On the ancestral process of long-range seedbank models

We present a new model for seed banks, where individuals may obtain their type from ancestors which have lived in the near as well as the very far past. We discern three parameter regimes of the seed bank age distribution, which lead to substantially different behaviour in terms of genetic variability, in particular with respect to fixation of types and time to the most recent common ancestor. The classical Wright-Fisher model, as well as a seed bank model with bounded age distribution considered by Kaj, Krone and Lascoux (2001) are boundary cases of our model. The mathematical methods are based on renewal theory as well as on a Gibbsian approach introduced by Hammond and Sheffield (2011) in a different context