A spatial model for selection and cooperation

Czuppon, Peter; Pfaffelhuber, Peter

doi:10.1017/jpr.2017.15

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A spatial model for selection and cooperation

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Czuppon, Peter
Department Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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https://www.cambridge.org/core/journals/journal-of-applied-probability/article/spatial-model-for-selection-and-cooperation/6AE45F14AA471867A90FDC1997CFC2DE
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Citation

Czuppon, P., & Pfaffelhuber, P. (2017). A spatial model for selection and cooperation. Journal of Applied Probability, 54(2), 522-539. doi:10.1017/jpr.2017.15.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002E-10A4-3

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.