Evolutionary dynamics of prey-predator systems with Holling type II functional response

Jian Zu; Wendi Wang; Bo Zu; Jian Zu; Wendi Wang; Bo Zu

doi:10.3934/mbe.2007.4.221

Mathematical Biosciences and Engineering

2007, Volume 4, Issue 2: 221-237. doi: 10.3934/mbe.2007.4.221

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Evolutionary dynamics of prey-predator systems with Holling type II functional response

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, PR
2.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715
3.
Chongqing University, Chongqing, 400030, PR

Received: 01 March 2006 Accepted: 29 June 2018 Published: 01 February 2007
MSC : 92D15.

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.
- adaptive dynamics.,
- continuously stable strategy,
- evolutionary branching,
- Hopf bifurcation,
- evolutionary dynamics
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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