2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216132Interacting 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.4 pages, 4 figures, accepted for publication in Phys. Rev. E as a Rapid CommunicationPopulations and Evolutiontext