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Allee effects and pulsed invasion by the gypsy moth

Abstract

Biological invasions pose considerable threats to the world’s ecosystems1 and cause substantial economic losses2. A prime example is the invasion of the gypsy moth in the United States, for which more than $194 million was spent on management and monitoring between 1985 and 2004 alone3. The spread of the gypsy moth across eastern North America is, perhaps, the most thoroughly studied biological invasion in the world, providing a unique opportunity to explore spatiotemporal variability in rates of spread. Here we describe evidence for periodic pulsed invasions, defined as regularly punctuated range expansions interspersed among periods of range stasis. We use a theoretical model with parameter values estimated from long-term monitoring data to show how an interaction between strong Allee effects (negative population growth at low densities)4 and stratified diffusion (most individuals disperse locally, but a few seed new colonies by long-range movement)5 can explain the invasion pulses. Our results indicate that suppressing population peaks along range borders might greatly slow invasion.

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Figure 1: Map showing the years of first quarantine of the gypsy moth in the eastern United States.
Figure 2: Nonparametric spatial correlation function showing geographically synchronized rates of invasion out to a distance of 600 km.
Figure 3: Periodic invasion pulses in the gypsy moth.
Figure 4: Simulation model.

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Acknowledgements

We thank L. Blackburn for invaluable assistance in manuscript preparation. B. Grenfell provided insightful comments that improved the manuscript. This work was supported by the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service Grants to O.N.B. and A.M.L. (2002), O.N.B., A.M.L. and P.C.T. (2006), and D.M.J. (2006). Author Contributions The original concept of the manuscript was conceived by A.M.L., O.N.B. and D.M.J., and all authors contributed to the development of that concept. A.M.L. provided expertise regarding the ecology of the gypsy moth. P.C.T. performed the analyses for estimates of the Allee effect and carrying capacity. A.M.L. and O.N.B. constructed the population equation, D.M.J. wrote the code for the spatial model and ran the spatial simulations, and performed tests for periodicity and sensitivity analysis. O.N.B. coded and ran the continuous-space model. D.M.J. was responsible for writing the manuscript, and all authors contributed equally to revisions.

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Correspondence to Derek M. Johnson.

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Supplementary information

Supplementary Notes

This file contains Supplementary Information A–E. Supplementary Information A: Estimation of the Allee threshold and carrying capacity in North American gypsy moth populations from pheromone-baited trap data. Supplementary Information B: Allee effects and stratified diffusion are critical for pulsed invasion, plus Supplementary Figures demonstrating the lack of pulses of invasion in the absence of an Allee effect, stratified diffusion, and both. Supplementary Information C: Approximation continuous space in a discrete invasion model Analyses suggesting that discretizing space has no affect on periodicity of invasion pulses. Supplementary Information D: Continuous space invasion model Analysis demonstrating periodic invasion pulses in a continuous-space invasion model with Allee effects. Supplementary Information E: Sensitivity analyses of invasion model parameters The effect of variation in model parameters on the periodicity of invasion pulses (DOC 166 kb)

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Johnson, D., Liebhold, A., Tobin, P. et al. Allee effects and pulsed invasion by the gypsy moth. Nature 444, 361–363 (2006). https://doi.org/10.1038/nature05242

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