Spatial populations with seed-bank: finite-systems scheme

This is the third in a series of four papers which we consider system interacting Fisher-Wright diffusions with seed-bank. Individuals carry type ♡ or ♢, live colonies, and are subject to resampling migration as long they active. Each colony has structured seed-bank into individuals can retreat become dormant, suspending their until active again. As geographic space labelling colonies countable Abelian group G endowed discrete topology. Our goal understand what way enhances genetic diversity causes new phenomena. In [GHO22b] showed that continuum stochastic differential equations, describing population large-colony-size limit, unique strong solution. We further if starts from an initial law invariant ergodic under translations density equal θ, then it converges equilibrium νθ whose also θ. Moreover, exhibits dichotomy coexistence (= locally multi-type equilibrium) versus clustering mono-type equilibrium). identified parameter regimes for these two phases occur, found different when mean wake-up time dormant individual finite infinite. The present paper establish finite-systems scheme, i.e., identify how truncation (both seed-bank) behaves both level tend infinity, properly tuned together. Since clustering, focus on regime where infinite coexistence, consists sub-regimes. If mean, scaling turns out be proportional volume truncated space, there single universality class namely, moves through succession equilibria evolves according renormalised diffusion ultimately gets trapped either 0 1. On other hand, grow faster than classes depending fast grows compared space. For slow growth limit same while different, initially remains fixed at afterwards makes random switches between 1 range scales, driven by deep seed-banks wake up, finally scale deepest up. Thus, sequence partial clusterings (or fixations) before reaches complete fixation).