2014/11/30 by Jochen Blath, Adrián González Casanova, Noemi Kurt +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #math.PR #q-bio.PE
paper · pdf · doi:10.1214/15-aap1106
published as Annals of Applied Probability 2016, Vol. 26, No. 2, 857-891 · 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)
arxiv created 2016/05/04 · arxiv updated 2016/08/10
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 loglog 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.