Extinctions in the random replicator model

Author(s)

De Oliveira‚ V.M. ; Fontanari‚ JF

• Document type: Journal article
• Source: Physical Review E; v. 64, n. 5, p. 051911, 2001.

Abstract

The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interactions are studied analytically with tools of equilibrium statistical mechanics of disordered systems. Emphasis is given to the effects of externally induced extinction of a fixed fraction of species at the outset of the evolutionary process. The manner the ecosystem copes with the initial extinction event depends on the degree of competition among the species as well is on the strength of that event. For instance, in the regime of high competition the ecosystem diversity, given by the fraction of surviving species, is practically insensitive to the strength of the initial extinction provided it is not too large, while in the less competitive regime the diversity decreases linearly with the size or the event. In the case or large extinction events we find that no further biotic extinctions take place and, furthermore, that rare species become very unlikely to be found in the ecosystem at equilibrium. In addition, we show that the reciprocal of the Edwards-Anderson order parameter yields a good measure of the diversity of the model ecosystem. (AU)

• FAPESP's process: 99/09644-9 - Theoretical Molecular Evolution
• Grantee: José Fernando Fontanari
• Support Opportunities: Research Projects - Thematic Grants