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

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.

21 pages, 5 figures

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Cited by in corpus (8)

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• Dynamical mean-field theory: from ecosystems to reaction networks
• Immigration-induced phase transition in a regulated multispecies birth-death process
• Exploiting fast-variables to understand population dynamics and evolution
• Demographic noise in complex ecological communities
• Critical Slowing Down along the Separatrix of Lotka-Volterra Model of Competition
• Survival of the densest accounts for the expansion of mitochondrial mutations in ageing
• Demographic noise slows down cycles of dominance