Spatially explicit non-Mendelian diploid model
N. Lanchier and C. Neuhauser
Source: Ann. Appl. Probab. Volume 19, Number 5 (2009), 1880-1920.
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.
Primary Subjects: 60K35, 82C22
Secondary Subjects: 92D25
Keywords: Voter model; annihilating branching process; non-Mendelian segregation
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1255699547
Digital Object Identifier: doi:10.1214/09-AAP598
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