Evolution of Genetic Architecture Under Directional Selection

Abstract

We investigate the multilinear epistatic model under mutation-limited directional selection. We confirm previous results that only directional epistasis, in which genes on average reinforce or diminish each other's effects, contribute to the initial evolution of mutational effects. Thus, either canalization or decanalization can occur under directional selection, depending on whether positive or negative epistasis is prevalent. We then focus on the evolution of the epistatic coefficients themselves. In the absence of higher-order epistasis, positive pairwise epistasis will tend to weaken relative to additive effects, while negative pairwise epistasis will tend to become strengthened. Positive third-order epistasis will counteract these effects, while negative third-order epistasis will reinforce them. More generally, gene interactions of all orders have an inherent tendency for negative changes under directional selection, which can only be modified by higher-order directional epistasis. We identify three types of nonadditive quasi-equilibrium architectures that, although not strictly stable, can be maintained for an extended time: (1) nondirectional epistatic architectures; (2) canalized architectures with strong epistasis; and (3) near-additive architectures in which additive effects keep increasing relative to epistasis.

Epistasis can accelerate adaptive diversification in haploid asexual populations

“…Prior theoretical work indicated that directional epistasis can facilitate the directional response of a population to selection [15,18]. Our model of epistasis that assumes independent effects ( f ¼ 0) is different from the model in references [15,18], which assumed a directional form of epistasis, such that alleles on average reinforce or suppress the effect of other alleles.…”

On the evolution of epistasis II: A generalized Wright–Kimura framework

“…This appears not to be the case in analysis of statistical epistasis (Barton and Turelli 2004, Carter et al 2005, Hansen et al 2006. Again, this is because we focus on initial perturbation of functional epistasis.…”

“…As pointed out by Hansen et al (2006), the evolution of epistasis is not part of the corpus of classical population genetics. The statistical framework, exemplified by the recent work of Hansen et al, defines epistasis with respect to a reference genotype.…”

“…The focus of these and subsequent studies (Hansen et al 2006) has been on the directionality of the epistasis, namely the extent to which effects of different genes reinforce each other along a trajectory of directional selection on a phenotype to which they contribute. Epistasis here is a component of the variance in the trait under selection, and its effect is modeled in the analysis of variance framework (see also Barton and Turelli 2005).…”

On the evolution of epistasis III: The haploid case with mutation

“…The evolution of epistasis is a topic largely absent from classical population genetic literature (Hansen et al, 2006). The subject has, however, received increased attention in the past decade as relevant data on haploid genetic systems have become available Lenski 1997, 2001;Wilke and Adami 2001;You and Yin 2002;Sanjuan et al 2004;Bonhoeffer et al 2004;Burch and Chao 2004;Shapiro et al 2006).…”