  Interacting populations often create complicated spatiotemporal behavior, and
understanding it is a basic problem in the dynamics of spatial systems. We
study the two-species case by simulations of a host--parasitoid model. In the
case of co-existence, there are spatial patterns leading to noise-sustained
oscillations. We introduce a new measure for the patterns, and explain the
oscillations as a consequence of a timescale separation and noise. They are
linked together with the patterns by letting the spreading rates depend on
instantaneous population densities. Applications are discussed.
