A branching process model of evolutionary rescue

Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of fitter genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such as the probability of rescue, the shape of the population growth curve of a rescued population, and the time until the first rescuing mutation occurs. Comparisons are made to existing results in the literature in cases where both the mutation rate and the selective advantage of the beneficial mutations are small.

Automated summary

Evolutionary rescue refers to the process in which a declining population may start growing again by increasing the frequency of fitter genotypes, thus avoiding extinction. This study presents a model to analyze the probability of rescue, the population growth curve of a rescued population, and the time until the first rescuing mutation occurs, under conditions of small mutation rate and selective advantage.