$\Lambda$-coalescents arising in populations with dormancy

TL;DR

This paper models population genealogies with seasonal dormancy and reproduction, showing that under certain conditions, the genealogy converges to a $ ext{Lambda}$-coalescent, including the beta coalescent, depending on wake-up rates.

Contribution

It introduces a population model with seasonal dormancy leading to $ ext{Lambda}$-coalescents, characterizing which coalescents can arise from this framework.

Findings

Genealogies can be described by $ ext{Lambda}$-coalescents under certain parameters.

Beta coalescent arises when wake-up rates increase exponentially.

Characterization of all $ ext{Lambda}$-coalescents compatible with the model.

Abstract

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 $\Lambda$-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 $\Lambda$-coalescents that can arise in this framework.