We survey a class of models for spatially structured populations which we have called
spatial Λ-Fleming–Viot processes. They arise from a flexible framework for modelling in …

Probabilistic cellular automata (PCA) are interacting discrete stochastic dynamical systems
used as a modeling tool for a wide range of natural and societal phenomena. Their key …

We consider random walks in dynamic random environments, with an environment
generated by the time-reversal of a Markov process from the oriented percolation …

We consider a model recently introduced by Barton & Etheridge for a population evolving in
a spatial continuum, in which a succession of catastrophic events of varying intensity allows …

We study a discrete-time branching annihilating random walk (BARW) on the d-dimensional
lattice. Each particle produces a Poissonian number of offspring with mean μ which …

Consider two ancestral lineages sampled from a system of two-dimensional branching
random walks with logistic regulation in the stationary regime. We study the asymptotics of …

These notes are intended to provide a very rapid introduction to some of the mathematical
models of theoretical population genetics. We shall be particularly concerned with models …

We consider random walks in dynamic random environments which arise naturally as
spatial embeddings of ancestral lineages in spatial locally regulated population models. In …

We consider systems of interacting diffusions with local population regulation representing
populations on countably many islands. Our main result shows that the total mass process of …

We give a short overview on our work on ancestral lineages in spatial population models
with local regulation. We explain how an ancestral lineage can be interpreted as a random …