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Small-amplitude cycles emerge from stage-structured interactions in Daphnia–algal systems


A long-standing issue in ecology is reconciling the apparent stability of many populations with robust predictions of large-amplitude population cycles from general theory on consumer–resource interactions1. Even when consumers are decoupled from dynamic resources, large-amplitude cycles can theoretically emerge from delayed feedback processes found in many consumers2,3. Here we show that resource-dependent mortality and a dynamic developmental delay in consumers produces a new type of small-amplitude cycle that coexists with large-amplitude fluctuations in coupled consumer–resource systems. A distinctive characteristic of the small-amplitude cycles is slow juvenile development for consumers, leading to a developmental delay that is longer than the cycle period. By contrast, the period exceeds the delay in large-amplitude cycles. These theoretical predictions may explain previous empirical results on coexisting attractors found in Daphnia–algal systems4,5. To test this, we used bioassay experiments that measure the growth rates of individuals in populations exhibiting each type of cycle. The results were consistent with predictions. Together, the new theory and experiments establish that two very general features of consumers—a resource-dependent juvenile stage duration and resource-dependent mortality—combine to produce small-amplitude resource–consumer cycles. This phenomenon may contribute to the prevalence of small-amplitude fluctuations in many other consumer–resource populations6,7.

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Figure 1: Multiple limit-cycle attractors in the structured predator–prey model.
Figure 2: Bioassay experiments for resource–consumer systems.
Figure 3: Egg density dynamics during cycles.
Figure 4: Comparison of individual growth rates in large- and small-amplitude cycles.


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We acknowledge feedback from A. de Roos, J. Fox, J. Casas, L. Persson and C. Briggs. A. Potapov provided advice on the bifurcation analysis. Experiments and theoretical analysis were supported by NSERC (Discovery Grants and Accelerator Award), Canada Foundation for Innovation, and the Canada Research Chairs Program to E.M. W.A.N. acknowledges support from Alberta Ingenuity. R.M.N. acknowledges support from the US National Science Foundation (Grant DEB-0717259).

Author Contributions All authors contributed to the planning, execution and analysis of theory and experiments.

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Correspondence to Edward McCauley.

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McCauley, E., Nelson, W. & Nisbet, R. Small-amplitude cycles emerge from stage-structured interactions in Daphnia–algal systems. Nature 455, 1240–1243 (2008).

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