The economic damage caused by episodic outbreaks of forest-defoliating insects has spurred much research1, yet why such outbreaks occur remains unclear2. Theoretical biologists argue that outbreaks are driven by specialist pathogens or parasitoids, because host–pathogen and host–parasitoid models show large-amplitude, long-period cycles resembling time series of outbreaks3,4. Field biologists counter that outbreaks occur when generalist predators fail, because predation in low-density defoliator populations is usually high enough to prevent outbreaks5,6,7,8. Neither explanation is sufficient, however, because the time between outbreaks in the data is far more variable than in host–pathogen and host–parasitoid models1,2, and far shorter than in generalist-predator models9,10,11. Here we show that insect outbreaks can be explained by a model that includes both a generalist predator and a specialist pathogen. In this host–pathogen–predator model, stochasticity causes defoliator densities to fluctuate erratically between an equilibrium maintained by the predator, and cycles driven by the pathogen12,13. Outbreaks in this model occur at long but irregular intervals, matching the data. Our results suggest that explanations of insect outbreaks must go beyond classical models to consider interactions among multiple species.
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We thank O. Bjornstad, P. Turchin and A. Hunter for comments. G.D. and J.D. were supported by grants from the US National Science Foundation. J.D. was also supported by the Andrew W. Mellon Foundation.
The authors declare that they have no competing financial interests.
Results for the combined model when a term for long-term pathogen survival is added to the pathogen equation. The file includes figures showing the model's multiple equilibria and stochastically-induced complex dynamics. (PDF 112 kb)
Equations and results for a host-parasitoid-predator model analogous to the combined host-pathogen-predator model in the main text. The file includes figures showing the model's multiple equilibria, and stochastically-induced complex dynamics. (PDF 96 kb)
Results for a spatial version of the combined model. The file includes a figure showing a realization of the model, as an example of how this version of the model usually allows for high levels of synchrony (correlation greater than 0.8) among sub-populations. (PDF 75 kb)
Figures showing that changes in the parameter values have only a modest effect on the upper bound of the CV of the time between outbreaks in the combined model. (PDF 295 kb)
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Dwyer, G., Dushoff, J. & Yee, S. The combined effects of pathogens and predators on insect outbreaks. Nature 430, 341–345 (2004). https://doi.org/10.1038/nature02569
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