Search Advanced

Mathematical Biosciences and Engineering

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

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.

    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

    Related Papers:

    [1] Jian Zu, Wendi Wang, Bo Zu . Letter to the editors. Mathematical Biosciences and Engineering, 2007, 4(4): 755-755. doi: 10.3934/mbe.2007.4.755
    [2] Lina Hao, Meng Fan, Xin Wang . Effects of nutrient enrichment on coevolution of a stoichiometric producer-grazer system. Mathematical Biosciences and Engineering, 2014, 11(4): 841-875. doi: 10.3934/mbe.2014.11.841
    [3] Saheb Pal, Nikhil Pal, Sudip Samanta, Joydev Chattopadhyay . Fear effect in prey and hunting cooperation among predators in a Leslie-Gower model. Mathematical Biosciences and Engineering, 2019, 16(5): 5146-5179. doi: 10.3934/mbe.2019258
    [4] Shuangte Wang, Hengguo Yu . Stability and bifurcation analysis of the Bazykin's predator-prey ecosystem with Holling type Ⅱ functional response. Mathematical Biosciences and Engineering, 2021, 18(6): 7877-7918. doi: 10.3934/mbe.2021391
    [5] Peter A. Braza . Predator-Prey Dynamics with Disease in the Prey. Mathematical Biosciences and Engineering, 2005, 2(4): 703-717. doi: 10.3934/mbe.2005.2.703
    [6] Yongli Cai, Malay Banerjee, Yun Kang, Weiming Wang . Spatiotemporal complexity in a predator--prey model with weak Allee effects. Mathematical Biosciences and Engineering, 2014, 11(6): 1247-1274. doi: 10.3934/mbe.2014.11.1247
    [7] Eric M. Takyi, Charles Ohanian, Margaret Cathcart, Nihal Kumar . Dynamical analysis of a predator-prey system with prey vigilance and hunting cooperation in predators. Mathematical Biosciences and Engineering, 2024, 21(2): 2768-2786. doi: 10.3934/mbe.2024123
    [8] Yajie Sun, Ming Zhao, Yunfei Du . Multiple bifurcations of a discrete modified Leslie-Gower predator-prey model. Mathematical Biosciences and Engineering, 2023, 20(12): 20437-20467. doi: 10.3934/mbe.2023904
    [9] Rujing Zhao, Xiulan Lai . Evolutionary analysis of replicator dynamics about anti-cancer combination therapy. Mathematical Biosciences and Engineering, 2023, 20(1): 656-682. doi: 10.3934/mbe.2023030
    [10] Sílvia Cuadrado . Stability of equilibria of a predator-prey model of phenotype evolution. Mathematical Biosciences and Engineering, 2009, 6(4): 701-718. doi: 10.3934/mbe.2009.6.701
  • 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.


  • This article has been cited by:

    1. YUN KANG, JENNIFER HARRISON FEWELL, CO-EVOLUTIONARY DYNAMICS OF A SOCIAL PARASITE-HOST INTERACTION MODEL: OBLIGATE VERSUS FACULTATIVE SOCIAL PARASITISM, 2015, 28, 08908575, 398, 10.1111/nrm.12078
    2. Jian Zu, Masayasu Mimura, Joe Yuichiro Wakano, The evolution of phenotypic traits in a predator–prey system subject to Allee effect, 2010, 262, 00225193, 528, 10.1016/j.jtbi.2009.10.022
    3. Vincent Calcagno, Marion Dubosclard, Claire de Mazancourt, Rapid Exploiter‐Victim Coevolution: The Race Is Not Always to the Swift, 2010, 176, 0003-0147, 198, 10.1086/653665
    4. Jian Zu, Masayasu Mimura, The impact of Allee effect on a predator–prey system with Holling type II functional response, 2010, 217, 00963003, 3542, 10.1016/j.amc.2010.09.029
    5. Mohammad A. Safi, Salisu M. Garba, Global Stability Analysis of SEIR Model with Holling Type II Incidence Function, 2012, 2012, 1748-670X, 1, 10.1155/2012/826052
    6. Muhammad Bilal Ghori, Parvaiz Ahmad Naik, Jian Zu, Zohreh Eskandari, Mehraj‐ud‐din Naik, Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate, 2022, 45, 0170-4214, 3665, 10.1002/mma.8010
    7. Yudan Ma, Ming Zhao, Yunfei Du, Impact of the strong Allee effect in a predator-prey model, 2022, 7, 2473-6988, 16296, 10.3934/math.2022890
    8. Bo Li, Mohammadreza Mahmoudi, Zohreh Eskandari, 2025, Chapter 7, 978-981-96-3093-6, 191, 10.1007/978-981-96-3094-3_7
  • Reader Comments
  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2361) PDF downloads(486) Cited by(8)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog