A mutualism-parasitism system modeling host and parasite withmutualism at low density
A mutualism-parasitism system of two species is considered, where mutualism is the dominant interaction when the predators (parasites) are at low density while parasitism is dominant when the predators are at high density. Our aim is to show that mutualism at low density promotes coexistence of the...
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AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.431 |
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| author | Yuanshi Wang Donald L. DeAngelis |
| author_facet | Yuanshi Wang Donald L. DeAngelis |
| author_sort | Yuanshi Wang |
| collection | DOAJ |
| description | A mutualism-parasitism system of two species is considered, where mutualism is the dominant interaction when the predators (parasites) are at low density while parasitism is dominant when the predators are at high density. Our aim is to show that mutualism at low density promotes coexistence of the species and leads to high production of the prey (host). The mutualism-parasitism system presented here is a combination of the Lotka-Volterra cooperative model and Lotka-Volterra predator-prey model. By comparing dynamics of this system with those of the Lotka-Volterra predator-prey model, we present the mechanisms by which the mutualism improves the coexistence of the species and production of the prey. Then the parameter space is divided into six regions, which correspond to the four outcomes of mutualism, commensalism, predation/parasitism and neutralism, respectively. When the parameters are varied continuously among the six regions, it is shown that the interaction outcomes of the system transition smoothly among the four outcomes. By comparing the dynamics of the specific system with those of the Lotka-Volterra cooperative model, we show that the parasitism at high density promotes stability of the system. A novel aspect of this paper is the simplicity of the model, which allows rigorous and thorough analysis and transparency of the results. |
| format | Article |
| id | doaj-art-6a24b0bc61d5483e8dffc15b141d8933 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6a24b0bc61d5483e8dffc15b141d89332025-01-24T02:05:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-02-019243144410.3934/mbe.2012.9.431A mutualism-parasitism system modeling host and parasite withmutualism at low densityYuanshi Wang0Donald L. DeAngelis1School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275A mutualism-parasitism system of two species is considered, where mutualism is the dominant interaction when the predators (parasites) are at low density while parasitism is dominant when the predators are at high density. Our aim is to show that mutualism at low density promotes coexistence of the species and leads to high production of the prey (host). The mutualism-parasitism system presented here is a combination of the Lotka-Volterra cooperative model and Lotka-Volterra predator-prey model. By comparing dynamics of this system with those of the Lotka-Volterra predator-prey model, we present the mechanisms by which the mutualism improves the coexistence of the species and production of the prey. Then the parameter space is divided into six regions, which correspond to the four outcomes of mutualism, commensalism, predation/parasitism and neutralism, respectively. When the parameters are varied continuously among the six regions, it is shown that the interaction outcomes of the system transition smoothly among the four outcomes. By comparing the dynamics of the specific system with those of the Lotka-Volterra cooperative model, we show that the parasitism at high density promotes stability of the system. A novel aspect of this paper is the simplicity of the model, which allows rigorous and thorough analysis and transparency of the results.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.431population dynamicscoexistence.parasitismmutualismlotka-volterra |
| spellingShingle | Yuanshi Wang Donald L. DeAngelis A mutualism-parasitism system modeling host and parasite withmutualism at low density Mathematical Biosciences and Engineering population dynamics coexistence. parasitism mutualism lotka-volterra |
| title | A mutualism-parasitism system modeling host and parasite withmutualism at low density |
| title_full | A mutualism-parasitism system modeling host and parasite withmutualism at low density |
| title_fullStr | A mutualism-parasitism system modeling host and parasite withmutualism at low density |
| title_full_unstemmed | A mutualism-parasitism system modeling host and parasite withmutualism at low density |
| title_short | A mutualism-parasitism system modeling host and parasite withmutualism at low density |
| title_sort | mutualism parasitism system modeling host and parasite withmutualism at low density |
| topic | population dynamics coexistence. parasitism mutualism lotka-volterra |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.431 |
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