Spatial populations with seed-bank: well-posedness, duality and equilibrium

@article{Greven2022SpatialPW,
  title={Spatial populations with seed-bank: well-posedness, duality and equilibrium},
  author={Andreas Greven and Frank den Hollander and Margriet Oomen},
  journal={Electronic Journal of Probability},
  year={2022}
}
We consider a system of interacting Fisher-Wright diffusions with seed-bank. Individuals live in colonies and are subject to resampling and migration as long as they are active. Each colony has a structured seed-bank into which individuals can retreat to become dormant, suspending their resampling and migration until they become active again. As geographic space labelling the colonies we consider a countable Abelian group $\mathbb{G}$ endowed with the discrete topology. The key example of… 

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References

SHOWING 1-10 OF 59 REFERENCES
Spatial Populations with seed-bank: renormalisation on the hierarchical group
We consider a system of interacting diffusions labeled by a geographic space that is given by the hierarchical group $\Omega_N$ of order $N\in\mathbb{N}$. Individuals live in colonies and are subject
A new coalescent for seed-bank models
TLDR
The seed-bank coalescent "does not come down from infinity," and the time to the most recent common ancestor of a sample of size $n$ grows like $\log\log n$, in line with the empirical observation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.
Structural properties of the seed bank and the two island diffusion
TLDR
It is shown that the Wright–Fisher diffusion with seed bank can be reformulated as a one-dimensional stochastic delay differential equation, providing an elegant interpretation of the age structure in the seed bank also forward in time in the spirit of Kaj et al. (J Appl Probab 38(2):285–300, 2001).
Renormalisation of hierarchically interacting Cannings processes
In order to analyse universal patterns in the large space-time behaviour of interacting multi-type stochastic populations on countable geographic spaces, a key approach has been to carry out a
Equilibria and Quasi-Equilibria for Infinite Collections of Interacting Fleming-Viot Processes
In this paper of infinite systems of interacting measure-valued diffusions each with state space ¿^([O, 1]), the set of probability measures on [0, 1], is constructed and analysed (Fleming-Viot
Genealogy of a Wright-Fisher Model with Strong SeedBank Component
TLDR
It is proved that the ancestral process of a sample of n individuals converges under a non-classical time-scaling to Kingman’s n−coalescent.
Coalescent theory for seed bank models
We study the genealogical structure of samples from a population for which any given generation is made up of direct descendants from several previous generations. These occur in nature when there
Renormalization of Hierarchically Interacting Isotropic Diffusions
AbstractWe study a renormalization transformation arising in an infinite system of interacting diffusions. The components of the system are labeled by the N-dimensional hierarchical lattice (N≥2) and
...
...