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October 2009 Spatially explicit non-Mendelian diploid model
N. Lanchier, C. Neuhauser
Ann. Appl. Probab. 19(5): 1880-1920 (October 2009). DOI: 10.1214/09-AAP598

Abstract

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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N. Lanchier. C. Neuhauser. "Spatially explicit non-Mendelian diploid model." Ann. Appl. Probab. 19 (5) 1880 - 1920, October 2009. https://doi.org/10.1214/09-AAP598

Information

Published: October 2009
First available in Project Euclid: 16 October 2009

zbMATH: 1195.60125
MathSciNet: MR2569811
Digital Object Identifier: 10.1214/09-AAP598

Subjects:
Primary: 60K35 , 82C22
Secondary: 92D25

Keywords: annihilating branching process , non-Mendelian segregation , voter model

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 5 • October 2009
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