The effect of gene interactions on the long-term response to selection

Abstract

The role of gene interactions in the evolutionary process has long been controversial. Although some argue that they are not of importance, because most variation is additive, others claim that their effect in the long term can be substantial. Here, we focus on the long-term effects of genetic interactions under directional selection assuming no mutation or dominance, and that epistasis is symmetrical overall. We ask by how much the mean of a complex trait can be increased by selection and analyze two extreme regimes, in which either drift or selection dominate the dynamics of allele frequencies. In both scenarios, epistatic interactions affect the long-term response to selection by modulating the additive genetic variance. When drift dominates, we extend Robertson's [Robertson A (1960) Proc R Soc Lond B Biol Sci 153(951):234−249] argument to show that, for any form of epistasis, the total response of a haploid population is proportional to the initial total genotypic variance. In contrast, the total response of a diploid population is increased by epistasis, for a given initial genotypic variance. When selection dominates, we show that the total selection response can only be increased by epistasis when some initially deleterious alleles become favored as the genetic background changes. We find a simple approximation for this effect and show that, in this regime, it is the structure of the genotype−phenotype map that matters and not the variance components of the population.T he relation between an organism's genotype and its phenotype is immensely complicated, yet quantitative genetics predicts the correlations between relatives, and the response to selection over tens of generations, based primarily on an additive model. How do interactions between genes affect the response to selection? This question is not easy to answer: Although the additive model can be represented by a few parameters, there are an enormous number of possible relationships between genotype and phenotype. Some insight may come from studying specific well-understood systems, for example, regulation of gene expression by binding of transcription factors, or folding of RNA molecules. Here, we take the alternative approach, seeking statistical regularities, while making minimal assumptions about the nature of epistasis.There has been a long-standing debate about the effect of genetic interactions on adaptation (1-7). Although some claim that they are unimportant because they contribute very little to the total genetic variance of a population, and consequently to its short-term response, others claim that their long-term effects can be substantial. At the heart of the debate is the distinction between what has been called physiological and statistical epistasis. The former is independent of the state of the population, whereas the latter is the statistical contribution of gene interactions to the trait variance, which depends on the allele frequencies (8, 9).In the absence of new mutations, the total response to selection is limited by the in...

How does epistasis influence the response to selection?

“…Therefore, epistasis reduces the information gain under directional selection. This argument is close to that made by Paixao and Barton (2016), in their extension of the selection limit of Robertson (1960).…”

“…The magnitude of this effect can be predicted if interactions among different sets of genes are independent of each other, and matches simulations of random pairwise epistasis well. Overall, however, the effect of epistasis on selection response is modest (Paixao and Barton, 2016; Figure 3). …”

“…This extension of the infinitesimal model immediately leads to a remarkably general expression for the effect of epistasis on the limits to directional selection on standing variation (Paixao and Barton, 2016). (Note that here, I use directional selection to refer to an exponential relation between fitness and trait; other forms of selection -for example, truncation selection-will select on the variance as well as the mean).…”

“…This standard infinitesimal model can be justified as the limit of an additive model, when the number of loci tends to infinity (Fisher, 1918;Bulmer, 1980). However, the model extends to allow for substantial epistasis Paixao and Barton, 2016). The key assumption is that phenotypes occupy a narrow range, relative to the range of multilocus genotypes that are possible, given the standing variation.…”

“…If epistatic interactions are random with respect to the marginal effects on the trait, and if the optimal genotype is the same under the epistatic and the corresponding additive models, then epistasis has no expected effect (Paixao and Barton, 2016). However, if epistasis is sufficiently strong, the marginal effects of alleles will change sign as allele frequencies change, so that a different optimal genotype will be reached.…”