Global dynamics for two-species competition in patchy environment
An ODE system modeling the competition between two species in a two-patch environment is studied.Both species move between the patches with the same dispersal rate. It is shown that the species with largerbirth rates in both patches drives the other species to extinction, regardless of the dispersal...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.947 |
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| author | Kuang-Hui Lin Yuan Lou Chih-Wen Shih Tze-Hung Tsai |
| author_facet | Kuang-Hui Lin Yuan Lou Chih-Wen Shih Tze-Hung Tsai |
| author_sort | Kuang-Hui Lin |
| collection | DOAJ |
| description | An ODE system modeling the competition between two species in a two-patch environment is studied.Both species move between the patches with the same dispersal rate. It is shown that the species with largerbirth rates in both patches drives the other species to extinction, regardless of the dispersal rate. The more interesting case is when both species have the same average birth rate but each species has larger birth rate in one patch. It has previously been conjectured by Gourley and Kuang that the species that can concentrate its birth in a single patch wins if the diffusion rate is large enough, and two species will coexist if the diffusion rate is small. We solve these two conjectures by applying the monotone dynamics theory, incorporated with a complete characterization of the positive equilibrium and a thorough analysis on the stability of the semi-trivial equilibria with respect to the dispersal rate. Our result on the winning strategy for sufficiently large dispersal rate might explain the group breeding behavior that is observed in some animals under certain ecological conditions. |
| format | Article |
| id | doaj-art-c24cba339ecd407680c2f5f754b37d1c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c24cba339ecd407680c2f5f754b37d1c2025-01-24T02:28:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-02-0111494797010.3934/mbe.2014.11.947Global dynamics for two-species competition in patchy environmentKuang-Hui Lin0Yuan Lou1Chih-Wen Shih2Tze-Hung Tsai3Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300Department of Mathematics, Mathematical Bioscience Institute, Ohio State University, Columbus, Ohio 43210Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300An ODE system modeling the competition between two species in a two-patch environment is studied.Both species move between the patches with the same dispersal rate. It is shown that the species with largerbirth rates in both patches drives the other species to extinction, regardless of the dispersal rate. The more interesting case is when both species have the same average birth rate but each species has larger birth rate in one patch. It has previously been conjectured by Gourley and Kuang that the species that can concentrate its birth in a single patch wins if the diffusion rate is large enough, and two species will coexist if the diffusion rate is small. We solve these two conjectures by applying the monotone dynamics theory, incorporated with a complete characterization of the positive equilibrium and a thorough analysis on the stability of the semi-trivial equilibria with respect to the dispersal rate. Our result on the winning strategy for sufficiently large dispersal rate might explain the group breeding behavior that is observed in some animals under certain ecological conditions.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.947monotone dynamicsglobal dynamicspatch modelcompetitionstability. |
| spellingShingle | Kuang-Hui Lin Yuan Lou Chih-Wen Shih Tze-Hung Tsai Global dynamics for two-species competition in patchy environment Mathematical Biosciences and Engineering monotone dynamics global dynamics patch model competition stability. |
| title | Global dynamics for two-species competition in patchy environment |
| title_full | Global dynamics for two-species competition in patchy environment |
| title_fullStr | Global dynamics for two-species competition in patchy environment |
| title_full_unstemmed | Global dynamics for two-species competition in patchy environment |
| title_short | Global dynamics for two-species competition in patchy environment |
| title_sort | global dynamics for two species competition in patchy environment |
| topic | monotone dynamics global dynamics patch model competition stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.947 |
| work_keys_str_mv | AT kuanghuilin globaldynamicsfortwospeciescompetitioninpatchyenvironment AT yuanlou globaldynamicsfortwospeciescompetitioninpatchyenvironment AT chihwenshih globaldynamicsfortwospeciescompetitioninpatchyenvironment AT tzehungtsai globaldynamicsfortwospeciescompetitioninpatchyenvironment |