Genetic drift in range expansions is very sensitive to density feedback in dispersal and growth

Abstract

AbstractTheory predicts rapid genetic drift in expanding populations due to the serial founder effect at the expansion front. Yet, many natural populations maintain high genetic diversity in the newly colonized regions. Here, we investigate whether density-dependent dispersal could provide a resolution of this paradox. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because many more migrants from the diverse, high-density regions arrive at the expansion edge. When density-dependence is weak or negative, the effective population size of the front scales only logarithmically with the carrying capacity. The dependence, however, switches to a sublinear power law and then to a linear increase as the density-dependence becomes strongly positive. To understand these results, we introduce a unified framework that predicts how the strength of genetic drift depends on the density-dependence in both dispersal and growth. This theory reveals that the transitions between different regimes of diversity loss are controlled by a single, universal parameter: the ratio of the expansion velocity to the geometric mean of dispersal and growth rates at expansion edge. Importantly, our results suggest that positive density-dependence could dramatically alter evolution in expanding populations even when its contributions to the expansion velocity is small.