Spatial populations with seed-bank
speaker: Margriet Oomen (Universiteit Leiden)abstract: We consider a system of interacting Wright-Fisher diffusions with seed-bank. Individuals are of two types, live in colonies 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. As geographic space we consider Zd. We endow the seed-bank with an internal structure that mimics fat tails but preserves the Markov property. The obtained model has a dual and exhibits a dichotomy of coexistence (multi-type equilibrium) versus clustering (mono-type equilibrium). We also establish the finite-systems scheme, we identify how a finite truncation of the system behaves as both the time and the truncation level tend to infinity, properly tuned together. It turns out that the seed-bank changes the long-time behavior of the system not only quantitatively but also qualitatively. Joint work with Andreas Greven.
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