  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.
