Critical patch-size for two-sex populations.

As environments become increasingly degraded, mainly due to human activities, species are often subject to isolated habitats surrounded by unfavorable regions. Since the pioneering work by Skellam [25] mathematical models have provided useful insights into the population persistence in such cases. Most of these models, however, neglect the sex structure of populations and the differences between males and females. In this work we investigate, through a reaction-diffusion system, the dynamics of a sex-structured population in a single semipermeable patch. The critical patch size for persistence is determined from implicit relationships between model parameters. The effects of the various growth and movement parameters are also investigated.