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Complex dynamics and phase synchronization in spatially extended ecological systems


Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma1,2,3,4,5,6,7,8,9,10,11. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual ‘4- and 10-year cycle’ of wildlife are often found. 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. In a spatial lattice of patches, only small amounts of local migration are required to induce broad-scale ‘phase synchronization’12,13, with all populations in the lattice phase-locking to the same collective rhythm. Peak population abundances, however, remain chaotic and largely uncorrelated. Although synchronization is often perceived as being detrimental to spatially structured populations14, phase synchronization leads to the emergence of complex chaotic travelling-wave structures which may be crucial for species persistence.

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Figure 1: Time series analysis.
Figure 2: Model time series of predator populations in a two-patch system ( b1 = 1.1, b2 = 1.055 ) under different synchronization regimes.
Figure 3: Phase analysis.
Figure 4: Effects of noise and seasonality.
Figure 5: Simulation results in a square lattice of 20 × 20 sites with periodic boundary conditions (Box 1).


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We thank MINERVA for their award of a Fellowship to B.B., and H. Bhasin for her comments on the manuscript.

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Correspondence to Lewi Stone.

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Blasius, B., Huppert, A. & Stone, L. Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399, 354–359 (1999).

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