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Survival and coexistence in stochastic spatial Lotka–Volterra models
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  • Published: 01 December 2006

Survival and coexistence in stochastic spatial Lotka–Volterra models

  • J. Theodore Cox1 &
  • Edwin A. Perkins2 

Probability Theory and Related Fields volume 139, pages 89–142 (2007)Cite this article

  • 190 Accesses

  • 11 Citations

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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

Authors and Affiliations

  1. Department of Mathematics, Syracuse University, Syracuse, 13244, NY, USA

    J. Theodore Cox

  2. Department of Mathematics, The University of British Columbia, Room 121, 1984 Mathematics Road, Vancouver, BC, V6T 1Z2, Canada

    Edwin A. Perkins

Authors
  1. J. Theodore Cox
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  2. Edwin A. Perkins
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Corresponding author

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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  • Received: 31 October 2005

  • Revised: 19 September 2006

  • Published: 01 December 2006

  • Issue Date: September 2007

  • DOI: 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
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