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Measurement of non-randomness in spatial distributions

Summary

The measurement of departure from randomness in spatial distributions has widespread application in ecological work. Several “indices of non-randomness” are compared with regard to their dependence on sample number, sample size and density. Criteria for the best choice of index for specific situations are discussed. A new coefficientC x is proposed for use with positively contagious distributions and tests of significance are given. WhenC x and another index (S 2/m−1) are used for positive and negative contagion respectively, values ranging from −1 through 0 (random) to +1 are obtained, regardless of sample number, sample size or density.

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Literature cited

  • Anscombe, F. J. (1949) The statistical analysis of insect counts based on the negative binomial distribution.Biometrics 5: 165–173.

    Article  Google Scholar 

  • Anscombe, F. J. (1950) Sampling theory of the negative binomial and logarithmic series distributions.Biometrika 37: 358–382.

    PubMed  CAS  Article  Google Scholar 

  • Beall, G. (1935) Study of arthropod populations by the method of sweeping.Ecology 16: 216–225.

    Article  Google Scholar 

  • Beall, G. (1940) The fit and significance of contagious distributions when applied to observations on larval insects.Ecology 21: 460–474.

    Article  Google Scholar 

  • Bliss, C. I. (1953) Fitting the negative binomial distribution to biological data.Biometrics 9: 176–196.

    Article  Google Scholar 

  • Cole, L. C. (1946) A study of the cryptozoa of an Illinois woodland.Ecol. Monogr. 16: 49–86.

    Article  Google Scholar 

  • David, F. N. andP. G. Moore. (1954) Notes on contagious distributions in plant populations.Ann. Botany, N. S.18: 47–53.

    Google Scholar 

  • Fisher, R. A. (1941) The negative binomial distribution.Ann. Eugenics 11: 182–187.

    Google Scholar 

  • Morisita, M. (1959) Measuring the dispersion of individuals and analysis of the distributional patterns.Mem. Fac. Sci., Kyushu Univ., Ser. E (Biol.),2: 215–235.

    Google Scholar 

  • Morisita, M. (1962) Iδ index, a measure of dispersion of individuals.Res. Popul. Ecol. 4: 1–7.

    Google Scholar 

  • Neyman, J. (1939) On a new class of contagious distributions applicable to entomology and bacteriology.Ann. Math. Stat. 10: 35–57.

    Google Scholar 

  • Oakland, G. B. (1950) An application of sequential analysis to whitefish sampling.Biometrics 6: 59–67.

    Article  Google Scholar 

  • Polya, G. (1931) Sur quelque points de la theorie des probabilites.Ann. de l’Inst. Henri Poincare 1: 117–162. (Original not seen).

    Google Scholar 

  • Wuenouille, M. H. (1949) A relation the between the logarithmic, poisson and negative binomial series.Biometrics 5: 162–164.

    Article  Google Scholar 

  • Steel, R. G. D., andJ. H. Torrie. (1960)Principles and procedures in statistics, etc. McGraw-Hill, New York.

    Google Scholar 

  • Student. (1919) An explanation of deviations from Poisson’s law in practice.Biometrika 12: 211–215.

    Article  Google Scholar 

  • Taylor, C. T. (1953) Nature of variability in trawl catches.Fishery Bull. 83, U. S. Fish and Wildlife Ser. 54.

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Green, R.H. Measurement of non-randomness in spatial distributions. Res Popul Ecol 8, 1–7 (1966). https://doi.org/10.1007/BF02524740

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  • DOI: https://doi.org/10.1007/BF02524740

Keywords

  • Negative Binomial Distribution
  • Negative Contagion
  • Larval Insect
  • Australia Introduction
  • Positive Contagion