Abstract
Genetic correlations between traits can strongly impact evolutionary responses to selection, and may thus impose constraints on adaptation. Theoretical and empirical work has made it clear that without strong linkage and with random mating, genetic correlations at evolutionary equilibrium result from an interplay of correlated pleiotropic effects of mutations, and correlational selection favoring combinations of trait values. However, it is not entirely clear how change in the overall strength of stabilizing selection across traits (breadth of the fitness peak, given its shape) influences this compromise between mutation and selection effects on genetic correlation. Here, we show that the answer to this question crucially depends on the intensity of genetic drift. In large, effectively infinite populations, genetic correlations are unaffected by the strength of selection, regardless of whether the genetic architecture involves common small‐effect mutations (Gaussian regime), or rare large‐effect mutations (House‐of‐Cards regime). In contrast in finite populations, the strength of selection does affect genetic correlations, by shifting the balance from drift‐dominated to selection‐dominated evolutionary dynamics. The transition between these domains depends on mutation parameters to some extent, but with a similar dependence of genetic correlation on the strength of selection. Our results are particularly relevant for understanding how senescence shapes patterns of genetic correlations across ages, and genetic constraints on adaptation during colonization of novel habitats.
Highlights
genetic correlations between traits shaped by natural selection
phenotypic (co)variances arise from an equilibrium between mutation
genetic correlations are a compromise between the correlation of pleitropic mutation effects
Summary
MODEL As in standard quantitative genetic models, we assume that the multivariate phenotype z can be partitioned into a breeding value x determined by the genotype, plus a residual component of variation e (often described as the environmental component), normally distributed with mean 0 and covariance matrix E. Mutation had additive effects on the traits, modifying the phenotypic value of the mutated allele by an amount drawn from a multivariate normal distribution, with mean zero (unbiased mutation) and mutation variance-covariance matrix M This life cycle, developed by Revell (2007), ensures that the population size N is constant and equal to the effective population size Ne in the absence of selection. Something that has been largely overlooked in previous studies on this topic (e.g., Lande 1976, 1979; Burger et al 1989), but becomes important under strong selection and low population size, is that selection on non-heritable phenotypic variation increases the intensity of genetic drift on heritable phenotypic variation This occurs because residual, non-heritable phenotypic variation, with covariance matrix E (usually denoted as Ve for single traits) causes variance in relative fitness among parents with a given breeding value x, increasing the amount of genetic drift, that is, random changes in the distribution of breeding values. To ensure that the expected genetic covariance matrix Gwas estimated after a pseudo-equilibrium is reached (i.e., at stationarity), only the 70,000 last iterations from the chain were used to estimate the mean
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