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Difference equations as models of evolutionary population dynamics.

J M Cushing1

  • 1a Department of Mathematics, Interdisciplinary Program in Applied Mathematics , University of Arizona , Tucson, AZ , USA.

Journal of Biological Dynamics
|February 5, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces evolutionary game theory to population dynamics, showing how Darwinian evolution shapes model coefficients. This approach reveals new survival strategies and evolutionary stable outcomes in classic ecological models.

Keywords:
39A2839A3039A6092D1592D25Darwinian dynamicsPopulation dynamicsbifurcationdifference equationsevolutionary dynamicsevolutionary game theorystability

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Area of Science:

  • Evolutionary biology
  • Mathematical ecology
  • Game theory

Background:

  • Population dynamic models are crucial for understanding ecological systems.
  • Incorporating evolutionary dynamics can reveal long-term population behavior.
  • Classic models like Beverton-Holt and Ricker lack evolutionary considerations.

Purpose of the Study:

  • To develop a methodology integrating evolutionary game theory with difference equation population models.
  • To analyze the impact of evolving model coefficients on population dynamics.
  • To investigate evolutionary stable strategies and bifurcations in ecological models.

Main Methods:

  • Extension of difference equation population models using evolutionary game theory.
  • Application of a general theorem on transcritical bifurcations.
  • Analysis of evolutionary versions of the discrete logistic (Beverton-Holt) and Ricker equations.

Main Results:

  • A method for accounting for Darwinian evolution of model coefficients is presented.
  • A theorem describes transcritical bifurcations leading to stable survival equilibria.
  • Applications demonstrate phenomena like Allee effects and adaptive landscapes.

Conclusions:

  • Evolutionary game theory provides a robust framework for extending population dynamic models.
  • Evolving coefficients lead to new stability properties and survival equilibria.
  • The methodology offers insights into complex biological phenomena and evolutionary stable strategies.