Evolutionary optimum for male sexual traits characterized using the multivariate Robertson-Price Identity

Phenotypes tend to remain relatively constant in natural populations, suggesting a limit to trait evolution. Although stationary phenotypes suggest stabilizing selection, directional selection is more commonly reported. However, selection on phenotypes will have no evolutionary consequence if the traits do not genetically covary with fitness, a covariance known as the Robertson-Price Identity. The nature of this genetic covariance determines if phenotypes will evolve directionally or whether they reside at an evolutionary optimum. Here, we show how a set of traits can be shown to be under net stabilizing selection through an application of the multivariate Robertson-Price Identity. We characterize how a suite of male sexual displays genetically covaries with fitness in a population of Drosophila serrata. Despite strong directional sexual selection on these phenotypes directly and significant genetic variance in them, little genetic covariance was detected with overall fitness. Instead, genetic analysis of trait deviations showed substantial stabilizing selection on the genetic variance of these traits with respect to overall fitness, indicating that they reside at an evolutionary optimum. In the presence of widespread pleiotropy, stabilizing selection on focal traits will arise through the net effects of selection on other, often unmeasured, traits and will tend to be stronger on trait combinations than single traits. Such selection may be difficult to detect in phenotypic analyses if the environmental covariance between the traits and fitness obscures the underlying genetic associations. The genetic analysis of trait deviations provides a way of detecting the missing stabilizing selection inferred by recent metaanalyses.