Mapping the regional transition to cyclicity inClethrionomys rufocanus: Spectral densities and functional data analysis

Abstract

We study the regional transitions in dynamics of the gray-sided vole,Clethrionomys rufocanus, within Hokkaido, Japan. The data-set consists of 225 time series of varying length (most from 23 to 31 years long) collected between 1962 and 1992 by the Forestry Agency of the Japanese Government. To see clearly how the periodic behavior changes geographically, we estimate the spectral density functions of the growth rates of all populations using a log-spline method. We subsequently apply functional data analysis to the estimated densities. The functional data analysis is, in this context, analogous to a principal component analysis applied to curves. We plot the results of the analysis on the map of Hokkaido, to reveal a clear transition from relatively stable populations in the southwest and west to populations undergoing 3–4 year cycles in the northeast and east. The degree of seasonality in the vegetation and the rodent demography appear to be strongest in the cyclic area. We briefly speculate that the destabilization of the rodent dynamics is linked to increased seasonalforcing on the trophic interactions in which the gray-sided voles are involved.

This is a preview of subscription content, log in to check access.

References

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

    Article  CAS  Google Scholar 

  2. Bjørnstad, O. N., W. Falck and N. C. Stenseth (1995) A geographic gradient in small rodent density fluctuations: a statistical modelling approach.Proceedings of the Royal Society of London B 262: 127–133.

    Article  Google Scholar 

  3. Bjørnstad, O. N., S. Champely, N. C. Stenseth and T. Saitoh (1996) Cyclicity and stability of grey-sided voles,Clethrionomys rufocanus, of Hokkaido: spectral and Principal components analyses.Philosophical Transactions of the Royal Society of London B 351: 867–875.

    Article  Google Scholar 

  4. Bjørnstad, O. N., N. C. Stenseth and T. Saitoh (1998) Synchrony and scaling in dynamics of voles and mice in northern Japan.Ecology (in press).

  5. Butler, L. (1951) Population cycles and colour phase genetics of the coloured fox in Quebec.Canadian Journal of Zoology 29: 24–41.

    Article  Google Scholar 

  6. Castro, P. E., W. H. Lawton and E. A. Sylvestre (1986) Principal modes of variation for processes with continuous sample curves.Technometrics 28: 329–337.

    Article  Google Scholar 

  7. Chatfield, C. (1989)The analysis of time series: an introduction, 4th edn. Chapman and Hall, London.

    Google Scholar 

  8. Dennis, B., R. A. Desharnais, J. M. Cushing and R. F. Costantino (1997) Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles.Journal of Animal Ecology 66: 704–729.

    Article  Google Scholar 

  9. Dobson, A. and P. Hudson (1994) The interaction between the parasites and predators of Red GrouseLagopus lagopus scoticus.Ibis 137: S87–96.

    Google Scholar 

  10. Erlinge, S. (1987) Predation and noncyclicity in a microtine population in Southern Sweden.Oikos 50: 347–352.

    Article  Google Scholar 

  11. Erlinge, S., G. Göransson, L. Hansson, G. Högstedt, O. Liberg, I. N. Nilsson, T. Nilsson, T. von Schantz and M. Sylven (1983) Predation as a regulating factor on small rodent populations in Southern Sweden.Oikos 40: 36–52.

    Article  Google Scholar 

  12. Fromentin, J.-M, N. C. Stenseth, J. Gjøsæter, O. N. Bjørnstad, W. Falck and T. Johannesen (1997) Spatial patterns of the temporal dynamics of three gadoid species along the Norwegian Skagerrak coast.Marine Ecological Progress Series 155: 209–222.

    Article  Google Scholar 

  13. Goodall, D. W. (1954) Objective methods for the classification of vegetation III. An essay in the use of factor analysis.Australian Journal of Botany 2: 304–324.

    Article  Google Scholar 

  14. Grenfell, B. T., B. M. Bolker and A. Kleczkowski (1995) Seasonality and extinction in chaotic metapopulations.Proceedings of the Royal Society of London B 259: 97–103.

    Article  Google Scholar 

  15. Hanski, I., L. Hansson and H. Henttonen (1991) Specialist predators, generalist predators, and the microtine rodent cycle.Journal of Animal Ecology 60: 353–367.

    Article  Google Scholar 

  16. Hanski, I. and E. Korpimäki (1995) Microtine rodent dynamics in Northern Europe: Parametrized models for the predator-prey interaction.Ecology 76: 840–850.

    Article  Google Scholar 

  17. Hanski, I., P. Turchin, E. Korpimäki and H. Henttonen (1993) Population oscillations of boreal rodents: Regulation by mustelid predators leads to chaos.Nature 364: 232–235.

    PubMed  Article  CAS  Google Scholar 

  18. Hansson, L. (1987) An interpretation of rodent dynamics as due to trophic interactions.Oikos 50: 308–318.

    Article  Google Scholar 

  19. Hansson, L. (1992) Small mammal communities on clearcuts in a latitudinal gradient.Acta Oecologia 13: 687–699.

    Google Scholar 

  20. Hansson, L. and H. Henttonen (1985a) Gradients in density variations of small rodents: the importance of latitude snow cover.Oecologia 67: 394–402.

    Article  Google Scholar 

  21. Hansson, L. and H. Henttonen (1985b) Regional differences in cyclicity and reproduction inClethrionomys species: Are they related?Annales Zoologica Fennici 22: 277–288.

    Google Scholar 

  22. Hansson, L. and H. Henttonen (1988) Rodent dynamics as community processes.Trends in Ecology and Evolution 3: 195–200.

    Article  Google Scholar 

  23. Hastie, T. and R. Tibshirani (1990)Generalized additive models. Chapman and Hall, London.

    Google Scholar 

  24. Hastings, A., C. L. Horn, S. Ellner, P. Turchin and H. C. J. Godfray (1993) Chaos in ecology: Is mother nature a strange attractor?Annual Review of Ecology and Systematics 24: 1–33.

    Google Scholar 

  25. Henttonen, H., D. McGuire and L. Hansson (1985) Comparisons of amplitude and frequencies (spectral analyses) of density variations in long-term data sets ofClethrionomys species.Annales Zoologica Fennici 22: 221–27.

    Google Scholar 

  26. Jedrzejewski, W. and B. Jedrzejewska (1996) Rodent cycles in relation to biomass and productivity of ground vegetation and predation in the Palearctic.Acta Theriologica 41: 1–34.

    Google Scholar 

  27. Kaneko, Y., K. Nakata, T. Saitoh, N. C. Stenseth and O. N. Bjørnstad (1998) The biology of the voleClethrionomys rufocanus: a review.Researches on Population Ecology 40: 21–37.

    Google Scholar 

  28. King, A. A., W. M. Schaffer, C. Gordon, J. Treat and M. Kot (1996) Weakly dissipative predator-prey systems.Bulletin of Mathematical Biology 58: 835–859.

    Article  Google Scholar 

  29. Kooperberg, C, C. J. Stone and Y. K. Truong (1995) Logspline estimation of a possibly mixed spectral distribution.Journal of Time Series Analysis 16: 359–388.

    Google Scholar 

  30. Manly, B. F. J. (1997)Randomization, bootstrap and Monte Carlo methods in biology, 2nd edn. Chapman and Hall, London.

    Google Scholar 

  31. May, R. M. (1976) Simple mathematical models with very complicated dynamics.Nature 261: 459–467.

    PubMed  Article  CAS  Google Scholar 

  32. Moss, R., A. Watson and R. Parr (1996) Experimental prevention of population cycle in red grouse.Ecology 77: 1512–1530.

    Article  Google Scholar 

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

    Article  Google Scholar 

  34. Myers, J. H. and L. D. Rothman (1995) Field experiments to study regulation of fluctuating populations. pp. 229–251.In N. Cappuccino and P. Price (eds.)Population dynamics. Academic Press, New York.

    Google Scholar 

  35. Priestley, M. B. (1981)Spectral analysis and time series. Academic Press, London.

    Google Scholar 

  36. Ramsay, J. O. and B. W. Silverman (1997)Functional data analysis. Springer-Verlag, New York.

    Google Scholar 

  37. Saitoh, T. and A. Nakatsu (1997) Impact of forest plantation on the community of small mammals in Hokkaido, Japan.Mammal Study 22: 27–38.

    Google Scholar 

  38. Saitoh, T., N. C. Stenseth and O. N. Bjørnstad (1997) Density dependence in fluctuating grey-sided vole populations.Journal of Animal Ecology 66: 14–24.

    Article  Google Scholar 

  39. Saitoh, T., O.N. Bjørnstad and N. C. Stenseth (1998a) Density-dependence in voles and mice: a comparative analysis.Ecology (in press).

  40. Saitoh, T., N. C. Stenseth and O. N. Bjørnstad (1998b) The population dynamics of the vole,Clethrionomys rufocanus, in Hokkaido Japan.Researches on Population Ecology 40: 61–76.

    Google Scholar 

  41. Selås, V. (1997) Cyclic population fluctuations of herbivores as an effect of cyclic seed cropping of plants: the mast depression hypothesis.Oikos 80: 257–268.

    Article  Google Scholar 

  42. Shepherd, R., D. D. Bennet, J. W. Dale, S. Tunnock, R. E. Dolph and R. W. Thier (1988) Evidence of synchronized cycles in outbreak patterns of Douglas-fir tussock moth,Orgyia pseudotsugata (McDunnough) (Lepidoptera: Lymantriidae).Memoirs of the Entomological Society of CanActa, Ottawa 146: 107–121.

    Google Scholar 

  43. Statistical Sciences (1995)S-plus guide to statistical and mathematical analysis, version 3.3. StatSci, MathSoft, Inc., Seattle.

    Google Scholar 

  44. Stenseth, N. C. (1985) Models of bank vole and wood mice.Symposium of the Zoological Society of London 55: 339–376.

    Google Scholar 

  45. Stenseth, N. C, O. N. Bjørnstad and T. Saitoh (1996a) A gradient from stable to cyclic populations ofClethrionomys rufocanus in Hokkaido, Japan.Proceedings of the Royal Society of London B 263: 1117–1126.

    Article  CAS  Google Scholar 

  46. Stenseth, N. C, O. N. Bjornstad and W. Falck (1996b) Is spacing behaviour coupled with predation causing the microtine density cycle? A synthesis of current process-oriented and pattern-oriented studies.Proceedings of the Royal Society of London B 263: 1423–1435.

    Article  CAS  Google Scholar 

  47. Stenseth, N. C, O. N. Bjørnstad and T. Saitoh (1998a) Seasonal forcing on the dynamics ofClethrionomys rufocanus: modeling geographic gradients in population dynamics.Researches on Population Ecology 40: 85–95.

    Google Scholar 

  48. Stenseth, N. C., T. Saitoh and N. G. Yoccoz (1998b) Frontiers of population ecology in microtine rodents: a pluralistic approach to the study of population ecology.Researches on Population Ecology 40: 5–20.

    Google Scholar 

  49. Turchin, P. and I. Hanski (1997) An empirically based model for latitudinal gradient in vole population dynamics.American Naturalist 149: 842–874.

    Article  PubMed  CAS  Google Scholar 

  50. Wahba, G. (1980) Automatic smoothing of the log periodogram.Journal of the American Statistical Association 75: 122–132.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ottar N. Bjørnstad.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bjørnstad, O.N., Stenseth, N.C., Saitoh, T. et al. Mapping the regional transition to cyclicity inClethrionomys rufocanus: Spectral densities and functional data analysis. Res Popul Ecol 40, 77–84 (1998). https://doi.org/10.1007/BF02765223

Download citation

Key words

  • biogeography
  • microtine cycle
  • population fluctuation
  • scale of regulation
  • seasonality