$Λ$ -休眠种群中产生的聚结剂
$Λ$-coalescents arising in populations with dormancy
摘要：
考虑一个种群在春、夏、冬三个季节中逐年演化。每年春天，$N$休眠的个体根据给定的分布彼此独立地醒来。一旦个体醒来，它就开始以恒定的速度繁殖。到春天结束时，所有的个体都醒了，并继续独立繁殖，就像整个夏天的圣诞节一样。在冬天，随机选择的$N$个体会沉睡到第二年春天，而其他个体则会死去。我们发现，因为一个人醒来异常早，可以有大量的幸存后代，对于一些选择的模型参数的人口的家谱将描述由一个$Λ$ -聚结。特别是，当个体醒来的速率随时间呈指数级增加时，β聚结可以描述谱系。我们还描述了一套所有的$Λ$ -聚结，可以出现在这个框架。
英文摘要：
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with $N$ dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake, it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, $N$ individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a $Λ$-coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all $Λ$-coalescents that can arise in this framework.
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