Generalized model of island biodiversity

The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics with four qualitatively distinct phases is unfolded. When the overall interspecies competition is weak, the island species recapitulate the mainland species. For higher values of the competition parameter, the system still admits an equilibrium community, but now some of the mainland species are absent on the island. Further increase in competition leads to an intermittent disordered phase, where the dynamics is controlled by invadable combinations of species and the turnover rate is governed by the migration. Finally, the strong competition phase is glasslike, dominated by uninvadable states and noise-induced transitions. Our model contains, as a special case, the celebrated neutral island theories of Wilson-MacArthur and Hubbell. Moreover, we show that slight deviations from perfect neutrality may lead to each of the phases, as the Hubbell point appears to be quadracritical.