DEGENERATE DIFFUSIONS ARISING FROM GENE DUPLICATION MODELS

• 成果类型: Article
• 署名作者: Durrett, Rick; Popovic, Lea
• 署名单位: Cornell University; Concordia University - Canada
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP530
• 发表日期: 2009
• 页码: 15-48
• 关键词: mutation pressure; tetraploid fish; yeast genome; loci; EVOLUTION; subfunctionalization; preservation; Fixation; allele; drift

摘要

We consider two processes that have been used to study gene duplication, Watterson's [Genetics 105 (1983) 745-766] double recessive null model and lynch and Force's [Genetics 154 (2000) 459-473] subfunctionalization model. Though the state spaces of these diffusions are two and six-dimensional, respectively, we show in each case that the diffusion stays close to a curve. Using ideas of Katzenberger [Ann. Probab. 19 (1991) 1587-1628] we show that one-dimensional projections converge to diffusion processes, and we obtain asymptotics for the time to loss of one gene copy. AS a corollary we find that the probability of subfunctionalization decreases exponentially fast as the population size increases. This rigorously confirms a result Ward and Durrett [Theor. Pop. Biol. 66 (2004) 93-100] found by simulation that the likelihood of subfunctionalization for gene duplicates decays exponentially fast as the population size increases.