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Patch Retention Times for the Ideal Free Distribution

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  • Vlastimil Křivan

    (University of South Bohemia
    Biology Centre, Czech Academy of Sciences)

Abstract

This article studies patch retention time dynamics for which dispersal dynamics converge on the Ideal Free Distribution. Two types of dispersal dynamics are considered: one that assumes immigration rates are random and the second where immigration rates depend on patch distances. Emigration rates are inversely proportional to patch retention times. Both these dispersal dynamics converge to a unique and stable population distribution equilibrium. Assuming that animal distribution tracks current retention times instantaneously, retention time dynamics are modeled by the canonical equation of adaptive dynamics. This general framework is applied to two negative density-dependent patch payoff functions, hyperbolic and linear. Patch retention time dynamics are unbounded for low population densities, meaning dispersal tends to stop, and the resulting population distribution is identical to the classic Ideal Free Distribution. For higher densities, retention time dynamics converge on an equilibrium where animal dispersal is balanced in that the net dispersal stops.

Suggested Citation

  • Vlastimil Křivan, 2025. "Patch Retention Times for the Ideal Free Distribution," Dynamic Games and Applications, Springer, vol. 15(4), pages 1186-1213, September.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:4:d:10.1007_s13235-025-00628-4
    DOI: 10.1007/s13235-025-00628-4
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