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


Constable, George W A; McKane, Alan J (2017). Mapping of the stochastic Lotka-Volterra model to models of population genetics and game theory. Physical review. E, 96(2):022416.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Evolutionary Biology and Environmental Studies
Dewey Decimal Classification:570 Life sciences; biology
590 Animals (Zoology)
Scopus Subject Areas:Physical Sciences > Statistical and Nonlinear Physics
Physical Sciences > Statistics and Probability
Physical Sciences > Condensed Matter Physics
Language:English
Date:2017
Deposited On:17 Jan 2018 19:07
Last Modified:28 Jul 2020 12:42
Publisher:American Physical Society
ISSN:2470-0045
OA Status:Green
Publisher DOI:https://doi.org/10.1103/PhysRevE.96.022416
PubMed ID:28950630

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