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Noise and determinism in synchronized sheep dynamics

Nature volume 394, pages 674–677 (1998)Cite this article

Abstract

A major debate in ecology concerns the relative importance of intrinsic factors and extrinsic environmental variations in determining population size fluctuations1,2,3,4,5,6. Spatial correlation of fluctuations in different populations caused by synchronous environmental shocks2,7,8 is a powerful tool for quantifying the impact of environmental variations on population dynamics8,9. However, interpretation of synchrony is often complicated by migration between populations8,10. Here we address this issue by using time series from sheep populations on two islands in the St Kilda archipelago11,12,13. Fluctuations in the sizes of the two populations are remarkably synchronized over a 40-year period. A nonlinear time-series model shows that a high and frequent degree of environmental correlation is required to achieve this level of synchrony. The model indicates that if there were less environmental correlation, population dynamics would be much less synchronous than is observed. This is because of a threshold effect that is dependent on population size; the threshold magnifies random differences between populations. A refined model showsthat part of the required environmental synchronicity can be accounted for by large-scale weather variations. These results underline the importance of understanding the interaction between intrinsic and extrinsic influences on population dynamics14.

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Figure 1: Feral sheep populations on Hirta and Boreray.
Figure 2: Modelling the Hirta time series.
Figure 3: Simulations of the observed correlation in sheep counts between islands.

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References

  1. May, R. M. Stability and Complexity in Model Ecosystems (Princeton University Press, NJ,(1973)).

    Google Scholar 

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

    Book  Google Scholar 

  3. Stenseth, N. C., Bjornstad, O. N. & Saitoh, T. Agradient from stable to cyclic populations of Clethrionomys rufocanus in Hokkaido, Japan. Proc. R. Soc. Lond. B 263, 1117–1126 (1996).

    Article  ADS  CAS  Google Scholar 

  4. Sugihara, G. Ecology — from out of the blue. Nature 378, 559–560 (1995).

    Article  ADS  CAS  Google Scholar 

  5. 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 

  6. Leirs, H. et al. Stochastic seasonality and nonlinear density-dependent factors regulate population size in an African rodent. Nature 389, 176–180 (1997).

    Article  ADS  CAS  Google Scholar 

  7. Moran, P. A. P. The statistical analysis of the Canadian lynx cycle: II syhchronisation and meteorology. Aust. J. Zool. 1, 291–298 (1953).

    Article  Google Scholar 

  8. Ranta, E., Kaitala, V., Lindstrom, J. & Helle, E. The Moran effect and synchrony in population dynamics. Oikos 78, 136–142 (1997).

    Article  Google Scholar 

  9. Hill, J. K., Thomas, C. D. & Lewis, O. T. Effects of habitat patch size and isolation on dispersal by Hesperia comma butterflies: implications for metapopulation structure. J. Anim. Ecol. 65, 725–735 (1996).

    Article  Google Scholar 

  10. Bjornstad, O. N., Falck, W. & Stenseth, N. C. Geographic gradient in small rodent density-fluctuations — a statistical modeling approach. Proc. R. Soc. Lond. B 262, 127–133 (1995).

    Article  ADS  CAS  Google Scholar 

  11. Jewell, P. A., Milner, C. & Morton-Boyd, J. Island Survivors (Athlone, London, (1974)).

    Google Scholar 

  12. Clutton-Brock, T. H., Price, O. F., Albon, S. D. & Jewell, P. A. Persistent instability and population regulation in Soay sheep. J. Anim. Ecol. 60, 593–608 (1991).

    Article  Google Scholar 

  13. Grenfell, B. T., Price, O. F., Albon, S. D. & Clutton-Brock, T. H. Overcompensation and population cycles in an ungulate. Nature 355, 823–826 (1992).

    Article  ADS  CAS  Google Scholar 

  14. Sugihara, G. Red/blue chaotic power spectra. Nature 381, 199–199 (1996).

    Article  ADS  CAS  Google Scholar 

  15. Grenfell, B. T. Chance and chaos in measles dynamics. J. R. Stat. Soc. B 54, 383–398 (1992).

    Google Scholar 

  16. Falck, W., Bjornstad, O. N. & Stenseth, N. C. Voles and lemmings — chaos and uncertainty in fluctuating populations. Proc. R. Soc. Lond. B 262, 363–370 (1995).

    Article  ADS  Google Scholar 

  17. Stenseth, N. C. Snowshoe hare populations — squeezed from below and above. Science 269, 1061–1062 (1995).

    Article  ADS  CAS  Google Scholar 

  18. Higgins, K., Hastings, A., Sarvela, J. N. & Botsford, L. W. Stochastic dynamics and deterministic skeletons: population behavior of Dungeness crab. Science 276, 1431–1435 (1997).

    Article  CAS  Google Scholar 

  19. Ranta, E., Kaitala, V., Lindstrom, J. & Linden, H. Synchrony in population dynamics. Proc. R. Soc. Lond. B 262, 113–118 (1995).

    Article  ADS  Google Scholar 

  20. Clutton-Brock, T. H. et al. Stability and instability in ungulate populations: an empirical analysis. Am. Nat. 149, 195–219 (1997).

    Article  Google Scholar 

  21. Hassell, M. P., Lawton, J. H. & May, R. M. Patterns of dynamical behaviour in single-species populations. J. Anim. Ecol. 45, 471–486 (1976).

    Article  Google Scholar 

  22. Turchin, P. Nonlinear time-series modeling of vole population fluctuations. Res. Pop. Ecol. 38, 121–132 (1996).

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  24. Tong, H. Non-linear Time Series: a Dynamical Systems Approach (Oxford Univ. Press, (1990)).

    MATH  Google Scholar 

  25. Tsay, R. S. Testing and modelling threshold autoregressive processes. J. Am. Stat. Assoc. 84, 230–240 (1989).

    Article  Google Scholar 

  26. Gulland, F. M. D. Role of nematode infections in mortality of Soay sheep during a population crash on St Kilda. Parasitology 105, 493–503 (1992).

    Article  Google Scholar 

  27. Grenfell, B. T., Wilson, K., Isham, V. S., Boyd, H. E. G. & Dietz, K. Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study. Parasitology 111, S135–S151 (1995).

    Article  Google Scholar 

  28. Framstad, E., Stenseth, N. C., Bjornstad, O. N. & Falck, W. Limit cycles in Norwegian lemmings: tensions between phase-dependence and density-dependence. Proc. R. Soc. Lond. B 264, 31–38 (1997).

    Article  ADS  Google Scholar 

  29. Cloete, S. W. P., Van Halderen, A. & Schneider, D. J. Causes of perinatal lamb mortality amongst dormer and SA mutton Merino lambs. J. S. Afr. Vet. Assoc. 64, 121–125 (1993).

    CAS  PubMed  Google Scholar 

  30. Champion, R. A., Rutter, S. M., Penning, P. D. & Rook, A. J. Temporal variation in grazing behavior of sheep and the reliability of sampling periods. Appl. Anim. Behav. Sci. 42, 99–108 (1994).

    Article  Google Scholar 

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Acknowledgements

We thank Scottish Natural Heritage and the National Trust for Scotland for permission to work on St Kilda, and their staff for assistance, support and encouragement; J. M. Pilkington, A. McColl, A. Robertson and I.R. Stevenson for help with the project; P. Rohani for comments on the manuscript; H. Tong for statistical advice and encouragement; and the Royal Artillery for logistical support on St Kilda. The work was funded by grants from the Natural Environment Research Council (to T.H.C.-B., M.J.C., B.T.G., K.W. and S.D.A.), the Royal Society (to M.J.C., K.W. and S.D.A.) and the Biotechnology and Biological Sciences Research Council (to J.M.P.).

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Authors and Affiliations

  1. Zoology Department, University of Cambridge, Downing Street, CB2 3EJ, Cambridge, UK

    B. T. Grenfell, B. F. Finkenstädt & T. H. Clutton-Brock

  2. Department of Biological and Molecular Sciences, University of Stirling, Stirling, FK9 4LA, UK

    K. Wilson

  3. Institute of Zoology, Zoological Society of London, Regent's Park, NW1 4RY, London, UK

    T. N. Coulson

  4. Scottish Natural Heritage, Clachcaran, Stilligarry, South Uist, HS8 5RS, Western Isles, UK

    S. Murray

  5. Institute of Terrestrial Ecology, Hill of Brathens, Glassel, AB31 4BY, Banchory, UK

    S. D. Albon

  6. Institute of Cell, Animal and Population Biology, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JT, UK

    J. M. Pemberton

  7. Imperial College, Silwood Park, Ascot, SL5 7PY, UK

    M. J. Crawley

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  1. B. T. Grenfell
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Correspondence to B. T. Grenfell.

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Grenfell, B., Wilson, K., Finkenstädt, B. et al. Noise and determinism in synchronized sheep dynamics. Nature 394, 674–677 (1998). https://doi.org/10.1038/29291

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