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Stability in N-species coevolutionary systems.

Ross Cressman1, József Garay

  • 1Department of Mathematics, Wilfrid Laurier University, Ont., N2L 3C5 Waterloo, Canada. rcressma@wlu.ca

Theoretical Population Biology
|November 25, 2003
PubMed
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This study generalizes coevolutionary stability criteria beyond linear fitness functions for Lotka-Volterra systems. It establishes that coevolutionary stability equals ecological and evolutionary stability on the stationary density surface for monomorphic systems.

Area of Science:

  • Ecology and Evolutionary Biology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • Recent advances provide stability criteria for coevolutionary Lotka-Volterra systems with linear individual fitness functions.
  • Existing models often simplify fitness functions, limiting applicability to complex ecological interactions.

Purpose of the Study:

  • To extend coevolutionary stability criteria to systems with arbitrary (nonlinear) fitness functions.
  • To develop a general theory of coevolution integrating ecological and evolutionary dynamics.
  • To analyze the role of the stationary density surface in coevolutionary stability.

Main Methods:

  • Generalization of existing stability criteria for coevolutionary Lotka-Volterra systems.
  • Development of a unified theory combining ecological and evolutionary effects.

Related Experiment Videos

  • Analysis of systems with a finite number of individual phenotypes.
  • Investigation of monomorphic resident systems and their stability properties.

    • Main Results:

    • Coevolutionary stability is demonstrated to be equivalent to the combination of ecological stability and evolutionary stability on the stationary density surface for monomorphic resident systems.
    • The theory accommodates arbitrary nonlinear fitness functions, broadening the scope of coevolutionary analysis.
    • The central importance of the stationary density surface for determining stability is highlighted.

    Conclusions:

    • The generalized theory provides a robust framework for studying coevolution with nonlinear fitness functions.
    • The findings offer new insights into the interplay between ecological and evolutionary processes in shaping species dynamics.
    • The study connects to adaptive dynamics approaches for phenotypic coevolution with continuous phenotypes.