Enhanced species coexistence in Lotka-Volterra competition models due to nonlocal interactions.

We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the nonlocal interactions. In both cases, nonlocal interactions can create spatial patterns of population densities in which highly populated clumps alternate with unpopulated regions. These non-populated regions provide spatial niches for a weaker competitor to establish in the community and persist in conditions in which local models predict competitive exclusion. Moreover, depending on the balance between local and nonlocal competition intensity, the clumps of the weaker competitor vary from M-like structures with higher densities of individuals accumulating at the edges of each clump to triangular structures with most individuals occupying their centers. These results suggest that long-range competition, through the creation of spatial patterns in population densities, might be a key driving force behind the rich diversity of species observed in natural ecological communities.

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.