Mathematical modeling of seed bank dynamics in population genetics

We study the genealogical structure of samples from a population for which any givengeneration is made up of direct descendants from one randomly chosen previousgeneration. These occur in nature when there are seed banks or egg banks allowingan individual to leave offspring several generations in the future. Kaj et al. studied in2001 the case where any given generation is made up of descendants from severalprevious generations and showed how this temporal structure in the reproductionmechanism causes a decrease in the coalescence rate. In this project we will showthat having all samples pick their parents in one randomly chosen generation will leadto a coalescent process which is equivalent to a time shifted version of Kingman’scoalescent, time shifted with the age distribution of the seed bank