Mathematical Sciences: Some Aspects of Markov Processes in Population Genetics

数学科学：群体遗传学中马尔可夫过程的某些方面

• 批准号: 8704369
• 负责人: Stewart Ethier
• 金额: $ 5.57万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-15 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8704369&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Aspects; Markov

This research will study stochastic models in mathematical population genetics. The first set of problems concerns measure- valued diffusion processes that generalize the usual K-allele diffusion model of population genetics. The investigator will study the ergodicity of the selective infinitely-many-alleles model, properties of the two-locus model, and existence of the infinitely-many-sites model with recombination. The second set of problems relates to Gaussian diffusion approximations of genetic models with two time scales, and convergence of an ancestral Markov chain related to the coalescent.

这项研究将研究数学种群遗传学中的随机模型。第一组问题涉及测量值扩散过程，它推广了通常的群体遗传学K等位基因扩散模型。研究者将研究选择性无限多个等位基因模型的遍历性，两个位点模型的性质，以及无限多个位点重组模型的存在性。第二组问题涉及具有两个时间尺度的遗传模型的高斯扩散近似，以及与合并相关的祖先马尔可夫链的收敛。