Natural enemies and victims interact over spatial and temporal scales, resulting in a variety of emerging patterns. We used a prey density-dependent Lotka –Volterra model to investigate space-time dynamics in a spatially-extended predator-prey system. Higher rates of predator and prey dispersal resulted in greater local spatial clustering of each; however, highly mobile predators that attack less mobile prey showed negative asymptotic local spatial cross-correlation. In cyclic populations, and in particular, dynamics characterized by 2-phase limit cycles and quasiperiodicity, predators and prey could achieve positive local cross-correlation regardless of dispersal rates, suggesting that in nature, prey and predator populations are likely governed by nonlinear dynamics if long-term consistent spatial and temporal overlap exists. Over regional scales, chaotic populations did not synchronize, even with high rates of dispersal. However, other types of nonlinear, nonchaotic dynamics allowed synchronization in prey, predators, and their space-time interaction. This work thus shows how in natural enemy-victim systems, spatial and temporal clustering between predators and prey, over both local and regional spatial scales, can be achieved in locally unstable populations that are linked through dispersal.
Keywords: spatial covariance function, coupled map lattice
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