0.0101   2.5500  0.0170 
##                                         ci.lb    ci.ub 
## intrcpt                               -0.0944   0.0324      
## outcomeUTL                            -0.1396   0.0379      
## taxonomic_groupvertebrate             -0.0351   0.0840      
## habitatterrestrial                    -0.0230   0.1018      
## originwild                            -0.0488   0.0918      
## z_acc_duration                        -0.0220  -0.0076  *** 
## outcomeUTL:habitatterrestrial         -0.0320   0.1471      
## outcomeUTL:originwild                 -0.0154   0.1717    . 
## outcomeUTL:taxonomic_groupvertebrate  -0.0782   0.0480      
## outcomeUTL:z_acc_duration              0.0050   0.0467    * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model selection and multi-model inference

We used the MuMin package to generate all possible moderator combinations, determine the importance of the moderators, and generate model-averaged estimates.

eval(metafor:::.MuMIn)

d.noNA <- d[!apply(d[,c("outcome", "taxonomic_group","habitat","origin", "z_acc_duration")], 1, anyNA),] # Remove rows with any NA value on one of these columns
d.noNA.TL<-subset(d.noNA, outcome!="PBT") # need a subset without PBT because we have interactions with outcome

d.noNA.TL<-as.data.frame(d.noNA.TL) # Convert to data frame to calculate the VCV matrix

VCV_ARRD_MuMIn<-make_VCV_matrix(d.noNA.TL, V="Var_ARRD", cluster="shared_measurement_ID", obs="es_ID") # Create a new VCV matrix with this reduced data set

full_model.MuMIn<- rma.mv(yi=ARRD, V=VCV_ARRD_MuMIn, 
                   method="ML", # maximum likelihood for model selection
                   mods= ~outcome+ # all moderators listed in the full model above
                         taxonomic_group+
                         habitat+
                         origin+
                         z_acc_duration+
                              outcome:habitat+
                              outcome:origin+
                              outcome:taxonomic_group+
                              outcome:z_acc_duration,
                   random=list(~1|species_ID,
                               ~1|genus_species,
                               ~1|es_ID), # all possible random effects
                   R = list(genus_species = phylo_matrix),
                   data=d.noNA.TL)
options(na.action = "na.fail") #required for dredge to run
candidate_models<-dredge(full_model.MuMIn) # Generate all possible combinations of moderators
options(na.action = "na.omit") #set back to default

subset(candidate_models, delta<=2) # Display all models within 2 values of AICc
## Global model call: rma.mv(yi = ARRD, V = VCV_ARRD_MuMIn, mods = ~outcome + taxonomic_group + 
##     habitat + origin + z_acc_duration + outcome:habitat + outcome:origin + 
##     outcome:taxonomic_group + outcome:z_acc_duration, random = list(~1 | 
##     species_ID, ~1 | genus_species, ~1 | es_ID), data = d.noNA.TL, 
##     method = "ML", R = list(genus_species = phylo_matrix))
## ---
## Model selection table 
##     (Int) hbt org otc txn_grp z_acc_drt hbt:otc org:otc otc:z_acc_drt df
## 376     +   +   +   +          -0.01163       +       +             + 11
## 104     +   +   +   +                         +       +                9
## 384     +   +   +   +       +  -0.01315       +       +             + 12
## 72      +   +   +   +                                 +                8
##      logLik   AICc delta weight
## 376 211.920 -400.6  0.00  0.414
## 104 209.036 -399.2  1.35  0.210
## 384 212.286 -399.1  1.51  0.195
## 72  207.802 -398.9  1.65  0.182
## Models ranked by AICc(x)
sw(model.avg(candidate_models, subset=delta<=2))# relative importance (sum of weights) of the moderators
##                      habitat origin outcome origin:outcome habitat:outcome
## Sum of weights:      1.00    1.00   1.00    1.00           0.82           
## N containing models:    4       4      4       4              3           
##                      z_acc_duration outcome:z_acc_duration taxonomic_group
## Sum of weights:      0.61           0.61                   0.19           
## N containing models:    2              2                      1
mod.avg<-summary(model.avg(candidate_models, subset=delta<=2)) # Generate model-averaged estimates 
mod.avg
## 
## Call:
## model.avg(object = candidate_models, subset = delta <= 2)
## 
## Component model call: 
## rma.mv(yi = ARRD, V = VCV_ARRD_MuMIn, mods = ~<4 unique rhs>, random = 
##      list(~1 | species_ID, ~1 | genus_species, ~1 | es_ID), data = 
##      d.noNA.TL, method = ML, R = list(genus_species = phylo_matrix))
## 
## Component models: 
##          df logLik    AICc delta weight
## 1235678  11 211.92 -400.56  0.00   0.41
## 12367     9 209.04 -399.21  1.35   0.21
## 12345678 12 212.29 -399.06  1.51   0.19
## 1237      8 207.80 -398.92  1.65   0.18
## 
## Term codes: 
##                habitat                 origin                outcome 
##                      1                      2                      3 
##        taxonomic_group         z_acc_duration        habitat:outcome 
##                      4                      5                      6 
##         origin:outcome outcome:z_acc_duration 
##                      7                      8 
## 
## Model-averaged coefficients:  
## (full average) 
##                                Estimate Std. Error z value Pr(>|z|)   
## intrcpt                       -0.015365   0.017390   0.884  0.37694   
## habitatterrestrial             0.028215   0.017233   1.637  0.10157   
## originwild                     0.016558   0.018276   0.906  0.36494   
## outcomeUTL                    -0.051740   0.024574   2.105  0.03525 * 
## z_acc_duration                -0.007368   0.007456   0.988  0.32306   
## habitatterrestrial:outcomeUTL  0.048052   0.032412   1.483  0.13819   
## originwild:outcomeUTL          0.067067   0.025129   2.669  0.00761 **
## outcomeUTL:z_acc_duration      0.014312   0.014067   1.017  0.30898   
## taxonomic_groupvertebrate      0.002524   0.008200   0.308  0.75824   
##  
## (conditional average) 
##                                Estimate Std. Error z value Pr(>|z|)   
## intrcpt                       -0.015365   0.017390   0.884  0.37694   
## habitatterrestrial             0.028215   0.017233   1.637  0.10157   
## originwild                     0.016558   0.018276   0.906  0.36494   
## outcomeUTL                    -0.051740   0.024574   2.105  0.03525 * 
## z_acc_duration                -0.012114   0.005824   2.080  0.03751 * 
## habitatterrestrial:outcomeUTL  0.058716   0.025642   2.290  0.02203 * 
## originwild:outcomeUTL          0.067067   0.025129   2.669  0.00761 **
## outcomeUTL:z_acc_duration      0.023530   0.010414   2.259  0.02386 * 
## taxonomic_groupvertebrate      0.012969   0.014493   0.895  0.37088   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
confint(mod.avg, full=TRUE) # Generate confidence intervals for the estimates averaged using full-averages procedures
##                                      2.5 %       97.5 %
## intrcpt                       -0.049448001  0.018718425
## habitatterrestrial            -0.005560977  0.061991256
## originwild                    -0.019262016  0.052377367
## outcomeUTL                    -0.099903987 -0.003575934
## z_acc_duration                -0.021982118  0.007245813
## habitatterrestrial:outcomeUTL -0.015473742  0.111578025
## originwild:outcomeUTL          0.017815532  0.116317821
## outcomeUTL:z_acc_duration     -0.013259872  0.041883577
## taxonomic_groupvertebrate     -0.013547784  0.018595532

Best models

Best model

best_model<-run.model(d.TL, ~habitat + # paste model structure of the best model identified
                             origin + 
                             outcome + 
                             z_acc_duration +
                                 outcome:habitat + 
                                 outcome:origin+ 
                                 outcome:z_acc_duration)

summary(best_model) # summary of the best model identified 
## 
## Multivariate Meta-Analysis Model (k = 219; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  197.5057  -395.0114  -373.0114  -336.1410  -371.6848   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0003  0.0179     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     36     no  genus_species  yes 
## sigma^2.3  0.0004  0.0187    219     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 211) = 318.5302, p-val < .0001
## 
## Test of Moderators (coefficients 2:8):
## QM(df = 7) = 26.3301, p-val = 0.0004
## 
## Model Results:
## 
##                                estimate      se     zval    pval    ci.lb 
## intrcpt                         -0.0169  0.0185  -0.9168  0.3593  -0.0531 
## habitatterrestrial               0.0286  0.0185   1.5469  0.1219  -0.0076 
## originwild                       0.0238  0.0197   1.2114  0.2258  -0.0147 
## outcomeUTL                      -0.0587  0.0221  -2.6606  0.0078  -0.1020 
## z_acc_duration                  -0.0123  0.0059  -2.0827  0.0373  -0.0239 
## habitatterrestrial:outcomeUTL    0.0638  0.0253   2.5221  0.0117   0.0142 
## originwild:outcomeUTL            0.0716  0.0238   3.0161  0.0026   0.0251 
## outcomeUTL:z_acc_duration        0.0250  0.0108   2.3104  0.0209   0.0038 
##                                  ci.ub 
## intrcpt                         0.0193     
## habitatterrestrial              0.0648     
## originwild                      0.0624     
## outcomeUTL                     -0.0155  ** 
## z_acc_duration                 -0.0007   * 
## habitatterrestrial:outcomeUTL   0.1134   * 
## originwild:outcomeUTL           0.1182  ** 
## outcomeUTL:z_acc_duration       0.0462   * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Assumptions


qplot(y = sqrt(residuals(best_model)^2), x = fitted(best_model)) +
  geom_point() +
  geom_smooth(method = "lm") +
  geom_hline(yintercept = 0, colour="red") # Assumption of residual homogeneity of variance seem violated

robust.rma.mv(best_model,cluster=d.TL$species_ID) # robust estimates
## 
## Number of outcomes:   219
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.08, median: 3)
## 
## Test of Moderators (coefficients 2:8):
## F(df1 = 7, df2 = 28) = 11.2393, p-val < .0001
## 
## Model Results:
## 
##                                estimate      se     tval    pval    ci.lb 
## intrcpt                         -0.0169  0.0359  -0.4714  0.6410  -0.0905 
## habitatterrestrial               0.0286  0.0335   0.8542  0.4003  -0.0400 
## originwild                       0.0238  0.0363   0.6556  0.5174  -0.0506 
## outcomeUTL                      -0.0587  0.0444  -1.3230  0.1965  -0.1497 
## z_acc_duration                  -0.0123  0.0037  -3.3627  0.0022  -0.0198 
## habitatterrestrial:outcomeUTL    0.0638  0.0454   1.4062  0.1707  -0.0292 
## originwild:outcomeUTL            0.0716  0.0460   1.5568  0.1308  -0.0226 
## outcomeUTL:z_acc_duration        0.0250  0.0082   3.0639  0.0048   0.0083 
##                                  ci.ub 
## intrcpt                         0.0566     
## habitatterrestrial              0.0971     
## originwild                      0.0982     
## outcomeUTL                      0.0322     
## z_acc_duration                 -0.0048  ** 
## habitatterrestrial:outcomeUTL   0.1568     
## originwild:outcomeUTL           0.1659     
## outcomeUTL:z_acc_duration       0.0417  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
r2_ml(best_model) # R-squared of the best model (the r2_ml function is part of the orchaRd package)
##   R2_marginal R2_coditional 
##     0.5120823     0.7448837

Second best model

best_model_n2<-run.model(d.TL, ~habitat + # paste model structure of the second best model
                                origin + 
                                outcome +
                                  outcome:habitat + 
                                  outcome:origin)
summary(best_model_n2)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  205.0360  -410.0719  -392.0719  -361.5293  -391.2148   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0002  0.0139     38     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     38     no  genus_species  yes 
## sigma^2.3  0.0004  0.0192    226     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 220) = 325.1693, p-val < .0001
## 
## Test of Moderators (coefficients 2:6):
## QM(df = 5) = 20.1951, p-val = 0.0011
## 
## Model Results:
## 
##                                estimate      se     zval    pval    ci.lb 
## intrcpt                         -0.0055  0.0167  -0.3269  0.7438  -0.0383 
## habitatterrestrial               0.0247  0.0173   1.4316  0.1523  -0.0091 
## originwild                       0.0060  0.0173   0.3469  0.7287  -0.0280 
## outcomeUTL                      -0.0565  0.0215  -2.6249  0.0087  -0.0988 
## habitatterrestrial:outcomeUTL    0.0440  0.0227   1.9381  0.0526  -0.0005 
## originwild:outcomeUTL            0.0746  0.0230   3.2395  0.0012   0.0295 
##                                  ci.ub 
## intrcpt                         0.0273     
## habitatterrestrial              0.0585     
## originwild                      0.0400     
## outcomeUTL                     -0.0143  ** 
## habitatterrestrial:outcomeUTL   0.0885   . 
## originwild:outcomeUTL           0.1198  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(best_model_n2)^2), x = fitted(best_model_n2)) +
  geom_point() +
  geom_smooth(method = "lm") +
  geom_hline(yintercept = 0, colour="red") # Assumption of residual homogeneity of variance seem violated

robust.rma.mv(best_model_n2,cluster=d.TL$species_ID) # robust estimates
## 
## Number of outcomes:   226
## Number of clusters:   38
## Outcomes per cluster: 1-30 (mean: 5.95, median: 3)
## 
## Test of Moderators (coefficients 2:6):
## F(df1 = 5, df2 = 32) = 6.7469, p-val = 0.0002
## 
## Model Results:
## 
##                                estimate      se     tval    pval    ci.lb 
## intrcpt                         -0.0055  0.0307  -0.1781  0.8598  -0.0681 
## habitatterrestrial               0.0247  0.0305   0.8094  0.4242  -0.0375 
## originwild                       0.0060  0.0310   0.1938  0.8476  -0.0572 
## outcomeUTL                      -0.0565  0.0453  -1.2473  0.2213  -0.1489 
## habitatterrestrial:outcomeUTL    0.0440  0.0457   0.9635  0.3425  -0.0490 
## originwild:outcomeUTL            0.0746  0.0459   1.6258  0.1138  -0.0189 
##                                 ci.ub 
## intrcpt                        0.0571    
## habitatterrestrial             0.0869    
## originwild                     0.0692    
## outcomeUTL                     0.0358    
## habitatterrestrial:outcomeUTL  0.1370    
## originwild:outcomeUTL          0.1681    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
r2_ml(best_model_n2) # R-squared
##   R2_marginal R2_coditional 
##     0.4417215     0.6346086

Third best model

best_model_n3<-run.model(d.TL, ~habitat + # paste model structure of the third best model
                                origin +
                                outcome + 
                                taxonomic_group + 
                                z_acc_duration +
                                     outcome:habitat + 
                                     outcome:origin + 
                                     outcome:z_acc_duration)

summary(best_model_n3)
## 
## Multivariate Meta-Analysis Model (k = 219; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  196.4572  -392.9144  -368.9144  -328.7491  -367.3306   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0004  0.0205     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     36     no  genus_species  yes 
## sigma^2.3  0.0003  0.0177    219     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 210) = 318.5300, p-val < .0001
## 
## Test of Moderators (coefficients 2:9):
## QM(df = 8) = 28.1135, p-val = 0.0005
## 
## Model Results:
## 
##                                estimate      se     zval    pval    ci.lb 
## intrcpt                         -0.0248  0.0206  -1.2068  0.2275  -0.0651 
## habitatterrestrial               0.0339  0.0197   1.7225  0.0850  -0.0047 
## originwild                       0.0237  0.0204   1.1599  0.2461  -0.0163 
## outcomeUTL                      -0.0631  0.0218  -2.9000  0.0037  -0.1058 
## taxonomic_groupvertebrate        0.0157  0.0162   0.9712  0.3315  -0.0160 
## z_acc_duration                  -0.0140  0.0061  -2.2961  0.0217  -0.0260 
## habitatterrestrial:outcomeUTL    0.0679  0.0250   2.7191  0.0065   0.0190 
## originwild:outcomeUTL            0.0781  0.0238   3.2846  0.0010   0.0315 
## outcomeUTL:z_acc_duration        0.0239  0.0112   2.1411  0.0323   0.0020 
##                                  ci.ub 
## intrcpt                         0.0155     
## habitatterrestrial              0.0725   . 
## originwild                      0.0637     
## outcomeUTL                     -0.0205  ** 
## taxonomic_groupvertebrate       0.0475     
## z_acc_duration                 -0.0021   * 
## habitatterrestrial:outcomeUTL   0.1169  ** 
## originwild:outcomeUTL           0.1247  ** 
## outcomeUTL:z_acc_duration       0.0458   * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(best_model_n3)^2), x = fitted(best_model_n3)) +
  geom_point() +
  geom_smooth(method = "lm") +
  geom_hline(yintercept = 0, colour="red") # Assumption of residual homogeneity of variance seem violated

robust.rma.mv(best_model_n3,cluster=d.TL$species_ID) # robust estimates
## 
## Number of outcomes:   219
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.08, median: 3)
## 
## Test of Moderators (coefficients 2:9):
## F(df1 = 8, df2 = 27) = 11.0616, p-val < .0001
## 
## Model Results:
## 
##                                estimate      se     tval    pval    ci.lb 
## intrcpt                         -0.0248  0.0307  -0.8084  0.4259  -0.0877 
## habitatterrestrial               0.0339  0.0299   1.1341  0.2667  -0.0274 
## originwild                       0.0237  0.0335   0.7066  0.4859  -0.0451 
## outcomeUTL                      -0.0631  0.0440  -1.4352  0.1627  -0.1534 
## taxonomic_groupvertebrate        0.0157  0.0204   0.7708  0.4475  -0.0262 
## z_acc_duration                  -0.0140  0.0035  -4.0158  0.0004  -0.0212 
## habitatterrestrial:outcomeUTL    0.0679  0.0452   1.5019  0.1447  -0.0249 
## originwild:outcomeUTL            0.0781  0.0464   1.6826  0.1040  -0.0171 
## outcomeUTL:z_acc_duration        0.0239  0.0093   2.5703  0.0160   0.0048 
##                                  ci.ub 
## intrcpt                         0.0381      
## habitatterrestrial              0.0952      
## originwild                      0.0924      
## outcomeUTL                      0.0271      
## taxonomic_groupvertebrate       0.0577      
## z_acc_duration                 -0.0069  *** 
## habitatterrestrial:outcomeUTL   0.1607      
## originwild:outcomeUTL           0.1733      
## outcomeUTL:z_acc_duration       0.0430    * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
r2_ml(best_model_n3) # R-squared
##   R2_marginal R2_coditional 
##     0.5658501     0.8142307

Fourth best model

best_model_n4 <- run.model(d.TL, ~habitat + origin + outcome + outcome:origin)
summary(best_model_n4)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  205.3629  -410.7258  -394.7258  -367.5405  -394.0466   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0118     38     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     38     no  genus_species  yes 
## sigma^2.3  0.0005  0.0231    226     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 221) = 336.5205, p-val < .0001
## 
## Test of Moderators (coefficients 2:5):
## QM(df = 4) = 14.8825, p-val = 0.0050
## 
## Model Results:
## 
##                        estimate      se     zval    pval    ci.lb   ci.ub 
## intrcpt                 -0.0209  0.0146  -1.4332  0.1518  -0.0495  0.0077     
## habitatterrestrial       0.0408  0.0146   2.7984  0.0051   0.0122  0.0695  ** 
## originwild               0.0177  0.0160   1.1089  0.2675  -0.0136  0.0491     
## outcomeUTL              -0.0187  0.0095  -1.9562  0.0504  -0.0374  0.0000   . 
## originwild:outcomeUTL    0.0388  0.0148   2.6197  0.0088   0.0098  0.0678  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
qplot(y = sqrt(residuals(best_model_n4)^2), x = fitted(best_model_n4)) + geom_point() +
    geom_smooth(method = "lm") + geom_hline(yintercept = 0, colour = "red")  # Assumption of residual homogeneity of variance seem violated

robust.rma.mv(best_model_n4, cluster = d.TL$species_ID)  # robust estimates
## 
## Number of outcomes:   226
## Number of clusters:   38
## Outcomes per cluster: 1-30 (mean: 5.95, median: 3)
## 
## Test of Moderators (coefficients 2:5):
## F(df1 = 4, df2 = 33) = 7.5165, p-val = 0.0002
## 
## Model Results:
## 
##                        estimate      se     tval    pval    ci.lb   ci.ub 
## intrcpt                 -0.0209  0.0164  -1.2744  0.2114  -0.0543  0.0125     
## habitatterrestrial       0.0408  0.0132   3.0981  0.0040   0.0140  0.0677  ** 
## originwild               0.0177  0.0201   0.8843  0.3829  -0.0231  0.0586     
## outcomeUTL              -0.0187  0.0145  -1.2880  0.2067  -0.0481  0.0108     
## originwild:outcomeUTL    0.0388  0.0177   2.1900  0.0357   0.0028  0.0748   * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
r2_ml(best_model_n4)  # R-squared
##   R2_marginal R2_coditional 
##     0.3246459     0.4642041

Publication bias

Data type

Data type: published (reported in the publication) or unpublished (not reported)

data.type_model <- run.model(d, ~data_type - 1)
summary(data.type_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  207.2339  -414.4678  -404.4678  -387.1275  -404.2080   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0000     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0086     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0279    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 378.0483, p-val < .0001
## 
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 1.5263, p-val = 0.4662
## 
## Model Results:
## 
##                       estimate      se    zval    pval    ci.lb   ci.ub 
## data_typepublished      0.0004  0.0072  0.0510  0.9593  -0.0137  0.0144    
## data_typeunpublished    0.0107  0.0092  1.1593  0.2464  -0.0074  0.0288    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot.two.levels(d, ~data_type - 1, "data_type")

Publication type

Publication type: peer-reviewed or not peer-reviewed (PhD and MSc dissertations)

peer_model <- run.model(d, ~peer_reviewed - 1)
summary(peer_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  206.8349  -413.6697  -403.6697  -386.3294  -403.4100   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0103     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0080     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0278    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 382.3276, p-val < .0001
## 
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 0.9145, p-val = 0.6330
## 
## Model Results:
## 
##                                 estimate      se    zval    pval    ci.lb 
## peer_reviewednot peer-reviewed    0.0061  0.0125  0.4933  0.6218  -0.0183 
## peer_reviewedpeer-reviewed        0.0069  0.0077  0.8972  0.3696  -0.0082 
##                                  ci.ub 
## peer_reviewednot peer-reviewed  0.0306    
## peer_reviewedpeer-reviewed      0.0220    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot.two.levels(d, ~peer_reviewed - 1, "peer_reviewed")

Publication year

We tested for the effect of publication year to identify a potential time lag bias

Because the pub_year was not significantly affecting ARRD we do not need to consider this variable in the analyses

year_model <- run.model(d, ~z_pub_year)
summary(year_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  207.1098  -414.2196  -404.2196  -386.8793  -403.9599   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0087     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0071     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0282    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 382.9603, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 0.5074, p-val = 0.4763
## 
## Model Results:
## 
##             estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt       0.0057  0.0065  0.8702  0.3842  -0.0071  0.0185    
## z_pub_year    0.0038  0.0054  0.7123  0.4763  -0.0067  0.0144    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pred_year_model <- predict.rma(year_model)

d.year <- subset(d, pub_year != "NA")
plot_continuous(d.year, year_model, d.year$pub_year, "Publication year")

Funnel Plot

Because funnel plots analyses assume the heterogeneity to be 0, we performed this analysis with the best model we identified.

funnel(best_model, 
      yaxis="seinv", # Inverse of standard error (precision) as the y axis
      level = c(90, 95, 99),  # levels of statistical significance highlighted 
      shade = c("white", "gray55", "gray75"), # shades for different levels of statistical significance
      refline = 0, # reference line at x = 0
      legend = TRUE, # display legend
      ylab="Precision (1/SE)", 
      cex.lab=1.5, 
      digits=1, 
      xlim=c(-2,2))

Egger’s regression

We performed an Egger’s regression by fitting standard error (sqrt(Var_ARRD)) as a moderator

Intercept model fitted with standard error

Egger_reg <- run.model(d, ~sqrt(Var_ARRD))  # standard error = sqrt(Var_ARRD)
summary(Egger_reg)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  208.3179  -416.6358  -406.6358  -389.2955  -406.3760   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0031     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0092     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0281    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 382.0780, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 0.4727, p-val = 0.4918
## 
## Model Results:
## 
##                 estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt           0.0009  0.0084  0.1110  0.9116  -0.0155  0.0174    
## sqrt(Var_ARRD)    0.0779  0.1133  0.6875  0.4918  -0.1441  0.2999    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pred_Egger_reg <- predict.rma(Egger_reg)  # to generate regression lines, confidence and prediction intervals

plot_continuous(d, Egger_reg, sqrt(d$Var_ARRD), "Standard error")

Best model fitted with standard error

Egger_reg.best<-run.model(d.TL, ~sqrt(Var_ARRD)+
                                 habitat + # structure of the best model identified
                                 origin + 
                                 outcome +
                                 z_acc_duration+
                                      outcome:habitat + 
                                      outcome:origin+ 
                                      outcome:z_acc_duration)
summary(Egger_reg.best)
## 
## Multivariate Meta-Analysis Model (k = 219; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  197.2494  -394.4987  -370.4987  -330.3334  -368.9150   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0004  0.0195     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     36     no  genus_species  yes 
## sigma^2.3  0.0003  0.0182    219     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 210) = 317.4596, p-val < .0001
## 
## Test of Moderators (coefficients 2:9):
## QM(df = 8) = 27.0551, p-val = 0.0007
## 
## Model Results:
## 
##                                estimate      se     zval    pval    ci.lb 
## intrcpt                         -0.0149  0.0194  -0.7686  0.4421  -0.0530 
## sqrt(Var_ARRD)                  -0.0805  0.1433  -0.5616  0.5744  -0.3614 
## habitatterrestrial               0.0294  0.0189   1.5572  0.1194  -0.0076 
## originwild                       0.0272  0.0206   1.3194  0.1870  -0.0132 
## outcomeUTL                      -0.0603  0.0219  -2.7563  0.0058  -0.1032 
## z_acc_duration                  -0.0127  0.0060  -2.1383  0.0325  -0.0244 
## habitatterrestrial:outcomeUTL    0.0668  0.0252   2.6492  0.0081   0.0174 
## originwild:outcomeUTL            0.0733  0.0236   3.1088  0.0019   0.0271 
## outcomeUTL:z_acc_duration        0.0259  0.0109   2.3730  0.0176   0.0045 
##                                  ci.ub 
## intrcpt                         0.0231     
## sqrt(Var_ARRD)                  0.2004     
## habitatterrestrial              0.0664     
## originwild                      0.0676     
## outcomeUTL                     -0.0174  ** 
## z_acc_duration                 -0.0011   * 
## habitatterrestrial:outcomeUTL   0.1162  ** 
## originwild:outcomeUTL           0.1196  ** 
## outcomeUTL:z_acc_duration       0.0474   * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
robust.rma.mv(Egger_reg.best,cluster=d.TL$species_ID)
## 
## Number of outcomes:   219
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.08, median: 3)
## 
## Test of Moderators (coefficients 2:9):
## F(df1 = 8, df2 = 27) = 9.2729, p-val < .0001
## 
## Model Results:
## 
##                                estimate      se     tval    pval    ci.lb 
## intrcpt                         -0.0149  0.0357  -0.4173  0.6798  -0.0883 
## sqrt(Var_ARRD)                  -0.0805  0.1158  -0.6952  0.4929  -0.3180 
## habitatterrestrial               0.0294  0.0331   0.8880  0.3824  -0.0386 
## originwild                       0.0272  0.0365   0.7450  0.4627  -0.0477 
## outcomeUTL                      -0.0603  0.0442  -1.3640  0.1838  -0.1510 
## z_acc_duration                  -0.0127  0.0036  -3.5098  0.0016  -0.0202 
## habitatterrestrial:outcomeUTL    0.0668  0.0454   1.4720  0.1526  -0.0263 
## originwild:outcomeUTL            0.0733  0.0459   1.5975  0.1218  -0.0209 
## outcomeUTL:z_acc_duration        0.0259  0.0084   3.0776  0.0047   0.0086 
##                                  ci.ub 
## intrcpt                         0.0584     
## sqrt(Var_ARRD)                  0.1570     
## habitatterrestrial              0.0974     
## originwild                      0.1021     
## outcomeUTL                      0.0304     
## z_acc_duration                 -0.0053  ** 
## habitatterrestrial:outcomeUTL   0.1599     
## originwild:outcomeUTL           0.1675     
## outcomeUTL:z_acc_duration       0.0432  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Sampling variance fitted as a moderator

Intercept model witted with sampling variance

Var_model <- run.model(d, ~Var_ARRD)
summary(Var_model)
## 
## Multivariate Meta-Analysis Model (k = 239; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  208.9114  -417.8227  -407.8227  -390.4824  -407.5630   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0073     44     no     species_ID   no 
## sigma^2.2  0.0001  0.0083     44     no  genus_species  yes 
## sigma^2.3  0.0008  0.0279    239     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 237) = 382.8744, p-val < .0001
## 
## Test of Moderators (coefficient 2):
## QM(df = 1) = 0.0309, p-val = 0.8605
## 
## Model Results:
## 
##           estimate      se    zval    pval    ci.lb   ci.ub 
## intrcpt     0.0054  0.0070  0.7699  0.4414  -0.0083  0.0190    
## Var_ARRD    0.0547  0.3115  0.1757  0.8605  -0.5558  0.6653    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Best model fitted with sampling variance

Var_model.best<-run.model(d.TL, ~Var_ARRD+
                                 habitat + # structure of the best model identified
                                 origin + 
                                 outcome +
                                 z_acc_duration+
                                      outcome:habitat + 
                                      outcome:origin+ 
                                      outcome:z_acc_duration)
summary(Var_model.best)
## 
## Multivariate Meta-Analysis Model (k = 219; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  197.8325  -395.6650  -371.6650  -331.4997  -370.0812   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0003  0.0180     36     no     species_ID   no 
## sigma^2.2  0.0000  0.0000     36     no  genus_species  yes 
## sigma^2.3  0.0003  0.0187    219     no          es_ID   no 
## 
## Test for Residual Heterogeneity:
## QE(df = 210) = 318.3734, p-val < .0001
## 
## Test of Moderators (coefficients 2:9):
## QM(df = 8) = 26.3902, p-val = 0.0009
## 
## Model Results:
## 
##                                estimate      se     zval    pval    ci.lb 
## intrcpt                         -0.0169  0.0185  -0.9111  0.3622  -0.0532 
## Var_ARRD                        -0.0463  0.3600  -0.1286  0.8977  -0.7518 
## habitatterrestrial               0.0286  0.0185   1.5455  0.1222  -0.0077 
## originwild                       0.0241  0.0198   1.2188  0.2229  -0.0146 
## outcomeUTL                      -0.0590  0.0221  -2.6724  0.0075  -0.1023 
## z_acc_duration                  -0.0124  0.0059  -2.0889  0.0367  -0.0240 
## habitatterrestrial:outcomeUTL    0.0643  0.0253   2.5351  0.0112   0.0146 
## originwild:outcomeUTL            0.0720  0.0238   3.0269  0.0025   0.0254 
## outcomeUTL:z_acc_duration        0.0251  0.0108   2.3167  0.0205   0.0039 
##                                  ci.ub 
## intrcpt                         0.0194     
## Var_ARRD                        0.6593     
## habitatterrestrial              0.0649     
## originwild                      0.0628     
## outcomeUTL                     -0.0157  ** 
## z_acc_duration                 -0.0008   * 
## habitatterrestrial:outcomeUTL   0.1139   * 
## originwild:outcomeUTL           0.1185  ** 
## outcomeUTL:z_acc_duration       0.0463   * 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
robust.rma.mv(Var_model.best,cluster=d.TL$species_ID)
## 
## Number of outcomes:   219
## Number of clusters:   36
## Outcomes per cluster: 1-30 (mean: 6.08, median: 3)
## 
## Test of Moderators (coefficients 2:9):
## F(df1 = 8, df2 = 27) = 9.5094, p-val < .0001
## 
## Model Results:
## 
##                                estimate      se     tval    pval    ci.lb 
## intrcpt                         -0.0169  0.0365  -0.4621  0.6477  -0.0918 
## Var_ARRD                        -0.0463  0.2115  -0.2188  0.8284  -0.4803 
## habitatterrestrial               0.0286  0.0340   0.8420  0.4072  -0.0411 
## originwild                       0.0241  0.0369   0.6527  0.5195  -0.0516 
## outcomeUTL                      -0.0590  0.0451  -1.3085  0.2017  -0.1515 
## z_acc_duration                  -0.0124  0.0037  -3.3348  0.0025  -0.0200 
## habitatterrestrial:outcomeUTL    0.0643  0.0462   1.3916  0.1754  -0.0305 
## originwild:outcomeUTL            0.0720  0.0468   1.5381  0.1357  -0.0240 
## outcomeUTL:z_acc_duration        0.0251  0.0083   3.0122  0.0056   0.0080 
##                                  ci.ub 
## intrcpt                         0.0581     
## Var_ARRD                        0.3878     
## habitatterrestrial              0.0983     
## originwild                      0.0997     
## outcomeUTL                      0.0335     
## z_acc_duration                 -0.0048  ** 
## habitatterrestrial:outcomeUTL   0.1590     
## originwild:outcomeUTL           0.1679     
## outcomeUTL:z_acc_duration       0.0422  ** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Sensitivity analyses

Leave-one-out analyses

Leave one study out

d<-as.data.frame(d) # Only work with a dataframe
VCV_matrix<-list() # will need new VCV matrices because the sample size will be iteratively reduced
Leave1studyout<-list() # create a list that will host the results of each model 
for(i in 1:length(levels(d$study_ID))){ # N models = N studies 
  VCV_matrix[[i]]<-make_VCV_matrix(d[d$study_ID != levels(d$study_ID)[i], ], V="Var_ARRD", cluster="shared_measurement_ID", obs="es_ID") # Create a new VCV matrix for each new model
  Leave1studyout[[i]] <- rma.mv(yi = ARRD, V = VCV_matrix[[i]], # Same model structure as all the models we fitted
                                random=list(~1|species_ID,
                                            ~1|genus_species,
                                            ~1|es_ID),
                                 R = list(genus_species = phylo_matrix),
                                method="REML",
                                data = d[d$study_ID != levels(d$study_ID)[i], ]) # Generate a new model for each new data (iterative removal of one study at a time)
}

# The output is a list so we need to summarise the coefficients of all the models performed

results.Leave1studyout<-as.data.frame(cbind(
                                           sapply(Leave1studyout, function(x) summary(x)$beta), # extract the beta coefficient from all models
                                           sapply(Leave1studyout, function(x) summary(x)$se), # extract the standard error from all models
                                           sapply(Leave1studyout, function(x) summary(x)$zval),  # extract the z value from all models
                                           sapply(Leave1studyout, function(x) summary(x)$pval), # extract the p value from all models
                                           sapply(Leave1studyout, function(x) summary(x)$ci.lb), # extract the lower confidence interval for all models
                                           sapply(Leave1studyout, function(x) summary(x)$ci.ub))) # extract the upper confidence interval for all models

colnames(results.Leave1studyout)=c("Estimate", "SE", "zval", "pval", "ci.lb", "ci.ub") # change column names 
kable(results.Leave1studyout)%>% kable_styling("striped", position="left") %>% scroll_box(width="100%", height="500px") # Table of the results from all models
Estimate SE zval pval ci.lb ci.ub
0.0080306 0.0092556 0.8676472 0.3855875 -0.0101101 0.0261713
0.0052709 0.0071667 0.7354644 0.4620567 -0.0087756 0.0193173
0.0054298 0.0070916 0.7656606 0.4438783 -0.0084695 0.0193291
0.0046161 0.0070690 0.6530044 0.5137535 -0.0092389 0.0184711
0.0067137 0.0072478 0.9263047 0.3542877 -0.0074918 0.0209192
0.0048080 0.0066615 0.7217633 0.4704400 -0.0082483 0.0178643
0.0054527 0.0070874 0.7693469 0.4416874 -0.0084384 0.0193437
0.0055409 0.0068885 0.8043665 0.4211853 -0.0079604 0.0190422
0.0061384 0.0069776 0.8797310 0.3790050 -0.0075375 0.0198144
0.0061617 0.0068123 0.9045010 0.3657298 -0.0071901 0.0195136
0.0045223 0.0072981 0.6196511 0.5354875 -0.0097817 0.0188262
0.0023465 0.0060866 0.3855156 0.6998554 -0.0095831 0.0142760
0.0052821 0.0073373 0.7199067 0.4715825 -0.0090986 0.0196629
0.0049186 0.0069233 0.7104405 0.4774310 -0.0086508 0.0184879
0.0063041 0.0065845 0.9574161 0.3383573 -0.0066013 0.0192096
0.0066613 0.0074735 0.8913164 0.3727594 -0.0079865 0.0213090
0.0053373 0.0072329 0.7379210 0.4605625 -0.0088389 0.0195134
0.0044828 0.0065228 0.6872465 0.4919274 -0.0083017 0.0172673
0.0062647 0.0071358 0.8779296 0.3799819 -0.0077212 0.0202506
0.0032875 0.0073974 0.4444136 0.6567436 -0.0112112 0.0177862
0.0061955 0.0069273 0.8943600 0.3711293 -0.0073817 0.0197726
0.0054246 0.0070718 0.7670769 0.4430358 -0.0084359 0.0192851
0.0043628 0.0070497 0.6188644 0.5360057 -0.0094544 0.0181800
0.0062202 0.0070814 0.8783802 0.3797374 -0.0076591 0.0200995
0.0061745 0.0067844 0.9100954 0.3627722 -0.0071228 0.0194717
0.0049251 0.0070798 0.6956555 0.4866446 -0.0089510 0.0188011
0.0056818 0.0069126 0.8219459 0.4111077 -0.0078667 0.0192302
0.0061529 0.0074865 0.8218676 0.4111522 -0.0085204 0.0208262
0.0060947 0.0070200 0.8681989 0.3852854 -0.0076642 0.0198536
0.0055954 0.0070447 0.7942727 0.4270367 -0.0082120 0.0194029
0.0072695 0.0066700 1.0898880 0.2757625 -0.0058034 0.0203424
0.0057441 0.0069308 0.8287705 0.4072343 -0.0078401 0.0193283
0.0044940 0.0063438 0.7084150 0.4786876 -0.0079395 0.0169276
0.0087544 0.0052998 1.6518420 0.0985668 -0.0016330 0.0191417
0.0107753 0.0054621 1.9727419 0.0485250 0.0000698 0.0214807
0.0056328 0.0068994 0.8164150 0.4142628 -0.0078898 0.0191554
0.0056543 0.0068973 0.8197947 0.4123332 -0.0078640 0.0191727
ggplot(results.Leave1studyout, aes(Estimate))+
       geom_histogram(fill="darkcyan", col="black",binwidth = 0.0001)+ # Simple plot of the distribution of estimates across the models generated
       theme_bw()+
       theme(text = element_text(size = 20, colour = "black", hjust = 0.5))

results.Leave1studyout %>% 
                          summarise(estimate= mean(Estimate), # calculate the mean coefficients across the models generated
                                    se=mean(SE), 
                                    zval=mean(zval), 
                                    pval=mean(pval), 
                                    ci.lb=mean(ci.lb), 
                                    ci.ub=mean(ci.ub)) %>% 
                                                          kable()%>% kable_styling("striped", position="left") 
estimate se zval pval ci.lb ci.ub
0.0057492 0.0069517 0.8383279 0.4181508 -0.0078758 0.0193742

Leave one species out

VCV_matrix <- list()
Leave1speciesout <- list()
for (i in 1:length(levels(d$species_ID))) {
    VCV_matrix[[i]] <- make_VCV_matrix(d[d$species_ID != levels(d$species_ID)[i],
        ], V = "Var_ARRD", cluster = "shared_measurement_ID", obs = "es_ID")
    Leave1speciesout[[i]] <- rma.mv(yi = ARRD, V = VCV_matrix[[i]], random = list(~1 |
        species_ID, ~1 | genus_species, ~1 | es_ID), R = list(genus_species = phylo_matrix),
        method = "REML", data = d[d$species_ID != levels(d$species_ID)[i], ])  # Generate a new model for each new data (iterative removal of one species at a time)
}

results.Leave1speciesout <- as.data.frame(cbind(sapply(Leave1speciesout, function(x) summary(x)$beta),
    sapply(Leave1speciesout, function(x) summary(x)$se), sapply(Leave1speciesout,
        function(x) summary(x)$zval), sapply(Leave1speciesout, function(x) summary(x)$pval),
    sapply(Leave1speciesout, function(x) summary(x)$ci.lb), sapply(Leave1speciesout,
        function(x) summary(x)$ci.ub)))

colnames(results.Leave1speciesout) = c("Estimate", "SE", "zval", "pval", "ci.lb",
    "ci.ub")
kable(results.Leave1speciesout) %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")
Estimate SE zval pval ci.lb ci.ub
0.0080306 0.0092556 0.8676472 0.3855875 -0.0101101 0.0261713
0.0056328 0.0068994 0.8164150 0.4142628 -0.0078898 0.0191554
0.0056543 0.0068973 0.8197947 0.4123332 -0.0078640 0.0191727
0.0052709 0.0071667 0.7354644 0.4620567 -0.0087756 0.0193173
0.0041047 0.0073383 0.5593540 0.5759201 -0.0102781 0.0184875
0.0070721 0.0066830 1.0582181 0.2899560 -0.0060264 0.0201705
0.0046161 0.0070690 0.6530044 0.5137535 -0.0092389 0.0184711
0.0067137 0.0072478 0.9263047 0.3542877 -0.0074918 0.0209192
0.0048080 0.0066615 0.7217633 0.4704400 -0.0082483 0.0178643
0.0054527 0.0070874 0.7693469 0.4416874 -0.0084384 0.0193437
0.0055409 0.0068885 0.8043665 0.4211853 -0.0079604 0.0190422
0.0023465 0.0060866 0.3855156 0.6998554 -0.0095831 0.0142760
0.0061384 0.0069776 0.8797310 0.3790050 -0.0075375 0.0198144
0.0061617 0.0068123 0.9045010 0.3657298 -0.0071901 0.0195136
0.0045223 0.0072981 0.6196511 0.5354875 -0.0097817 0.0188262
0.0052821 0.0073373 0.7199067 0.4715825 -0.0090986 0.0196629
0.0065703 0.0074792 0.8784742 0.3796864 -0.0080887 0.0212293
0.0047462 0.0067005 0.7083378 0.4787355 -0.0083865 0.0178790
0.0055993 0.0068673 0.8153507 0.4148716 -0.0078604 0.0190590
0.0050221 0.0067013 0.7494222 0.4536028 -0.0081122 0.0181564
0.0063041 0.0065845 0.9574161 0.3383573 -0.0066013 0.0192096
0.0066613 0.0074735 0.8913164 0.3727594 -0.0079865 0.0213090
0.0053373 0.0072329 0.7379210 0.4605625 -0.0088389 0.0195134
0.0047565 0.0066206 0.7184437 0.4724837 -0.0082196 0.0177326
0.0062647 0.0071358 0.8779296 0.3799819 -0.0077212 0.0202506
0.0032875 0.0073974 0.4444136 0.6567436 -0.0112112 0.0177862
0.0054246 0.0070718 0.7670769 0.4430358 -0.0084359 0.0192851
0.0043628 0.0070497 0.6188644 0.5360057 -0.0094544 0.0181800
0.0057115 0.0068950 0.8283612 0.4074660 -0.0078024 0.0192254
0.0060571 0.0070732 0.8563364 0.3918117 -0.0078062 0.0199204
0.0057153 0.0068920 0.8292681 0.4069527 -0.0077927 0.0192233
0.0061745 0.0067844 0.9100954 0.3627722 -0.0071228 0.0194717
0.0062771 0.0069620 0.9016175 0.3672601 -0.0073682 0.0199224
0.0049251 0.0070798 0.6956555 0.4866446 -0.0089510 0.0188011
0.0056818 0.0069126 0.8219459 0.4111077 -0.0078667 0.0192302
0.0063404 0.0073506 0.8625634 0.3883776 -0.0080666 0.0207474
0.0057254 0.0068932 0.8305852 0.4062080 -0.0077850 0.0192358
0.0053589 0.0070610 0.7589395 0.4478888 -0.0084805 0.0191983
0.0072695 0.0066700 1.0898880 0.2757625 -0.0058034 0.0203424
0.0056788 0.0069076 0.8221132 0.4110125 -0.0078598 0.0192174
0.0049944 0.0065586 0.7615024 0.4463570 -0.0078602 0.0178490
0.0053309 0.0066512 0.8014919 0.4228470 -0.0077053 0.0183671
0.0087544 0.0052998 1.6518420 0.0985668 -0.0016330 0.0191417
0.0105997 0.0054653 1.9394678 0.0524444 -0.0001120 0.0213114
ggplot(results.Leave1speciesout, aes(Estimate)) + geom_histogram(fill = "darkcyan",
    col = "black", binwidth = 1e-04) + theme_bw() + theme(text = element_text(size = 20,
    colour = "black", hjust = 0.5))

results.Leave1speciesout %>%
    summarise(estimate = mean(Estimate), se = mean(SE), zval = mean(zval), pval = mean(pval),
        ci.lb = mean(ci.lb), ci.ub = mean(ci.ub)) %>%
    kable() %>%
    kable_styling("striped", position = "left")
estimate se zval pval ci.lb ci.ub
0.0057336 0.0069427 0.8356278 0.4173508 -0.0078738 0.019341

Leave one effect size out

VCV_matrix <- list()
Leave1effectout <- list()
for (i in 1:length(levels(d$es_ID))) {
    VCV_matrix[[i]] <- make_VCV_matrix(d[d$es_ID != levels(d$es_ID)[i], ], V = "Var_ARRD",
        cluster = "shared_measurement_ID", obs = "es_ID")
    Leave1effectout[[i]] <- rma.mv(yi = ARRD, V = VCV_matrix[[i]], random = list(~1 |
        species_ID, ~1 | genus_species, ~1 | es_ID), R = list(genus_species = phylo_matrix),
        method = "REML", data = d[d$es_ID != levels(d$es_ID)[i], ])
}

results.Leave1effectout <- as.data.frame(cbind(sapply(Leave1effectout, function(x) summary(x)$beta),
    sapply(Leave1effectout, function(x) summary(x)$se), sapply(Leave1effectout, function(x) summary(x)$zval),
    sapply(Leave1effectout, function(x) summary(x)$pval), sapply(Leave1effectout,
        function(x) summary(x)$ci.lb), sapply(Leave1effectout, function(x) summary(x)$ci.ub)))

colnames(results.Leave1effectout) = c("Estimate", "SE", "zval", "pval", "ci.lb",
    "ci.ub")
kable(results.Leave1effectout) %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")
Estimate SE zval pval ci.lb ci.ub
0.0054737 0.0069434 0.7883189 0.4305102 -0.0081353 0.0190826
0.0054214 0.0069978 0.7747333 0.4384972 -0.0082940 0.0191368
0.0065632 0.0070632 0.9292116 0.3527794 -0.0072805 0.0204070
0.0054647 0.0068693 0.7955223 0.4263098 -0.0079989 0.0189283
0.0063437 0.0070266 0.9028092 0.3666272 -0.0074282 0.0201155
0.0051634 0.0068185 0.7572592 0.4488946 -0.0082007 0.0185274
0.0047288 0.0067498 0.7005846 0.4835623 -0.0085005 0.0179581
0.0062664 0.0070135 0.8934730 0.3716039 -0.0074798 0.0200125
0.0042357 0.0066858 0.6335308 0.5263871 -0.0088683 0.0173396
0.0064678 0.0070476 0.9177292 0.3587607 -0.0073452 0.0202808
0.0049550 0.0067800 0.7308382 0.4648780 -0.0083334 0.0182435
0.0060580 0.0069813 0.8677445 0.3855342 -0.0076251 0.0197411
0.0054431 0.0069747 0.7804046 0.4351527 -0.0082271 0.0191132
0.0061333 0.0069913 0.8772837 0.3803326 -0.0075693 0.0198360
0.0063116 0.0070259 0.8983389 0.3690049 -0.0074589 0.0200822
0.0060067 0.0069654 0.8623577 0.3884907 -0.0076453 0.0196587
0.0055409 0.0068885 0.8043665 0.4211853 -0.0079604 0.0190422
0.0056899 0.0069057 0.8239513 0.4099672 -0.0078449 0.0192248
0.0056847 0.0069053 0.8232345 0.4103746 -0.0078495 0.0192188
0.0056371 0.0068957 0.8174862 0.4136506 -0.0078782 0.0191524
0.0057727 0.0069212 0.8340586 0.4042479 -0.0077926 0.0193380
0.0057877 0.0069239 0.8358978 0.4032124 -0.0077829 0.0193582
0.0056288 0.0068947 0.8164070 0.4142674 -0.0078844 0.0191421
0.0055458 0.0068898 0.8049229 0.4208642 -0.0079580 0.0190496
0.0055694 0.0068820 0.8092650 0.4183627 -0.0079191 0.0190578
0.0055816 0.0068849 0.8106935 0.4175417 -0.0079126 0.0190758
0.0057275 0.0069131 0.8285080 0.4073829 -0.0078218 0.0192769
0.0057699 0.0069172 0.8341453 0.4041991 -0.0077875 0.0193274
0.0057143 0.0069107 0.8268837 0.4083030 -0.0078304 0.0192591
0.0056347 0.0068933 0.8174112 0.4136935 -0.0078760 0.0191454
0.0055750 0.0068838 0.8098713 0.4180141 -0.0079170 0.0190671
0.0057357 0.0069134 0.8296495 0.4067370 -0.0078143 0.0192856
0.0055842 0.0068857 0.8109847 0.4173745 -0.0079116 0.0190800
0.0057185 0.0069093 0.8276572 0.4078647 -0.0078235 0.0192605
0.0054562 0.0069630 0.7836043 0.4332723 -0.0081910 0.0191034
0.0055758 0.0069166 0.8061421 0.4201609 -0.0079805 0.0191321
0.0057521 0.0068740 0.8367817 0.4027153 -0.0077208 0.0192249
0.0062440 0.0067744 0.9217101 0.3566798 -0.0070335 0.0195215
0.0057340 0.0068789 0.8335611 0.4045284 -0.0077484 0.0192163
0.0056869 0.0068887 0.8255497 0.4090596 -0.0078146 0.0191885
0.0055906 0.0069165 0.8083058 0.4189146 -0.0079654 0.0191466
0.0056732 0.0068933 0.8230049 0.4105052 -0.0078374 0.0191839
0.0056334 0.0069023 0.8161629 0.4144070 -0.0078949 0.0191618
0.0057017 0.0068860 0.8280146 0.4076622 -0.0077946 0.0191979
0.0056645 0.0068938 0.8216821 0.4112578 -0.0078471 0.0191762
0.0056174 0.0068414 0.8210918 0.4115940 -0.0077915 0.0190264
0.0056492 0.0068968 0.8191052 0.4127264 -0.0078682 0.0191666
0.0057509 0.0068780 0.8361289 0.4030824 -0.0077298 0.0192316
0.0055309 0.0069297 0.7981435 0.4247872 -0.0080511 0.0191130
0.0056149 0.0069062 0.8130244 0.4162040 -0.0079210 0.0191508
0.0056278 0.0069031 0.8152574 0.4149250 -0.0079021 0.0191577
0.0056541 0.0068963 0.8198762 0.4122867 -0.0078623 0.0191705
0.0056459 0.0068980 0.8184880 0.4130786 -0.0078739 0.0191658
0.0056345 0.0069015 0.8164272 0.4142558 -0.0078921 0.0191612
0.0054508 0.0069545 0.7837697 0.4331752 -0.0081799 0.0190814
0.0043431 0.0071975 0.6034117 0.5462349 -0.0097638 0.0184499
0.0055963 0.0068432 0.8177929 0.4134754 -0.0078161 0.0190087
0.0060281 0.0068773 0.8765117 0.3807519 -0.0074513 0.0195074
0.0057779 0.0069137 0.8357092 0.4033185 -0.0077728 0.0193285
0.0056950 0.0068767 0.8281545 0.4075830 -0.0077831 0.0191730
0.0062603 0.0066256 0.9448654 0.3447276 -0.0067257 0.0192464
0.0052866 0.0070943 0.7451876 0.4561583 -0.0086180 0.0191913
0.0054965 0.0069793 0.7875480 0.4309612 -0.0081826 0.0191756
0.0061144 0.0066836 0.9148296 0.3602811 -0.0069853 0.0192140
0.0057616 0.0068418 0.8421084 0.3997273 -0.0076482 0.0191714
0.0057740 0.0068470 0.8432914 0.3990655 -0.0076459 0.0191939
0.0059698 0.0067588 0.8832629 0.3770943 -0.0072772 0.0192168
0.0056128 0.0068453 0.8199437 0.4122482 -0.0078038 0.0190294
0.0052967 0.0070963 0.7464042 0.4554233 -0.0086118 0.0192052
0.0058565 0.0068161 0.8592147 0.3902221 -0.0075028 0.0192158
0.0055670 0.0069403 0.8021303 0.4224776 -0.0080357 0.0191697
0.0057932 0.0068271 0.8485536 0.3961297 -0.0075878 0.0191742
0.0056904 0.0068781 0.8273213 0.4080550 -0.0077904 0.0191712
0.0053823 0.0070466 0.7638207 0.4449741 -0.0084287 0.0191934
0.0047090 0.0075261 0.6256905 0.5315180 -0.0100419 0.0194600
0.0057182 0.0068697 0.8323740 0.4051979 -0.0077462 0.0191826
0.0056691 0.0068875 0.8230995 0.4104514 -0.0078301 0.0191682
0.0057325 0.0069689 0.8225856 0.4107437 -0.0079262 0.0193912
0.0054330 0.0069814 0.7782125 0.4364438 -0.0082503 0.0191164
0.0064490 0.0074284 0.8681564 0.3853087 -0.0081103 0.0210083
0.0056400 0.0068480 0.8235958 0.4101693 -0.0077819 0.0190619
0.0056766 0.0069214 0.8201542 0.4121282 -0.0078891 0.0192423
0.0056242 0.0068682 0.8188860 0.4128515 -0.0078371 0.0190856
0.0054580 0.0068534 0.7963931 0.4258036 -0.0079744 0.0188904
0.0046897 0.0066620 0.7039553 0.4814606 -0.0083675 0.0177470
0.0059989 0.0070027 0.8566528 0.3916368 -0.0077262 0.0197240
0.0053399 0.0067448 0.7917121 0.4285285 -0.0078796 0.0185594
0.0059590 0.0070317 0.8474502 0.3967442 -0.0078229 0.0197410
0.0059918 0.0070060 0.8552439 0.3924161 -0.0077396 0.0197232
0.0055156 0.0069024 0.7990846 0.4242414 -0.0080128 0.0190439
0.0054984 0.0068541 0.8022075 0.4224329 -0.0079354 0.0189322
0.0055797 0.0068875 0.8101172 0.4178728 -0.0079196 0.0190789
0.0050027 0.0066827 0.7486056 0.4540950 -0.0080952 0.0181006
0.0055822 0.0068788 0.8115101 0.4170728 -0.0079000 0.0190644
0.0058641 0.0068178 0.8601234 0.3897210 -0.0074985 0.0192267
0.0060169 0.0066863 0.8998815 0.3681833 -0.0070880 0.0191217
0.0068523 0.0075673 0.9055122 0.3651941 -0.0079794 0.0216840
0.0055965 0.0068260 0.8198813 0.4122838 -0.0077822 0.0189752
0.0056224 0.0068923 0.8157514 0.4146423 -0.0078862 0.0191310
0.0054189 0.0069594 0.7786457 0.4361884 -0.0082213 0.0190591
0.0054889 0.0069219 0.7929650 0.4277982 -0.0080779 0.0190556
0.0053698 0.0069652 0.7709478 0.4407379 -0.0082817 0.0190212
0.0061723 0.0068020 0.9074336 0.3641775 -0.0071593 0.0195039
0.0054943 0.0069244 0.7934632 0.4275080 -0.0080773 0.0190659
0.0054574 0.0069529 0.7849133 0.4325044 -0.0081700 0.0190849
0.0052308 0.0070428 0.7427115 0.4576564 -0.0085729 0.0190344
0.0058092 0.0068964 0.8423504 0.3995919 -0.0077075 0.0193259
0.0065199 0.0067356 0.9679771 0.3330558 -0.0066816 0.0197214
0.0056268 0.0068928 0.8163295 0.4143117 -0.0078828 0.0191364
0.0044949 0.0065273 0.6886319 0.4910550 -0.0082984 0.0172882
0.0065139 0.0072269 0.9013324 0.3674116 -0.0076506 0.0206783
0.0056522 0.0068191 0.8288869 0.4071684 -0.0077129 0.0190174
0.0057507 0.0067735 0.8489933 0.3958850 -0.0075252 0.0190265
0.0055086 0.0068156 0.8082263 0.4189603 -0.0078498 0.0188669
0.0032875 0.0073974 0.4444136 0.6567436 -0.0112112 0.0177862
0.0073081 0.0074263 0.9840822 0.3250751 -0.0072472 0.0218635
0.0057608 0.0069172 0.8328309 0.4049401 -0.0077966 0.0193182
0.0049228 0.0063984 0.7693778 0.4416691 -0.0076179 0.0174635
0.0054246 0.0070718 0.7670769 0.4430358 -0.0084359 0.0192851
0.0043509 0.0070501 0.6171450 0.5371391 -0.0094669 0.0181688
0.0053953 0.0069305 0.7784896 0.4362804 -0.0081882 0.0189789
0.0056113 0.0068564 0.8184050 0.4131260 -0.0078270 0.0190497
0.0057476 0.0069351 0.8287674 0.4072360 -0.0078450 0.0193402
0.0021176 0.0060148 0.3520692 0.7247864 -0.0096712 0.0139064
0.0059932 0.0070507 0.8500149 0.3953168 -0.0078259 0.0198124
0.0056967 0.0069173 0.8235481 0.4101964 -0.0078609 0.0192543
0.0057736 0.0069243 0.8338165 0.4043844 -0.0077978 0.0193450
0.0055900 0.0068670 0.8140390 0.4156226 -0.0078690 0.0190490
0.0059531 0.0068305 0.8715389 0.3834600 -0.0074345 0.0193406
0.0058436 0.0068561 0.8523117 0.3940411 -0.0075942 0.0192813
0.0049251 0.0070798 0.6956555 0.4866446 -0.0089510 0.0188011
0.0056599 0.0069035 0.8198599 0.4122960 -0.0078708 0.0191906
0.0056594 0.0069034 0.8197901 0.4123358 -0.0078711 0.0191899
0.0056559 0.0069020 0.8194551 0.4125268 -0.0078718 0.0191835
0.0062487 0.0071197 0.8776653 0.3801254 -0.0077056 0.0202031
0.0056272 0.0068789 0.8180315 0.4133392 -0.0078553 0.0191097
0.0058558 0.0070501 0.8305994 0.4062000 -0.0079621 0.0196737
0.0059001 0.0070826 0.8330504 0.4048163 -0.0079814 0.0197817
0.0057795 0.0069979 0.8258924 0.4088651 -0.0079361 0.0194950
0.0057483 0.0069410 0.8281665 0.4075762 -0.0078559 0.0193525
0.0053133 0.0067422 0.7880651 0.4306586 -0.0079012 0.0185279
0.0065023 0.0072364 0.8985564 0.3688890 -0.0076808 0.0206854
0.0057274 0.0069326 0.8261425 0.4087232 -0.0078604 0.0193151
0.0060446 0.0070628 0.8558362 0.3920884 -0.0077982 0.0198873
0.0049976 0.0065455 0.7635129 0.4451576 -0.0078314 0.0178265
0.0051142 0.0069385 0.7370804 0.4610735 -0.0084849 0.0187133
0.0044022 0.0070384 0.6254518 0.5316746 -0.0093928 0.0181971
0.0073144 0.0067626 1.0816065 0.2794274 -0.0059400 0.0205689
0.0063198 0.0068596 0.9213056 0.3568909 -0.0071247 0.0197643
0.0048269 0.0069704 0.6924790 0.4886366 -0.0088349 0.0184887
0.0063839 0.0068544 0.9313460 0.3516746 -0.0070506 0.0198183
0.0055652 0.0068753 0.8094450 0.4182592 -0.0079101 0.0190405
0.0061870 0.0070432 0.8784307 0.3797100 -0.0076175 0.0199914
0.0055954 0.0070447 0.7942727 0.4270367 -0.0082120 0.0194029
0.0064796 0.0067674 0.9574725 0.3383288 -0.0067843 0.0197435
0.0057120 0.0069212 0.8252818 0.4092116 -0.0078534 0.0192773
0.0061372 0.0068506 0.8958601 0.3703275 -0.0072898 0.0195642
0.0056788 0.0069076 0.8221132 0.4110125 -0.0078598 0.0192174
0.0055029 0.0068496 0.8033981 0.4217447 -0.0079220 0.0189279
0.0056735 0.0069037 0.8218033 0.4111889 -0.0078575 0.0192045
0.0058236 0.0069488 0.8380834 0.4019839 -0.0077957 0.0194430
0.0051232 0.0067273 0.7615545 0.4463260 -0.0080621 0.0183086
0.0056511 0.0068221 0.8283621 0.4074654 -0.0077198 0.0190221
0.0059976 0.0069966 0.8572210 0.3913228 -0.0077154 0.0197106
0.0048122 0.0066150 0.7274683 0.4669391 -0.0081529 0.0177773
0.0045900 0.0065296 0.7029613 0.4820799 -0.0082077 0.0173878
0.0068564 0.0072283 0.9485520 0.3428485 -0.0073107 0.0210235
0.0058646 0.0069599 0.8426262 0.3994375 -0.0077765 0.0195056
0.0058366 0.0069522 0.8395315 0.4011711 -0.0077895 0.0194626
0.0058063 0.0069522 0.8351806 0.4036160 -0.0078197 0.0194323
0.0055371 0.0068573 0.8074772 0.4193916 -0.0079029 0.0189771
0.0055548 0.0068632 0.8093511 0.4183132 -0.0078969 0.0190065
0.0060017 0.0070146 0.8556028 0.3922175 -0.0077466 0.0197500
0.0056082 0.0068395 0.8199801 0.4122275 -0.0077969 0.0190134
0.0064898 0.0071724 0.9048259 0.3655576 -0.0075679 0.0205475
0.0047966 0.0065291 0.7346455 0.4625554 -0.0080002 0.0175934
0.0059098 0.0069773 0.8470063 0.3969916 -0.0077654 0.0195850
0.0055132 0.0068349 0.8066315 0.4198788 -0.0078829 0.0189094
0.0052111 0.0067253 0.7748407 0.4384338 -0.0079703 0.0183925
0.0055324 0.0068514 0.8074905 0.4193840 -0.0078960 0.0189609
0.0055991 0.0066465 0.8424113 0.3995577 -0.0074278 0.0186259
0.0055835 0.0067961 0.8215642 0.4113250 -0.0077367 0.0189037
0.0056130 0.0065669 0.8547288 0.3927013 -0.0072580 0.0184839
0.0056079 0.0066092 0.8485059 0.3961563 -0.0073458 0.0185617
0.0056868 0.0068046 0.8357262 0.4033090 -0.0076500 0.0190235
0.0055864 0.0068633 0.8139504 0.4156734 -0.0078654 0.0190382
0.0056997 0.0071114 0.8014888 0.4228487 -0.0082384 0.0196379
0.0055903 0.0068916 0.8111685 0.4172689 -0.0079171 0.0190977
0.0055816 0.0068700 0.8124595 0.4165280 -0.0078833 0.0190465
0.0055983 0.0066694 0.8393959 0.4012472 -0.0074735 0.0186701
0.0055822 0.0068363 0.8165435 0.4141894 -0.0078168 0.0189811
0.0056249 0.0065343 0.8608266 0.3893335 -0.0071821 0.0184318
0.0056485 0.0064875 0.8706811 0.3839283 -0.0070667 0.0183638
0.0056102 0.0066330 0.8458126 0.3976573 -0.0073901 0.0186106
0.0055905 0.0068507 0.8160448 0.4144745 -0.0078367 0.0190177
0.0053930 0.0070658 0.7632552 0.4453112 -0.0084557 0.0192416
0.0055801 0.0068262 0.8174510 0.4136707 -0.0077990 0.0189592
0.0055810 0.0068353 0.8164955 0.4142168 -0.0078159 0.0189779
0.0056083 0.0069266 0.8096825 0.4181227 -0.0079675 0.0191842
0.0057591 0.0071793 0.8021866 0.4224450 -0.0083120 0.0198303
0.0059528 0.0074045 0.8039441 0.4214293 -0.0085597 0.0204653
0.0059585 0.0074101 0.8040987 0.4213400 -0.0085651 0.0204821
0.0056115 0.0066172 0.8480111 0.3964318 -0.0073581 0.0185811
0.0055684 0.0068299 0.8152930 0.4149046 -0.0078180 0.0189548
0.0055737 0.0068155 0.8178004 0.4134712 -0.0077844 0.0189319
0.0055743 0.0068285 0.8163248 0.4143144 -0.0078093 0.0189578
0.0054540 0.0069514 0.7845873 0.4326956 -0.0081705 0.0190785
0.0056756 0.0070239 0.8080423 0.4190662 -0.0080910 0.0194422
0.0057793 0.0071955 0.8031750 0.4218736 -0.0083237 0.0198822
0.0056790 0.0064886 0.8752344 0.3814464 -0.0070384 0.0183964
0.0056240 0.0067623 0.8316720 0.4055941 -0.0076298 0.0188778
0.0057148 0.0070980 0.8051242 0.4207480 -0.0081970 0.0196266
0.0057485 0.0071793 0.8006998 0.4233055 -0.0083227 0.0198197
0.0073664 0.0057158 1.2887766 0.1974758 -0.0038364 0.0185692
0.0056738 0.0074158 0.7650965 0.4442141 -0.0088609 0.0202084
0.0087605 0.0050792 1.7247930 0.0845648 -0.0011945 0.0187155
0.0065066 0.0082214 0.7914301 0.4286931 -0.0096070 0.0226203
0.0054053 0.0072414 0.7464437 0.4553994 -0.0087876 0.0195982
0.0056328 0.0068994 0.8164150 0.4142628 -0.0078898 0.0191554
0.0056543 0.0068973 0.8197947 0.4123332 -0.0078640 0.0191727
0.0058213 0.0068208 0.8534630 0.3934026 -0.0075472 0.0191898
0.0056294 0.0069030 0.8154991 0.4147867 -0.0079003 0.0191591
0.0052790 0.0071205 0.7413795 0.4584634 -0.0086769 0.0192348
0.0052609 0.0071377 0.7370506 0.4610916 -0.0087288 0.0192506
0.0057203 0.0068570 0.8342294 0.4041517 -0.0077191 0.0191597
0.0057585 0.0068392 0.8419864 0.3997956 -0.0076461 0.0191631
0.0057779 0.0068874 0.8389129 0.4015182 -0.0077211 0.0192769
0.0049119 0.0070808 0.6936813 0.4878821 -0.0089664 0.0187901
0.0055645 0.0068693 0.8100622 0.4179044 -0.0078990 0.0190280
0.0063263 0.0067903 0.9316643 0.3515101 -0.0069824 0.0196350
0.0056747 0.0068827 0.8244853 0.4096639 -0.0078151 0.0191644
0.0046161 0.0070690 0.6530044 0.5137535 -0.0092389 0.0184711
0.0054513 0.0068642 0.7941595 0.4271026 -0.0080023 0.0189049
0.0070945 0.0073719 0.9623771 0.3358602 -0.0073541 0.0215432
0.0055332 0.0068682 0.8056209 0.4204615 -0.0079283 0.0189947
0.0055969 0.0068901 0.8123136 0.4166117 -0.0079074 0.0191012
0.0058442 0.0069628 0.8393577 0.4012686 -0.0078025 0.0194910
0.0051139 0.0067525 0.7573302 0.4488520 -0.0081208 0.0183485
0.0047330 0.0067489 0.7013044 0.4831131 -0.0084945 0.0179606
ggplot(results.Leave1effectout, aes(Estimate)) + geom_histogram(fill = "darkcyan",
    col = "black", binwidth = 1e-04) + theme_bw() + theme(text = element_text(size = 20,
    colour = "black", hjust = 0.5))

results.Leave1effectout %>%
    summarise(estimate = mean(Estimate), se = mean(SE), zval = mean(zval), pval = mean(pval),
        ci.lb = mean(ci.lb), ci.ub = mean(ci.ub)) %>%
    kable() %>%
    kable_styling("striped", position = "left")
estimate se zval pval ci.lb ci.ub
0.0056545 0.0069012 0.8205943 0.4140513 -0.0078716 0.0191806

Analysis with the full data set (without removing the outlier from Hernandez et al. (2002))

d.raw<-read_csv("data/Raw_data.csv") # Load the raw data with this outlier

d.raw<-d.raw %>% # calculate effect sizes
                mutate(ARR_f=((mean_high_f-mean_low_f)/(acc_temp_high-acc_temp_low)),
                       ARR_m=((mean_high_m-mean_low_m)/(acc_temp_high-acc_temp_low)),
                       ARRD=ARR_f - ARR_m,
                       Var_ARRD=((1/(acc_temp_high-acc_temp_low))^2*(sd_low_f^2/n_low_f_adj+sd_high_f^2/n_high_f_adj+sd_low_m^2/n_low_m_adj+sd_high_m^2/n_high_m_adj)),
                       precision=(1/sqrt(Var_ARRD))) 


d.raw$es_ID=as.factor(d.raw$es_ID) # convert to factors the variables used as random effects
d.raw$species_ID=as.factor(d.raw$species_ID)
d.raw$shared_measurement_ID=as.factor(d.raw$shared_measurement_ID)
  
### Create a new phylogenetic variance covariance matrix 
d.raw$genus_species<-as.factor(d.raw$genus_species) 
taxa.raw <- tnrs_match_names(names = levels(d.raw$genus_species), context_name = "Animals") 

d.raw$genus_species<-str_replace(d.raw$genus_species, "Gammarus marinus", "Marinogammarus marinus") 
d.raw$genus_species<-str_replace(d.raw$genus_species, "Hyale hirtipalma", "Apohyale hirtipalma") 
d.raw$genus_species<-str_replace(d.raw$genus_species, "Uca panacea", "Leptuca panacea") 

phylo_tree.raw<-tol_induced_subtree(ott_ids=taxa.raw$ott_id, label_format = "name") 
set.seed(1234)
binary_tree.raw<-multi2di(phylo_tree.raw,random=TRUE) 

d.raw$genus_species<-as.factor(d.raw$genus_species) 
binary_tree.raw$tip.label<-as.factor(binary_tree.raw$tip.label) 

levels(binary_tree.raw$tip.label)<-levels(d.raw$genus_species) 
binary_tree.raw$tip.label<-as.character(binary_tree.raw$tip.label) 

phylo_branch.raw<-compute.brlen(binary_tree.raw,method="Grafen",power=1)

phylo_matrix.raw<-vcv(phylo_branch.raw,cor=T) 



###

d.raw<-as.data.frame(d.raw) # convert to dataframe to calculate the VCV matrix
VCV_ARRD.raw<- make_VCV_matrix(d.raw, V = "Var_ARRD", cluster = "shared_measurement_ID", obs = "es_ID") # generate the VCV matrix



meta_ana_model.all<-rma.mv(yi=ARRD~1, V=VCV_ARRD.raw, # run the meta-analytic model with the same structure as before
                           method="REML",
                           random=list(~1|species_ID,
                                            ~1|genus_species,
                                            ~1|es_ID),
                                  R = list(genus_species = phylo_matrix.raw),
                           data=d.raw)

summary(meta_ana_model.all) # results of the model
## 
## Multivariate Meta-Analysis Model (k = 240; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  174.0176  -348.0351  -340.0351  -326.1293  -339.8642   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0090  0.0948     45     no     species_ID   no 
## sigma^2.2  0.0000  0.0037     45     no  genus_species  yes 
## sigma^2.3  0.0007  0.0265    240     no          es_ID   no 
## 
## Test for Heterogeneity:
## Q(df = 239) = 482.8002, p-val < .0001
## 
## Model Results:
## 
## estimate      se     zval    pval    ci.lb   ci.ub 
##  -0.0035  0.0169  -0.2070  0.8360  -0.0366  0.0296    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Plot the results 

orchard_plot(meta_ana_model.all,mod="Int",xlab="ARRD")+ 
        annotate(geom = "text", x = -0.5, y = 1.5, label = paste0("italic(I)^{2} == ", round(i2_ml(meta_ana_model.all)[1] * 100, 2)), color = "black", parse = TRUE, size = 5) + # display heterogeneity
        geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6)+  # change the thickness of prediction intervals
        geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.04, show.legend = FALSE, size = 1)+ # change the thickness of confidence intervals
        annotate(geom = "text", x = -0.32, y = 1.49, label = "%", color = "black", parse = FALSE, size = 5) + 
        geom_point(aes(fill = name), size = 4.6, shape = 21)+ # change mean estimate point size 
        scale_colour_manual(values = "darkcyan")+ # change colour of data points
        scale_fill_manual(values="gold") +  # change colour of the mean estimate
        scale_y_discrete(labels = "Overall mean")+ # rename y label
        scale_size_continuous(range = c(1, 9)) + # change scaling of data points
        theme(text = element_text(size = 20, colour = "black", hjust = 0.5),
              axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
              legend.title = element_text(size=16))

Analysis without the PBT data

The sample size of PBT data was low so we decided to see if including these values influenced our interpretations

meta_ana_model.TL<-run.model(d.TL, ~1) # run the meta-analytic model with the data subset of thermal limits
summary(meta_ana_model.TL)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  205.8310  -411.6620  -403.6620  -389.9976  -403.4801   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0000  0.0069     38     no     species_ID   no 
## sigma^2.2  0.0001  0.0092     38     no  genus_species  yes 
## sigma^2.3  0.0007  0.0271    226     no          es_ID   no 
## 
## Test for Heterogeneity:
## Q(df = 225) = 365.0356, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0056  0.0073  0.7658  0.4438  -0.0087  0.0198    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
orchard_plot(meta_ana_model.TL,mod="Int",xlab="ARRD")+ 
        annotate(geom = "text", x = -0.5, y = 1.5, label = paste0("italic(I)^{2} == ", round(i2_ml(meta_ana_model.TL)[1] * 100, 2)), color = "black", parse = TRUE, size = 5) + # display heterogeneity
        geom_errorbarh(aes(xmin = lowerPR,  xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6)+  # change the thickness of prediction intervals
        geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.04, show.legend = FALSE, size = 1)+ # change the thickness of confidence intervals
        annotate(geom = "text", x = -0.32, y = 1.49, label = "%", color = "black", parse = FALSE, size = 5) + 
        geom_point(aes(fill = name), size = 4.6, shape = 21)+ # change mean estimate point size 
        scale_colour_manual(values = "darkcyan")+ # change colour of data points
        scale_fill_manual(values="gold") +  # change colour of the mean estimate
        scale_y_discrete(labels = "Overall mean")+ # rename y label
        scale_size_continuous(range = c(1, 9)) + # change scaling of data points
        theme(text = element_text(size = 20, colour = "black", hjust = 0.5),
              axis.text.y = element_text(size = 15,colour = "black", hjust = 0.5),
              legend.title = element_text(size=16))

Analyses without the data having major concerns

The major concerns identified in the data were:

  • Mixed varieties : data from two different varieties (which may differ in their thermal tolerance) were pooled in the original study
  • Peculiar methods for estimating Ctmax : CTmax was considered as the temperature at which 50% of the animals reach the endpoint, following an incremental increase in temperature.
  • Peculiar methods for estimating Ctmin : CTmin was considered as the temperature at which 50% of the animals reach the endpoint, following an incremental decrease in temperature.
  • Unequal duration of acclimation : The animals tested in this study were not acclimated for the same absolute duration, but were acclimated for an equivalent proportion of development (i.e. temperature influences development time, so animals acclimated to higher temperature were acclimated for shorter durations to obtain animals at the same developmental stage at the end of the acclimation period)
kable(d$major_concern[d$major_concern != "NA"]) %>%
    kable_styling("striped", position = "left") %>%
    scroll_box(width = "100%", height = "500px")
x
NA
NA
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Unequal duration of acclimation.
Unequal duration of acclimation.
Unequal duration of acclimation.
Unequal duration of acclimation.
NA
NA
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Peculiar method for estimating Ctmin
NA
NA
NA
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Peculiar method for estimating Ctmax
Peculiar method for estimating Ctmax
Peculiar method for estimating Ctmax
Peculiar method for estimating Ctmax
Peculiar method for estimating Ctmax
Peculiar method for estimating Ctmax
NA
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Mixed varieties
NA
NA
d.concerns <- subset(d, ref != "Piyaphongkul et al. 2014")  # remove studies with major concerns
d.concerns <- subset(d.concerns, ref != "Kubisch et al. 2016")
d.concerns <- subset(d.concerns, ref != "Worthen and Haney 1999")
d.concerns <- subset(d.concerns, ref != "Cortemeglia and Beitinger 2006")

meta_ana_model.concerns <- run.model(d.concerns, ~1)  # run the meta-analytic model with this curated data set
summary(meta_ana_model.concerns)
## 
## Multivariate Meta-Analysis Model (k = 226; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  189.2344  -378.4687  -370.4687  -356.8043  -370.2869   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed         factor    R 
## sigma^2.1  0.0001  0.0074     40     no     species_ID   no 
## sigma^2.2  0.0000  0.0069     40     no  genus_species  yes 
## sigma^2.3  0.0009  0.0297    226     no          es_ID   no 
## 
## Test for Heterogeneity:
## Q(df = 225) = 374.3997, p-val < .0001
## 
## Model Results:
## 
## estimate      se    zval    pval    ci.lb   ci.ub 
##   0.0040  0.0065  0.6145  0.5389  -0.0088  0.0168    
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
orchard_plot(meta_ana_model.concerns, mod = "Int", xlab = "ARRD") + annotate(geom = "text",
    x = -0.5, y = 1.5, label = paste0("italic(I)^{2} == ", round(i2_ml(meta_ana_model.concerns)[1] *
        100, 2)), color = "black", parse = TRUE, size = 5) + geom_errorbarh(aes(xmin = lowerPR,
    xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6) +
    geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.04, show.legend = FALSE,
        size = 1) + annotate(geom = "text", x = -0.32, y = 1.49, label = "%", color = "black",
    parse = FALSE, size = 5) + geom_point(aes(fill = name), size = 4.6, shape = 21) +
    scale_colour_manual(values = "darkcyan") + scale_fill_manual(values = "gold") +
    scale_y_discrete(labels = "Overall mean") + scale_size_continuous(range = c(1,
    9)) + theme(text = element_text(size = 20, colour = "black", hjust = 0.5), axis.text.y = element_text(size = 15,
    colour = "black", hjust = 0.5), legend.title = element_text(size = 16))

Graphs for publication

We modified the orchard_plot function to personalise graphs

my.orchard<-function (object, mod = "Int", xlab, N = "none", 
    alpha = 0.5, angle = 90, cb = TRUE, k = TRUE, transfm = c("none", 
        "tanh")) 
{
  
  mod_results<-function (model, mod) ### Changed the mod_results function to incorporate "robust.rma"
{
    if (all(class(model) %in% c("robust.rma", "rma.mv", "rma")) == 
        FALSE) {
        stop("Sorry, you need to fit a metafor model of class rma.mv or rma")
    }
    data <- get_data(model, mod)
    CI <- get_est(model, mod)
    PI <- get_pred(model, mod)
    model_results <- list(mod_table = cbind(CI, PI[, -1]), data = data)
    class(model_results) <- "orchard"
    return(model_results)
  }
  
    transfm <- match.arg(transfm)
    if (any(class(object) %in% c("robust.rma","rma.mv", "rma"))) {
        if (mod != "Int") {
            object <- mod_results(object, mod)
        }
        else {
            object <- mod_results(object, mod = "Int")
        }
    }
    mod_table <- object$mod_table
    data <- object$data
    data$moderator <- factor(data$moderator, levels = mod_table$name, 
        labels = mod_table$name)
    data$scale <- (1/sqrt(data[, "vi"]))
    legend <- "Precision (1/SE)"
    if (any(N != "none")) {
        data$scale <- N
        legend <- "Sample Size (N)"
    }
    if (transfm == "tanh") {
        cols <- sapply(mod_table, is.numeric)
        mod_table[, cols] <- Zr_to_r(mod_table[, cols])
        data$yi <- Zr_to_r(data$yi)
        label <- xlab
    }
    else {
        label <- xlab
    }
    mod_table$K <- as.vector(by(data, data[, "moderator"], 
        function(x) length(x[, "yi"])))
    group_no <- nrow(mod_table)
    cbpl <- c("#E69F00", "#009E73", "#F0E442", 
        "#0072B2", "#D55E00", "#CC79A7", "#56B4E9", 
        "#999999")
    plot <- ggplot2::ggplot(data = mod_table, aes(x = estimate, 
        y = name)) + ggbeeswarm::geom_quasirandom(data = data, 
        aes(x = yi, y = moderator, size = scale, col = moderator), 
        groupOnX = FALSE, alpha = alpha) + ggplot2::geom_errorbarh(aes(xmin = lowerPR, 
        xmax = upperPR), height = 0, show.legend = FALSE, size = 0.5, 
        alpha = 0.6) + ggplot2::geom_errorbarh(aes(xmin = lowerCL, 
        xmax = upperCL), height = 0, show.legend = FALSE, size = 1.2) + 
        ggplot2::geom_vline(xintercept = 0, linetype = 2, colour = "black", 
            alpha = alpha) + ggplot2::geom_point(aes(fill = name), 
        size = 3, shape = 21) + ggplot2::theme_bw() + ggplot2::guides(fill = "none", 
        colour = "none") + ggplot2::theme(legend.position = c(1, 
        0), legend.justification = c(1, 0)) + ggplot2::theme(legend.title = element_text(size = 14)) + #size changed to 14
        ggplot2::theme(legend.direction = "horizontal") + 
        ggplot2::theme(legend.background = element_blank()) + 
        ggplot2::labs(x = label, y = "", size = legend) + 
        ggplot2::theme(axis.text.y = element_text(size = 14, #size changed to 14
            colour = "black", hjust = 0.5, angle = angle))
    if (cb == TRUE) {
        plot <- plot + scale_fill_manual(values = cbpl) + scale_colour_manual(values = cbpl)
    }
    if (k == TRUE) {
        plot <- plot + ggplot2::annotate("text", x = (max(data$yi) - 
            (max(data$yi) * 0.05)), y = (seq(1, group_no, 1) + 
            0.3), label = paste("italic(k)==", mod_table$K), 
            parse = TRUE, hjust = "right", size = 5.5) # size changed to 5.5
    }
    return(plot)
}

FIGURE 2: Overall meta-analytic mean and distribution of effect sizes across the phylogeny

Species-specific estimates were added to the phylogenetic tree and the plot of the meta-analytic mean in Powerpoint. Comestic adjustments were also performed in Powerpoint.

The phylogenetic tree can be found in Phylogenetic tree and variance-covariance matrices

  • Gammarus marinus = considered to be Marinogammarus marinus in the Tree of Life taxonomy
  • Hyale hirtipalma = taken to be Apohyale hirtipalma in the Tree of Life taxonomy
  • Uca panacea = taken to be Leptuca panacea in the Tree of Life taxonomy

Species-specific estimates

d.species.plot<-d # Duplicate dataset to avoid modifications of the original one

d.species.plot$genus_species <- factor(d.species.plot$genus_species,c('Terrapene ornata','Terrapene carolina','Anolis sagrei','Liolaemus pictus','Eutropis longicaudata','Eutropis multifasciata',"Lampropholis coggeri", "Cordylus oelofseni","Hyperolius marmoratus","Pleurodema thaul","Eleutherodactylus coqui","Triturus dobrogicus","Dionda diaboli","Danio rerio","Acanthochromis polyacanthus","Poecilia reticulata","Gambusia affinis","Fundulus heteroclitus","Dasyatis sabina","Ophryotrocha labronica","Helicoverpa zea","Drosophila tripunctata","Drosophila putrida","Drosophila falleni","Drosophila melanogaster","Drosophila simulans","Anopheles funestus","Anopheles arabiensis","Tenebrio molitor", "Harmonia axyridis","Enochrus politus", "Hydroporus sabaudus","Nilaparvata lugens","Exosphaeroma gigas","Exosphaeroma laeviusculum","Apohyale hirtipalma","Hyale grandicornis",'Gammarus chevreuxi','Marinogammarus marinus','Corophium volutator','Crangon crangon','Leptuca panacea','Carcinus maenas','Pardosa furcifera')) # Re-order species name in the same order as the phylogenetic tree


mod.species<-run.model(d.species.plot, ~genus_species-1) # run the model with species name as a moderator to obtain species-specific estimates

result.mod.species<-mod_results(mod.species, "genus_species") # mod_results is a function from the orchaRd package (creates a table of model results)
mod.species.table<-result.mod.species$mod_table # coefficients for each species
data.species <- result.mod.species$data # all data points (used to display individual data points used to generate mean estimates


mod.species.table<-mod.species.table %>%  mutate(taxon=c("Reptiles", "Reptiles", "Reptiles", "Reptiles", "Reptiles","Reptiles", "Reptiles", "Reptiles", "Amphibians", "Amphibians", "Amphibians", "Amphibians","Fishes", "Fishes","Fishes", "Fishes","Fishes", "Fishes","Fishes", "Aquatic Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Terrestrial Invertebrates", "Aquatic Invertebrates", "Aquatic Invertebrates", "Terrestrial Invertebrates", "Aquatic Invertebrates", "Aquatic Invertebrates","Aquatic Invertebrates","Aquatic Invertebrates","Aquatic Invertebrates","Aquatic Invertebrates","Aquatic Invertebrates","Aquatic Invertebrates","Aquatic Invertebrates", "Aquatic Invertebrates", "Terrestrial Invertebrates")) # Add the taxonomic group of each species to the data set to colour points differently for each taxonomic group 


data.species$moderator <- factor(data.species$moderator, levels = mod.species.table$name, labels = mod.species.table$name) # convert the "moderator" (i.e. species name) as a factor and match it with the mod.species.table data 
data.species$precision <- (1/sqrt(data.species[, "vi"])) # calculate the precision of the data points to scale the points on the plot
legend <- "Precision (1/SE)"

mod.species.table$K <- as.vector(by(data.species, data.species[, "moderator"], function(x) length(x[,"yi"]))) # calculate the number of effect sizes for each species
group_no <- nrow(mod.species.table) # number of species
cbpl <- viridis(5) # number of colors, here we took 5 discrete values from the viridis package
    
phylo.plot<-ggplot(data = mod.species.table, aes(x = estimate, y = name)) + 
                   ggbeeswarm::geom_quasirandom(data = data.species, aes(x = yi, y = moderator, size = precision), groupOnX = FALSE, alpha=0.6, colour="grey40") + # geom_quasi random generates some random variation around the points so they do not overlap too much
                   geom_errorbarh(aes(xmin = lowerPR, xmax = upperPR), height = 0, show.legend = FALSE, size = 0.8, alpha = 0.6) + # prediction intervals
                   geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), alpha=0.7, height = 0.2, show.legend = FALSE, size = 1.5) + # confidence intervals
                   geom_vline(xintercept = 0, linetype = 2, colour = "black") + # vertical line at x = 0 (ARRD = 0)
                   geom_point(aes(fill = taxon), size = 6, shape = 21, alpha=1, stroke=1) + # colour each point as a function of the taxonomic group
                   scale_fill_manual(values = cbpl) + # colour the plots according to the cbpl we assigned (viridis(5))
                   labs(x = "ARRD", y = "") +
                   xlim(-1,1.4)+ # change the limit to make it match with the following plot (meta-analytic mean)
                   annotate("text", x = (max(data.species$yi) + (max(data.species$yi) * 0.6)), # add the number of effect sizes to the right panel of the plot
                                    y = (seq(1, group_no, 1) + 0.33), 
                                    label = paste("italic(k)==", mod.species.table$K), 
                                    parse = TRUE, hjust = "right", size = 4.5)+
                   theme_classic()+ # classic theme
                   theme(legend.title = element_text(size = 14), # change font
                         legend.text = element_text(size = 14),
                         legend.background = element_blank(), # remove the background of the legend
                         axis.text.y = element_text(size = 12, colour = "black", hjust = 0.5, angle = 0, face="italic"), # italic
                         panel.background = element_rect(fill="transparent"), # make it transparent
                         plot.background = element_rect(fill="transparent", color=NA))
                         



d.species.plot %>% 
                   group_by(genus_species) %>% # calculate whether UTL, LTL and/or PBT were tested for each species (data used for the symbols displayed on the right side of FIGURE 2)
                                              summarise(
                                                        `LTL` = n_distinct(es_ID[outcome=="LTL"]), 
                                                        `UTL` = n_distinct(es_ID[outcome=="UTL"]),
                                                        `PBT` = n_distinct(es_ID[outcome=="PBT"]))
## # A tibble: 44 x 4
##    genus_species            LTL   UTL   PBT
##    <fct>                  <int> <int> <int>
##  1 Terrapene ornata           0     0     2
##  2 Terrapene carolina         0     0     2
##  3 Anolis sagrei              9     0     0
##  4 Liolaemus pictus           1     0     3
##  5 Eutropis longicaudata      1     0     0
##  6 Eutropis multifasciata     2     0     0
##  7 Lampropholis coggeri       0     2     0
##  8 Cordylus oelofseni         0     0     1
##  9 Hyperolius marmoratus      9     9     0
## 10 Pleurodema thaul           0     0     1
## # ... with 34 more rows

Plot of the meta-analytic mean

ma.plot<-my.orchard(meta_ana_model,mod="Int",xlab="ARRD", alpha=0.2)+
                    scale_y_discrete(labels = "")+ # no labels
                    geom_vline(xintercept = 0, linetype = 2, colour = "black")+ # vertical line at ARRD = 0
                    geom_errorbarh(aes(xmin = lowerPR, xmax = upperPR), height = 0, show.legend = FALSE, size = 0.75, alpha = 0.6)+ # prediction intervals
                    geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.1, show.legend = FALSE, size = 1, alpha=0.85)+ # confidence intervals
                    geom_point(aes(fill = name),size = 4, shape = 23, alpha=1)+ # change shape to a triangle
                    scale_fill_manual(values="red") + # change colour of the estimate
                    scale_colour_manual(values="grey40") + # change colour of the data points
                    xlim(-1,1.4)+ # match xlim with phylo_plot
                    theme_classic()+ # classic theme
                    theme(panel.background = element_rect(fill="transparent"), # personalise theme 
                          plot.background = element_rect(fill="transparent", color=NA),
                          axis.text.x = element_text(size = 16, colour = "black", hjust = 0.5, angle = 0),
                          text = element_text(size = 20, hjust=0.42, vjust=-0.4),
                          legend.position="none")

Combine the species-specific estimates with the meta-analytic mean

phylo.plot/ma.plot + plot_layout(heights = c(15, 1.8))  # combine the two plots

ggsave("output/Fig_2.png", width = 10, height = 16.8, dpi = 800, bg = "transparent")  # save the plot. Cosmetics modifications were then performed in Powerpoint

FIGURE 3: Mean acclimation response ratio (ARR) of males and females

We created an alternative data set d.fm where the ARR was not separated according to the animal’ sex and “sex” was coded as a moderator. The formula to calculate the sampling variance of ARR, Var_ARR was adjusted (see below)

# Mean ARR values of males and females

d.fm<-read_csv("data/data_plot_fm.csv") # load the data set 
d.fm<-subset(d.fm, ref!="Hernandez et al. 2002") # Remove the outlier 

d.fm<-d.fm %>% # calculate effect sizes
              mutate(ARR=(mean_high-mean_low)/(acc_temp_high - acc_temp_low),
                     Var_ARR=((1/(acc_temp_high-acc_temp_low))^2*(sd_low^2/n_low_adj+sd_high^2/n_high_adj)), # The formula of 'Var_ARR" was modified because it was not calculated on a comparison
                     precision=(1/sqrt(Var_ARR)))
                     


  d.fm$es_ID=as.factor(d.fm$es_ID) # Convert to factors the variables used as random effects
  d.fm$species_ID=as.factor(d.fm$species_ID)
  d.fm$shared_measurement_ID=as.factor(d.fm$shared_measurement_ID)
  d.fm$sex=as.factor(d.fm$sex)
  


d.fm<-as.data.frame(d.fm) # convert to a data frame
VCV_ARR<- make_VCV_matrix(d.fm, V = "Var_ARR", cluster = "shared_measurement_ID", obs = "es_ID") # calculate a VCV matrix for the sampling variance of ARR

fm.model<-rma.mv(yi=ARR~sex-1, V=VCV_ARR, # the random effect structure was used, but here the response variable is ARR and the sampling variance is different. 
                   method="REML",
                   random=list(~1|species_ID,
                               ~1|es_ID), # all possible random effects
                   data=d.fm)
summary(fm.model) # Summary of the model
## 
## Multivariate Meta-Analysis Model (k = 478; method: REML)
## 
##    logLik   Deviance        AIC        BIC       AICc 
##  198.8744  -397.7487  -389.7487  -373.0871  -389.6638   
## 
## Variance Components:
## 
##             estim    sqrt  nlvls  fixed      factor 
## sigma^2.1  0.0197  0.1403     44     no  species_ID 
## sigma^2.2  0.0083  0.0913    478     no       es_ID 
## 
## Test for Residual Heterogeneity:
## QE(df = 476) = 16529.3011, p-val < .0001
## 
## Test of Moderators (coefficients 1:2):
## QM(df = 2) = 25.7472, p-val < .0001
## 
## Model Results:
## 
##            estimate      se    zval    pval   ci.lb   ci.ub 
## sexfemale    0.1194  0.0236  5.0565  <.0001  0.0731  0.1657  *** 
## sexmale      0.1121  0.0236  4.7431  <.0001  0.0658  0.1584  *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Plot the results

my.orchard(fm.model,mod="sex",xlab="ARR")+
           geom_errorbarh(aes(xmin = lowerPR, xmax = upperPR), height = 0, show.legend = FALSE, size = 0.75, alpha = 0.5)+ # prediction intervals
           geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.05, show.legend = FALSE, size = 1.75)+ # confidence intervals
           geom_point(aes(fill = name),  size = 6, shape = 21, stroke=1.2)+ # mean estimate
           scale_colour_manual(values = c("darkorange","purple"))+ # change colours
           scale_fill_manual(values=c("darkorange","purple"))+ 
           scale_size_continuous(range = c(1, 9))+ # change point scaling
           scale_x_continuous(breaks = c(-0.5,0,0.5,1, 1.5))+ # change cuts on the x axis
           theme(text = element_text(size = 24), # change font sizes
                 legend.title = element_text(size = 15),
                 legend.text = element_text(size = 13))

ggsave("output/Fig_3.png", width=10, height=7, dpi=1200, bg="transparent") # save the plot

FIGURE 4: Sexual dimorphism in acclimation capacity for different types of outcome variable, as a function of the habitat (A), origin (B), extent of sexual size dimorphism (C) and duration of acclimation (D)

Figure 4A and Figure 4B

# Create a function to run both plots with the same structure 

plot.four.levels.pub<-function(data,formula,moderator){
  model<-run.model(data,formula) #Run the model that will be used for the plot (must be a model without intercept)
          my.orchard(model, mod=moderator,xlab="ARRD")+ #Create an orchard plot
          geom_errorbarh(aes(xmin = lowerPR, xmax = upperPR), height = 0, show.legend = FALSE, size = 0.75, alpha = 0.5)+
          geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.075, show.legend = FALSE, size = 1.25)+
          geom_point(aes(fill = name), size = 3.8, shape = 21, stroke=1.2)+
          scale_size_continuous(range = c(1, 10))+  
          scale_colour_manual(values = c("dodgerblue2","royalblue2","orange2","sienna2"))+
          scale_fill_manual(values=c("dodgerblue2","royalblue2","orange2","sienna2"))+
          xlim(-0.6, 0.87)+
          theme(text = element_text(size = 24), 
                legend.position = c(1,0.01), 
                panel.border = element_rect(colour = "black", fill=NA, size=1), 
                axis.text.y = element_text(size = 16,colour = "black", hjust = 0.5, angle = 0), 
                axis.text.x=element_text(size=16),
                legend.text=element_text(size=15))
}


p4A<-plot.four.levels(d.TL,~int.habitat_outcome-1,"int.habitat_outcome")+
          geom_errorbarh(aes(xmin = lowerPR, xmax = upperPR), height = 0, show.legend = FALSE, size = 0.75, alpha = 0.5)+
          geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.075, show.legend = FALSE, size = 1.25)+
          geom_point(aes(fill = name), size = 3.8, shape = 21, stroke=1.2)+
          scale_size_continuous(range = c(1, 10))+  
          scale_colour_manual(values = c("#00BFC4","#00BBD8","coral1","coral2"))+
          scale_fill_manual(values=c("#00BFC4","#00BBD8","coral1","coral2"))+
          xlim(-0.6, 0.87)+
          theme(text = element_text(size = 24), 
                legend.position = c(1,0.01), 
                panel.border = element_rect(colour = "black", fill=NA, size=1), 
                axis.text.y = element_text(size = 16,colour = "black", hjust = 0.5, angle = 0), 
                axis.text.x=element_text(size=16),
                legend.text=element_text(size=15))+
                         annotate("text", x=0.87,y=0.65, label="A", size=8)+
                         annotate("text", x=0.4,y=2, label="*", size=18 ,col="#00BBD8")+
                         coord_flip()


p4B<-my.orchard(robust.rma.mv(run.model(d.TL, ~int.origin_outcome - 1), cluster = d.TL$species_ID), mod="int.origin_outcome", xlab="ARRD")+
          geom_errorbarh(aes(xmin = lowerPR, xmax = upperPR), height = 0, show.legend = FALSE, size = 0.75, alpha = 0.5)+
          geom_errorbarh(aes(xmin = lowerCL, xmax = upperCL), height = 0.075, show.legend = FALSE, size = 1.25)+
          geom_point(aes(fill = name), size = 3.8, shape = 21, stroke=1.2)+
          scale_size_continuous(range = c(1, 10))+
          scale_colour_manual(values = c("#00BFC4","#00BBD8","coral1","coral2"))+
          scale_fill_manual(values=c("#00BFC4","#00BBD8","coral1","coral2"))+
          xlim(-0.6, 0.87)+
          theme(text = element_text(size = 24),
                legend.position = c(1,0.01),
                panel.border = element_rect(colour = "black", fill=NA, size=1),
                axis.text.y = element_text(size = 16,colour = "black", hjust = 0.5, angle = 0),
                axis.text.x=element_text(size=16),
                legend.text=element_text(size=15))+
                         annotate("text", x=0.87,y=0.65, label="B", size=8)+
                         annotate("text", x=0.5,y=4,label="*", size=18, col="coral2")+
                         coord_flip()



p4A+p4B # combine plots 

ggsave("output/Fig_4AB.png", width=14, height=8, dpi=1200)

Figures 4C and 4D

The four figures were then combined in Powerpoint and we made some cosmetics adjustments. For some reason, this part of the code, although working, does not knit. Therefore, I pasted the code as comments for it to appear in the knitted file.

# ##### Figure 4C ##### MDI_model<-run.model(d,~MDI) pred_MDI_model <-
# predict.rma(robust.rma.mv(MDI_model, cluster=d$species_ID))
# d.MDI<-subset(d,MDI!='NA') d.MDI <- mutate(d.MDI, ci.lb =
# pred_MDI_model$ci.lb, ci.ub = pred_MDI_model$ci.ub, fit =
# pred_MDI_model$pred) p4C<-ggplot(d,aes(x = MDI, y = ARRD, fill=outcome)) +
# geom_point(aes(size=(1/sqrt(Var_ARRD)), col=outcome), shape=21, alpha=0.7,
# col='gray35', stroke=0.1) + geom_ribbon(data=d.MDI,aes(ymin = ci.lb, ymax =
# ci.ub, color = NULL), alpha = .3, fill = 'grey30') +
# geom_line(data=d.MDI,aes(y = fit), size = 1.5, colour = 'black')+
# scale_fill_manual(values=c('#00BDD0','#CF78FF','coral2'))+ labs(x = 'Body
# mass dimorphism index', y = 'ARRD', size = 'Precision (1/SE)') +
# scale_size_continuous(range = c(1, 11)) + annotate('text', x=-3,y=0.87,
# label='C', size=8)+ annotate('text', x=-2.5,y=-0.15, label='*', size=18,
# col='black')+ geom_hline(yintercept = 0,linetype = 2, colour = 'black',
# alpha=0.8)+ geom_vline(xintercept = 0,linetype = 2, colour =
# 'black',alpha=0.5) + ylim(-0.6,0.87) + theme_bw() + theme(text =
# element_text(size = 24), axis.text.y = element_text(size = 16, colour =
# 'black', hjust = 0.5, angle = 0), axis.text.x = element_text(size = 16,
# colour = 'black', hjust = 0.5, angle = 0), axis.title.x =
# element_text(hjust=0.6,vjust=-0.5), legend.title = element_text(size = 14),
# legend.text = element_text(size = 14), legend.position = c(1, 1),
# legend.justification = c(1,1), legend.box.just = 'right', legend.direction =
# 'horizontal', legend.background = element_blank(), panel.border =
# element_rect(colour = 'black', fill=NA, size=1))+ guides(fill = 'none',
# colour = 'none') # Remove legend (they were added manually in Powerpoint)
# #### Figure 4D #### d.acc.UTL<-subset(d.UTL,acc_duration!='NA')
# d.acc.LTL<-subset(d.LTL,acc_duration!='NA') ## Prediction: Outcome = UTL
# acc_model.UTL<-run.model(d.acc.UTL,~z_acc_duration) pred_acc_model.UTL<-
# predict.rma(robust.rma.mv(acc_model.UTL, cluster=d.acc.UTL$species_ID))
# d.acc.UTL <- mutate(d.acc.UTL, ci.lb = pred_acc_model.UTL$ci.lb, ci.ub =
# pred_acc_model.UTL$ci.ub, fit = pred_acc_model.UTL$pred) ## Prediction:
# Outcome = LTL acc_model.LTL<-run.model(d.acc.LTL,~z_acc_duration)
# pred_acc_model.LTL<- predict.rma(robust.rma.mv(acc_model.LTL,
# cluster=d.acc.LTL$species_ID)) d.acc.LTL <- mutate(d.acc.LTL, ci.lb =
# pred_acc_model.LTL$ci.lb, ci.ub = pred_acc_model.LTL$ci.ub, fit =
# pred_acc_model.LTL$pred) p4D<-ggplot(data=d.TL, aes(x=acc_duration, y=ARRD,
# fill=outcome))+ geom_point(aes(size=(1/sqrt(Var_ARRD)), col=outcome),
# shape=21, alpha=0.7, col='gray35', stroke=0.1) +
# geom_ribbon(data=d.acc.UTL,aes(ymin = ci.lb, ymax = ci.ub, color = NULL),
# alpha = .3) + geom_ribbon(data= d.acc.LTL,aes(ymin = ci.lb, ymax = ci.ub,
# color = NULL), alpha = .3) + geom_line(data=d.acc.UTL,aes(y = fit), size =
# 1.5, col='coral2')+ geom_line(data= d.acc.LTL,aes(y = fit), size = 1.5,
# col='#00BDD0')+ scale_fill_manual(values=c('#00BDD0','coral2'))+
# scale_color_manual(values=c('#00BDD0','coral2'))+ labs(x = 'Duration of
# acclimation (days)', y = 'ARRD', size = 'Precision (1/SE)') +
# scale_size_continuous(range = c(1, 11)) + scale_x_continuous(breaks =
# c(0,50,100))+ annotate('text', x=0,y=0.87, label='D', size=8)+
# annotate('text', x=70,y=-0.18, label='*', size=18 ,col='#00BDD0')+
# geom_hline(yintercept = 0,linetype = 2, colour = 'black', alpha=0.8)+
# ylim(-0.6,0.87) + theme_bw() + theme(text = element_text(size = 24),
# axis.text.y = element_text(size = 16, colour = 'black', hjust = 0.5, angle =
# 0), axis.text.x = element_text(size = 16, colour = 'black', hjust = 0.5,
# angle = 0), axis.title.x = element_text(hjust=0.6,vjust=-0.5), legend.title =
# element_text(size = 14), legend.text = element_text(size = 14),
# legend.position = c(1, 1), legend.justification = c(1,1), legend.box.just =
# 'right', legend.direction = 'horizontal', legend.background =
# element_blank(), panel.border = element_rect(colour = 'black', fill=NA,
# size=1))+ guides(fill = 'none', colour = 'none') # Remove legend (they were
# added manually in Powerpoint) p4C+p4D

Software and packages versions

sessionInfo()
## R version 4.1.0 (2021-05-18)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19042)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_Australia.1252  LC_CTYPE=English_Australia.1252   
## [3] LC_MONETARY=English_Australia.1252 LC_NUMERIC=C                      
## [5] LC_TIME=English_Australia.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] GGally_2.1.1       MuMIn_1.43.17      car_3.0-11         carData_3.0-4     
##  [5] orchaRd_0.0.0.9000 patchwork_1.1.1    metafor_2.4-0      Matrix_1.3-3      
##  [9] ape_5.5            rotl_3.0.11        maps_3.3.0         cowplot_1.1.1     
## [13] viridis_0.6.1      viridisLite_0.4.0  DataExplorer_0.8.2 kableExtra_1.3.4  
## [17] forcats_0.5.1      stringr_1.4.0      dplyr_1.0.6        purrr_0.3.4       
## [21] readr_1.4.0        tidyr_1.1.3        tibble_3.1.2       ggplot2_3.3.3     
## [25] tidyverse_1.3.1   
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-152       fs_1.5.0           lubridate_1.7.10   RColorBrewer_1.1-2
##  [5] webshot_0.5.2      progress_1.2.2     httr_1.4.2         tools_4.1.0       
##  [9] backports_1.2.1    bslib_0.2.5.1      utf8_1.2.1         R6_2.5.0          
## [13] DBI_1.1.1          colorspace_2.0-1   withr_2.4.2        tidyselect_1.1.1  
## [17] gridExtra_2.3      prettyunits_1.1.1  curl_4.3.1         compiler_4.1.0    
## [21] cli_3.0.0          rvest_1.0.0        formatR_1.11       xml2_1.3.2        
## [25] bookdown_0.22      sass_0.4.0         scales_1.1.1       systemfonts_1.0.2 
## [29] digest_0.6.27      foreign_0.8-81     rmarkdown_2.9      svglite_2.0.0     
## [33] rio_0.5.27         rentrez_1.2.3      pkgconfig_2.0.3    htmltools_0.5.1.1 
## [37] dbplyr_2.1.1       htmlwidgets_1.5.3  rlang_0.4.11       readxl_1.3.1      
## [41] rstudioapi_0.13    jquerylib_0.1.4    generics_0.1.0     jsonlite_1.7.2    
## [45] zip_2.2.0          magrittr_2.0.1     Rcpp_1.0.7         munsell_0.5.0     
## [49] fansi_0.4.2        abind_1.4-5        lifecycle_1.0.0    stringi_1.6.1     
## [53] yaml_2.2.1         plyr_1.8.6         grid_4.1.0         parallel_4.1.0    
## [57] crayon_1.4.1       rncl_0.8.4         lattice_0.20-44    haven_2.4.1       
## [61] hms_1.1.0          knitr_1.33         pillar_1.6.1       igraph_1.2.6      
## [65] stats4_4.1.0       reprex_2.0.0       XML_3.99-0.6       glue_1.4.2        
## [69] evaluate_0.14      data.table_1.14.0  modelr_0.1.8       vctrs_0.3.8       
## [73] rmdformats_1.0.2   networkD3_0.4      cellranger_1.1.0   gtable_0.3.0      
## [77] reshape_0.8.8      assertthat_0.2.1   openxlsx_4.2.4     xfun_0.23         
## [81] broom_0.7.8        ellipsis_0.3.2