Evolution and the duration of a doomed population

Many populations are doomed to extinction, but little is known about how evolution contributes to their longevity. We address this by modeling an asexual population consisting of genotypes whose abundances change independently according to a system of continuous branching diffusions. Each genotype is characterized by its initial abundance, growth rate, and reproductive variance. The latter two components determine the genotype's “risk function” which describes its per capita probability of extinction at any time. We derive the probability distribution of extinction times for a polymorphic population, which can be expressed in terms of genotypic risk functions. We use this to explore how spontaneous mutation, abrupt environmental change, or population supplementation and removal affect the time to extinction. Results suggest that evolution based on new mutations does little to alter the time to extinction. Abrupt environmental changes that affect all genotypes can have more substantial impact, but, curiously, a beneficial change does more to extend the lifetime of thriving than threatened populations of the same initial abundance. Our results can be used to design policies that meet specific conservation goals or management strategies that speed the elimination of agricultural pests or human pathogens.