A new coalescent for seed-bank models

Abstract

We identify a new natural coalescent structure, which we call the seed-bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where "dormant forms" of individuals (such as seeds or spores) may jump a significant number of generations before joining the "active" population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright-Fisher model with geometric seed-bank age structure if the average time of seed dormancy scales with the order of the total population size $N$. This extends earlier results of Kaj, Krone and Lascoux [J. Appl. Probab. 38 (2011) 285-300] who show that the genealogy of a Wright-Fisher model in the presence of a "weak" seed-bank effect is given by a suitably time-changed Kingman coalescent. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. In particular, the seed-bank coalescent "does not come down from infinity," and the time to the most recent common ancestor of a sample of size $n$ grows like $\log \log n$. This is in line with the empirical observation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.

Published at http://dx.doi.org/10.1214/15-AAP1106 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Random recursive trees and the Bolthausen-Sznitman coalescent

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• Stability of fixed life histories to perturbation by rare diapause
• Structural properties of the seed bank and the two-island diffusion
• Spatial populations with seed-banks in random environment: III. Convergence towards mono-type equilibrium
• Two-type branching processes with immigration, and the structured coalescents