How much does evolution delay extinction when it cannot be
avoided?
Richard Gomulkiewicz
School of Biological Sciences
Washington State University
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. This
is joint work with Steve Krone and Chris Remien.