A NEW COALESCENT FOR SEED-BANK MODELS

• 成果类型: Article
• 署名作者: Blath, Jochen; Casanova, Adrian Gonzalez; Kurt, Noemi; Wilke-Berenguer, Maite
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1106
• 发表日期: 2016
• 页码: 857-891
• 关键词: consequences; inference

摘要

We identify a new natural coalescent structure, which we call the seed bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where dormant forms of individuals (such as seeds or spores) may jump a significant number of generations before joining the active population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright-Fisher model with geometric seed-bank age structure if the average time of seed dormancy scales with the order of the total population size N. This extends earlier results of Kaj, Krone and Lascoux [J. Appl. Probab. 38 (2011) 285-300] who show that the genealogy of a Wright-Fisher model in the presence of a weak seed-bank effect is given by a suitably time-changed Kingman coalescent. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. In particular, the seed-bank coalescent does not come down from infinity, and the time to the most recent common ancestor of a sample of size n grows like log log n. This is in line with the empirical observation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.