IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v268y2013icp25-36.html
   My bibliography  Save this article

Dynamics of a predator–prey interaction with seasonal reproduction and continuous predation

Author

Listed:
  • Zhou, Can
  • Fujiwara, Masami
  • Grant, William E.

Abstract

Dynamics of predator–prey systems are affected by life history attributes of both predator and prey. We compare performance of several different models of one specific type of predator–prey interaction in which both predator and prey exhibit seasonal reproduction and predation is continuous. We show that use of a discrete-time model that preserves seasonal reproduction, whether stage-structured or non-stage-structured, always produces equilibria that are locally stable, whereas use of a continuous-time predator–prey model with an instantaneous approximation of seasonal reproduction can produce a limit cycle (self-sustained population fluctuations). This difference in dynamics results from the mismatch of life history properties between the mathematical model and the biological system under the continuous time model. We conclude that seasonal reproduction may be an important stabilizing factor in predator–prey interactions. Finally, with stage-structured predator–prey models, we show how life history parameters affect asymptotic dynamics of the system. Discrete-time models provide a more natural match to the biology of these systems. Our results suggest that discrete-time models have the potential for reducing the gap between theoretical models and empirical observations for these systems.

Suggested Citation

  • Zhou, Can & Fujiwara, Masami & Grant, William E., 2013. "Dynamics of a predator–prey interaction with seasonal reproduction and continuous predation," Ecological Modelling, Elsevier, vol. 268(C), pages 25-36.
    • Handle: RePEc:eee:ecomod:v:268:y:2013:i:c:p:25-36
    DOI: 10.1016/j.ecolmodel.2013.07.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380013003840
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2013.07.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    2. Masami Fujiwara & Hal Caswell, 2001. "Demography of the endangered North Atlantic right whale," Nature, Nature, vol. 414(6863), pages 537-541, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sun, Zepeng & de Roos, André M., 2015. "Alternative stable states in a stage-structured consumer–resource biomass model with niche shift and seasonal reproduction," Theoretical Population Biology, Elsevier, vol. 103(C), pages 60-70.
    2. Fujiwara, Masami, 2016. "Incorporating demographic diversity into food web models: Effects on community structure and dynamics," Ecological Modelling, Elsevier, vol. 322(C), pages 10-18.
    3. Kvamsdal, Sturla & Maroto, José M. & Morán, Manuel & Sandal, Leif K., 2017. "A bridge between continuous and discrete-time bioeconomic models: Seasonality in fisheries," Ecological Modelling, Elsevier, vol. 364(C), pages 124-131.
    4. Rao, B. Veena Shankara Narayana & Walton, J.R. & Fujiwara, M., 2022. "A mathematical model to investigate the effects of fishing zone configurations and mass dependent rates on biomass yield: Application to brown shrimp in Gulf of Mexico," Ecological Modelling, Elsevier, vol. 463(C).
    5. Barraquand, Frédéric & Gimenez, Olivier, 2019. "Integrating multiple data sources to fit matrix population models for interacting species," Ecological Modelling, Elsevier, vol. 411(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Weiming & Wang, Xiaoqin & Lin, Yezhi, 2008. "Complicated dynamics of a predator–prey system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1427-1441.
    2. Song, Xinyu & Li, Yongfeng, 2007. "Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 463-478.
    3. Hernandez-Suarez, Carlos & Rabinovich, Jorge, 2024. "Exact confidence intervals for population growth rate, longevity and generation time," Theoretical Population Biology, Elsevier, vol. 155(C), pages 1-9.
    4. Sun, Chengjun & Loreau, Michel, 2009. "Dynamics of a three-species food chain model with adaptive traits," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2812-2819.
    5. Huo, Liang’an & Jiang, Jiehui & Gong, Sixing & He, Bing, 2016. "Dynamical behavior of a rumor transmission model with Holling-type II functional response in emergency event," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 228-240.
    6. Chiquet, Ross A. & Ma, Baoling & Ackleh, Azmy S. & Pal, Nabendu & Sidorovskaia, Natalia, 2013. "Demographic analysis of sperm whales using matrix population models," Ecological Modelling, Elsevier, vol. 248(C), pages 71-79.
    7. Wang, Weiming & Wang, Hailing & Li, Zhenqing, 2007. "The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1772-1785.
    8. Liu, Zhijun & Tan, Ronghua, 2007. "Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 454-464.
    9. Banks, J.E. & Dick, L.K. & Banks, H.T. & Stark, J.D., 2008. "Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics," Ecological Modelling, Elsevier, vol. 210(1), pages 155-160.
    10. Bramanti, Lorenzo & Iannelli, Mimmo & Santangelo, Giovanni, 2009. "Mathematical modelling for conservation and management of gorgonians corals: youngs and olds, could they coexist?," Ecological Modelling, Elsevier, vol. 220(21), pages 2851-2856.
    11. Guo, Hongjian & Song, Xinyu, 2008. "An impulsive predator–prey system with modified Leslie–Gower and Holling type II schemes," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1320-1331.
    12. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2008. "Chaotic behavior of a Watt-type predator–prey system with impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 706-718.
    13. Yongzhen, Pei & Yong, Yang & Changguo, Li, 2009. "Dynamics of an impulsive control system which prey species share a common predator," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2429-2436.
    14. Kendall, Bruce E. & Fujiwara, Masami & Diaz-Lopez, Jasmin & Schneider, Sandra & Voigt, Jakob & Wiesner, Sören, 2019. "Persistent problems in the construction of matrix population models," Ecological Modelling, Elsevier, vol. 406(C), pages 33-43.
    15. Barabás, György & Meszéna, Géza & Ostling, Annette, 2014. "Fixed point sensitivity analysis of interacting structured populations," Theoretical Population Biology, Elsevier, vol. 92(C), pages 97-106.
    16. Han, Xinli & Teng, Zhidong & Xiao, Dongmei, 2006. "Persistence and average persistence of a nonautonomous Kolmogorov system," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 748-758.
    17. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Chaotic behavior of a chemostat model with Beddington–DeAngelis functional response and periodically impulsive invasion," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 474-482.
    18. Wang, Xiaoqin & Wang, Weiming & Lin, Xiaolin, 2009. "Dynamics of a two-prey one-predator system with Watt-type functional response and impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2392-2404.
    19. Rouby, Etienne & Authier, Matthieu & Cam, Emmanuelle & Siebert, Ursula & Plard, Floriane, 2024. "Addressing temporal trends in survivorship from cross-sectional sampling designs: A modelling framework with applications for megafauna conservation," Ecological Modelling, Elsevier, vol. 490(C).
    20. Mullen, Kaitlyn A. & Peterson, Michael L. & Todd, Sean K., 2013. "Has designating and protecting critical habitat had an impact on endangered North Atlantic right whale ship strike mortality?," Marine Policy, Elsevier, vol. 42(C), pages 293-304.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:268:y:2013:i:c:p:25-36. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.