Habitat size and extinction in population dynamics

Carlos Escudero; Javier Buceta; Francisco Javier de la Rubia; Katja Lindenberg

doi:10.1117/12.537570

25 May 2004 Habitat size and extinction in population dynamics

Carlos Escudero, Javier Buceta, Francisco Javier de la Rubia, Katja Lindenberg

Proceedings Volume 5467, Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II; (2004) https://doi.org/10.1117/12.537570
Event: Second International Symposium on Fluctuations and Noise, 2004, Maspalomas, Gran Canaria Island, Spain

Abstract

We review the critical patch size problem, already classic in the mathematical biology literature. We consider a logistic population living in a finite patch of length L and undergoing random dispersal. The patch presents good conditions for life, while the conditions are so harsh outside that they lead to certain extinction. The usual mean field approach leads to a critical patch size L_c, such that if the actual length of the patch is smaller than L_c the population becomes extinct with certainty, whereas a longer patch leads to certain survival. We study the fluctuations in the population due to its low density near extinction and analyze their effects on the probability of extinction. We find that there is no patch size that can be considered absolutely safe for the population and that, under certain circumstances, the population is under risk of extinction for any patch size.

Citation Download Citation

Carlos Escudero, Javier Buceta, Francisco Javier de la Rubia, and Katja Lindenberg "Habitat size and extinction in population dynamics", Proc. SPIE 5467, Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II, (25 May 2004); https://doi.org/10.1117/12.537570

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