The diversity of evolutionary dynamics on epistatic versus non-epistatic fitness landscapes

Although the role of epistasis in evolution has received considerable attention from experimentalists and theorists alike, it is unknown which aspects of adaptation are in fact sensitive to epistasis. Here, we address this question by comparing the evolutionary dynamics on all finite epistatic landscapes versus all finite non-epistatic landscapes, under weak mutation. We first analyze the fitness trajectory—that is, the time course of the expected fitness of a population. We show that for any epistatic fitness landscape and choice of starting genotype, there always exists a non-epistatic fitness landscape and starting genotype that produces the exact same fitness trajectory. Thus, surprisingly, the presence or absence of epistasis is irrelevant to the first-order dynamics of adaptation. On the other hand, we show that the time evolution of the variance in fitness across replicate populations can be sensitive to epistasis: some epistatic fitness landscapes produce variance trajectories that cannot be produced by any non-epistatic landscape. Likewise, the mean substitution trajectory—that is, the expected number of mutations that fix over time—is also sensitive to epistasis. These results on identifiability have direct implications for efforts to infer epistasis from the types of data often measured in experimental populations. ∗To whom correspondence should be addressed. E-mail: [email protected] 1 ar X iv :1 41 0. 25 08 v1 [ qbi o. PE ] 9 O ct 2 01 4