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.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Murdoch, W. W. Population regulation in theory and practise. Ecology 75, 271–287 (1994)
Murdoch, W. W., Briggs, C. J. & Nisbet, R. M. Consumer-Resource Dynamics (Princeton Univ. Press, 2003)
de Roos, A. M. & Persson, L. Competition in size-structured populations, mechanisms inducing cohort formation and population cycles. Theor. Popul. Biol. 63, 1–16 (2003)
McCauley, E., Nisbet, R. M., Murdoch, W. W., de Roos, A. M. & Gurney, W. S. C. Large amplitude cycles of Daphnia and its algal prey in enriched environments. Nature 402, 653–656 (1999)
Bjornstad, O. N. & Grenfell, B. T. Noisy clockwork: Time-series analysis of population fluctuations in animals. Science 293, 638–643 (2001)
McCauley, E. & Murdoch, W. W. Cyclic and stable populations: Plankton as paradigm. Am. Nat. 129, 97–121 (1987)
McCauley, E. & Murdoch, W. W. Predator–prey dynamics in environments rich and poor in nutrients. Nature 343, 455–457 (1990)
Claessen, D., de Roos, A. M. & Persson, L. Population dynamic theory of size-dependent cannibalism. Proc. R. Soc. Lond. B 271, 333–340 (2004)
Medvinsky, A. B., Tikhonova, I. A., Li, B. L. & Malchow, H. Time delay as a key factor in model plankton dynamics. C. R. Biologies 327, 277–282 (2004)
Hastings, A. & Wollkind, D. Age structure in predator-prey systems. Theor. Pop. Biol. 21, 44–56 (1982)
De Roos, A. M., Metz, J. A. J., Evers, E. & Leipoldt, A. A size-dependent predator-prey interaction: who pursues whom? J. Math. Biol. 28, 609–643 (1990)
McCauley, E., Nisbet, R. M., de Roos, A. M., Murdoch, W. W. & Gurney, W. S. C. Structured population models of herbivorous zooplankton. Ecol. Monogr. 66, 479–501 (1996)
Nelson, W. A., McCauley, E. & Nisbet, R. M. Stage-structured cycles generate strong fitness-equalizing mechanisms. Evol. Ecol. 21, 499–515 (2007)
Kretzschmar, M., Nisbet, R. M. & McCauley, E. A predator-prey model for zooplankton grazing on competing algal populations. Theor. Pop. Biol. 44, 32–66 (1993)
Grover, J. P. Assembly rules for communities of nutrient-limited plants and specialist herbivores. Am. Nat. 143, 258–282 (1994)
Abrams, P. A. & Holt, R. D. The impact of consumer-resource cycles on the coexistence of competing consumers. Theor. Pop. Biol. 62, 281–295 (2002)
Murdoch, W. W. & McCauley, E. Three distinct types of dynamic behaviour shown by a single planktonic system. Nature 316, 628–630 (1985)
Kendall, B. E. et al. Why do populations cycle? A synthesis of statistical and mechanistic modelling approaches. Ecology 80, 1789–1805 (1999)
Murdoch, W. W. et al. Single-species models for many-species food webs. Nature 417, 541–543 (2002)
Benton, T. G., Plaistow, S. J. & Coulson, T. N. Complex population dynamics and complex causation: devils, details and demography. Proc. R. Soc. B 273, 1173–1181 (2006)
Dennis, B., Desharnais, R. A., Cushing, J. M., Henson, S. M. & Constantino, R. F. Estimating chaos and complex dynamics in an insect population. Ecol. Monogr. 71, 277–303 (2001)
Yoshida, T., Jones, L. E., Ellner, S. P., Fussmann, G. F. & Hairston, N. G. Rapid evolution drives ecological dynamics in a predator–prey system. Nature 424, 303–306 (2003)
Persson, L. et al. Culling prey promotes predator recovery-alternative states in a whole-lake experiment. Science 316, 1743–1746 (2007)
Nisbet, R. M., McCauley, E., Gurney, W. S. C., Murdoch, W. W. & Wood, S. N. Formulating and testing a partially specified Dynamic Energy Budget Model. Ecology 85, 3132–3139 (2004)
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.
About this article
Cite this article
McCauley, E., Nelson, W. & Nisbet, R. Small-amplitude cycles emerge from stage-structured interactions in Daphnia–algal systems. Nature 455, 1240–1243 (2008). https://doi.org/10.1038/nature07220
Journal of Theoretical Biology (2019)
Journal of Theoretical Biology (2019)
Asymmetric interactions and their consequences for vital rates and dynamics: the smaller tea tortrix as a model system
Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods
Journal of Mathematical Biology (2019)
Offspring size-number tradeoffs and food quality feedbacks impact population dynamics in a Daphnia- algae system