Genetic (co)variance selection response
To test whether genetic variances decreased with selection and whether the structure of the genetic variance-covariance matrix was affected by selection, we first ran multi-response animal models implemented in the R-package ‘MCMCglmm’. We limited our analyses to the four components that have been show to affect male response: Z9-16:Ald, Z11-16:Ald, Z11-16:OAc, and Z11-16:OH (in all cases, the log-contrast to 14:Ald was used). Model formulation roughly followed the MCMCglmm manual (Hadfield, 2010) and Jarrod Hadfield’s course notes (Hadfield, 2012), as well as the animal model tutorial by Pierre de Villemereuil (Villemereuil, 2012). High and low line individuals had separate pedigrees, but shared ancestors for which we had pedigree data up to three generations prior to the onset of the experiment (in total 1,065 breeding females). To minimize the influence from priors on the covariances, for which we had no prior expectations with high degrees of belief, we formulated flat, uninformative priors for the variance-covariance structure of the random effect (‘animal’). To evaluate the models, we checked chain convergence and assessed effective sample sizes and levels of autocorrelation. To check whether the prior did not contribute unduly to posterior estimates, we also compared genetic (co)variance estimates among univariate, bi-variate, and full (tetra-variate) models and using different, more informative priors. We found models with flat priors to perform best.
To observe changes in genetic (co)variances at higher sample sizes, we partitioned the data in the starting generation (generation 0) and generation blocks of three generations each (1 – 3, 4 – 6, 7 – 9) for both the high and low line. For each generation block, we obtained posterior estimates of the additive genetic variance, VAfor each of the four log-contrasts from the multi-response animal model. For each posterior sample of VA, we calculated the coefficient of additive genetic variance, CVA (where\(\text{CV}_{\text{A\ }}=\frac{V_{A}}{\text{phenotypic\ mean}}\)), which provides a standardized measure of the evolvability of a trait that is independent of other variance components. We also extracted the posterior genetic correlations and visually inspected pairwise genetic correlations between Z11-16:OAc and each of the other three components. Lastly, we examined changes in the G matrix by inspecting the trait loadings on genetic principle components. The four genetic principle components were obtained for every posterior sample using the ‘eigen’ function. We focused on the first two axes, gPC1 (also known asgmax , the direction in phenotypic space containing the largest fraction of the genetic variance) and gPC2, because these axes jointly described > 90% of the genetic variance (see Results).