Evolution of Quantitative Traits under a Migration-Selection Balance: When Does Skew Matter?

Abstract

Quantitative-genetic models of differentiation under migration-selection balance often rely on the assumption of normally distributed genotypic and phenotypic values. When a population is subdivided into demes with selection toward different local optima, migration between demes may result in asymmetric, or skewed, local distributions. Using a simplified two-habitat model, we derive formulas without a priori assuming a Gaussian distribution of genotypic values, and we find expressions that naturally incorporate higher moments, such as skew. These formulas yield predictions of the expected divergence under migration-selection balance that are more accurate than models assuming Gaussian distributions, which illustrates the importance of incorporating these higher moments to assess the response to selection in heterogeneous environments. We further show with simulations that traits with loci of large effect display the largest skew in their distribution at migration-selection balance. Online enhancement: appendix.abstract: Quantitative-genetic models of differentiation under migration-selection balance often rely on the assumption of normally distributed genotypic and phenotypic values. When a population is subdivided into demes with selection toward different local optima, migration between demes may result in asymmetric, or skewed, local distributions. Using a simplified two-habitat model, we derive formulas without a priori assuming a Gaussian distribution of genotypic values, and we find expressions that naturally incorporate higher moments, such as skew. These formulas yield predictions of the expected divergence under migration-selection balance that are more accurate than models assuming Gaussian distributions, which illustrates the importance of incorporating these higher moments to assess the response to selection in heterogeneous environments. We further show with simulations that traits with loci of large effect display the largest skew in their distribution at migration-selection balance.

Remarkable life history polymorphism may be evolving under divergent selection in the silverleaf sunflower

“…6 of 14 quantitative traits in this study) or traits evolving under migration‐selection balance (Débarre et al . ). Unfortunately, an appropriate model also capable of accounting for this study design does not yet exist.…”

Genetics of dispersal

“…Furthermore, when loci contribute unequally to trait variation, the shape of the phenotypic distribution may depart from normality, and become skewed, or have higher kurtosis. For example, Débarre, Yeaman & Guillaume () showed that when traits are affected by a few loci of large effect (i. E. major loci) together with many loci of small effect (i. E. minor loci), they are better able to resist homogenization by gene flow and lead to better local adaptation under diversifying selection between divergent habitats than when only minor loci are considered. In Débarre et al .…”

Modern Approaches to Local Adaptation

“…When there is substantial variation in the effect sizes of alleles, the distribution of breeding values in populations experiencing local adaptation and recurrent migration can become skewed, sometimes strikingly, as Florence Débarre, Sam Yeaman, and Fred Guillaume show in this issue (Débarre et al 2015). This is caused by the interaction of local selection and migration, as a result of which the descendants of recent migrants can be far from the local mean.…”