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Ideal free dispersal in integrodifference models.

Robert Stephen Cantrell1, Chris Cosner2, Ying Zhou3

  • 1Department of Mathematics, University of Miami, Coral Gables, FL, USA.

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Summary

Dispersal strategies are evolutionarily stable when habitats vary seasonally or spatially. Ideal free distributions, including partial occupation, are evolutionarily stable, ensuring population viability in changing environments.

Keywords:
DispersalIdeal free distributionIntegrodifferenceMigrationPopulation dynamicsSpatial ecology

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Area of Science:

  • Ecology
  • Evolutionary Biology
  • Mathematical Biology

Background:

  • Habitat suitability can vary spatially and seasonally, influencing population dynamics.
  • Dispersal is a key strategy influencing species survival and distribution.
  • Understanding evolutionarily stable strategies (ESS) is crucial for predicting ecological persistence.

Purpose of the Study:

  • To determine evolutionarily stable dispersal strategies under spatial heterogeneity and seasonal habitat variation.
  • To investigate the role of dispersal in sustaining populations in non-viable or seasonally shifting habitats.
  • To connect dispersal strategies with ideal free distribution models.

Main Methods:

  • Utilized an integrodifference equation model.
  • Employed pairwise invasion analysis to identify evolutionarily stable strategies (ESS).
  • Applied properties of line sum symmetric functions for mathematical proofs.

Main Results:

  • Dispersal strategies linked to ideal free distributions are evolutionarily stable.
  • Partial occupation ideal free distributions are ESS in habitats with non-viable regions.
  • Dispersal can be essential for population persistence when viable regions shift seasonally.

Conclusions:

  • The study confirms and extends previous findings on ESS dispersal strategies.
  • Mathematical modeling provides robust insights into ecological strategy evolution.
  • Ideal free distributions offer a framework for understanding adaptive dispersal in heterogeneous environments.