  Starting from the well-known field theory for directed percolation, we
describe an evolving population, near extinction, in an environment with its
own nontrivial spatio-temporal dynamics. Here, we consider the special case
where the environment follows a simple relaxational (Model A) dynamics. Two new
operators emerge, with upper critical dimension of four, which couple the two
theories in a nontrivial way. While the Wilson-Fisher fixed point remains
completely unaffected, a mismatch of time scales destabilizes the usual DP
fixed point, suggesting a crossover to a first order transition from the active
(surviving) to the inactive (extinct) state.
