The Changing Geometry of a Fitness Landscape Along an Adaptive Walk

It has recently been noted that the relative prevalence of the various kinds of epistasis varies along an adaptive walk. This has been explained as a result of mean regression in NK model fitness landscapes. Here we show that this phenomenon occurs quite generally in fitness landscapes. We propose a simple and general explanation for this phenomenon, confirming the role of mean regression. We provide support for this explanation with simulations, and discuss the empirical relevance of our findings.Author Summary: The main result concerns the changing geometry along an adaptive walk in a fitness landscape. An adaptive walk is described by a sequence of genotypes of increasing fitness, where two consecutive genotypes differ by a point mutation. We compare patterns of epistasis, or gene interactions, along adaptive walks. Roughly, epistasis is antagonistic (rather than synergistic) if the double mutant combining two beneficial mutations has lower fitness than expected. In the extreme case that the double mutant has lower fitness than one (or both) of the single mutants, one has sign epistasis. We claim that the further one is along an adaptive walk, the larger the frequency of sign epistasis and the smaller the relative amount of antagonistic epistasis relative to synergistic epistasis. We provide a simple and general argument for our claim, which hence likely applies to empirical fitness landscapes. Our claims can readily be checked by empirical biologists. Potential theoretical progress related to our work includes a better understanding of the role of recombination in evolution.