The distribution of epistasis on simple fitness landscapes

Abstract

Fitness interactions between mutations can influence a population’s evolution in many different ways. While epistatic effects are difficult to measure precisely, important information is captured by the mean and variance of log fitnesses for individuals carrying different numbers of mutations. We derive predictions for these quantities from a class of simple fitness landscapes, based on models of optimizing selection on quantitative traits. We also explore extensions to the models, including modular pleiotropy, variable effect sizes, mutational bias and maladaptation of the wild type. We illustrate our approach by reanalysing a large dataset of mutant effects in a yeast snoRNA (small nucleolar RNA). Though characterized by some large epistatic effects, these data give a good overall fit to the non-epistatic null model, suggesting that epistasis might have limited influence on the evolutionary dynamics in this system. We also show how the amount of epistasis depends on both the underlying fitness landscape and the distribution of mutations, and so is expected to vary in consistent ways between new mutations, standing variation and fixed mutations.

The geometry and genetics of hybridization

“…Finally, both of our extensions illustrate how existing work on quantitative traits can be used with Fisher's model -even when, as here, the model is treated as a fitness landscape, and the "traits" are not taken too literally (Martin 2014;Fraïsse and Welch 2019). In future, the approach might be extended to landscapes with multiple phenotypic optima (Whitlock 1997), or to populations that diverged phenotypically via linkage disequilibria, rather than allelic substitutions (Kremer & Le Corre 2012;Savolainen et al 2013).…”

“…where k denotes the curvature of the fitness landscape, i.e. how quickly fitness declines with the distance from the optimum (Peck et al 1997;Tenaillon et al 2007;Fraïsse et al 2016;Fraïsse and Welch 2019). In the remainder of the paper, following common practice (Turelli and Orr 2000;Wade and Demuth 2005; Moyle 2007), we will not work with fitness directly.…”

“…First, the model assumes that fitness is determined by a few quantitative traits, each with additive genetics. This assumption is less restrictive than it seems, because the "traits" need not be identified with standard quantitative traits (such as height or weight), but might emerge from a variety of more complex underlying phenotypic models (Martin 2014;Schiffman and Ralph 2017;Fraïsse and Welch 2019). Nevertheless, additivity leads to some questionable predictions, especially for the initial F1 cross (Fraïsse et al 2016).…”

The geometry and genetics of hybridization

“…where α is a constant, and k denotes the curvature of the fitness landscape, that is, how quickly fitness declines with the distance from the optimum (Peck et al 1997;Tenaillon et al 2007;Fraïsse et al 2016;Fraïsse and Welch 2019). This model assumes a single phenotypic optimum at any given time and location, but the position of the optimum can vary in space and time, so that we can investigate divergence and hybridization under different environmental conditions.…”

Phenotypic and genotypic parallel evolution in parapatric ecotypes ofSenecio

“…Such a system would imply that evolution is extremely repeatable and predicable at the level of the phenotype (Blount et al, 2018), where every instance of repeated evolution has resulted in the same phenotypic adaptations. However, this may be highly unlikely within natural systems due to a range of factors such as environmental heterogeneity within each habitat, the interplay between the genotype, phenotype and fitness landscapes, genetic constraints, and stochastic forces such as genetic drift (Lenormand et al, 2009(Lenormand et al, , 2016Rosenblum et al, 2014;Fraïsse & Welch, 2019).…”