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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...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2015
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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. |
format | Online Article Text |
id | pubmed-4643889 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2015 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
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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