Predictability of evolution depends nonmonotonically on population size

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 Nμ2, 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.