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Survival and coexistence in stochastic spatial Lotka–Volterra models

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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.

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Author information

Correspondence to Edwin A. Perkins.

Additional information

Supported in part by NSF grants DMS-024422/DMS-0505439. Part of the research was done while the author was visiting The University of British Columbia.

Supported in part by an NSERC Research grant.

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Cox, J.T., Perkins, E.A. Survival and coexistence in stochastic spatial Lotka–Volterra models. Probab. Theory Relat. Fields 139, 89–142 (2007). https://doi.org/10.1007/s00440-006-0040-3

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Keywords

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

Mathematics Subject Classification (2000)

  • Primary 60K35
  • Primary 60G57
  • Secondary 60F05
  • Secondary 60J80