ASYMPTOTICS FOR THE SITE FREQUENCY SPECTRUM ASSOCIATED WITH THE GENEALOGY OF A BIRTH AND DEATH PROCESS

• 成果类型: Article
• 署名作者: Schweinsberg, Jason; Shuai, Yubo
• 署名单位: University of California System; University of California San Diego
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2110
• 发表日期: 2025
• 页码: 99-141
• 关键词: coalescent structure; splitting trees; neutral mutations; models

摘要

Consider a birth and death process started from one individual in which each individual gives birth at rate lambda and dies at rate mu, so that the population size grows at rater = lambda - mu. Lambert (Theor. Popul. Biol. 122 (2018) 30-35) and Harris, Johnston, and Roberts (Ann. Appl. Probab. 30 (2020) 1368-1414) came up with methods for constructing the exact genealogy of a sample of size n taken from this population at time T. We use the construction of Lambert, which is based on the coalescent point process, to obtain asymptotic results for the site frequency spectrum associated with this sample. In the supercritical case r > 0, our results extend results of Durrett (Ann. Appl. Probab. 23 (2013) 230-250) for exponentially growing populations. In the critical case r = 0, our results parallel those that Dahmer and Kersting (Ann. Appl. Probab. 25 (2015) 1325-1348) obtained for Kingman's coalescent.