Genealogy of a Wright-Fisher Model with Strong SeedBank Component
- Cite this paper as:
- Blath J., Eldon B., González Casanova A., Kurt N. (2015) Genealogy of a Wright-Fisher Model with Strong SeedBank Component. In: Mena R., Pardo J., Rivero V., Uribe Bravo G. (eds) XI Symposium on Probability and Stochastic Processes. Progress in Probability, vol 69. Birkhäuser, Cham
We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seedbank effect. More precisely, we consider a simple seedbank age distribution with two atoms, leading to either classical or long genealogical jumps (the latter modeling the effect of seed-dormancy). We assume that the length of these long jumps scales like a power Nβ of the population size N, thus giving rise to a ‘strong’ seedbank effect. For a certain range of β, we prove that the ancestral process of a sample of n individuals converges under a non-classical time-scaling to Kingman’s n−coalescent. Further, for a wider range of parameters, we analyze the time to the most recent common ancestor of two individuals analytically and by simulation.