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Asymmetric dispersal in the multi-patch logistic equation.

Roger Arditi1, Claude Lobry2, Tewfik Sari3

  • 1University of Fribourg, Department of Biology, Chemin du Musée 10, 1700 Fribourg, Switzerland; Sorbonne Université, Institute of Ecology and Environmental Sciences (iEES-Paris), 75252 Paris cedex 05, France.

Theoretical Population Biology
|December 27, 2017
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Summary

Population fragmentation and dispersal dynamics were analyzed in a two-patch model. Asymmetric dispersal rates significantly influence whether fragmentation benefits or harms total population abundance.

Keywords:
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Area of Science:

  • Ecology
  • Population Dynamics
  • Mathematical Biology

Background:

  • The standard model for fragmented populations uses coupled logistic models with migration.
  • This model, widely used since the 1970s, lacks full analysis in two-patch systems.
  • Asymmetric dispersal rates are common but their impact is not fully understood.

Purpose of the Study:

  • To fully analyze the standard population dynamics model in a two-patch scenario.
  • To determine conditions where population fragmentation aids or hinders total abundance.
  • To investigate the specific role of asymmetric dispersal.

Main Methods:

  • Mathematical analysis of a two-patch logistic model with migration.
  • Focus on density-dependent population dynamics.
  • Examination of symmetric and asymmetric dispersal rates.

Main Results:

  • Fragmentation's effect on population abundance depends on specific conditions.
  • Asymmetric dispersal rates can critically alter the impact of fragmentation.
  • The analysis provides a comprehensive understanding of dispersal effects in fragmented populations.

Conclusions:

  • Dispersal in fragmented populations can be either beneficial or detrimental to total abundance.
  • Asymmetric dispersal is a key factor influencing population outcomes.
  • This study offers a complete analysis of a widely used ecological model.