  We consider random walks in dynamic random environments which arise naturally
as spatial embeddings of ancestral lineages in spatial locally regulated
population models. In particular, as the main result, we prove the quenched
central limit theorem for a random walk in dynamic random environment generated
by time reversal of logistic branching random walks in a regime where the
population density is sufficiently high. As an important tool we consider as
auxiliary models random walks in dynamic random environments defined in terms
of the time-reversal of oriented percolation. We show that the quenched central
limit theorem holds if the influence of the random medium on the walks is
suitably weak. The proofs of the quenched central limit theorems in these
models rely on coarse-graining arguments and a construction of regeneration
times for a pair of conditionally independent random walks in the same medium,
combined with a coupling that relates them to a pair of independent random
walks in two independent copies of the medium.
