A new coalescent for seed-bank models

We identify a new natural coalescent structure, the seed-bank coalescent, which describes the gene genealogy of populations under the influence of a strong seedbank 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 WrightFisher 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 Lascaux (2001) 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, which is the order also observed for the Bolthausen-Sznitman coalescent. 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. 2010 Mathematics Subject Classification: Primary 60K35, Secondary 92D10.