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Strong effect of dispersal network structure on ecological dynamics

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Abstract

A central question in ecology with great importance for management, conservation and biological control is how changing connectivity affects the persistence and dynamics of interacting species. Researchers in many disciplines have used large systems of coupled oscillators to model the behaviour of a diverse array of fluctuating systems in nature1,2,3,4. In the well-studied regime of weak coupling, synchronization is favoured by increases in coupling strength and large-scale network structures (for example ‘small worlds’) that produce short cuts and clustering5,6,7,8,9. Here we show that, by contrast, randomizing the structure of dispersal networks in a model of predators and prey tends to favour asynchrony and prolonged transient dynamics, with resulting effects on the amplitudes of population fluctuations. Our results focus on synchronization and dynamics of clusters in models, and on timescales, more appropriate for ecology, namely smaller systems with strong interactions outside the weak-coupling regime, rather than the better-studied cases of large, weakly coupled systems. In these smaller systems, the dynamics of transients and the effects of changes in connectivity can be well understood using a set of methods including numerical reconstructions of phase dynamics, examinations of cluster formation and the consideration of important aspects of cyclic dynamics, such as amplitude.

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Figure 1: Sample dispersal networks for systems with ten patches.
Figure 2: Total predator amplitude (summed over all patches) as a function of time for cluster solutions.
Figure 3: Distribution of cluster states as a function of time.
Figure 4: Predator amplitude and transient duration.

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Acknowledgements

We thank M. Holyoak for comments on an earlier version of the manuscript and D. Wysham for discussions. M.D.H. was funded by a Quantitative Environmental and Integrative Biology grant to A.H. and M. Holyoak from the National Science Foundation.

Author Contributions M.D.H. wrote custom software, ran simulations and analyzed data. M.D.H. and A.H. designed the study and wrote the paper.

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  1. Department of Environmental Science and Policy, University of California, Davis, One Shields Avenue, Davis, California 95616, USA,

    Matthew D. Holland & Alan Hastings

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  1. Matthew D. Holland
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  2. Alan Hastings
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Correspondence to Matthew D. Holland.

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Holland, M., Hastings, A. Strong effect of dispersal network structure on ecological dynamics. Nature 456, 792–794 (2008). https://doi.org/10.1038/nature07395

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