A new coalescent for seed-bank models

TL;DR

This paper introduces the seed-bank coalescent, a new genealogical model for populations with dormant seed or spore stages, showing it significantly alters ancestral lineage behavior and increases genetic diversity.

Contribution

The paper develops the seed-bank coalescent as a novel scaling limit for populations with seed banks, extending previous models to account for strong seed-bank effects.

Findings

Seed-bank coalescent does not come down from infinity.

Time to MRCA grows like log log n.

Seed-banks increase genetic variability.

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.