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 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.
Funding Statement
FC was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) – SFB 1283, Project C1. AGC was supported in part by CONACYT CIENCIA BASICA A1-S-14615. JS was supported in part by NSF Grant DMS-1707953.
Acknowledgments
The authors thank Jochen Blath for bringing to their attention the reference [33]. They also thank Anton Wakolbinger for a fruitful discussion over Zoom during the Bernoulli-IMS One World Symposium, and they thank a referee for helpful comments.
Citation
Fernando Cordero. Adrián González Casanova. Jason Schweinsberg. Maite Wilke-Berenguer. "Λ-coalescents arising in a population with dormancy." Electron. J. Probab. 27 1 - 34, 2022. https://doi.org/10.1214/22-EJP739
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