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Synchrony and second order spatial correlation in host-parasitoid systems

O.N. Bjørnstad and J. Bascompte: Synchrony and second order spatial correlation in host-parasitoid systems

Journal of Animal Ecology (2001) 70: 924-933

Abstract

1.Recent theoretical studies on population synchrony have focused on the role of dispersal, environmental correlation, and density dependence in single species. Trophic interactions have received less attention. Here we explore how trophic interactions affect spatial synchrony.

2. We consider a host-parasitoid coupled map lattice to understand how the self-organizing spatial patterns generated by such dynamics affect synchrony. In particular, we calculate the spatial correlation functions (SCFs) associated with traveling waves, spatial chaos, and crystal lattices.

3. Traveling waves are associated with cyclic SCFs (coined second-order SCFs) that differ greatly from those seen in spatial chaos or crystal lattices. Such U-shaped pattern of spatial synchrony, which has not been predicted by single-species models, has been recently reported in real data. Thus, the shape of the SCF can provide a test for trophically generated spatiotemporal dynamics.

4. We also calculate the cross-correlation function between the parasitoid and the host. Relatively high parasitoid mobility results in high within-patch synchrony of the dynamics of the two species. However with relatively high host mobility, the parasitoid dynamics begins to lag spatially behind that of the host.

5. We speculate that this spatial lag between the host and parasitoid is the ultimate source of traveling waves, because the spatial cross-correlation in turn affects host dynamics.

6. A new method to estimate the spatial cross-correlation function between two species is developed as an integral part of the paper.

Keyword: Spatial dynamics; Autocorrelation; Reaction-Diffusion; cross-correlation; coupled map lattice models; nonparametric covariance function; trophic interaction