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Extended Lotka–Volterra equations incorporating population heterogeneity: Derivation and analysis of the predator–prey case

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  • Waters, Edward K.
  • Sidhu, Harvinder S.
  • Sidhu, Leesa A.
  • Mercer, Geoffry N.

Abstract

Extended logistic and competitive Lotka–Volterra equations were developed by Eizi Kuno to understand the implications of population heterogeneity (especially spatial) for population growth. Population heterogeneity, defined as the presence of individuals in some patches of population and not others, is the resulting expression of a number of processes, including dispersal, habitat heterogeneity and searching behaviour. Kuno's models allow the effect of population heterogeneity (thus defined) on a population at equilibrium to be accounted for without using multi-patch models. This paper demonstrates this for the first time using numerical simulations and presents a more complete mathematical derivation of his models. An extension of Kuno's equations to model predator–prey scenarios with heterogeneity in the prey population is also developed. Analysis of this predator–prey case shows that a patchy distribution of prey facilitates their stable coexistence with predators. This paper has broad implications for ecological modelling because it shows how the effects of a number of population processes, including dispersal, are reflected in the density of populations at equilibrium. Therefore, by adjusting the equilibrium solutions of models, the effects of a number of processes are captured without representing the processes themselves in an explicit way.

Suggested Citation

  • Waters, Edward K. & Sidhu, Harvinder S. & Sidhu, Leesa A. & Mercer, Geoffry N., 2015. "Extended Lotka–Volterra equations incorporating population heterogeneity: Derivation and analysis of the predator–prey case," Ecological Modelling, Elsevier, vol. 297(C), pages 187-195.
    • Handle: RePEc:eee:ecomod:v:297:y:2015:i:c:p:187-195
    DOI: 10.1016/j.ecolmodel.2014.11.019
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    References listed on IDEAS

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    1. Matthieu Bouaziz & Caroline Paccard & Mickael Guedj & Christophe Ambroise, 2012. "SHIPS: Spectral Hierarchical Clustering for the Inference of Population Structure in Genetic Studies," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-17, October.
    2. Thomas Eichner & Rüdiger Pethig, 2006. "An Analytical Foundation of the Ratio-Dependent Predator-Prey Model," Journal of Bioeconomics, Springer, vol. 8(2), pages 121-132, August.
    3. Nagurney, Anna & Nagurney, Ladimer S., 2012. "Dynamics and equilibria of ecological predator–prey networks as nature’s supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 89-99.
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    Cited by:

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    2. Xuan Huang & Yuting Ding & Ning Pan, 2023. "Dynamic Analysis of Delayed Two-Species Interaction Model with Age Structure: An Application to Larch-Betula Platyphylla Forests in the Daxing’an Mountains, Northeast China," Mathematics, MDPI, vol. 11(11), pages 1-20, May.

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