The impact of specialized enemies on the dimensionality of host dynamics


Although individual species persist within a web of interactions with other species, data are usually gathered only from the focal species itself. We ask whether evidence of a species’ interactions be detected and understood from patterns in the dynamics of that species alone. Theory predicts that strong coupling between a prey and a specialist predator/parasite should lead to an increase in the dimensionality of the prey's dynamics, whereas weak coupling should not. Here we describe a rare test of this prediction. Two natural enemies were added separately to replicate populations of a moth. For biological reasons that we identify here, the prediction of increased dimensionality was confirmed when a parasitoid wasp was added (although this increase had subtleties not previously appreciated), but the prediction failed for an added virus. Thus, an imprint of the interactions may be discerned within time-series data from component species of a system.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Abundances of the host (thin black line).
Figure 2: Cross-validation for the order of density dependence according to the method of Tong and co-workers21–23 (Box 1).
Figure 3: The estimated functions.
Figure 4


  1. 1

    Hassell, M. P. & May, R. M. Generalist and specialist natural enemies in insect predator–prey interactions. J. Anim. Ecol. 55, 923–940 (1986).

    Article  Google Scholar 

  2. 2

    Begon, M., Sait, S. M. & Thompson, D. J. Predator–prey cycles with period shifts between two- and three-species systems. Nature 381, 311–315 (1996).

    ADS  CAS  Article  Google Scholar 

  3. 3

    Murdoch, W. W. & Stewart-Oaten, A. Predation and population stability. Adv. Ecol. Res. 9, 1–131 (1975).

    Article  Google Scholar 

  4. 4

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

    Google Scholar 

  5. 5

    Turchin, P. Rarity of density dependence or population regulation with lags? Nature 344, 660–663 (1990).

    ADS  Article  Google Scholar 

  6. 6

    Stenseth, N. C., Falck, W., Bjørnstad, O. N. & Krebs, C. J. Population regulation in snowshoe hare and lynx populations: asymmetric food web configurations between the snowshoe hare and the lynx. Proc. Natl Acad. Sci. USA 94, 5147–5152 (1997).

    ADS  CAS  Article  Google Scholar 

  7. 7

    Schaffer, W. M. Ecological abstraction: The consequence of reduced dimensionality in ecological models. Ecol. Monogr. 51, 383–401 (1981).

    Article  Google Scholar 

  8. 8

    Berryman, A. A. Population Systems: a General Introduction (Plenum, New York, 1981).

    Google Scholar 

  9. 9

    Sait, S. M., Begon, M. & Thompson, D. J. Long-term population dynamics of the Indian meal worm moth Plodia interpunctella and its granulosis virus. J. Anim. Ecol. 63, 861–870 (1994).

    Article  Google Scholar 

  10. 10

    Sait, S. M., Begon, M. & Thompson, D. J. The influence of larval age on the response of Plodia interpunctella to a granulosis virus. J. Invert. Pathol. 63, 107–110 (1994).

    Article  Google Scholar 

  11. 11

    Sait, S. M., Begon, M. & Thompson, D. J. The effect of a sublethal baculovirus infection in the Indian meal moth, Plodia interpunctella. J. Anim. Ecol. 63, 541–550 (1994).

    Article  Google Scholar 

  12. 12

    Gurney, W. S. C., Nisbet, R. M. & Lawton, J. H. The systematic formulation of tractable single-species population models incorporating age structure. J. Anim. Ecol. 52, 479–495 (1983).

    Article  Google Scholar 

  13. 13

    Gurney, W. S. C. & Nisbet, R. M. Fluctuation periodicity, generation separation, and the expression of larval competition. Theor. Popul. Biol. 28, 150–180 (1985).

    MathSciNet  Article  Google Scholar 

  14. 14

    Briggs, C. J., Sait, S. M., Begon, M., Thompson, D. J. & Godfray, H. C. J. What causes generation cycles in populations of stored product moths? J. Anim. Ecol. 69, 352–366 (2000).

    Article  Google Scholar 

  15. 15

    Bjørnstad, O. N. et al. Population dynamics of the Indian meal moth: demographic stochasticity and delayed regulatory mechanisms. J. Anim. Ecol. 67, 110–126 (1998).

    Article  Google Scholar 

  16. 16

    Sait, S. M. et al. Venturia canescens parasitizing Plodia interpunctella: host vulnerability – a matter of degree. Ecol. Entomol. 20, 199–201 (1995).

    Article  Google Scholar 

  17. 17

    Sait, S. M., Begon, M., Thompson, D. J., Harvey, J. A. & Hails, R. S. Factors affecting host selection in an insect host–parasitoid interaction. Ecol. Entomol. 22, 225–230 (1997).

    Article  Google Scholar 

  18. 18

    Harvey, J. A., Harvey, I. F. & Thompson, D. J. Flexible larval growth allows use of a range of host sizes by a parasitoid wasp. Ecology 75, 1420–1428 (1994).

    Article  Google Scholar 

  19. 19

    Boots, M. Cannibalism and the stage-dependent transmission of a viral pathogen of the Indian meal moth, Plodia interpunctella. Ecol. Entomol. 23, 118–122 (1998).

    Article  Google Scholar 

  20. 20

    Knell, R. J., Begon, M. & Thompson, D. J. Transmission of Plodia interpunctella granulosis virus does not conform to the mass action model. J. Anim. Ecol. 67, 592–599 (1998).

    Article  Google Scholar 

  21. 21

    Cheng, B. & Tong, H. On consistent nonparametric order determination and chaos. J. R. Statist. Soc. B 54, 427–449 (1992).

    MathSciNet  MATH  Google Scholar 

  22. 22

    Cheng, B. & Tong, H. Orthogonal projection, embedding dimension and sample size in chaotic time series from a statistical perspective. Phil. Trans. R. Soc. Lond. A 348, 325–341 (1994).

    ADS  MathSciNet  Article  Google Scholar 

  23. 23

    Yao, Q. & Tong, H. Quantifying the influence of initial values on non-linear prediction. J. R. Statist. Soc. B 56, 701-725 (1994).

    MathSciNet  MATH  Google Scholar 

  24. 24

    Ellner, S. P. et al. Noise and nonlinearity in measles epidemics: Combining mechanistic and statistical approaches to population modeling. Am. Nat. 151, 425–440 (1998).

    CAS  Article  Google Scholar 

  25. 25

    Bjørnstad, O. N., Fromentin, J.-M., Stenseth, N. C. & Gjøsaeter, J. A new test for density-dependent survival: the case of coastal cod populations. Ecology 80, 1278–1288 (1999).

    Article  Google Scholar 

  26. 26

    Free, C. A., Beddington, J. R. & Lawton, J. H. Inadequacy of simple-models of mutual interference for parasitism and predation. J. Anim. Ecol. 46, 543–554 (1977).

    Article  Google Scholar 

  27. 27

    Sokal, R. R. & Rohlf, F. J. in Biometry 1 Ch. XIX, 887 (W. H. Freeman, New York, 1995).

    Google Scholar 

  28. 28

    Murdoch, W. W. & Briggs, C. J. Theory of biological control: recent developments. Ecology 77, 2001–2013 (1996).

    Article  Google Scholar 

  29. 29

    Tabashnik, B. E. & McGaughey, W. H. Resistance risk assessment for single and multiple insecticides: Responses of Indian meal moth (Lepidoptera: Pyralidae) to Bacillus thuringiensis. J. Econ. Entomol. 87, 835–841 (1994).

    Article  Google Scholar 

  30. 30

    Costantino, R. F., Desharnais, R. A., Cushing, J. M. & Dennis, B. Chaotic dynamics in an insect population. Science 275, 389–391 (1997).

    CAS  Article  Google Scholar 

  31. 31

    Bjørnstad, O. N., Fromentin, J.-M., Stenseth, N. C. & Gjøsaeter, J. Cycles and trends in cod population. Proc. Natl Acad. Sci. USA 96, 5066–5071 (1999).

    ADS  Article  Google Scholar 

  32. 32

    Grenfell, B. T. & Dobson, A. P. Ecology of infectious diseases in natural populations. (Cambridge Univ. Press, Cambridge, 1995).

  33. 33

    Nicholson, A. J. & Bailey, V. A. The balance of animal populations. Proc. Zool. Soc. Lond. 3, 551–598 (1935).

    Article  Google Scholar 

  34. 34

    Venables, W. N. & Ripley, B. D. in Modern Applied Statistics with S-plus 1–462 (Springer, New York, 1994).

    Google Scholar 

  35. 35

    Wei, W. W. Time Series Analysis (Addison Wesley, California, 1989).

    Google Scholar 

  36. 36

    Green, P. J. & Silverman, B. W. in Nonparametric Regression and Generalized Linear Models: a Roughness Penalty Approach Ch. 1-IX, 182 (Chapman & Hall, London, 1994).

    Google Scholar 

  37. 37

    Ellner, S. & Turchin, P. Chaos in a noisy world: New methods and evidence from time-series analysis. Am. Nat. 145, 343–375 (1995).

    Article  Google Scholar 

  38. 38

    Ricker, W. E. Stock and recruitment. J. Fish. Res. Board Canada 11, 559–623 (1954).

    Article  Google Scholar 

Download references


Funding was received from the National Center for Ecological Analysis and Synthesis (O.N.B.) (a Center funded by the NSF, the University of California Santa Barbara and the State of California), from the Norwegian National Science Foundation (O.N.B., N.C.S.) and from NERC (M.B., S.M.S. and D.J.T.). P. Amarasekare, A. Dobson and B. Grenfell commented on the manuscript.

Author information



Corresponding author

Correspondence to Ottar N. Bjørnstad.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bjørnstad, O., Sait, S., Stenseth, N. et al. The impact of specialized enemies on the dimensionality of host dynamics. Nature 409, 1001–1006 (2001).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing