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A new coalescent for seed-bank models. (English) Zbl 1339.60137
Summary: 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 I. Kaj et al. [J. Appl. Probab. 38, No. 2, 285–300 (2001; Zbl 0989.92017)] 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
92D10 Genetics and epigenetics
17D92 Genetic algebras
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