Evolutionary dynamics of a quantitative trait in a finite asexual population

In finite populations, mutation limitation and genetic drift can hinder evolutionary diversification. We consider the evolution of a quantitative trait in an asexual population whose size can vary and depends explicitly on the trait. Previous work showed that evolutionary branching is certain ("deterministic branching") above a threshold population size, but uncertain ("stochastic branching") below it. Using the stationary distribution of the population's trait variance, we identify three qualitatively different sub-domains of "stochastic branching" and illustrate our results using a model of social evolution. We find that in very small populations, branching will almost never be observed; in intermediate populations, branching is intermittent, arising and disappearing over time; in larger populations, finally, branching is expected to occur and persist for substantial periods of time. Our study provides a clearer picture of the ecological conditions that facilitate the appearance and persistence of novel evolutionary lineages in the face of genetic drift.