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Adaptive dynamics of saturated polymorphisms.

Éva Kisdi1, Stefan A H Geritz2

  • 1Department of Mathematics and Statistics, University of Helsinki, PO Box 68, 00014, Helsinki, Finland. eva.kisdi@helsinki.fi.

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|December 18, 2015
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Summary
This summary is machine-generated.

This study explores adaptive dynamics in saturated ecological systems, revealing unique characteristics in host-pathogen-predator models and general polymorphisms. It establishes a new condition for stability in evolutionary dynamics, applicable to saturated systems.

Keywords:
Adaptive dynamicsCoevolutionCompetitive exclusion principleEnvironmental feedbackSaturated community

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Area of Science:

  • Evolutionary Biology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • The competitive exclusion principle limits the number of coexisting strategies in ecosystems.
  • Saturated systems, where the maximum number of strategies coexist, exhibit unique adaptive dynamics.
  • Understanding these dynamics is crucial for predicting ecosystem stability and evolution.

Purpose of the Study:

  • To characterize the adaptive dynamics of saturated polymorphisms in general.
  • To investigate convergence stability of these dynamics.
  • To develop methods for analyzing evolutionary stability in specific ecological models.

Main Methods:

  • Analysis of joint adaptive dynamics for n scalar-valued strategies.
  • Demonstration using a host-pathogen-predator model example.
  • Derivation of a new sufficient condition for absolute stability of polymorphic singularities.

Main Results:

  • Saturated evolutionarily stable polymorphisms satisfy the newly derived condition for absolute stability.
  • A method is introduced to construct pairwise invasibility plots for monomorphic populations in saturated dimorphisms.
  • The study reveals special characteristics of adaptive dynamics in saturated ecological systems.

Conclusions:

  • The findings provide a deeper understanding of evolutionary stability in complex ecological systems.
  • The new stability condition offers a valuable tool for analyzing adaptive dynamics.
  • The developed methods facilitate the study of evolutionary trajectories in saturated polymorphisms.