Data from: Detecting epistasis from an ensemble of adapting populations

The role that epistasis plays during adaptation remains an outstanding problem, which has received considerable attention in recent years. Most of the recent empirical studies are based on ensembles of replicate populations that adapt in a fixed, laboratory controlled condition. Researchers often seek to infer the presence and form of epistasis in the fitness landscape from the time-evolution of various statistics averaged across the ensemble of populations. Here we provide a rigorous analysis of what quantities, drawn from time-series of such ensembles, can be used to infer epistasis for populations evolving under weak mutation on finite-site fitness landscapes. First we analyze the mean fitness trajectory—that is, the time course of the ensemble average fitness. We show that for any epistatic fitness landscape and starting genotype, there always exists a non-epistatic fitness landscape that produces the exact same mean fitness trajectory. Thus, the presence of epistasis is not identifiable from the mean fitness trajectory. By contrast, we show that two other ensemble statistics—the time evolution of the fitness variance across populations, and the time evolution of the mean number of substitutions—can detect certain forms of epistasis in the underlying fitness landscape.上位性（epistasis）在适应性演化过程中所发挥的作用仍是一项尚未解决的重要问题，近年来已受到学界的广泛关注。当前绝大多数实证研究均基于在固定且受实验室严格控制的条件下演化的重复种群集合开展。研究者通常尝试通过跨种群集合平均得到的各类统计量的时间演化过程，推断适应度景观（fitness landscape）中上位性的存在及其具体形式。本文针对有限位点适应度景观上、在弱突变条件下演化的种群，严谨分析了可从这类种群集合的时间序列中提取哪些量可用于推断上位性。首先，我们分析了平均适应度轨迹——即种群集合平均适应度的时间演化过程。研究表明，对于任意上位性适应度景观与初始基因型，总能找到一个非上位性适应度景观，使其产生完全一致的平均适应度轨迹。因此，仅通过平均适应度轨迹无法辨识上位性的存在。与之相对，我们证明另外两类集合统计量——种群间适应度方差的时间演化，以及平均替代数的时间演化——可检测对应适应度景观中的特定上位性形式。