Predictability of evolution depends nonmonotonically on population size

Abstract

To gauge the relative importance of contingency and determinism in evolution is a fundamental problem that continues to motivate much theoretical and empirical research. In recent evolution experiments with microbes, this question has been explored by monitoring the repeatability of adaptive changes in replicate populations. Here, we present the results of an extensive computational study of evolutionary predictability based on an experimentally measured eight-locus fitness landscape for the filamentous fungus Aspergillus niger. To quantify predictability, we define entropy measures on observed mutational trajectories and endpoints. In contrast to the common expectation of increasingly deterministic evolution in large populations, we find that these entropies display an initial decrease and a subsequent increase with population size N, governed, respectively, by the scales Nμ and Nμ 2 , corresponding to the supply rates of single and double mutations, where μ denotes the mutation rate. The amplitude of this pattern is determined by μ. We show that these observations are generic by comparing our findings for the experimental fitness landscape to simulations on simple model landscapes.clonal interference | epistasis | experimental evolution E volutionary adaptations arise from an intricate interplay of deterministic selective forces and random reproductive or mutational events, and the relative roles of these two types of influences on the outcome of evolution has been subject to longstanding controversy with significant philosophical implications (1, 2). Although the vision of "replaying the tape of life" on Earth or on some extrasolar planet remains confined to the realm of imagination (3, 4), evolution experiments with microbial populations have begun to address predictability of adaptation on a microevolutionary scale (5-9). In particular, strong signatures of parallel evolution have been observed in the context of the evolution of antibiotic resistance in pathogens, a finding that is of direct relevance to strategies of drug design and deployment (10-14). As lack of knowledge of crucial parameters (e.g., the frequency of beneficial mutations) in such experiments prevents forward predictions, predictability is used in a weaker, a posteriori sense implying repeatability of evolutionary trajectories in replicate populations. For this reason, the two terms will often be used interchangeably in the following (15).The repeatability of adaptive trajectories is expected to depend on the genetic constraints imposed by epistatic interactions as well as on parameters such as population size N, mutation rate μ, and the typical scale s of selection coefficients (16-18). To be specific, consider a population evolving in the regime of strong selection and weak mutation (SSWM), where mutations are so rare that normally not more than one mutant is present simultaneously and the population can be represented as a single entity that performs an adaptive walk in the space of genotypes (19)(20)(21). Such walks are constrained to ...

Adaptation of Enterococcus faecalis to Daptomycin Reveals an Ordered Progression to Resistance

“…Similarly, the same mutation in cls was also observed in three different genetic backgrounds in the turbidostat, which in the absence of sexual recombination suggests independent and parallel evolution of this mutation. While the number of permutations open to a genome is vast, it is clear from our work and that of others that adaptation to strong selection can follow reproducible and predictable paths essential for prediction (13,48,49).…”

Repeatability of adaptation in experimental populations of different sizes

“…Differences in the amount of convergence or divergence in fitness among populations of different sizes could be due to differences in rates of adaptation [19,33] or the ability to cross fitness valleys in rugged fitness landscapes [18]. The initial variance among starting genotypes was reduced after evolution in medium and large populations, which is expected if the different histories were converging on the same trait combination.…”

“…In large populations, the higher supply of mutations will increase the probability of there being multiple different individuals each carrying a different beneficial mutation. Clonal interference [5][6][7] will tend to lead to the fixation of the mutations with largest beneficial effect [21,22] and to a reduction in the number of different trajectories taken by independent lineages [18]. As such, adaptation in large populations is predicted to be more repeatable because of the greater efficiency of selection and lower contribution of chance [18][19][20].…”

Rate of Adaptation in Sexuals and Asexuals: A Solvable Model of the Fisher–Muller Effect

“…The essence of the FM mechanism is the competition between independently arising beneficial mutations, termed clonal interference, which slows down the adaptation of large asexual populations (Gerrish and Lenski 1998;Miralles et al 1999;Wilke 2004;Kim and Orr 2005;Park and Krug 2007;Fogle et al 2008;Sniegowski and Gerrish 2010;Schiffels et al 2011). The concept of clonal interference has played an important role in interpreting the behavior observed in laboratory selection experiments (Lenski et al 1991;Lenski and Travisano 1994;Barrick et al 2009) and has also been invoked in explaining the population-size dependence of evolutionary predictability in rugged fitness landscapes (Jain et al 2011;Szendro et al 2013a). Although in its original formulation clonal interference theory neglects the occurrence of secondary beneficial mutations within a growing clone (Gerrish and Lenski 1998;Gerrish 2001), in general the coexistence of multiple beneficial mutations cannot be neglected in large populations (Park and Krug 2007).…”

“…The concept of clonal interference has played an important role in interpreting the behavior observed in laboratory selection experiments (Lenski et al 1991;Lenski and Travisano 1994;Barrick et al 2009) and has also been invoked in explaining the population-size dependence of evolutionary predictability in rugged fitness landscapes (Jain et al 2011;Szendro et al 2013a). Although in its original formulation clonal interference theory neglects the occurrence of secondary beneficial mutations within a growing clone (Gerrish and Lenski 1998;Gerrish 2001), in general the coexistence of multiple beneficial mutations cannot be neglected in large populations (Park and Krug 2007).…”