Spatial populations with seed-bank
A talk in the Keine Reihe series by
Frank den Hollander
| Abstract: | In this lecture we consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals carry one of two types, live in colonies labelled by countable Abelian group playing the role of geographic space, and are subject to resampling and migration as long as they are active. Each colony has a seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. Our goal is to understand in what way the seed-bank enhances genetic diversity. When individuals become dormant they adopt a random colour that determines their wake-up time. The system of continuum stochastic differential equations describing the population in the large-colony-size limit has a unique strong solution that converges to an equilibrium parametrised by the initial type densities. This equilibrium exhibits a dichotomy between two phases: coexistence (= locally multi-type equilibrium) versus clustering (= locally mono-type equilibrium). We identify the parameter regimes for which these two phases occur. We also establish the finite-systems scheme, i.e., identify how a finite truncation of the system (both in the geographic space and in the seed-bank) behaves as both the time and the truncation level tend to infinity, properly tuned together. Joint work with Andreas Greven (Erlangen) and Margriet Oomen (Leiden) Registration via email to popgen.conference@techfak.de |