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Invasion dynamics and attractor inheritance.

S A H Geritz1, M Gyllenberg, F J A Jacobs

  • 1Department of Mathematics, University of Turku, FIN-20014 Turku, Finland. stefan.geritz@utu.fi

Journal of Mathematical Biology
|July 12, 2002
PubMed
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In population dynamics, a new mutant typically inherits the established population

Area of Science:

  • Evolutionary dynamics
  • Population genetics
  • Mathematical biology

Background:

  • Understanding how populations change over time is crucial in evolutionary biology.
  • Investigating the dynamics of invasion by new mutants provides insights into evolutionary stability.

Purpose of the Study:

  • To analyze the population dynamics during invasion by a rare mutant.
  • To determine conditions under which population size and density remain stable.
  • To explore the role of strategy similarity and bifurcation points in evolutionary outcomes.

Main Methods:

  • Mathematical modeling of population dynamics.
  • Analysis of deterministic and stochastic systems.
  • Investigation of mutant-resident interactions and attractor stability.

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Main Results:

  • Under mild conditions, population size remains close to the resident's initial attractor if the mutant strategy is similar.
  • For stochastic systems, probability densities approximate the monomorphic resident's stationary density.
  • Attractor switching and evolutionary suicide occur mainly near bifurcation points; otherwise, the new resident inherits the attractor.

Conclusions:

  • Population attractors are generally inherited by successful mutants, ensuring stability away from bifurcation points.
  • Discontinuous changes in strategy space (bifurcation points) are critical for phenomena like attractor switching.
  • This study clarifies invasion dynamics and attractor inheritance in evolutionary game theory.