Coexistence in locally regulated competing populations and survival of branching annihilating random walk

DOI10.1214/105051607000000267zbMath1145.92032arXiv0710.5380OpenAlexW2058570807WikidataQ60500185 ScholiaQ60500185MaRDI QIDQ2475029

Alison M. Etheridge, Mark Meredith, Jochen Blath

Publication date: 20 March 2008

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.5380

zbMATH Keywords

survivalstepping stone modelinteracting diffusionscompeting speciesFeller diffusionheteromyopiaregulated populationsWright-Fisher distribution

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Applications of branching processes (60J85) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Ecology (92D40) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

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Cites Work

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• Continuous time multi-allelic stepping stone models in population genetics
• Infinite dimensional stochastic differential equations and their applications
• An interacting system in population genetics. I
• Field theory of branching and annihilating random walks
• Survival and extinction in a locally regulated population
• An explicitly spatial version of the Lotka-Volterra model with interspecific competition
• Rescaled Lotka-Volterra models converge to super-Brownian motion
• Coexistence in locally regulated competing populations and survival of branching annihilating random walk
• Survival and coexistence in stochastic spatial Lotka-Volterra models