Evolutionary games on minimally structured populations

Gergely J. Szöllosi, I. Derényi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects have, however, proved to be sensitive to the details of the underlying topology and dynamics. Here we introduce a minimal population structure that is described by two distinct hierarchical levels of interaction, similar to the structured metapopulation concept of ecology and island models in population genetics. We believe this model is able to identify effects of spatial structure that do not depend on the details of the topology. While effects depending on such details clearly lie outside the scope of our approach, we expect that those we are able to reproduce should be generally applicable to a wide range of models. We derive the dynamics governing the evolution of a system starting from fundamental individual level stochastic processes through two successive mean-field approximations. In our model of population structure the topology of interactions is described by only two parameters: the effective population size at the local scale and the relative strength of local dynamics to global mixing. We demonstrate, for example, the existence of a continuous transition leading to the dominance of cooperation in populations with hierarchical levels of unstructured mixing as the benefit to cost ratio becomes smaller then the local population size. Applying our model of spatial structure to the repeated prisoner's dilemma we uncover a counterintuitive mechanism by which the constant influx of defectors sustains cooperation. Further exploring the phase space of the repeated prisoner's dilemma and also of the "rock-paper-scissor" game we find indications of rich structure and are able to reproduce several effects observed in other models with explicit spatial embedding, such as the maintenance of biodiversity and the emergence of global oscillations.

Original languageEnglish
Article number031919
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume78
Issue number3
DOIs
Publication statusPublished - Sep 23 2008

Fingerprint

Evolutionary Game
Structured Populations
games
Population Structure
Prisoners' Dilemma
Spatial Structure
Population Size
topology
Topology
embedding
Interaction
Model
Island Model
Metapopulation
Biodiversity
Population Genetics
biological diversity
Successive Approximation
Mean-field Approximation
ecology

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Evolutionary games on minimally structured populations. / Szöllosi, Gergely J.; Derényi, I.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 78, No. 3, 031919, 23.09.2008.

Research output: Contribution to journalArticle

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