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Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model

In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual’s phenotype. Our...

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Detalles Bibliográficos
Autores principales: Li, Qing, Zhang, Jiahua, Zhang, Boyu, Cressman, Ross, Tao, Yi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4643889/
https://www.ncbi.nlm.nih.gov/pubmed/26566219
http://dx.doi.org/10.1371/journal.pone.0142929
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author Li, Qing
Zhang, Jiahua
Zhang, Boyu
Cressman, Ross
Tao, Yi
author_facet Li, Qing
Zhang, Jiahua
Zhang, Boyu
Cressman, Ross
Tao, Yi
author_sort Li, Qing
collection PubMed
description In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual’s phenotype. Our main goal is to reveal the dynamical properties of the evolutionary game in a heterogeneous patchy environment. By analyzing the equilibria and their stabilities, we find that the dynamical behavior of the evolutionary game dynamics could be very complicated. Numerical analysis shows that the simple model can have twelve equilibria where four of them are stable. This implies that spatial dispersion can significantly complicate the evolutionary game, and the evolutionary outcome in a patchy environment should depend sensitively on the initial state of the patches.
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spelling pubmed-46438892015-11-18 Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model Li, Qing Zhang, Jiahua Zhang, Boyu Cressman, Ross Tao, Yi PLoS One Research Article In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual’s phenotype. Our main goal is to reveal the dynamical properties of the evolutionary game in a heterogeneous patchy environment. By analyzing the equilibria and their stabilities, we find that the dynamical behavior of the evolutionary game dynamics could be very complicated. Numerical analysis shows that the simple model can have twelve equilibria where four of them are stable. This implies that spatial dispersion can significantly complicate the evolutionary game, and the evolutionary outcome in a patchy environment should depend sensitively on the initial state of the patches. Public Library of Science 2015-11-13 /pmc/articles/PMC4643889/ /pubmed/26566219 http://dx.doi.org/10.1371/journal.pone.0142929 Text en © 2015 Li et al http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Li, Qing
Zhang, Jiahua
Zhang, Boyu
Cressman, Ross
Tao, Yi
Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model
title Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model
title_full Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model
title_fullStr Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model
title_full_unstemmed Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model
title_short Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model
title_sort effect of spatial dispersion on evolutionary stability: a two-phenotype and two-patch model
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4643889/
https://www.ncbi.nlm.nih.gov/pubmed/26566219
http://dx.doi.org/10.1371/journal.pone.0142929
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