SPATIALLY EXPLICIT NON-MENDELIAN DIPLOID MODEL

• 成果类型: Article
• 署名作者: Lanchier, N.; Neuhauser, C.
• 署名单位: Arizona State University; Arizona State University-Tempe; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP598
• 发表日期: 2009
• 页码: 1880-1920
• 关键词: house mouse; mus-musculus; polymorphism; maintenance; populations; migration; STABILITY; DYNAMICS

摘要

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: an, 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.