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.
Highlights
Λ-coalescents arising in a population with dormancy the fields of population genetics and beyond
The impact of dormancy at different scales on the coalescent processes describing the genealogies of populations were investigated in [19, 3, 4, 5]
Branching processes in random environment explain how dormancy can be selectively advantageous under fluctuating environmental conditions [6] while models from adaptive dynamics uncover that dormancy can arise from competition [7]
Summary
The mechanisms for leaving a dormant state have been observed to be under selective pressure in the case of mosquitos [32] and in different contexts such as experimental evolution; see, for example, figure 2 of [23] and [24] In such experiments, individuals reproduce until the resources are depleted, and after that some of them are sampled and propagated to fresh identical media. Wright and Vetsigian [33] postulated that the randomness in the times when individuals emerge from a dormant state could cause the distribution of the numbers of offspring produced by different individuals to become highly skewed They demonstrated in their bacterial experiments that “the heavy-tailed nature of the distribution of descendants can, in our case, be largely explained by phenotypic variability in lag time before exponential growth.”. We find that Λ-coalescent genealogies can appear if some rare individuals emerge from dormancy sufficiently early
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