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What makes ecological systems reactive?

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  • Snyder, Robin E.

Abstract

Although perturbations from a stable equilibrium must ultimately vanish, they can grow initially, and the maximum initial growth rate is called reactivity. Reactivity thus identifies systems that may undergo transient population surges or drops in response to perturbations; however, we lack biological and mathematical intuition about what makes a system reactive. This paper presents upper and lower bounds on reactivity for an arbitrary linearized model, explores their strictness, and discusses their biological implications. I find that less stable systems (i.e. systems with long transients) have a smaller possible range of reactivities for which no perturbations grow. Systems with more species have a higher capacity to be reactive, assuming species interactions do not weaken too rapidly as the number of species increases. Finally, I find that in discrete time, reactivity is determined largely by mean interaction strength and neither discrete nor continuous time reactivity are sensitive to food web topology.

Suggested Citation

  • Snyder, Robin E., 2010. "What makes ecological systems reactive?," Theoretical Population Biology, Elsevier, vol. 77(4), pages 243-249.
    • Handle: RePEc:eee:thpobi:v:77:y:2010:i:4:p:243-249
    DOI: 10.1016/j.tpb.2010.03.004
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    Cited by:

    1. Yuguang Yang & Katharine Z. Coyte & Kevin R. Foster & Aming Li, 2023. "Reactivity of complex communities can be more important than stability," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    2. Jianguo Tan & Wenjuan Wang & Jianfeng Feng, 2022. "Transient Dynamics Analysis of a Predator-Prey System with Square Root Functional Responses and Random Perturbation," Mathematics, MDPI, vol. 10(21), pages 1-12, November.
    3. Wen Liu & Jianfeng Feng, 2021. "Analysis of Asymptotic and Transient Behaviors of Stochastic Ratio-Dependent Predator–Prey Model," Mathematics, MDPI, vol. 9(21), pages 1-13, November.

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