Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems. In the proposed spatial model, each local patch sustains a three-level trophic system composed of interacting predators, consumers and vegetation. Populations oscillate regularly and periodically in phase, but with irregular and chaotic peaks together in abundance—twin realistic features that are not found in standard ecological models...