A predator-2 prey fast-slow dynamical system for rapid predator evolution
We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast–3 slow dynamical system to describe the dynamics of the three populations amidst continuous but rapid evolution of the predator’s diet choice. The two extrem...
| Main Authors: | , , , |
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2017
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| _version_ | 1797052921193431040 |
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| author | Piltz, S Veerman, F Maini, P Porter, M |
| author_facet | Piltz, S Veerman, F Maini, P Porter, M |
| author_sort | Piltz, S |
| collection | OXFORD |
| description | We consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast–3 slow dynamical system to describe the dynamics of the three populations amidst continuous but rapid evolution of the predator’s diet choice. The two extremes at which the predator’s diet is composed solely of one prey correspond to two branches of the three-branch critical manifold of the fast–slow system. By calculating the points at which there is a fast transition between these two feeding choices (i.e., branches of the critical manifold), we prove that the system has a two-parameter family of periodic orbits for sufficiently large separation of the time scales between the evolutionary and ecological dynamics. Using numerical simulations, we show that these periodic orbits exist, and that their phase difference and oscillation patterns persist, when ecological and evolutionary interactions occur on comparable time scales. Our model also exhibits periodic orbits that agree qualitatively with oscillation patterns observed in experimental studies of the coupling between rapid evolution and ecological interactions. |
| first_indexed | 2024-03-06T18:37:21Z |
| format | Journal article |
| id | oxford-uuid:0bb1fd40-2c0f-483f-82d0-a356bb78400f |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:37:21Z |
| publishDate | 2017 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:0bb1fd40-2c0f-483f-82d0-a356bb78400f2022-03-26T09:30:52ZA predator-2 prey fast-slow dynamical system for rapid predator evolutionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0bb1fd40-2c0f-483f-82d0-a356bb78400fSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2017Piltz, SVeerman, FMaini, PPorter, MWe consider adaptive change of diet of a predator population that switches its feeding between two prey populations. We develop a novel 1 fast–3 slow dynamical system to describe the dynamics of the three populations amidst continuous but rapid evolution of the predator’s diet choice. The two extremes at which the predator’s diet is composed solely of one prey correspond to two branches of the three-branch critical manifold of the fast–slow system. By calculating the points at which there is a fast transition between these two feeding choices (i.e., branches of the critical manifold), we prove that the system has a two-parameter family of periodic orbits for sufficiently large separation of the time scales between the evolutionary and ecological dynamics. Using numerical simulations, we show that these periodic orbits exist, and that their phase difference and oscillation patterns persist, when ecological and evolutionary interactions occur on comparable time scales. Our model also exhibits periodic orbits that agree qualitatively with oscillation patterns observed in experimental studies of the coupling between rapid evolution and ecological interactions. |
| spellingShingle | Piltz, S Veerman, F Maini, P Porter, M A predator-2 prey fast-slow dynamical system for rapid predator evolution |
| title | A predator-2 prey fast-slow dynamical system for rapid predator evolution |
| title_full | A predator-2 prey fast-slow dynamical system for rapid predator evolution |
| title_fullStr | A predator-2 prey fast-slow dynamical system for rapid predator evolution |
| title_full_unstemmed | A predator-2 prey fast-slow dynamical system for rapid predator evolution |
| title_short | A predator-2 prey fast-slow dynamical system for rapid predator evolution |
| title_sort | predator 2 prey fast slow dynamical system for rapid predator evolution |
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