The Influence of Higher-Order Epistasis on Biological Fitness Landscape Topography

Abstract

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.Electronic supplementary materialThe online version of this article (10.1007/s10955-018-1975-3) contains supplementary material, which is available to authorized users.

Minimum epistasis interpolation for sequence-function relationships

“…in partial factorial designs where they are purposefully confounded with main effects and lower-order interactions, [63]). However, there is a growing consensus that such higher-order interactions are not only common in genotype-phenotype maps [10,18,29,32,38] but are expected even for very simple, smooth genotype-phenotype relationships such as where the observed phenotype is just an additive trait that has been run through a nonlinear transformation [31,32,40,[64][65][66]. Our results contribute to this view by showing that the incorporation of higher-order interactions in fact allows substantially less epistatic fits than standard pairwise models.…”

“…In the special case where such interactions are limited to occurring between pairs of sites, the prediction problem can be solved using regularized regression [26] a technique that has sometimes performed quite well [27,28]. However, there is now abundant evidence that adding pair-wise interaction terms to an otherwise additive model is not sufficient to capture the complex interdependencies between mutations observed in empirical data [10,24,[29][30][31][32][33][34][35][36][37][38][39].…”

Lexical landscapes as largein silicodata for examining advanced properties of fitness landscapes

“…Epistasis remains a cutting-edge topic in evolutionary biology that continues to be the object of study for a variety of reasons, and measured using diverse methods [10,[19][20][21]. For our purposes, we use a Walsh-Hadamard transformation of the fitness values, scaled by an additional diagonal matrix, as presented in Poelwijk et al [19].…”

“…They were critical for introducing the concept of the adaptive trajectory, and have since been used as an innovation space for methods to detect higher-order epistasis [7], for metrics to calculate the speed of adaptive evolution [8], and for more rigorous attempts at predicting evolution. The limitations of combinatorial data sets are that they tend to only focus on suites of mutations within a single gene of interest, and that there are relatively few such data sets in existence [9][10][11]. Regardless of source, fitness measurements for these landscapes are often taken in a small number of environments, which limits our understanding of how the effect of mutations might be affected by environments.…”

Higher-order epistatic networks underlie the evolutionary fitness landscape of a xenobiotic-degrading enzyme

“…Adaptive fitness landscapes, which can be determined by generating and functionally assaying all possible combinations of the mutations responsible for a new function, have become a powerful tool for studying the evolutionary and biophysical origins of novel functions by unveiling the potential adaptive pathways that connect the ancestral and derived genotypes [10][11][12]14,[16][17][18] . Recently developed statistical methods enable us to assess and quantify the degree of epistasis, including high-order interactions (those that involve interactions between more than two mutations), which provide a comprehensive view of epistasis and the dominant interactions that drive it [19][20][21][22] . Moreover, because epistasis reflects interactions between amino acid changes, adaptive landscapes also provide critical insight into the underlying molecular interactions both within an enzyme and between enzyme and substrate.…”