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Single-species models for many-species food webs

Abstract

Most species live in species-rich food webs; yet, for a century, most mathematical models for population dynamics have included only one or two species1,2,3. We ask whether such models are relevant to the real world. Two-species population models of an interacting consumer and resource collapse to one-species dynamics when recruitment to the resource population is unrelated to resource abundance, thereby weakening the coupling between consumer and resource4,5,6. We predict that, in nature, generalist consumers that feed on many species should similarly show one-species dynamics. We test this prediction using cyclic populations, in which it is easier to infer underlying mechanisms7, and which are widespread in nature8. Here we show that one-species cycles can be distinguished from consumer–resource cycles by their periods. We then analyse a large number of time series from cyclic populations in nature and show that almost all cycling, generalist consumers examined have periods that are consistent with one-species dynamics. Thus generalist consumers indeed behave as if they were one-species populations, and a one-species model is a valid representation for generalist population dynamics in many-species food webs.

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Figure 1: Cycles classified by period.

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Acknowledgements

We thank C. Godfray for permission to analyse time series from the Global Population Dynamics Database (GPDD). We thank J. Fryxell, B.K. Gilbert, S. Henke, P.J. Hudson, C.J. Krebs, L. Oksanen, B. Sanderson, S. Taylor and M. Tewes for discussions on particular taxa, and J.A.J. Metz for discussions of cycle periods. The research was supported by grants from the NSF and United States Department of Agriculture (USDA).

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Correspondence to W. W. Murdoch.

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Murdoch, W., Kendall, B., Nisbet, R. et al. Single-species models for many-species food webs. Nature 417, 541–543 (2002). https://doi.org/10.1038/417541a

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