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Allee effects and pulsed invasion by the gypsy moth

Naturevolume 444pages361363 (2006) | Download Citation



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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  1. 1

    Vitousek, P. M., D'Antonio, C. M., Loope, L. L. & Westbrooks, R. Biological invasions as global environmental change. Am. Sci. 84, 468–478 (1996)

  2. 2

    Barbier, E. B. A note on the economics of biological invasions. Ecol. Econ. 39, 197–202 (2001)

  3. 3

    Mayo, J. H., Straka, T. J. & Leonard, D. S. The cost of slowing the spread of the gypsy moth (Lepidoptera: Lymantriidae). J. Econ. Entomol. 96, 1448–1454 (2003)

  4. 4

    Allee, W. C. The Social Life of Animals (Norton, New York, 1938)

  5. 5

    Liebhold, A. M., Halverson, J. A. & Elmes, G. A. Gypsy moth invasion in North America: a quantitative analysis. J. Biogeogr. 19, 513–520 (1992)

  6. 6

    Montgomery, M. E. & Wallner, W. E. in Dynamics of Forest Insect Populations: Patterns, Causes, Implications (ed. Berryman, A. A.) 253–375 (Plenum, New York, 1988)

  7. 7

    Sharov, A. A., Leonard, D., Liebhold, A. M., Roberts, E. A. & Dickerson, W. “Slow the Spread”: A national program to contain the gypsy moth. J. For. 100, 30–35 (2002)

  8. 8

    Tobin, P. C. et al. Management of the gypsy moth through a decision algorithm under the Slow-the-Spread project. Am. Entomol. 50, 200–209 (2004)

  9. 9

    Dwyer, G., Dushoff, J. & Yee, S. H. The combined effects of pathogens and predators on insect outbreaks. Nature 430, 341–345 (2004)

  10. 10

    Johnson, D. M., Liebhold, A. M. & Bjørnstad, O. N. Circumpolar variation in periodicity and synchrony among gypsy moth populations. J. Anim. Ecol. 74, 882–892 (2005)

  11. 11

    Sharov, A. A. & Liebhold, A. M. Bioeconomics of managing the spread of exotic pest species with barrier zones. Ecol. Appl. 8, 833–845 (1998)

  12. 12

    Skellam, J. G. Random dispersal in theoretical populations. Biometrika 38, 196–218 (1951)

  13. 13

    Shigesada, N., Kawasaki, K. & Takeda, Y. Modeling stratified diffusion in biological invasions. Am. Nat. 146, 229–251 (1995)

  14. 14

    Neubert, M. G., Kot, M. & Lewis, M. A. Invasion speeds in fluctuating environments. Proc. R. Soc. Lond. B 267, 1603–1610 (2000)

  15. 15

    Sharov, A. A. & Liebhold, A. M. Model of slowing the spread of gypsy moth (Lepidoptera: Lymantriidae) with a barrier zone. Ecol. Appl. 8, 1170–1179 (1998)

  16. 16

    Keitt, T. H., Lewis, M. A. & Holt, R. D. Allee effects, invasion pinning, and species' borders. Am. Nat. 157, 203–216 (2001)

  17. 17

    Wang, M. H. & Kot, M. Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 171, 83–97 (2001)

  18. 18

    Lewis, M. A. & Kareiva, P. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 43, 141–158 (1993)

  19. 19

    Taylor, C. M., Davis, H. G., Civille, J. C., Grevstad, F. S. & Hastings, A. Consequences of an Allee effect in the invasion of a Pacific estuary by Spartina alterniflora. Ecology 85, 3254–3266 (2004)

  20. 20

    Veit, R. R. & Lewis, M. A. Dispersal, population growth, and the Allee effect: Dynamics of the House Finch invasion of eastern North America. Am. Nat. 148, 255–274 (1996)

  21. 21

    Taylor, C. M. & Hastings, A. Allee effects in biological invasions. Ecol. Lett. 8, 895–908 (2005)

  22. 22

    Liebhold, A. & Bascompte, J. The Allee effect, stochastic dynamics and the eradication of alien species. Ecol. Lett. 6, 133–140 (2003)

  23. 23

    Sharov, A. A., Liebhold, A. M. & Ravlin, F. W. Prediction of gypsy-moth (Lepidoptera, Lymantriidae) mating success from pheromone trap counts. Environ. Entomol. 24, 1239–1244 (1995)

  24. 24

    Whitmire, S. L. & Tobin, P. C. Persistence of invading gypsy moth colonies in the United States. Oecologia 147, 230–237 (2006)

  25. 25

    Dwyer, G. & Morris, W. F. Resource-dependent dispersal and the speed of biological invasions. Am. Nat. 167, 165–176 (2006)

  26. 26

    Royama, T. Analytical Population Dynamics (Chapman & Hall, London, 1992)

  27. 27

    Peltonen, M., Liebhold, A. M., Bjørnstad, O. N. & Williams, D. W. Spatial synchrony in forest insect outbreaks: roles of regional stochasticity and dispersal. Ecology 83, 3120–3129 (2002)

  28. 28

    Deutsch, C. V. & Journel, A. G. GSLIB: Geostatistical Software Library and User's Guide (Oxford Univ. Press, New York, 1992)

  29. 29

    Sharov, A. A., Roberts, E. A., Liebhold, A. M. & Ravlin, R. W. Gypsy moth (Lepidoptera: Lymantriidae) spread in the central Appalachians: three methods for species boundary estimation. Environ. Entomol. 24, 1529–1538 (1995)

  30. 30

    Bjørnstad, O. N. & Falck, W. Nonparametric spatial covariance functions: estimation and testing. Environ. Ecol. Stat. 8, 53–70 (2001)

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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.

Author information


  1. Department of Biology, University of Louisiana, PO Box 42451, Louisiana, 70504, Lafayette, USA

    • Derek M. Johnson
  2. United States Department of Agriculture, Forest Service, Northern Research Station, 180 Canfield Street, West Virginia, 26505, Morgantown, USA

    • Andrew M. Liebhold
    •  & Patrick C. Tobin
  3. 501 ASI Building, Departments of Entomology and Biology, Pennsylvania State University, Pennsylvania, 16802, University Park, USA

    • Ottar N. Bjørnstad


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Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Corresponding author

Correspondence to Derek M. Johnson.

Supplementary information

  1. 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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