The genetic basis of phenotypic adaptation II: The distribution of adaptive substitutions in the moving optimum model

Abstract

We consider a population that adapts to a gradually changing environment. Our aim is to describe how ecological and genetic factors combine to determine the genetic basis of adaptation. Specifically,we consider the evolution of a polygenic trait that is under stabilizing selection with a moving optimum. The ecological dynamics are defined by the strength of selection, σ, and the speed of the optimum, υ; the key genetic parameters are the mutation rate Θ and the variance of the effects of new mutations, ω. We develop analytical approximations within an "adaptive-walk" framework and describe how selection acts as a sieve that transforms a given distribution of new mutations into the distribution of adaptive substitutions. Our analytical results are complemented by individual-based simulations. We find that (i) the ecological dynamics have a strong effect on the distribution of adaptive substitutions and their impact depends largely on a single composite measure γ = υ/(σΘω3), which combines the ecological and genetic parameters; (ii) depending on g, we can distinguish two distinct adaptive regimes: for large γ the adaptive process is mutation limited and dominated by genetic constraints, whereas for small γ it is environmentally limited and dominated by the external ecological dynamics; (iii) deviations from the adaptive-walk approximation occur for large mutation rates, when different mutant alleles interact via linkage or epistasis; and (iv) in contrast to predictions from previous models assuming constant selection, the distribution of adaptive substitutions is generally not exponential. Copyright © 2009 by the Genetics Society of America.