Environmental and Ecological Statistics

, Volume 2, Issue 3, pp 225–237 | Cite as

Using selection functions to describe changes in environmental variables

  • L. L. McDonald
  • L. Gonzalez
  • B. F. J. Manly


The selection function (which shows how the frequency of sampling units with the value X = x at one point in time must change in order to produce the distribution that occurs at a later point in time) is proposed for describing the changes over time in an environmentally important variable X. It is shown that the theory of selection functions as used in the study of natural selection and resource selection by animals requires some modifications in this new application and that a selection function is a useful tool in long-term monitoring studies because all changes in a distribution can be examined (rather than just changes in single parameters such as the mean), and because graphical presentations of the selection function are easy for non-statisticians to understand. Estimation of the selection function is discussed using a method appropriate for normal distributions and bootstrapping is suggested as a method for assessing the precision of estimates and for testing for significant differences between samples taken at different times. Methods are illustrated using data on water chemical variables from a study of the effects of acid precipitation in Norway.


environmental monitoring selection function natural selection EMAP environmental assessment fitness function 


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  1. Anderson, J.A. and Blair, V. (1982) Penalized maximum likelihood estimation in logistic regression and discrimination. Biometrika, 69, 123–36.Google Scholar
  2. Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, London.Google Scholar
  3. Kullback, S. (1983) Kullback information. Encyclopedia of Statistical Sciences, 4, 421–5.Google Scholar
  4. Manly, B.F.J. (1985) The Statistics of Natural Selection on Animal Populations. Chapman and Hall, London.Google Scholar
  5. Manly, B.F.J., McDonald, L.L. and Thomas, D.L. (1993) Resource Selection by Animals: Statistical Design and Analysis for Field Studies. Chapman and Hall, London.Google Scholar
  6. Mohn, E. and Volden, R. (1985) Acid precipitation: effects on small lake chemistry. In Data Analysis in Real Life Environment: Ins and Outs of Solving Problems, J.F. Marcotorchino, J.M. Proth and J. Janssen (eds), pp. 191–6.Google Scholar
  7. Overrein, L.N., Seip, H.M. and Tollan, A. (1980) Acid Precipitation — Effects on Forest and Fish: Final Report. Norwegian Institute for Water Research, Oslo.Google Scholar
  8. Overton, W.S., White, D. and Stevens, D.L. (1990) Design Report for EMAP. Report EPA/600/3-91/053, United States Environmental Protection Agency.Google Scholar
  9. Patil, G.P. (1991) Encounter data, statistical ecology, environmental statistics, and weighted distribution methods. Environmetrics, 2, 377–423.Google Scholar
  10. Patil, G.P. and Rao, C.R. (1978) Weighted distributions and size-biased sampling with applications to wildlife populations and human families. Biometrics, 34, 179–89.Google Scholar
  11. Pearson, K. (1903) Mathematical contributions to the theory of evolution. XI. On the influence of natural selection on the variability and correlation of organisms. Philosophical Transactions of the Royal Society of London, Series A, 200, 1–66.Google Scholar
  12. Seber, G.A.F. (1984) Multivariate Observations. Wiley, New York.Google Scholar
  13. Wichmann, B.A. and Hill, I.D. (1982) Algorithm AS183: an efficient and portable pseudo-random number generator. Applied Statistics, 31, 188–90.Google Scholar

Copyright information

© Chapman & Hall 1995

Authors and Affiliations

  • L. L. McDonald
    • 1
  • L. Gonzalez
    • 2
  • B. F. J. Manly
    • 2
  1. 1.WEST Inc.CheyenneUSA
  2. 2.University of OtagoDunedinNew Zealand

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