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Modelling Population Change From Time Series Data

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Wildlife 2001: Populations

Abstract

Information on change in population size over time is among the most basic inputs for population management. Unfortunately, population changes are generally difficult to identify, and once identified difficult to explain. Sources of variation (patterns) in population data include: changes in environment that affect carrying capacity and produce trend, autocorrelative processes, irregular environmentally induced perturbations, and stochasticity arising from population processes. In addition, populations are almost never censused and many surveys (e.g., the North American Breeding Bird Survey) produce multiple, incomplete time series of population indices, providing further sampling complications. We suggest that each source of pattern should be used to address specific hypotheses regarding population change, but that failure to correctly model each source can lead to false conclusions about the dynamics of populations. We consider hypothesis tests based on each source of pattern, and the effects of autocorrelated observations and sampling error. We identify important constraints on analyses of time series that limit their use in identifying underlying relationships.

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Literature Cited

  • Bulmer, M. G. 1975. The statistical analysis of density dependence. Biometrics 31: 901–911.

    Article  CAS  Google Scholar 

  • Cochran, W. G. 1977. Sampling techniques. Wiley and Sons, New York, New York, USA.

    Google Scholar 

  • Dagum, C. and E. B. Dagum. 1988. Trend. Pages 321–324 in S. Kotz, and N. L. Johnson, editors. Encyclopedia of statistical sciences, Volume 9. John Wiley and Sons, New York, New York, USA.

    Google Scholar 

  • Dennis, B., P. L. Munholland, and J. M. Scott. 1991. Estimation of growth and extinction parameters for endangered species. Ecological Monographs 61: 115–144.

    Article  Google Scholar 

  • Draper, N. R., and H. Smith. 1981. Applied regression analysis, second edition. John Wiley and Sons, New York, New York, USA.

    Google Scholar 

  • Droege, S., and J. R. Sauer. 1990. North American Breeding Bird Survey annual summary, 1989. U. S. Fish and Wildlife Service Biological Report 90(8). Washington, D. C, USA.

    Google Scholar 

  • Faanes, C. A., and D. Bystrak. 1981. The role of observer bias in the North American Breeding Bird Survey. Pages 353-359 in C. J. Ralph, and J. M. Scott, editors. Estimating the numbers of terrestrial birds. Studies in Avian Biology 6: 353–359.

    Google Scholar 

  • Fuller, W. A. 1976. Introduction to statistical time series. John Wiley and Sons, New York, New York, USA.

    Google Scholar 

  • Geissler, P. H., and J. R. Sauer. 1990. Topics in route-regression analysis. Pages 54–57 in J. R. Sauer, and S. Droege, editors. Survey designs and statistical methods for the estimation of avian population trends. U. S. Fish and Wildlife Service, Biological Report 90(1), Washington, D. C, USA.

    Google Scholar 

  • Gerrodette, T. 1987. A power analysis for detecting trends. Ecology 68: 1364–1372.

    Article  Google Scholar 

  • Jassby, A. D., and T. M. Powell. 1990. Detecting changes in ecological time series. Ecology 71: 2044–2052.

    Article  Google Scholar 

  • Keller-McNulty, S., and M. McNulty. 1987. The independent pairs assumption in hypothesis tests based on rank correlation coefficients. The American Statistician 41: 40–41.

    Article  Google Scholar 

  • Kuno, E. 1971. Sampling error as a misleading artifact in “key factor analysis”. Researches on Population Ecology 13: 28–45.

    Article  Google Scholar 

  • Lebreton, J-D. 1990. Modelling density-dependence, environmental variability, and demographic stochasticity from population counts: an example using Wytham Wood great tits. Pages 89–102 in J. Blondel, A. Gosier, J-D Lebreton, and R. McCleery, editors. Population biology of passerine birds. Springer-Verlag, Berlin, Germany.

    Google Scholar 

  • Link, W. A., and J. S. Hatfield. 1990. Power calculations and model selection for trend analysis: a comment. Ecology 71: 1217–1220.

    Article  Google Scholar 

  • Maelzer, D. A. 1970. The regression of log N n+1 lon log N nas a test of density dependence: an exercise with computer-constructed density-independent populations. Ecology 51: 810–822.

    Article  Google Scholar 

  • Marchant, J. H., R. Hudson, S. P. Carter, and P. Whittington. 1990. Population trends in British breeding birds. British Trust for Ornithology, Tring, England.

    Google Scholar 

  • Pollard, E., K. H. Lakhani, and P. Rothery. 1987. The detection of density-dependence from a series of annual censuses. Ecology 68: 2046–2055.

    Article  Google Scholar 

  • Reynolds, R. E., and J. R. Sauer. 1991. Changes in mallard breeding populations in relation to harvest and productivity rates. Journal of Wildlife Management 55: 483–487.

    Article  Google Scholar 

  • Robbins, C. S., D. Bystrak, and P. H. Geissler. 1986. The breeding bird survey: its first fifteen years, 1965–1979. U. S. Fish and Wildlife Service, Resource Publication 157. Washington, D. C, USA.

    Google Scholar 

  • Robbins, C. S., J. R. Sauer, R. S. Greenberg, and S. Droege. 1989. Population declines in North American birds that migrate to the neotropics. Proceedings of the National Academy of Sciences 86: 7658–7662.

    Article  CAS  Google Scholar 

  • Sauer, J. R., R. J. Barker, and P. H. Geissler. 1992. Statistical aspects of modeling population changes from population size data. In W. Kendall, and R. Lacher, editors. The population ecology and wildlife toxicology of agricultural pesticide use: a modelling initiative for avian species.

    Google Scholar 

  • Sauer, J. R., and S. Droege. 1990. Recent population trends of the eastern bluebird. Wilson Bulletin 102: 239–252.

    Google Scholar 

  • Sauer, J. R., S. Droege, and D. D. Dolton. In review. A comparison of mourning dove population trend estimates from the call count and North American Breeding Bird Surveys.

    Google Scholar 

  • Sauer, J. R.,and S. Droege. In press. Geographic patterns of population trends of neotropical migrants in North America. Proceedings of a Conference on the Conservation and Ecology of Neotropical Migrants.

    Google Scholar 

  • Slade, N. A. 1977. Statistical detection of density dependence from a series of sequential censuses. Ecology 58: 1094–1102.

    Article  Google Scholar 

  • Solow, A. R. 1990. Testing for density dependence-a cautionary note. Oecologia 83: 47–49.

    Article  Google Scholar 

  • St. Amant, J. L. S. 1970. The detection of regulation in animal populations. Ecology 51: 823–828.

    Article  Google Scholar 

  • Sykes, Z. M. 1969. Some stochastic versions of the matrix model for population dynamics. Journal of the American Statistical Association 64: 111–130.

    Article  Google Scholar 

  • Temple, S. A., and J. A. Weins. 1989. Bird populations and environmental changes: can birds be bio-indicators? American Birds 43: 260–270.

    Google Scholar 

  • Thompson, K. R., and F. H. Page. 1989. Detecting synchrony of recruitment using short, autocorrelated time series. Canadian Journal of Fisheries and Aquatic Sciences 46: 1831–1838.

    Article  Google Scholar 

  • Vickery, W. L., and T. D. Nudds. 1984. Detection of density-dependent effects in annual duck censuses. Ecology 65: 96–104.

    Article  Google Scholar 

  • Walters, C. J. 1985. Bias in the estimation of functional relationships from time series data. Canadian Journal of Fisheries and Aquatic Sciences 41: 147–149.

    Article  Google Scholar 

  • Yule, G. U. 1926. Why do we sometimes get nonsense-correlations between time-series? — A study in sampling and the nature of time-series. Journal of the Royal Statistical Society 89: 1–69.

    Article  Google Scholar 

  • Zeger, S. L. 1988. A regression model for time series of counts. Biometrika 75: 621–629.

    Article  Google Scholar 

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© 1992 Elsevier Science Publishers Ltd

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Barker, R.J., Sauer, J.R. (1992). Modelling Population Change From Time Series Data. In: McCullough, D.R., Barrett, R.H. (eds) Wildlife 2001: Populations. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2868-1_17

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  • DOI: https://doi.org/10.1007/978-94-011-2868-1_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-876-2

  • Online ISBN: 978-94-011-2868-1

  • eBook Packages: Springer Book Archive

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