EXTINCTION IN A SIMPLE SOURCE SINK SYSTEM - APPLICATION OF NEW MATHEMATICAL RESULTS/

I used a stochastic model to study extinction probabilities in a simpl e subdivided population composed of a source population regulated by d ensity-dependent processes connected by varying patterns of dispersal to a density-independent sink population. The only kind of stochastici ty incorporated was demographic, and only one type of individual was c onsidered in each population. Mathematical results are presented which demonstrate that in this model (i) extinction is, ultimately, certain ; (ii) time to extinction has an approximately geometric distribution; and (iii) the probability distribution of population size conditional on non-extinction converges, as time increases, to a fixed probabilit y distribution. Monte-Carlo simulations show that density-dependent di spersal minimises the probability of extinction. Among types of densit y-independent dispersal, two situations yield lower extinction probabi lities: (i) no dispersal; and (ii) weak dispersal from the source to t he sink and strong dispersal from the sink to the source. These result s raise a number of questions, especially about the meaning of source and sink populations in conservation biology.