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 explore whether natural selection may have contributed to this finding, and conclude by highlight opportunities for further work dissecting the influence that epistasis of all orders has on the efficiency of natural selection.

Idiosyncratic epistasis leads to global fitness-correlated trends

“…Nevertheless, the overall contribution from different epistatic orders shows some similarities across ploidies and environments (the magnitudes do differ; Fig. 2D), with additive and pairwise terms explaining most of the variance in the data, third-order terms contributing minorly, and the remaining orders making little difference, consistent with earlier studies ( 40 ). Across all epistatic orders, inferred effects were highly skewed, with a small number of terms explaining disproportionate variance (Fig.…”

“…2D). Additive and pairwise terms explained most of the variance in the data, third-order terms contributed minorly, and the remaining orders made little difference, consistent with earlier studies (32). Across all epistatic orders, inferred effects were highly skewed, with a small number of terms explaining disproportionate variance (Fig.…”

Minimum epistasis interpolation for sequence-function relationships

“…in partial factorial designs where higher-order interactions are purposefully confounded with main effects and lower-order interactions 73 ). 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,[74][75][76] . 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 occuring 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 pairwise interaction terms to an otherwise additive model is not sufficient to capture the complex interdependencies between mutations observed in the empirical data 10,24,[29][30][31][32][33][34][35][36][37][38][39] .…”

Evolutionary constraints in fitness landscapes

“…We computed the accessible direct paths (number and similarity) and the chain measure (number of chains, steps and origins, as well as maximum depth) on 38 experimentally biallelic resolved landscapes (Malcolm et al 1990;Whitlock and Bourguet 2000;Lunzer et al 2005;Weinreich et al 2006;O'maille et al 2008;Bridgham et al 2009;Lozovsky et al 2009;de Visser et al 2009;Hall et al 2010;da Silva et al 2010;Tan et al 2011;Chou et al 2011;Khan et al 2011;Flynn et al 2013;Jiang et al 2013;Meini et al Mira et al 2015;Palmer et al 2015). They differ on their number of loci: 1 landscape has 3 loci, 20 have 4 loci, 9 have 5 loci, and 8 have 6 loci and their general features are summarized in Weinreich et al (2017). Results can be seen in Fig.…”