论文标题

$λ$ -Coalescents在休眠的种群中产生

$Λ$-coalescents arising in populations with dormancy

论文作者

Cordero, Fernando, Casanova, Adrián González, Schweinsberg, Jason, Wilke-Berenguer, Maite

论文摘要

考虑一个人口,每年都会发展到三个季节:春季,夏季和冬季。每年春季,$ n $休眠的人会根据给定的分布互相独立醒来。一旦一个人醒来,它就会开始以恒定的速度重现。到春季结束时,所有个人都已经清醒,并继续在整个夏季作为Yule过程独立繁殖。在冬天,$ n $的个人在随机的随机中均匀选择,直到第二春天,其他人死亡。我们表明,由于一个异常醒来的个体可以拥有大量幸存的后代,因此,对于某些模型参数,人口的家谱将由$λ$ - coalescent描述。特别是,当个体醒来的速度随着时间的推移呈指数增长时,β结合可以描述谱系。我们还表征了在此框架中可能会出现的所有$λ$ coalescents的集合。

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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