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A game-theoretic mechanism for aggregation and dispersal of interacting populations

Russ deForest,A. Belmonte

Published 2018 in arXiv: Populations and Evolution

ABSTRACT

We adapt a fitness function from evolutionary game theory as a mechanism for aggregation and dispersal in a partial differential equation (PDE) model of two interacting populations, described by density functions $u$ and $v$. We consider a spatial model where individuals migrate up local fitness gradients, seeking out locations where their given traits are more advantageous. The resulting system of fitness gradient equations is a degenerate system having spatially structured, smooth, steady state solutions characterized by constant fitness throughout the domain. When populations are viewed as predator and prey, our model captures prey aggregation behavior consistent with Hamilton's selfish herd hypothesis. We also present weak steady state solutions in 1d that are continuous but in general not smooth everywhere, with an associated fitness that is discontinuous, piecewise constant. We give numerical examples of solutions that evolve toward such weak steady states. We also give an example of a spatial Lotka--Volterra model, where a fitness gradient flux creates instabilities that lead to spatially structured steady states. Our results also suggest that when fitness has some dependence on local interactions, a fitness-based dispersal mechanism may act to create spatial variation across a habitat.

PUBLICATION RECORD

  • Publication year

    2018

  • Venue

    arXiv: Populations and Evolution

  • Publication date

    2018-03-15

  • Fields of study

    Biology, Mathematics, Economics

  • Identifiers
    arXiv 1803.05855
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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