Evolutionary dynamics of prey-predator systems with Holling type II functional response
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School of Mathematics and Statistics, Southwest University, Chongqing, 400715, PR
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School of Mathematics and Statistics, Southwest University, Chongqing, 400715
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Chongqing University, Chongqing, 400030, PR
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Received:
01 March 2006
Accepted:
29 June 2018
Published:
01 February 2007
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MSC :
92D15.
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This paper considers the coevolution of phenotypes in a community
comprising the populations of predators and prey. The evolutionary
dynamics is constructed from a stochastic process of mutation and
selection. We investigate the ecological and evolutionary conditions
that allow for continuously stable strategy and evolutionary
branching. It is shown that branching in the prey can induce
secondary branching in the predators. Furthermore, it is shown that
the evolutionary dynamics admits a stable limit cycle. The
evolutionary cycle is a likely outcome of the process, which
requires higher evolutionary speed of prey than of predators. It
is also found that different evolutionary rates and conversion
efficiencies can influence the lengths of evolutionary cycles.
Citation: Jian Zu, Wendi Wang, Bo Zu. Evolutionary dynamics of prey-predator systems with Holling type II functional response[J]. Mathematical Biosciences and Engineering, 2007, 4(2): 221-237. doi: 10.3934/mbe.2007.4.221
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Abstract
This paper considers the coevolution of phenotypes in a community
comprising the populations of predators and prey. The evolutionary
dynamics is constructed from a stochastic process of mutation and
selection. We investigate the ecological and evolutionary conditions
that allow for continuously stable strategy and evolutionary
branching. It is shown that branching in the prey can induce
secondary branching in the predators. Furthermore, it is shown that
the evolutionary dynamics admits a stable limit cycle. The
evolutionary cycle is a likely outcome of the process, which
requires higher evolutionary speed of prey than of predators. It
is also found that different evolutionary rates and conversion
efficiencies can influence the lengths of evolutionary cycles.
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