Adaptive dynamics of saturated polymorphisms

J Math Biol. 2016 Mar;72(4):1039-1079. doi: 10.1007/s00285-015-0948-2. Epub 2015 Dec 16.

Abstract

We study the joint adaptive dynamics of n scalar-valued strategies in ecosystems where n is the maximum number of coexisting strategies permitted by the (generalized) competitive exclusion principle. The adaptive dynamics of such saturated systems exhibits special characteristics, which we first demonstrate in a simple example of a host-pathogen-predator model. The main part of the paper characterizes the adaptive dynamics of saturated polymorphisms in general. In order to investigate convergence stability, we give a new sufficient condition for absolute stability of an arbitrary (not necessarily saturated) polymorphic singularity and show that saturated evolutionarily stable polymorphisms satisfy it. For the case [Formula: see text], we also introduce a method to construct different pairwise invasibility plots of the monomorphic population without changing the selection gradients of the saturated dimorphism.

Keywords: Adaptive dynamics; Coevolution; Competitive exclusion principle; Environmental feedback; Saturated community.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Ecosystem
  • Evolution, Molecular
  • Feedback, Physiological
  • Food Chain
  • Genetics, Population
  • Host-Pathogen Interactions
  • Mathematical Concepts
  • Models, Genetic*
  • Polymorphism, Genetic*