  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.
