A generalized model of island biodiversity

TL;DR

This paper introduces a generalized competitive Lotka-Volterra model to describe island biodiversity, revealing four distinct dynamic phases influenced by competition strength and connecting to neutral theory.

Contribution

It extends existing neutral models by incorporating demographic noise and competition, uncovering complex phase behavior and transitions in island biodiversity dynamics.

Findings

Weak competition results in island species mirroring mainland species.

Higher competition leads to partial species exclusion on islands.

Strong competition induces a glassy, noise-dominated phase.

Abstract

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 structure with four qualitatively distinct phases is unfolded. When the overall interspecies competition is weak, the island species are a sample of the mainland species. For higher values of the competition parameter the system still admit an equilibrium community, but now some of the mainland species are absent on the island. Further increase in competition leads to an intermittent "chaotic" 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 glassy, dominated by uninvadable state and noise-induced transitions. Our model contains, as a spatial 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.