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Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model

Author

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  • Galina Neverova

    (Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, 690041 Vladivostok, Russia)

  • Oksana Zhdanova

    (Institute of Automation and Control Processes, Far Eastern Branch, Russian Academy of Sciences, 690041 Vladivostok, Russia)

Abstract

This study proposes a discrete-time eco-genetic model of a planktonic community that includes zooplankton and two competing phytoplankton haplotypes with and without a toxicity trait. The Holling type II response function describes predator consumption. We use the Ricker model to consider density limitation and regulation. The model is analytically and numerically studied. The loss of stability of fixed points occurs via the Neimark–Sacker scenario and a cascade of period-doubling bifurcations. The model reveals bistability and multistability. Therefore, the initial conditions can determine which of the coexisting dynamic modes will be attracted. If the competition of haplotypes is weaker than their self-regulation, then the variation in the current densities of community components can shift the observed dynamics, while the evolution direction remains unchanged. The ratio of haplotype fitnesses and predator pressure generally determines the asymptotic genetic composition of phytoplankton. If competition of haplotypes is higher than their self-regulation, then the bistability of monomorphic fixed points occurs when the displacement of one haplotype by another depends on initial conditions. The presence of predators can maintain the genetic polymorphism of the prey. This system shows dynamic modes similar to experimental dynamics: oscillation with delay, long-period antiphase fluctuations, and cryptic cycles emerging due to rapid evolution.

Suggested Citation

  • Galina Neverova & Oksana Zhdanova, 2023. "Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model," Mathematics, MDPI, vol. 11(22), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4673-:d:1281839
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    References listed on IDEAS

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    1. Michael J. Behrenfeld & Peter Gaube & Alice Penna & Robert T. O’Malley & William J. Burt & Yongxiang Hu & Paula S. Bontempi & Deborah K. Steinberg & Emmanuel S. Boss & David A. Siegel & Chris A. Hoste, 2019. "Global satellite-observed daily vertical migrations of ocean animals," Nature, Nature, vol. 576(7786), pages 257-261, December.
    2. Mehbuba Rehim & Weixin Wu & Ahmadjan Muhammadhaji, 2015. "On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-13, February.
    3. Pak, S.Ya. & Abakumov, A.I., 2020. "PHYTOPLANKTON in the SEA of OKHOTSK along WESTERN KAMCHATKA: WARM vs COLD YEARS," Ecological Modelling, Elsevier, vol. 433(C).
    4. Montagnes, David J.S. & Fenton, Andy, 2012. "Prey-abundance affects zooplankton assimilation efficiency and the outcome of biogeochemical models," Ecological Modelling, Elsevier, vol. 243(C), pages 1-7.
    5. Takehito Yoshida & Laura E. Jones & Stephen P. Ellner & Gregor F. Fussmann & Nelson G. Hairston, 2003. "Rapid evolution drives ecological dynamics in a predator–prey system," Nature, Nature, vol. 424(6946), pages 303-306, July.
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