Deterministic and stochastic regimes of asexual evolution on rugged fitness landscapes

We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length $L$. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance $d_{\mathrm{eff}}$ upto which the population can spread in genotype space. For $d_{\mathrm{eff}}=L$, the deterministic quasispecies theory operates while for $d_{\mathrm{eff}} < 1$, the evolution is completely stochastic. Between these two limiting cases, the dynamics are described by a local quasispecies theory below a crossover time $T_{\times}$ while above $T_{\times}$, the population gets trapped at a local fitness peak and manages to find a better peak either via stochastic tunneling or double mutations. In the stochastic regime $d_\mathrm{eff} < 1$, we identify two subregimes associated with clonal interference and uphill adaptive walks, respectively. We argue that our findings are relevant to the interepretation of evolution experiments with microbial populations.Comment: Revised version, to appear in Genetics. Note on the role of selection in defining d_eff added; new figure 4 include

Rapid adaptation of a polygenic trait after a sudden environmental shift

Although a number of studies have shown that natural and laboratory populations initially well-adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a population genetic model of polygenic selection is analyzed to describe the short-term response of a quantitative trait after a sudden shift of the phenotypic optimum. We provide explicit analytical expressions for the time scales over which the trait mean approaches the new optimum. We find that when the effect sizes are small relative to a scaled mutation rate, the genomic signatures of polygenic selection are small to moderate allele frequency changes that occur in the short-term phase in a synergistic fashion. In contrast, selective sweeps, i.e., dramatic changes in the allele frequency may occur provided the size of the effect is sufficiently large. Applications of our theoretical results to the relationship between QTL and selective sweep mapping and to tests of fast polygenic adaptation are discussed