A transition function expansion for a diffusion model with selection

• 成果类型: Article
• 署名作者: Barbour, AD; Ethier, SN; Griffiths, RC
• 署名单位: University of Zurich; Utah System of Higher Education; University of Utah; Monash University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1019737667
• 发表日期: 2000
• 页码: 123-162
• 关键词: descent

摘要

Using duality, an expansion is found for the transition function of the reversible K-allele diffusion model in population genetics. In the neutral case, the expansion is explicit but already known. When selection is present, it depends on the distribution at time t of a specified R-type birth-and-death process starting at infinity. The latter process is constructed by means of a coupling argument and characterized as the Ray process corresponding to the Ray-Knight compactification of the K-dimensional nonnegative-integer lattice.