Skip to main content
SpringerLink
Log in

Comparison of ordinations and classifications of vegetation data

  • Chapter
Progress in theoretical vegetation science

Part of the book series: Advances in vegetation science ((AIVS,volume 11))

  • 279 Accesses

Abstract

The methodology of comparing the results of multivariate community studies (resemblance matrices, ordinations, hierarchical and nonhierarchical classifications) is reviewed from two viewpoints: basic strategy and measure employed. The basic strategy is determined by 7 choices concerning the type of results, consensus methods or resemblance measures, hypothesis testing or exploratory analysis, lack or presence of reference basis, data set congruence or algorithmic effects, number of factors responsible for differences among results, and the number of properties considered in the comparison. Included is a brief summary of methods applicable to vegetation studies. Examples from a grassland survey demonstrate the utility of comparisons in evaluating the effects of plot size, data type, standardization, taxonomic level and number of species on classifications and ordinations.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Abbreviations

OUC:

Operational Unit of Comparison

PCA:

Principal Components Analysis

PCoA:

Principal Coordinates Analysis

SSA:

Incremental Sum of Squares Agglomeration

References

  • Adams III, E. N. 1972. Consensus techniques and the comparison of taxonomic trees. Syst. Zool. 21: 390–397.

    Article  Google Scholar 

  • Anderberg, M. R. 1973. Cluster analysis for applications. Academic Press, New York.

    Google Scholar 

  • André, H. M. 1988. Variable centered methods and community classification. Coenoses 3: 69–78.

    Google Scholar 

  • Arabie, P. & Boorman, S. A. 1973. Multidimensional scaling of measures of distance between partitions. J. Math. Psychol. 10: 148–203.

    Article  Google Scholar 

  • Austin, M. P. 1976. Performance of four ordination techniques assuming different non-linear species response models. Vegetado 33: 43–49.

    Article  Google Scholar 

  • Avena, G., Blasi, C., Feoli, E. & Scoppola, A. 1981. Measurement of the predictive value of species lists for species cover in phytosociological samples. Vegetatio 45: 77–84.

    Article  Google Scholar 

  • Barthélemy, J. P. & Monjardet, B. 1988. The median procedure in data analysis: new results and open problems. In: Bock, H. H. (ed.), Classification and related methods of data analysis, pp. 309–316. North-Holland, Amsterdam.

    Google Scholar 

  • Bayne, C. K., Beauchamp, J. J., Begovich, C. L. & Kane, V. E. 1980. Monte Carlo comparisons of selected clustering procedures. Pattern Recognition 12: 51–62.

    Article  Google Scholar 

  • Booth, T. H. 1978. Numerical classification techniques applied to forest tree distribution data. I. A comparison of methods. Australian J. Ecol. 3: 297–306.

    Article  Google Scholar 

  • Burgman, M. A. 1987. An analysis of the distribution of plants on granite outcrops in southern Western Australia using Mantel tests. Vegetatio 71: 79–86.

    Google Scholar 

  • Carroll, J. D. & Chang, J. J. 1970. Analysis of individual differences in multidimensional scaling via an N-way generalization of ‘Eckart-Young’ decomposition. Psychometrika 35: 283–319.

    Article  Google Scholar 

  • Crovello, T. J. 1981. Quantitative biogeography: an overview. Taxon 30: 563–575.

    Article  Google Scholar 

  • Cunningham, K. M. & Ogilvie, J. C. 1972. Evaluation of hierarchical grouping techniques. A preliminary study. Computer J. 15: 209–213.

    Article  Google Scholar 

  • Dale, M. B. & Clifford, H. T. 1976. On the effectiveness of higher taxonomic ranks for vegetation analysis. Australian J. Ecol. 1: 37–62.

    Article  Google Scholar 

  • Dale, M. R. T. & Moon, J. W. 1988. Statistical tests on two characteristics of the shapes of cluster diagrams. J. Classification 5: 21–38.

    Article  Google Scholar 

  • Day, W. H. E. 1981. The complexity of computing metric distances between partitions. Math. Soc. Sci. 1: 269–287.

    Article  Google Scholar 

  • Day, W. H. E. 1983. Distributions of distances between pairs of classifications. In: Felsenstein, J. (ed.), Numerical taxonomy, pp. 127–131. Springer, Berlin.

    Google Scholar 

  • Day, W. H. E. 1988. Consensus methods as tools for data analysis. In: Bock, H. H. (ed.), Classification and related methods of data analysis, pp. 317–324. North-Holland, Amsterdam.

    Google Scholar 

  • del Moral, R. & Watson, A. F. 1978. Gradient structure of forest vegetation in the central Washington Cascades. Vegetatio 32: 29–48.

    Article  Google Scholar 

  • Dickinson, T. A., Knowles, P. & Parker, W. H. 1988. Data set congruence in northern Ontario tamarack (Larix laricina, Pinaceae). Syst. Bot. 13: 442–455.

    Article  Google Scholar 

  • Diday, E. & Simon, J. C. 1976. Clustering analysis. In: Fu, K. S. (ed.), Digital pattern recognition, pp. 47–94. Springer, New York.

    Google Scholar 

  • Dietz, E. J. 1983. Permutation tests for association between two distance matrices. Syst. Zool. 32: 21–26.

    Article  Google Scholar 

  • Digby, P. G. N. & Gower, J. C. 1986. Ordination and classification. Univ. Montreal Press, Montreal.

    Google Scholar 

  • Digby, P. G. N. & Kempton, R. A. 1987. Multivariate analysis of ecological communities. Chapman & Hall, London.

    Google Scholar 

  • Dobson, A. J. 1975. Comparing the shapes of trees. In: Dold, A. & Eckmann, B. (eds), Lecture notes in mathematics 452: 95–100. Springer, Berlin.

    Google Scholar 

  • Dubes, R. & Jain, A. K. 1976. Clustering techniques: the user’s dilemma. Pattern Recognition 8: 247–260.

    Article  Google Scholar 

  • Duncan, T. & Estabrook, G. F. 1976. An operational method for evaluating classifications. Syst. Bot. 1: 373–382.

    Article  Google Scholar 

  • Duncan, T., Phillips, R. B. & Wagner, W. H. 1980. A comparison of branching diagrams derived by various phonetic and cladistic methods. Syst. Bot. 5: 264–293.

    Article  Google Scholar 

  • Engler, A. 1964. Syllabus der Pflanzenfamilien. Gebrüder Borntraeger, Berlin.

    Google Scholar 

  • Faith, D. P. 1988. Consensus applications in the biological sciences. In: Bock, H. H. (ed.), Classification and related methods of data analysis, pp. 325–332. North-Holland, Amsterdam.

    Google Scholar 

  • Faith, D. P. & Beibin, L. 1986. Comparison of classifications using measures intermediate between metric dissimilarity and consensus similarity. J. Classification 3: 257–280.

    Article  Google Scholar 

  • Farris, J. S. 1973. On comparing the shapes of taxonomic trees. Syst. Zool. 22: 50–54.

    Article  Google Scholar 

  • Fasham, M. J. R. 1977. A comparison of nonmetric multidimensional scaling, principal components and reciprocal averaging for the ordination of simulated coenoclines, and coenoplanes. Ecology 58: 551–561.

    Article  Google Scholar 

  • Felsenstein, J. 1985. Confidence limits on phylogenies: an approach using the bootstrap. Evolution 39: 783–791.

    Article  Google Scholar 

  • Feoli, E. 1983. Predictive use of classification and ordination methods in plant community ecology. A summary with examples. In: Ferrari, G., Gentile, S., Pignatti, S. & PoliMarchese, E. (eds), Le communità vegetali come indicatori ambientali, pp. 83–108. Bologna.

    Google Scholar 

  • Feoli, E., Lagonegro, M. & Orlóci, L. 1984a. Information analysis of vegetation data. Junk, The Hague.

    Google Scholar 

  • Feoli, E., Orlóci, L. & Scimone, M. 1984b. Comparison of ordinations of some Apennine forest communities based on different characters and methods. Studia Geobot. 4: 137–145.

    Google Scholar 

  • Ferraris, J. 1983. Comparison of classifications with the data from which they are derived. In: Felsenstein, J. (ed.), Numerical taxonomy, pp. 174–178. Springer, Berlin.

    Google Scholar 

  • Fish, E. B. 1976. Comparisons of phytosociological methods of classification on a desert grassland site. Agro-Ecosystems 2: 173–194.

    Article  Google Scholar 

  • Fowlkes, E. B. & Mallows, C. L. 1980. A method for comparing two hierarchical clusterings. Manuscript, Bell Laboratories, Murray Hill, N. J., USA. Abstract in: Classification Soc. Bull. 4: 54.

    Google Scholar 

  • Gauch, H. G. 1982. Multivariate analysis of community data. Cambridge Univ. Press, Cambridge, Mass., USA.

    Google Scholar 

  • Gauch, H. G. 1980. Rapid initial clustering of large data sets. Vegetatio 42: 103–111.

    Article  Google Scholar 

  • Gauch, H. G. & Whittaker, R. H. 1972. Comparison of ordination techniques. Ecology 53: 868–875.

    Article  Google Scholar 

  • Gauch, H. G. & Whittaker, R. H. 1981. Hierarchical classification of community data. J. Ecol. 69: 537–557.

    Article  Google Scholar 

  • Gauch, H. G., Whittaker, R. H. & Wentworth, T. R. 1977. A comparative study of reciprocal averaging and other ordination techniques. J. Ecol. 65: 157–174.

    Article  Google Scholar 

  • Goodman, L. A. & Kruskal, W. H. 1954. Measures of association for cross-classifications. J. Amer. Stat. Assoc. 49: 732–764.

    Article  Google Scholar 

  • Gordon, A. D. 1980. On the assessment and comparison of classifications. In: Tomassone, R. (ed.), Analyse de données et informatique, pp. 161–171. I.R.I.A., Le Chesnay.

    Google Scholar 

  • Gordon, A. D. 1981. Classification. Chapman & Hall, London.

    Google Scholar 

  • Gower, J. C. 1971. Statistical methods of comparing different multivariate analyses of the same data. In: Hodson, F. R., Kendall, D. G. & Tautu, P. (eds), Mathematics in the archaeological sciences, pp. 138–149. Edinburgh Univ. Press, Edinburgh.

    Google Scholar 

  • Gower, J. C. 1975. Generalized Procrustes analysis. Psychometrika 40: 33–51.

    Article  Google Scholar 

  • Gower, J. C. 1983. Comparing classifications. In: Felsenstein, J. (ed.), Numerical taxonomy, pp. 137–155. Springer, Berlin.

    Google Scholar 

  • Greig-Smith, P. 1983. Quantitative plant ecology. 3rd ed. Blackwell, Oxford.

    Google Scholar 

  • Grigal, D. F. & Goldstein, R. A. 1971. An integrated ordination-classification analysis of an intensively sampled oak-hickory forest. J. Ecol. 59: 481–492.

    Article  Google Scholar 

  • Hubert, L. J. 1978. Generalized proximity function comparisons. Br. J. Math. Statist. Psychol. 31: 179–192.

    Article  Google Scholar 

  • Hubert, L. J. 1983. Inference procedures for the evaluation and comparison of proximity matrices. In: Felsenstein, J. (ed.), Numerical taxonomy, pp. 209–228. Springer, Berlin.

    Google Scholar 

  • Hubert, L. & Arabie, P. 1985. Comparing partitions. J. Classification 2: 193–218.

    Article  Google Scholar 

  • Jackson, D. N. 1969. Comparison of classifications. In: Cole, A.J. (ed.), Numerical taxonomy, pp. 91–113. Academic Press, New York.

    Google Scholar 

  • Jeglum, J. K., Wehrhahn, G F. & Swan, J. M. A. 1971. Comparisons of environmental ordinations with principal component vegetational ordinations for sets of data having different degrees of complexity. Can. J. Forest Res. 1: 99–112.

    Article  Google Scholar 

  • Kenkel, N. C. & Booth, T. 1987. A comparison of presenceabsence resemblance coefficients for use in biogeographical studies. Coenoses 2: 25–30.

    Google Scholar 

  • Kenkel, N. C. & Orlóci, L. 1986. Applying metric and nonmetric multidimensional scaling to ecological studies: some new results. Ecology 67: 919–928.

    Article  Google Scholar 

  • Kershaw, K. A. & Looney, J. H. H. 1985. Quantitative and dynamic plant ecology. 3rd ed. E. Arnold, London.

    Google Scholar 

  • Kessell, S. R. & Whittaker, R. H. 1976. Comparison of three ordination techniques. Vegetado 32: 21–29.

    Article  Google Scholar 

  • Kruskal, J. B. 1964. Nonmetric multidimensional scaling: a numerical method. Psychometrika 29: 115–129.

    Article  Google Scholar 

  • Lefkovitch, L. P. 1984. A nonparametric method for comparing dissimilarity matrices, a general measure of biogeographic distance, and their application. Am. Nat. 123: 484–499.

    Article  Google Scholar 

  • Lefkovitch, L. P. 1985a. Euclidean consensus dendrograms and other classification structures. Math. Biosci. 74: 1–15.

    Article  Google Scholar 

  • Lefkovitch, L. P. 1985b. Further nonparametric tests for comparing dissimilarity matrices based on the relative neighborhood graph. Math. Biosci. 73: 71–88.

    Article  Google Scholar 

  • Legendre, L. & Legendre, P. 1983. Numerical ecology. Elsevier, Amsterdam.

    Google Scholar 

  • Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Res. 27: 209–220.

    PubMed  CAS  Google Scholar 

  • Milligan, G. W. & Isaac, P. D. 1980. The validation of four ultrametric clustering algorithms. Pattern Recognition 12: 41–50.

    Article  Google Scholar 

  • Minchin, P. R. 1987. An evaluation of the relative robustness of techniques for ecological ordination. Vegetado 69: 89–107.

    Article  Google Scholar 

  • Mucina, L. 1982. Numerical classification and ordination of ruderal plant communities (Sisymbrietalia, Onopordetalia) in the western part of Slovakia. Vegetado 48: 267–275.

    Google Scholar 

  • Orlóci, L. 1976. An agglomerative method for classification of plant communities. J. Ecol. 55: 193–205.

    Google Scholar 

  • Orlóci, L. 1978. Multivariate analysis in vegetation research. 2nd ed. Junk, The Hague.

    Google Scholar 

  • Orlóci, L., Kenkel, N. C. & Fewster, P. H. 1984. Probing simulated vegetation data for complex trends by linear and nonlinear ordination methods. Abstr. Bot. 8: 163–172.

    Google Scholar 

  • Orlóci, L. & Mukkattu, M. M. 1973. The effect of species number and type of data on the resemblance structure of a phytosociological collection. J. Ecol. 61: 37–46.

    Article  Google Scholar 

  • Paule, L. & Gömöry, D. 1987. Comparison of different clustering methods applied to matrices of genetic distances based on allelic frequencies. Abstr. Bot. 11: 43–51.

    Google Scholar 

  • Penny, D., Foulds, L. R. & Hendy, M. D. 1982. Testing the theory of evolution by comparing phylogenetic trees constructed from five different protein sequences. Nature 297: 197–200.

    Article  PubMed  CAS  Google Scholar 

  • Phipps, J. B. 1971. Dendrogram topology. Syst. Zool. 20: 306–308.

    Article  Google Scholar 

  • Pielou, E. C. 1984. The interpretation of ecological data. Wiley, New York.

    Google Scholar 

  • Podani, J. 1984. Spatial processes in the analysis of vegetation: theory and review. Acta Bot. Hung. 30: 75–118.

    Google Scholar 

  • Podani, J. 1985. Syntaxonomic congruence in a small-scale vegetation survey. Abstr. Bot. 9: 99–128.

    Google Scholar 

  • Podani, J. 1986. Comparison of partitions in vegetation studies. Abstr. Bot. 10: 235–290.

    Google Scholar 

  • Podani, J. 1988. SYN-TAX III. A package of programs for data analysis in community ecology and systematics. Coenoses 3: 111–119.

    Google Scholar 

  • Podani, J. 1989a. A method for generating consensus partitions and its application to community classification. Coenoses 4: 1–10.

    Google Scholar 

  • Podani, J. 1989b. New combinatorial clustering methods. Vegetatio 81: 61–77.

    Article  Google Scholar 

  • Podani, J. & Dickinson, T. A. 1984. Comparison of dendrograms: a multivariate approach. Can. J. Bot. 62: 2765–2778.

    Article  Google Scholar 

  • Pritchard, N. M. & Anderson, A. J. B. 1971. Observations on the use of cluster analysis in botany with an ecological example. J. Ecol. 59: 727–747.

    Article  Google Scholar 

  • Rand, W. M. 1971. Objective criteria for the evaluation of clustering methods. J. Amer. Stat. Assoc. 66: 846–850.

    Article  Google Scholar 

  • Robertson, P. A. 1978. Comparisons of techniques for ordinating and classifying old-growth floodplain forests in southern Illinois. Vegetatio 37: 43–51.

    Google Scholar 

  • Robertson, P. A. 1979. Comparisons among three hierarchical classification techniques using simulated coenoplanes. Vegetatio 40: 175–183.

    Google Scholar 

  • Robinson, D. F. & Foulds, L. R. 1979. Comparison of weighted labelled trees. In: Horadam, A. F. & Wallis, W. D. (eds), Lecture notes in mathematics 748: 119–126. Springer, Berlin.

    Google Scholar 

  • Robinson, D. F. & Foulds, L. R. 1981. Comparison of phylogenetic trees. Math. Biosci. 53: 131–147.

    Article  Google Scholar 

  • Rohlf, F. J. 1974. Methods of comparing classifications. Annual Rev. Ecol. Syst. 5: 101–113.

    Article  Google Scholar 

  • Rohlf, F. J. 1982. Consensus indices for comparing classifications. Math. Biosci. 59: 131–144.

    Article  Google Scholar 

  • Rohlf, F. J. & Sokal, R. R. 1981. Comparing numerical taxonomic studies. Syst. Zool. 30: 459–490.

    Article  Google Scholar 

  • Schnell, G. D. 1970. A phenetic study of the suborder Lari (Aves). II. Phenograms, discussion and conclusions. Syst. Zool. 19: 264–302.

    Article  PubMed  CAS  Google Scholar 

  • Schönemann, P. H. & Carroll, R. M. 1970. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika 35: 245–256.

    Article  Google Scholar 

  • Shao, K. & Rohlf, F. J. 1983. Sampling distribution of consensus indices when all bifurcating trees are equally likely. In: Felsenstein, J. (ed.), Numerical taxonomy, pp. 132–136. Springer, Berlin.

    Google Scholar 

  • Sneath, P. H. A. & Sokal, R. R. 1973. Numerical taxonomy. 2nd ed. Freeman, San Francisco.

    Google Scholar 

  • Sokal, R. R. 1979. Testing statistical significance of geographic variation patterns. Syst. Zool. 28: 227–232.

    Article  Google Scholar 

  • Sokal, R. R. & Rohlf, F. J. 1962. The comparison of dendrograms by objective methods. Taxon 11: 33–40.

    Article  Google Scholar 

  • Sokal, R. R. & Rohlf, F. J. 1981. Taxonomic congruence in the Leptopodomorpha re-examined. Syst. Zool. 30: 309–324.

    Article  Google Scholar 

  • Stanek, W. 1973. A comparison of Braun-Blanquet’s method with sum of squares agglomeration for vegetation classification. Vegetatio 27: 323–345.

    Article  Google Scholar 

  • van der Maarel, E. 1979. Multivariate methods in phytosociology, with reference to the Netherlands. In: Werger, M. J. A. (ed.), The study of vegetation, pp. 161–225. Junk, The Hague.

    Google Scholar 

  • Virágh, K. 1987. The effect of herbicides on vegetation dynamics: comparison of classifications. Abstr. Bot. 11: 53–70.

    Google Scholar 

  • Zólyomi, B. 1958. The natural vegetation of Budapest and its environs. In: Pécsi, M. (ed.), Natural history of Budapest (in Hungarian), pp. 508–642. Akadémiai, Budapest.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Plant Taxonomy and Ecology, L. Eötvös University, Kun B. tér 2, H-1083, Budapest, Hungary

    János Podani

Authors
  1. János Podani
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

G. Grabherr L. Mucina M. B. Dale C. J. F. Ter Braak

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Kluwer Academic Publishers

About this chapter

Cite this chapter

Podani, J. (1990). Comparison of ordinations and classifications of vegetation data. In: Grabherr, G., Mucina, L., Dale, M.B., Ter Braak, C.J.F. (eds) Progress in theoretical vegetation science. Advances in vegetation science, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1934-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1934-1_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7363-9

  • Online ISBN: 978-94-009-1934-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation