The tree length of an evolving coalescent

• 成果类型: Article
• 署名作者: Pfaffelhuber, P.; Wakolbinger, A.; Weisshaupt, H.
• 署名单位: University of Freiburg; Goethe University Frankfurt; University of Freiburg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0307-6
• 发表日期: 2011
• 页码: 529-557
• 关键词: genetic diversity; branch length

摘要

A well-established model for the genealogy of a large population in equilibrium is Kingman's coalescent. For the population together with its genealogy evolving in time, this gives rise to a time-stationary tree-valued process. We study the sum of the branch lengths, briefly denoted as tree length, and prove that the (suitably compensated) sequence of tree length processes converges, as the population size tends to infinity, to a limit process with cA dlA g paths, infinite infinitesimal variance, and a Gumbel distribution as its equilibrium.