The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 14, Number 1 (2004), 188-214.
Survival and extinction in a locally regulated population
Bolker and Pacala recently introduced a model of an evolving population in which an individual's fecundity is reduced in proportion to the "local population density." We consider two versions of this model and prove complementary extinction/persistence results, one for each version. Roughly, if individuals in the population disperse sufficiently quickly relative to the range of the interaction induced by the density dependent regulation, then the population has positive chance of survival, whereas, if they do not, then the population will die out.
Ann. Appl. Probab. Volume 14, Number 1 (2004), 188-214.
First available in Project Euclid: 3 February 2004
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes [See also 92Dxx] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Etheridge, A. M. Survival and extinction in a locally regulated population. Ann. Appl. Probab. 14 (2004), no. 1, 188--214. doi:10.1214/aoap/1075828051. https://projecteuclid.org/euclid.aoap/1075828051