Voter models with heterozygosity selection

Abstract

This paper studies variations of the usual voter model that favor types that are locally less common. Such models are dual to certain systems of branching annihilating random walks that are parity preserving. For both the voter models and their dual branching annihilating systems we determine all homogeneous invariant laws, and we study convergence to these laws started from other initial laws.

Published in at http://dx.doi.org/10.1214/07-AAP444 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Theory of Branching and Annihilating Random Walks
• Field Theory of Branching and Annihilating Random Walks
• Coexistence in locally regulated competing populations and survival of branching annihilating random walk
• Scale invariance and dynamic phase transitions in diffusion-limited reactions
• Rescaled Lotka-Volterra models converge to super-Brownian motion

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• Systems of branching, annihilating, and coalescing particles
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• Numerical analysis of the rebellious voter model
• Branching random walk with non-local competition
• Dependent Double Branching Annihilating Random Walk
• A complete convergence theorem for voter model perturbations