The role of epistatic gene interactions in the response to selection and the evolution of evolvability

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.…”

“…The fitness scheme (1.2) is the most general two-locus two-allele fitness scheme with no fitness differences between coupling and repulsion genotypes such that the row-wise additive epistasis measures, defined by Bodmer and Felsenstein (1967) (1.3) satisfy e 1 = -e 2 = -e 3 = e 4 = 4ε (see also Puniyani et al 2004). The epistatic parameter ε = e 1 /4 plays a key role in our model but is difficult to characterize as directional or nondirectional, in the terms of Carter et al (2005). We shall see, however, that the Δ matrix which determines how ε affects the fitnesses, can play an important role in its evolution.…”

“…The term "evolvability" has been used to describe the potential for change in the additive genotypic contribution to phenotypic variance (e.g., Carter et al 2005 and references therein). Hansen and Wagner (2001) proposed that the role of epistasis in evolvability could be studied by allowing the effect of each gene to be a linear function of the effects of other genes-the "multilinear genotype-phenotype" map.…”

“…Hansen and Wagner (2001) proposed that the role of epistasis in evolvability could be studied by allowing the effect of each gene to be a linear function of the effects of other genes-the "multilinear genotype-phenotype" map. This model was also used by Carter et al (2005) to claim that one form of linear interaction, called "directional epistasis," is important in evolution and, in particular, the evolution of the additive component of genotypic variance. Both linkage and linkage disequilibrium were claimed to be unimportant to response to multilinear epistatic selection.…”

“…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). This kind of epistasis is called "statistical" (e.g., Carter et al 2005, Weinreich et al 2005) because of its essential dependence on allele frequencies at the interacting loci. "Physiological" (Cheverud and Routman 1995) or "functional" (Hansen and Wagner 2001) epistasis, on the other hand, describes how the loci interact functionally, in our case to produce individual fitnesses.…”