Viability of Small Populations Experiencing Recurring Catastrophes

Abstract

Some small populations are characterized by periods of exponential growth interrupted by sudden drops. These drops can be linked to the population size itself, for example, through overexploitation of local resources. The long-term population extinction risk and the time to extinction for such a repeatedly collapsing population are estimated from general branching processes. The latter allows realistic modeling of lifespan distributions and reproduction patterns, litter (or brood or clutch) sizes as long as individuals reproduce freely and density effects are absent. As the population grows, the carrying capacity of the habitat increasingly matters. This is modeled as a drop after reaching a ceiling. The probability of recovery is then determined by the population size after the drop and by the risk of extinction of branching processes. The reproductive behavior of individuals during the periods free of density effects determines the intrinsic rate of increase of populations close to the carrying capacity. The details of life history which produce demographic stochasticity remain important in systems with density effects. Finally, the time to extinction of a single system with a high carrying capacity is compared to that of a population distributed over several small patches. For systems not allowing migration, survival is favored by a single large habitat rather than by several small habitats.