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Spatial Clustering of Species Based on Quadrat Sampling

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Information and Classification

Part of the book series: Studies in Classification, Data Analysis and Knowledge Organization ((STUDIES CLASS))

Abstract

The quadrat sampling technique is frequently used in ecology for estimating diversity or analyzing the spatial point pattern of a population. For testing the null hypothesis of spatial randomness against cluster alternatives, Solow and Smith (1991) applied the species-area curve, i.e. the mean number of species in q quadrats. The authors proposed to use a simulation procedure because the calculation of the exact quantiles of the test is computationally costly for large numbers of quadrats, species, and individuals. As an alternative, we propose the use of maximum statistics, and we derive upper and lower bounds for the upper P-values. By combining the upper bounds for the different species we derive tests for spatial clusters. An extension similar to the species-area curve is suggested. The procedures are illustrated by analyzing two data sets from ecological studies.

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References

  • Edgington, E.S. (1972), An Additive Method for Combining Probability Values for Independent Experiments, Journal of Psychology, 80, 351–363.

    Article  Google Scholar 

  • Fisher, R.A., Corbet, A.S. and Williams, C.B. (1943), The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population, Journal of Animal Ecology, 12, 42–58.

    Article  Google Scholar 

  • Galambos, J. (1977), Bonferroni Inequalities, Annals of Probability, 5, 577–581.

    Article  Google Scholar 

  • Heltshe, J.F. and Forrester, N.E. (1983a), Estimating Species Richness Using the Jackknife Procedure, Biometrics, 39, 1–11.

    Article  Google Scholar 

  • Heltshe, J.F. and Forrester, N.E. (1983b), Estimating Diversity Using Quadrat Sampling, Biometrics, 39, 1073–1076.

    Article  Google Scholar 

  • Heltshe, J.F. and Ritchey, T.A. (1984), Spatial Pattern Detection Using Quadrat Samples, Biometrics, 40, 877–885.

    Article  Google Scholar 

  • Holm, S. (1979), A Simple Sequentially Rejective Multiple Test Procedure, Scandinavian Journal of Statistics, 6, 65–70.

    Google Scholar 

  • Hurlbert, S.H. (1971), The Nonconcept of Species Diversity: a Critique and Alternative Parameters, Ecology, 58, 577–586.

    Article  Google Scholar 

  • Jogdeo, K. and Patil, G.P. (1975), Probability Inequalities for Certain Multivariate Discrete Distributions, Sankhyā, Series B, 37, 158–164.

    Google Scholar 

  • Kounias, E. and Marin, D. (1974), Best Linear Bonferroni Bounds, in: Proceedings of the Prague Symposium on Asymptotic Statistics, Volume II, Charles University, Prague, 179–213.

    Google Scholar 

  • Krauth, J. (1988), Distribution-Free Statistics: An Application-Oriented Approach, Elsevier, Amsterdam.

    Google Scholar 

  • Mallows, C.L. (1968), An Inequality Involving Multinomial Probabilities, Biometrika, 55, 422–424.

    Article  Google Scholar 

  • Solow, A.R. and Smith, W. (1991), Detecting Cluster in a Heterogeneous Community Sampled by Quadrats, Biometrics, 47, 311–317.

    Article  Google Scholar 

  • Tipper, J.C. (1979), Rarefaction and Rarefiction — the Use and Abuse of a Method in Paleoecology, Paleobiology, 5, 423–434.

    Google Scholar 

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© 1993 Springer-Verlag Berlin · Heidelberg

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Krauth, J. (1993). Spatial Clustering of Species Based on Quadrat Sampling. In: Opitz, O., Lausen, B., Klar, R. (eds) Information and Classification. Studies in Classification, Data Analysis and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50974-2_2

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  • DOI: https://doi.org/10.1007/978-3-642-50974-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56736-3

  • Online ISBN: 978-3-642-50974-2

  • eBook Packages: Springer Book Archive

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