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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 4: 859-875. doi: 10.3934/mbe.2008.5.859
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Variation in risk in single-species discrete-time models

  • 1.
    Department of Ecology, Evolution and Marine Biology, University of California at Santa Barbara, CA 93106-9610
  • Received: 01 January 2008 Accepted: 29 June 2018 Published: 01 October 2008

  • MSC : Primary: 92D25, 92D40; Secondary: 92B05

  • Simple, discrete-time, population models typically exhibit complex dynamics, like cyclic oscillations and chaos, when the net reproductive rate, , is large. These traditional models generally do not incorporate variability in juvenile "risk,'' defined to be a measure of a juvenile's vulnerability to density-dependent mortality. For a broad class of discrete-time models we show that variability in risk across juveniles tends to stabilize the equilibrium. We consider both density-independent and density-dependent risk, and for each, we identify appropriate shapes of the distribution of risk that will stabilize the equilibrium for all values of . In both cases, it is the shape of the distribution of risk and not the amount of variation in risk that is crucial for stability.

    Citation: Abhyudai Singh, Roger M. Nisbet. Variation in risk in single-species discrete-time models[J]. Mathematical Biosciences and Engineering, 2008, 5(4): 859-875. doi: 10.3934/mbe.2008.5.859

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  • Simple, discrete-time, population models typically exhibit complex dynamics, like cyclic oscillations and chaos, when the net reproductive rate, , is large. These traditional models generally do not incorporate variability in juvenile "risk,'' defined to be a measure of a juvenile's vulnerability to density-dependent mortality. For a broad class of discrete-time models we show that variability in risk across juveniles tends to stabilize the equilibrium. We consider both density-independent and density-dependent risk, and for each, we identify appropriate shapes of the distribution of risk that will stabilize the equilibrium for all values of . In both cases, it is the shape of the distribution of risk and not the amount of variation in risk that is crucial for stability.


  • This article has been cited by:

    1. Abhyudai Singh, Attack by a common parasitoid stabilizes population dynamics of multi-host communities, 2021, 531, 00225193, 110897, 10.1016/j.jtbi.2021.110897
    2. Abhyudai Singh, Brooks Emerick, 2020, Hybrid systems framework for modeling host-parasitoid population dynamics, 978-1-7281-7447-1, 4628, 10.1109/CDC42340.2020.9304450
    3. Abhyudai Singh, Brooks Emerick, Generalized stability conditions for host–parasitoid population dynamics: Implications for biological control, 2021, 456, 03043800, 109656, 10.1016/j.ecolmodel.2021.109656
    4. Abhyudai Singh, Stochasticity in host-parasitoid models informs mechanisms regulating population dynamics, 2021, 11, 2045-2322, 10.1038/s41598-021-96212-y
    5. Abhyudai Singh, Lucas D. B. Faria, A comparative approach to stabilizing mechanisms between discrete- and continuous-time consumer-resource models, 2022, 17, 1932-6203, e0265825, 10.1371/journal.pone.0265825
    6. Abhyudai Singh, Brooks Emerick, Coexistence conditions in generalized discrete-time models of insect population dynamics, 2022, 474, 03043800, 110148, 10.1016/j.ecolmodel.2022.110148
    7. Abhyudai Singh, Lucas D. B. Faria, Fundamental limits of parasitoid-driven host population suppression: Implications for biological control, 2023, 18, 1932-6203, e0295980, 10.1371/journal.pone.0295980
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  • © 2008 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)
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