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A spatial model for selection and cooperation

Published online by Cambridge University Press:  22 June 2017

Peter Pfaffelhuber*
Affiliation:
University of Freiburg
*
** Postal address: Department of Mathematical Stochastics, University of Freiburg, 79104 Freiburg, Germany.

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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