Background/Question/Methods Rapid adaptation may help some species avoid extinction. Despite significant progress in our theoretical understanding of evolutionary rescue, few studies have examined how a population behaves during the critical phase when it is no longer declining, but remains small and vulnerable to extinction. Demographic stochasticity and genetic drift are well known causes of extinction in small populations, but typically are studied independently. However, during evolutionary rescue the rate of evolution and the magnitude of stochasticity can become highly coupled. Here I examine the relative contributions of genetic drift and demographic stochasticity to extinction risk during evolutionary rescue and how these contributions depend on the strength and mode of selection. I calculate the effect of demographic stochasticity and genetic drift on the probability of extinction by comparing a fully individual-based model to reduced models that average over demographic stochasticity or genetic drift. I decompose the realized effects of the two processes on per-capita growth rate, and use this decomposition to determine the contribution of demographic stochasticity and genetic drift to individual extinction events. Because life history and the timing of selection affect stochasticity, I compare survival selection and fecundity selection, and populations with low and high per-capita growth rates. Results/Conclusions I found that as a population’s maximum per-capita growth rate decreases, demographic stochasticity has an increasingly large effect on extinction risk relative to genetic drift. This was confirmed at the level of individual rescue events; for slow-growing population experiencing weak selection, the effect of demographic stochasticity on growth rate was larger in magnitude and on average more negative than the effect of genetic drift. Further, as the strength of selection increases, so too does the effect of the timing of selection on extinction risk, with survival selection causing greater extinction risk than fecundity selection. This is consistent with the observation that survival selection results in greater demographic variance than fecundity selection. These results demonstrate that demographic stochasticity and genetic drift are critically important during evolutionary rescue and that their relationship with extinction risk is complex. While life history is known to influence extinction risk during evolutionary rescue by affecting the rate of evolution, these results suggest a secondary pathway, mediated by stochasticity, by which life history affects the likelihood of evolutionary rescue. This work represents an important first step in understanding the intricacies of this pathway.
