Survival and coexistence in stochastic spatial Lotka-Volterra models

J. Theodore Cox, Edwin A. Perkins

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

A spatially explicit, stochastic Lotka-Volterra model was introduced by Neuhauser and Pacala in Neuhauser and Pacala (Ann. Appl. Probab. 9, 1226-1259, 1999). A low density limit theorem for this process was proved by the authors in Cox and Perkins (Ann. Probab. 33, 904-947, 2005), showing that certain generalized rescaled Lotka-Volterra models converge to super-Brownian motion with drift. Here we use this convergence result to extend what is known about the parameter regions for the Lotka-Volterra process where (i) survival of one type holds, and (ii) coexistence holds.

Original languageEnglish (US)
Pages (from-to)89-142
Number of pages54
JournalProbability Theory and Related Fields
Volume139
Issue number1-2
DOIs
StatePublished - Sep 1 2007

Keywords

  • Lotka-Volterra
  • Super-Brownian motion
  • Voter model

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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