Annals of Applied Probability

Spatially explicit non-Mendelian diploid model

N. Lanchier and C. Neuhauser

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We introduce a spatially explicit model for the competition between type a and type b alleles. Each vertex of the d-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: aa, ab or bb. We are interested in the long-term behavior of the gene frequencies when Mendel’s law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition between genes during meiosis. We prove that with or without a spatial structure, type a and type b alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.

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Ann. Appl. Probab., Volume 19, Number 5 (2009), 1880-1920.

First available in Project Euclid: 16 October 2009

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C22: Interacting particle systems [See also 60K35]
Secondary: 92D25: Population dynamics (general)

Voter model annihilating branching process non-Mendelian segregation


Lanchier, N.; Neuhauser, C. Spatially explicit non-Mendelian diploid model. Ann. Appl. Probab. 19 (2009), no. 5, 1880--1920. doi:10.1214/09-AAP598.

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