Extinctions in the random replicator model

Viviane M. de Oliveira and J. F. Fontanari
Phys. Rev. E 64, 051911 – Published 25 October 2001
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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 as 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 of the event. In the case of 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.

  • Received 23 April 2001

DOI:https://doi.org/10.1103/PhysRevE.64.051911

©2001 American Physical Society

Authors & Affiliations

Viviane M. de Oliveira and J. F. Fontanari

  • Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos São Paolo, Brazil

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Issue

Vol. 64, Iss. 5 — November 2001

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