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Supplementary material reporting R code for the manuscript ‘Stronger net selection on males across animals’.

Phenotypic gambit

Statistical analyses were carried out in two steps. First, we examined the key assumption of the ‘phenotypic gambit’ by testing whether estimates of phenotypic variance predict the estimated genetic variance. For this we computed the Pearson correlation coefficient r, testing the relationship between CVP and CVG for both sexes and the two fitness components separately. In addition, we tested whether the sex bias in CVP translates into a sex bias in CVG by correlating the coefficient of variation ratio lnCVR (Nakagawa et al. 2015), which refers to the ln-transformed ratio of male CV to female CV, with positive values indicating a male bias. The analyses on the phenotypic gambit were motivated from a methodological perspective and we did not expect that inter-specific variation in the difference between CVP and CVG can be explained by a shared phylogenetic history. However, for completeness, we also ran correlations on phylogenetic independent contrasts (PICs; computed using the ape R-package (version 5.4.1) in R (Paradis & Schliep 2019)) to test whether our findings were robust when accounting for potential phylogenetic non-independence. We report Pearson’s correlation coefficients r for normally distributed data and Spearman’s rho if assumptions of normality were violated.

Load and prepare data

Stronger net selection on males (PGLMMs)

In this second part of the anlysis, we tested the hypothesis that net selection is stronger on males by testing for a male bias in CVP and CVG. Specifically, we ran Phylogenetic General Linear Mixed-Effects Models (PGLMMs) with CVP or CVG as the response variable, and sex as a fixed effect. To account for the paired data structure, we added an observation identifier as a random effect. Moreover, all models included a study identifier and the phylogeny (transformed into a correlation matrix) as random effects to account for statistical non-independence arising from shared study design or phylogenetic history, respectively. Note that the latter also accounts for the non-independence of estimates obtained from the same species as some studies estimated genetic variances from distinct field populations (Fox et al. 2004) or different experimental treatments under laboratory conditions such as food stress (Holman & Jacomb 2017) and temperature stress (Berger et al. 2014). In an additional series of PGLMMs we tested whether our proxy of sexual selection explained inter-specific variation in the sex-differences of CVP or CVG by adding mating system and its interaction with sex as fixed effects to the models. Finally, given that primary studies varied in the empirical approach used to quantify CVP and CVG, we also used PGLMMs to test whether study type (23 field studies versus 32 laboratory studies) represented a methodological determinant of the observed sex-differences in CVP and CVG. All PGLMMs were ran with the MCMCglmm R-package (version 2.2.9) (Hadfield 2010), using uninformative priors (V = 1, nu = 0.002) and an effective sample size of 20000 (number of iterations = 11000000, burn-in = 1000000, thinning interval = 500). We computed the proportion of variance explained by fixed factors (‘marginal R2’) (Nakagawa & Schielzeth 2013). In addition, we quantified the phylogenetic signal as the phylogenetic heritability H2 (i.e., proportional variance in CVP or CVG explained by species identity), which is equivalent to Pagel’s 𝜆 (de Villemereuil & Nakagawa 2014). In a previous study testing for sex-specific phenotypic variances in reproductive success (Janicke et al. 2016), we ran formal meta-analyses using lnCVR as the tested effect size (Nakagawa et al. 2015). This is potentially a more powerful approach for comparing phenotypic variances but rendered unsuitable when comparing genetic variances. This is because the computation of the sampling variance of lnCVR is a function of the sample size of the sampled population and the point estimate of lnCVR (Nakagawa et al. 2015). However, genetic variances are estimates from statistical models and notorious for being estimated with low precision (i.e. have large confidence intervals). Therefore, using a meta-analytic approach for genetic variances using lnCVR as an effect size leads to overconfident estimation of the global effect size and is therefore likely to result in type-II-errors. However, to allow comparison with the previous meta-analysis, we report the outcome of phylogenetic meta-analyses on phenotypic variances using lnCVR in the Supplementary Material (Table S2), which largely reflects the results on the point estimates of CVP from PGLMMs.

Run MCMC models

We then ran MCMC models to test for differences in the phenotypic and genetic variances in males and females for the fitness categories reproductive success and lifespan.

First we prune the phylogenetic tree to the data subset.

We then check if the phylogenetic tree was correctly build.

Next, we set the priors for the MCMC models using uninformative priors (V = 1, nu = 0.002) and an effective sample size of 20000 (number of iterations = 11000000, burn-in = 1000000, thinning interval = 500). We also set the index and study ID as factors.

MCMC models for reproductive success

First, we ran the MCMC testing for overall differences in phenotypic variance in reproductive success (‘phenCV’) between males and females (‘Sex’). The model includes the species (‘animal’), estimate ID (‘Index’) and study ID (‘Study_ID’) as random factors.


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 Iterations = 10001:109501
 Thinning interval  = 500
 Sample size  = 200 

 DIC: 50.08103 

 G-structure:  ~animal

       post.mean  l-95% CI u-95% CI eff.samp
animal    0.0215 0.0004836  0.08548      200

               ~Index

      post.mean l-95% CI u-95% CI eff.samp
Index   0.05882 0.001148   0.1242    267.8

               ~Study_ID

         post.mean l-95% CI u-95% CI eff.samp
Study_ID   0.06306 0.000233   0.1526    200.3

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units   0.06034  0.03996  0.08267    117.8

 Location effects: phenCV ~ factor(Sex) 

                       post.mean l-95% CI u-95% CI eff.samp  pMCMC   
(Intercept)               0.6897   0.5147   0.9442      200 <0.005 **
factor(Sex)phenCV_male    0.2316   0.1426   0.2996      200 <0.005 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

We then expanded the model to include the matingsytem as a covariate (‘Mating_system’).


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 Iterations = 10001:109501
 Thinning interval  = 500
 Sample size  = 200 

 DIC: 31.00689 

 G-structure:  ~animal

       post.mean  l-95% CI u-95% CI eff.samp
animal    0.0415 0.0009463   0.1245      200

               ~Index

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Index   0.06553 0.0006622   0.1327    345.3

               ~Study_ID

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Study_ID   0.05893 0.0002484   0.1553      139

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units   0.05102   0.0327   0.0685      200

 Location effects: phenCV ~ factor(Sex) * factor(Mating_system) 

                                                     post.mean  l-95% CI
(Intercept)                                           0.705011  0.331216
factor(Sex)phenCV_male                               -0.008772 -0.203472
factor(Mating_system)polygamy                         0.008150 -0.297388
factor(Sex)phenCV_male:factor(Mating_system)polygamy  0.319035  0.120912
                                                      u-95% CI eff.samp  pMCMC
(Intercept)                                           1.091192      200   0.01
factor(Sex)phenCV_male                                0.136592      200   0.94
factor(Mating_system)polygamy                         0.489325      200   0.98
factor(Sex)phenCV_male:factor(Mating_system)polygamy  0.483260      200 <0.005
                                                       
(Intercept)                                          * 
factor(Sex)phenCV_male                                 
factor(Mating_system)polygamy                          
factor(Sex)phenCV_male:factor(Mating_system)polygamy **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

In an additional model, we included the study type (‘StudyType’), i.e. if the data were obtained in laboratory or field experiments.


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 Iterations = 10001:109501
 Thinning interval  = 500
 Sample size  = 200 

 DIC: 51.0445 

 G-structure:  ~animal

       post.mean  l-95% CI u-95% CI eff.samp
animal   0.01296 0.0002984  0.04841      200

               ~Index

      post.mean l-95% CI u-95% CI eff.samp
Index   0.06457 0.005559   0.1166    228.2

               ~Study_ID

         post.mean  l-95% CI u-95% CI eff.samp
Study_ID   0.04607 0.0004687   0.1219      200

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units   0.05913  0.03754  0.08295      200

 Location effects: phenCV ~ factor(Sex) * factor(StudyType) 

                                                   post.mean l-95% CI u-95% CI
(Intercept)                                          0.88229  0.69786  1.13647
factor(Sex)phenCV_male                               0.19596  0.07779  0.32654
factor(StudyType)Laboratory                         -0.32085 -0.60583 -0.04419
factor(Sex)phenCV_male:factor(StudyType)Laboratory   0.06189 -0.11074  0.21244
                                                   eff.samp  pMCMC   
(Intercept)                                           215.5 <0.005 **
factor(Sex)phenCV_male                                200.0   0.01 * 
factor(StudyType)Laboratory                           200.0   0.03 * 
factor(Sex)phenCV_male:factor(StudyType)Laboratory    200.0   0.45   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Next, we ran the MCMC models examining the genetic variance in reproductive success (‘genCV’). First, the overall model for a sex difference.


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 Iterations = 10001:109501
 Thinning interval  = 500
 Sample size  = 200 

 DIC: -130.0802 

 G-structure:  ~animal

       post.mean  l-95% CI u-95% CI eff.samp
animal   0.01198 0.0004535  0.04331      200

               ~Index

      post.mean  l-95% CI u-95% CI eff.samp
Index  0.003847 0.0003005 0.009868      200

               ~Study_ID

         post.mean l-95% CI u-95% CI eff.samp
Study_ID   0.01471 0.004494  0.02548    248.7

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units   0.01497 0.009596  0.02006      200

 Location effects: genCV ~ factor(Sex) 

                      post.mean l-95% CI u-95% CI eff.samp  pMCMC   
(Intercept)             0.24615  0.13462  0.37596    200.0 <0.005 **
factor(Sex)genCV_male   0.08424  0.04133  0.12205    149.8 <0.005 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Secondly, including the matingsytem as a covariate (‘Mating_system’).


                       MCMC iteration = 0

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                       MCMC iteration = 110000

 Iterations = 10001:109501
 Thinning interval  = 500
 Sample size  = 200 

 DIC: -138.7594 

 G-structure:  ~animal

       post.mean  l-95% CI u-95% CI eff.samp
animal   0.01056 0.0002717  0.03152      200

               ~Index

      post.mean  l-95% CI u-95% CI eff.samp
Index  0.004712 0.0004249  0.01062      200

               ~Study_ID

         post.mean l-95% CI u-95% CI eff.samp
Study_ID   0.01545 0.005762  0.03144    156.5

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units   0.01356 0.009133  0.01777      200

 Location effects: genCV ~ factor(Sex) * factor(Mating_system) 

                                                    post.mean  l-95% CI
(Intercept)                                          0.254980  0.103623
factor(Sex)genCV_male                               -0.015821 -0.088028
factor(Mating_system)polygamy                       -0.007049 -0.146419
factor(Sex)genCV_male:factor(Mating_system)polygamy  0.135581  0.032283
                                                     u-95% CI eff.samp  pMCMC
(Intercept)                                          0.455024    200.0 <0.005
factor(Sex)genCV_male                                0.071933    200.0   0.74
factor(Mating_system)polygamy                        0.143565    272.4   0.98
factor(Sex)genCV_male:factor(Mating_system)polygamy  0.232928    246.3 <0.005
                                                      
(Intercept)                                         **
factor(Sex)genCV_male                                 
factor(Mating_system)polygamy                         
factor(Sex)genCV_male:factor(Mating_system)polygamy **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

And finally, we included the study type (‘StudyType’), i.e. if the data were obtained in laboratory or field experiments.


                       MCMC iteration = 0

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                       MCMC iteration = 110000

 Iterations = 10001:109501
 Thinning interval  = 500
 Sample size  = 200 

 DIC: -127.4064 

 G-structure:  ~animal

       post.mean  l-95% CI u-95% CI eff.samp
animal   0.01346 0.0004328  0.03499      200

               ~Index

      post.mean  l-95% CI u-95% CI eff.samp
Index  0.003754 0.0003163  0.00981    142.8

               ~Study_ID

         post.mean l-95% CI u-95% CI eff.samp
Study_ID    0.0143 0.003386   0.0273      200

 R-structure:  ~units

      post.mean l-95% CI u-95% CI eff.samp
units   0.01555  0.01059  0.02143      200

 Location effects: genCV ~ factor(Sex) * factor(StudyType) 

                                                  post.mean  l-95% CI  u-95% CI
(Intercept)                                        0.171715 -0.088682  0.386666
factor(Sex)genCV_male                              0.080874  0.023493  0.161411
factor(StudyType)Laboratory                        0.127308 -0.071792  0.395470
factor(Sex)genCV_male:factor(StudyType)Laboratory  0.002628 -0.074388  0.084146
                                                  eff.samp pMCMC  
(Intercept)                                          142.8  0.11  
factor(Sex)genCV_male                                258.0  0.04 *
factor(StudyType)Laboratory                          129.2  0.27  
factor(Sex)genCV_male:factor(StudyType)Laboratory    246.0  0.95  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

R version 4.0.0 (2020-04-24)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19041)

Matrix products: default

locale:
[1] LC_COLLATE=German_Germany.1252  LC_CTYPE=German_Germany.1252   
[3] LC_MONETARY=German_Germany.1252 LC_NUMERIC=C                   
[5] LC_TIME=German_Germany.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] readr_1.4.0                ggplot2_3.3.3             
 [3] data.table_1.14.0          stargazer_5.2.2           
 [5] dplyr_1.0.5                MCMCglmm_2.32             
 [7] coda_0.19-4                tidyr_1.1.3               
 [9] PerformanceAnalytics_2.0.4 xts_0.12.1                
[11] zoo_1.8-9                  matrixcalc_1.0-3          
[13] outliers_0.14              psych_2.1.3               
[15] multcomp_1.4-16            TH.data_1.0-10            
[17] survival_3.1-12            mvtnorm_1.1-1             
[19] pwr_1.3-0                  MASS_7.3-51.5             
[21] metafor_2.4-0              Matrix_1.2-18             
[23] ape_5.4-1                  workflowr_1.6.2           

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.6        lattice_0.20-41   corpcor_1.6.9     assertthat_0.2.1 
 [5] rprojroot_2.0.2   digest_0.6.27     utf8_1.2.1        R6_2.5.0         
 [9] evaluate_0.14     highr_0.8         pillar_1.5.1      rlang_0.4.10     
[13] cubature_2.0.4.1  whisker_0.4       rmarkdown_2.7     splines_4.0.0    
[17] stringr_1.4.0     munsell_0.5.0     compiler_4.0.0    httpuv_1.6.1     
[21] xfun_0.22         pkgconfig_2.0.3   mnormt_2.0.2      tmvnsim_1.0-2    
[25] htmltools_0.5.1.1 tidyselect_1.1.0  tibble_3.1.0      tensorA_0.36.2   
[29] quadprog_1.5-8    codetools_0.2-16  fansi_0.4.2       withr_2.4.1      
[33] crayon_1.4.1      later_1.2.0       grid_4.0.0        gtable_0.3.0     
[37] nlme_3.1-147      lifecycle_1.0.0   DBI_1.1.1         git2r_0.28.0     
[41] magrittr_2.0.1    scales_1.1.1      stringi_1.5.3     fs_1.5.0         
[45] promises_1.2.0.1  ellipsis_0.3.1    vctrs_0.3.6       generics_0.1.0   
[49] sandwich_3.0-0    tools_4.0.0       glue_1.4.2        purrr_0.3.4      
[53] hms_1.0.0         parallel_4.0.0    yaml_2.2.1        colorspace_2.0-0 
[57] knitr_1.31