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).