Probing chaos and biodiversity in a simple competition model

Lionel Roques (1) , Mickaël D. Chekroun (2)

1 BioSP - Biostatistique et Processus Spatiaux
2 CERES-ERTI - Centre d'Enseignement et de Recherche sur l'Environnement et la Societé / Environmental Research and Teaching Institute

Recent theoretical work has reported that chaos facilitates biodiversity. In this paper, we study the lowest-dimensional Lotka-Volterra competition model that exhibits chaotic trajectories, a model with four species. We observe that interaction and growth parameters leading respectively to extinction of three species, or coexistence of two, three or four species, are for the most part arranged in large regions with clear boundaries. Small islands of parameters that lead to chaos are also found. These regions where chaos occurs are, in the three cases presented here, situated at the interface between a non-chaotic four-species region and a region where extinction occurs. This implies a high sensitivity of biodiversity with respect to parameter variations in the chaotic regions. Additionally, in regions where extinction occurs which are adjacent to chaotic regions, the computation of local Lyapunov exponents reveals that a possible cause of extinction is the overly strong fluctuations in species abundances induced by local chaos at the beginning of the interval of study. For this model, we conclude that biodiversity is a necessary condition for chaos rather than a consequence of chaos, which can be seen as a signal of a high extinction risk.

Mots clés: Biodiversity; Chaos; Lotka-Volterra; Competition model; Lyapunov exponent; Local Lyapunov exponent; Simulated annealing

Domaines: Systèmes dynamiques [math.DS]; Biodiversité et Ecologie; Biodiversité; Ecosystèmes

Lionel Roques, Mickaël D. Chekroun. Probing chaos and biodiversity in a simple competition model. 2010. ⟨hal-00511225⟩