Spatially explicit non-Mendelian diploid model


We introduce a spatially explicit model for the competition between type aa and type bb alleles. Each vertex of the dd-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: aaaa, abab or bbbb. 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 aa and type bb alleles coexist at equilibrium when homozygotes are poor competitors. The inclusion of a spatial structure, however, reduces the parameter region where coexistence occurs.Comment: Published in at the Annals of Applied Probability ( by the Institute of Mathematical Statistics (

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    Last time updated on 05/06/2019