Spatially explicit non-mendelian diploid model

N. Lanchier, C. Neuhauser

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1880-1920
Number of pages41
JournalAnnals of Applied Probability
Issue number5
StatePublished - Oct 2009
Externally publishedYes


  • Annihilating branching process
  • Non-Mendelian segregation
  • Voter model


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