Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory

George W A Constable, Alan J. McKane

Research output: Contribution to journalArticle

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Abstract

The relationship between the M-species stochastic Lotka-Volterra competition (SLVC) model and the M-allele Moran model of population genetics is explored via timescale separation arguments. When selection for species is weak and the population size is large but finite, precise conditions are determined for the stochastic dynamics of the SLVC model to be mappable to the neutral Moran model, the Moran model with frequency-independent selection, and the Moran model with frequency-dependent selection (equivalently a game-theoretic formulation of the Moran model). We demonstrate how these mappings can be used to calculate extinction probabilities and the times until a species’ extinction in the SLVC model.
LanguageEnglish
Article number022416
Pages1-19
Number of pages19
JournalPhysical Review E (PRE)
Volume96
DOIs
StatusPublished - 29 Aug 2017

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Lotka-Volterra model
game theory
population genetics
extinction
population size
allele
timescale

Keywords

  • Ecological population dynamics
  • Ecology & evolution
  • Evolutionary dynamics
  • Fluctuations & noise
  • Noise
  • Population genetics
  • Statistical Physics
  • Biological Physics

Cite this

Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory. / Constable, George W A; McKane, Alan J.

In: Physical Review E (PRE), Vol. 96, 022416, 29.08.2017, p. 1-19.

Research output: Contribution to journalArticle

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