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A spatial model for selection and cooperation

  • Peter Czuppon and Peter Pfaffelhuber (a1)
Abstract

We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias α with respect to the other type (called cooperator). However, a cooperator helps a neighbor (either defector or cooperator) to reproduce at rate γ. We prove that the one-dimensional nearest-neighbor interacting dynamical system exhibits a phase transition at α = γ. A special choice of interaction kernels yield that for α > γ cooperators always die out, but if γ > α, cooperation is the winning strategy.

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Corresponding author
* Current address: Max-Planck-Institute for Evolutionary Biology, August-Thienemann-Str. 2, 24306 Plön, Germany. Email address: czuppon@evolbio.mpg.de
** Postal address: Department of Mathematical Stochastics, University of Freiburg, 79104 Freiburg, Germany.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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