Ancestral lineages in spatial population models with local regulation

TL;DR

This paper studies ancestral lineages in spatial population models with local regulation, modeling them as random walks in dynamic environments, and proves convergence results including the Brownian web for coalescing lineages.

Contribution

It introduces a novel interpretation of ancestral lineages as random walks in dynamic environments and establishes central limit theorems and convergence to the Brownian web.

Findings

Ancestral lineages can be modeled as random walks in dynamic environments.

Regeneration times enable proof of central limit theorems for these walks.

Coalescing lineages in one dimension converge to the Brownian web.

Abstract

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 walk in a dynamic random environment. Defining regeneration times allows to prove central limit theorems for such walks. We also consider several ancestral lineages in the same population and show for one prototypical example that in one dimension the corresponding system of coalescing walks converges to the Brownian web.