Evolutionary dynamics of prey-predator systems with Holling type II functional response
This paper considers the coevolution of phenotypes in a communitycomprising the populations of predators and prey. The evolutionarydynamics is constructed from a stochastic process of mutation andselection. We investigate the ecological and evolutionary conditionsthat allow for continuously stable s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.221 |
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| _version_ | 1832590277799313408 |
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| author | Jian Zu Wendi Wang Bo Zu |
| author_facet | Jian Zu Wendi Wang Bo Zu |
| author_sort | Jian Zu |
| collection | DOAJ |
| description | This paper considers the coevolution of phenotypes in a communitycomprising the populations of predators and prey. The evolutionarydynamics is constructed from a stochastic process of mutation andselection. We investigate the ecological and evolutionary conditionsthat allow for continuously stable strategy and evolutionarybranching. It is shown that branching in the prey can inducesecondary branching in the predators. Furthermore, it is shown thatthe evolutionary dynamics admits a stable limit cycle. Theevolutionary cycle is a likely outcome of the process, whichrequires higher evolutionary speed of prey than of predators. Itis also found that different evolutionary rates and conversionefficiencies can influence the lengths of evolutionary cycles. |
| format | Article |
| id | doaj-art-abf85a1ba2da42ddbe5509addf78c9f4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-abf85a1ba2da42ddbe5509addf78c9f42025-01-24T01:53:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-01-014222123710.3934/mbe.2007.4.221Evolutionary dynamics of prey-predator systems with Holling type II functional responseJian Zu0Wendi Wang1Bo Zu2School of Mathematics and Statistics, Southwest University, Chongqing, 400715, PRSchool of Mathematics and Statistics, Southwest University, Chongqing, 400715, PRSchool of Mathematics and Statistics, Southwest University, Chongqing, 400715, PRThis paper considers the coevolution of phenotypes in a communitycomprising the populations of predators and prey. The evolutionarydynamics is constructed from a stochastic process of mutation andselection. We investigate the ecological and evolutionary conditionsthat allow for continuously stable strategy and evolutionarybranching. It is shown that branching in the prey can inducesecondary branching in the predators. Furthermore, it is shown thatthe evolutionary dynamics admits a stable limit cycle. Theevolutionary cycle is a likely outcome of the process, whichrequires higher evolutionary speed of prey than of predators. Itis also found that different evolutionary rates and conversionefficiencies can influence the lengths of evolutionary cycles.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.221adaptive dynamics.continuously stable strategyevolutionary branchinghopf bifurcationevolutionary dynamics |
| spellingShingle | Jian Zu Wendi Wang Bo Zu Evolutionary dynamics of prey-predator systems with Holling type II functional response Mathematical Biosciences and Engineering adaptive dynamics. continuously stable strategy evolutionary branching hopf bifurcation evolutionary dynamics |
| title | Evolutionary dynamics of prey-predator systems with Holling type II functional response |
| title_full | Evolutionary dynamics of prey-predator systems with Holling type II functional response |
| title_fullStr | Evolutionary dynamics of prey-predator systems with Holling type II functional response |
| title_full_unstemmed | Evolutionary dynamics of prey-predator systems with Holling type II functional response |
| title_short | Evolutionary dynamics of prey-predator systems with Holling type II functional response |
| title_sort | evolutionary dynamics of prey predator systems with holling type ii functional response |
| topic | adaptive dynamics. continuously stable strategy evolutionary branching hopf bifurcation evolutionary dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.221 |
| work_keys_str_mv | AT jianzu evolutionarydynamicsofpreypredatorsystemswithhollingtypeiifunctionalresponse AT wendiwang evolutionarydynamicsofpreypredatorsystemswithhollingtypeiifunctionalresponse AT bozu evolutionarydynamicsofpreypredatorsystemswithhollingtypeiifunctionalresponse |