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Community Ecology

, Volume 14, Issue 2, pp 164–171 | Cite as

Fuzzy sets and eigenanalysis in community studies: classification and ordination are “two faces of the same coin”

  • E. FeoliEmail author
  • V. Zuccarello
Article

Abstract

With this paper we want to stress that, on the basis of some matrix algebraic theorems, eigenvectors of similarity matrices are strictly related with clusters that we can obtain with clustering procedures applied to the same similarity matrices and that the fuzzy sets obtained by cluster analysis can be efficiently used as ordination axes and also as tools to measure the diagnostic value (or the indicator value) of attributes (species or other characters) of the ecological systems.

Keywords

Clusters Data matrices Diagnostic value Indicator value Ordination axes Similarity matrices Vegetation 

Abbreviations

CA

Correspondence analysis

FS

Fuzzy set

OBC

Ordination based on classification

PCA

Principal component analysis

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References

  1. Amadei, M., R. Bagnaia, L. Laureti, F. Lugeri, N. Lugeri, E. Feoli, M. Dragan and M. Fernetti. 2003. Il progetto Carta della natura alla scala 1:250,000. Metodologia di realizzazione. APAT Manuali e Linee Guida 17/2003Google Scholar
  2. Andreucci, F., E. Biondi, E. Feoli and V. Zuccarello. 2000. Modeling environmental responses of plant associations by fuzzy set theory. Community Ecol. 1: 73–80.CrossRefGoogle Scholar
  3. Banykwa, F., E. Feoli and V. Zuccarello. 1990. Fuzzy set system ordination of Serengeti short grasslands, Tanzania. J. Veg. Sci. 1: 97–104.CrossRefGoogle Scholar
  4. Biondi, E., E. Feoli and V. Zuccarello. 2004. Modeling environmental responses of plant associations: A review of some critical concepts in vegetation study. Crit. Rev. Plant. Sci. 23: 149–156.CrossRefGoogle Scholar
  5. Burba, N., E. Feoli and M. Malaroda. 2008. MATEDIT: A software tool to integrate information in decision making processes. In: R. Neves, J.W. Baretta and M. Mateus (eds.), Perspectives on Integrated Coastal Zone Management in South America. IST PRESS, Lisbon, pp. 123–127.Google Scholar
  6. Ceschin, S., V. Zuccarello and G. Caneva. 2010. Role of macrophyte communities as bioindicators of water quality: application on the Tiber River basin (Italy). Plant Biosyst. 144: 528–536.CrossRefGoogle Scholar
  7. Dale, M. B. 1988. Knowing when to stop: cluster concept–concept cluster. Coenoses 1: 11–31.Google Scholar
  8. De Cáceres, M. and P. Legendre. 2009. Associations between species and groups of sites: indices and statistical inference. Ecology 90: 3566–3574.CrossRefGoogle Scholar
  9. De Cacéres, M., Legendre, P., Wiser, S.K. and Brotons, L. 2012. Using species combinations in indicator value analysis. Methods Ecol. Evol. 3: 973–982.CrossRefGoogle Scholar
  10. Dufrêne, M and P. Legendre. 1997. Species assemblages and indicator species: the need for a flexible assymetrical approach. Ecol. Monogr. 67: 345–366.Google Scholar
  11. Feoli E. 1973a. Un esempio di ordinamento di tipi fitosociologici mediante l’analisi delle componenti principali. Not. Fitosoc. 7:21–27.Google Scholar
  12. Feoli E. 1973b. Un indice che stima il peso dei caratteri per classificazioni monotetiche. Giorn. Bot. Ital. 107:263–268.CrossRefGoogle Scholar
  13. Feoli, E. 1976. Correlation between single ecological variables and vegetation by means of cluster analysis. Not. Fitosoc, 12: 77–82.Google Scholar
  14. Feoli, E. 1977a. On the resolving power of principal component analysis in plant community ordination. Vegetatio 33: 119–125.Google Scholar
  15. Feoli, E. 1977b. A criterion for monothetic classification of phytosociological entities based on species ordination. Vegetatio 33:147–152.Google Scholar
  16. Feoli, E. 1984. Some aspects of classification and ordination of vegetation data in perspective. Stud. Geobot. 4: 7–21.Google Scholar
  17. Feoli, E. 2012. Diversity patterns of vegetation systems from the perspective of similarity theory. Plant Biosyst. 146: 797–804.CrossRefGoogle Scholar
  18. Feoli, E. and G. Bressan. 1972. Affinità floristica dei tipi di vegetazione bentonica della Cala di Mitigliano (Massa Lubrense, Napoli). Giorn. Bot. Ital. 106:245–256.CrossRefGoogle Scholar
  19. Feoli, E. and L. Feoli Chiapella. 1980. Evaluation of ordination methods through simulated coenoclines: some comments. Vegetatio 42: 35–41.CrossRefGoogle Scholar
  20. Feoli, E. and D. Lausi. 1980. Hierarchical levels in syntaxonomy based on information functions. Vegetatio 42: 113–115.CrossRefGoogle Scholar
  21. Feoli, E. and L. Orlóci. 1979. Analysis of concentration and detection of underlying factors in structured tables. Vegetatio 40: 49–54.CrossRefGoogle Scholar
  22. Feoli, E. and L. Orlóci (eds.) 1991. Computer Assisted Vegetation Analysis. Kluwer, Boston.Google Scholar
  23. Feoli, E. and L. Orlóci. 2011. Can similarity theory contribute to the development of a general theory of the plant community? Community Ecol. 12: 135–141.CrossRefGoogle Scholar
  24. Feoli, E. and V. Zuccarello. 1986. Ordination based on classification: yet another solution? Abstr. Bot. 10: 203–219.Google Scholar
  25. Feoli, E. and V. Zuccarello. 1988. Syntaxonomy: A source of useful fuzzy sets of environmental analysis? Coenoses 3: 141–147.Google Scholar
  26. Feoli, E. and V. Zuccarello. 1994. Naivete of fuzzy system space in vegetation dinamics? Coenoses 9: 25–3.Google Scholar
  27. Feoli, E. and Zerihun Woldu. 2000. Fuzzy set analysis of the Ethiopian Rift Valley vegetation. Plant Ecol. 147: 219–22.CrossRefGoogle Scholar
  28. Feoli, E., G. Ferro and P. Ganis. 2006. Validation of phytosociological classifications based on a fuzzy set approach. Community Ecol. 7: 98–117.CrossRefGoogle Scholar
  29. Gauch, H.G. and R.H. Whittaker. 1972. Coenocline simulation. Ecology 53: 446–451.CrossRefGoogle Scholar
  30. Gauch, H.G. 1982. Multivariate Analysis in Community Ecology. Cambridge University Press, New York.CrossRefGoogle Scholar
  31. Goodall, D.W. 1964. A probabilistic similarity index. Nature 203:1098.CrossRefGoogle Scholar
  32. Goodall, D.W. 1966. A new similarity index based on probability. Biometrics 22:882–907.CrossRefGoogle Scholar
  33. Goodall, D.W. 1993. Probabilistic indices for classification – Some extensions. Abstr. Bot. 17:125–132.Google Scholar
  34. Gower, J.C. 1971. A general coefficient of similarity and some of its properties. Biometrics 27:857–871.CrossRefGoogle Scholar
  35. Hill, M.O., R.G.H. Bunce and M.V. Shaw. 1975. Indicator species analysis, a divisive polythetic method of classification, and its application to survey of native pinewoods in Scotland. J. Ecol. 63: 597–613.CrossRefGoogle Scholar
  36. Hill, M. O. 1979. TWINSPAN - A FORTRAN programme for arranging multivariate data in an ordered two-way table by classification of individuals and attributes. Cornell University, Ithaca, New York.Google Scholar
  37. Kenkel, N.C. and L. Orlóci. 1986. Applying metric and nonmetric multidimensional scaling to ecological studies: some new results. Ecology 67: 919–928.CrossRefGoogle Scholar
  38. Mantel, N. 1967. The detection of disease clustering and a generalized regression approach. Cancer Res. 27: 209–220.PubMedPubMedCentralGoogle Scholar
  39. Marsili-Libelli, S. 1989. Fuzzy clustering of ecological data. Coenoses 4: 95–106.Google Scholar
  40. Moraczewski, I.R. 1993a. Fuzzy logic for phytosociology. 1 Syntaxa as vague concept. Vegetatio 106:1–11.CrossRefGoogle Scholar
  41. Moraczewski, I.R. 1993b. Fuzzy logic for phytosociology. 2 Generalizations and prediction. Vegetatio 106:13–20.CrossRefGoogle Scholar
  42. Moraczewski, I.R. 1996. Fuzzy rough set as a tool for ecological data analysis. Coenoses 11:55–67.Google Scholar
  43. Noy-Meir, I. 1973. Data transformation in ecological ordination. I. Some advantages of non-centering. J. Ecol. 61:329–341.CrossRefGoogle Scholar
  44. Olano, J.M., J.J. Loidi, A. González and A. Escudero. 1998. Improving the interpretation of fuzzy partitions in vegetation science with constrained ordinations. Plant Ecol. 134:113–118.CrossRefGoogle Scholar
  45. Orlóci, L. 1967. Data centering: a review and evaluation with reference to component analysis. Syst. Zool. 16:208–212.CrossRefGoogle Scholar
  46. Orlóci, L. 1972. On objective functions of phytosociological resemblance. Am. Midl. Nat. 88:28–55.CrossRefGoogle Scholar
  47. Orlóci, L. 1978. Multivariate Analysis in Vegetation Research. 2nd ed. Junk, The Hague.Google Scholar
  48. Pillar, V.D. 1999. How sharp are classifications? Ecology 80: 2508–2516.CrossRefGoogle Scholar
  49. Podani, J. 2000. Introduction to the Exploration of Multivariate Biological Data. Backhuys, Leiden.Google Scholar
  50. Podani, J. and B. Csányi. 2010. Detecting indicator species: some extensions of the IndVal measure. Ecol. Indic. 10: 1119–1124.CrossRefGoogle Scholar
  51. Podani, J. and E. Feoli. 1991. A general strategy for the simultaneous classification of variables and objects in ecological data tables. J. Veg. Sci. 2:435–444.CrossRefGoogle Scholar
  52. Roberts, D.W. 1986. Ordination on the basis of fuzzy set theory. Vegetatio 66: 123–143.CrossRefGoogle Scholar
  53. Roberts, D.W. 2008. Statistical analysis of multidimensional fuzzy set ordinations. Ecology 89: 1246–1260.CrossRefPubMedPubMedCentralGoogle Scholar
  54. Roberts, D.W. 2009. Comparison of multidimensional fuzzy set ordination with CCA and DB-RDA. Ecology 90: 2622–2634.CrossRefPubMedPubMedCentralGoogle Scholar
  55. Shu, L., A. Chen, M. Xiong and W. Meng. 2011. Efficient SPectrAl neighborhood blocking for entity resolution. Proceedings IEEE 27th International Conference on Data Engineering. pp. 1063–1078.Google Scholar
  56. von Luxburg, U. 2007. A tutorial on spectral clustering. Statistics and Computing 17:395–416.CrossRefGoogle Scholar
  57. van der Maarel, E., L. Orlóci and S. Pignatti. 1980. Data Processing in Phytosociology: Retrospect and Anticipation. Junk, The Hague.CrossRefGoogle Scholar
  58. Wilkinson, J.H. 1965. The Algebraic Eigenvalue Problem. Oxford University Press, London.Google Scholar
  59. Wildi, O. 2010. Data Analysis in Vegetation Ecology. John Wiley & Sons, Padstow.CrossRefGoogle Scholar
  60. Woldu, Zerihun, Feoli, E. and L. Nigatu. 1989. Partitioning an elevation gradient of vegetation from South-eastern Ethiopia by probabilistic methods. Vegetatio 81: 189–198.CrossRefGoogle Scholar
  61. Zimmerman, H.G. 1996. Fuzzy Set Theory and its Applications. 3rd ed. Kluwer Academic Publishers, Dordrecht.CrossRefGoogle Scholar
  62. Zuccarello, V., M. Allegrezza, E. Biondi and R. Calandra. 1999. Valenza ecologica di specie e di associazioni prative e modelli di distribuzione lungo gradienti sulla base della teoria degli insiemi sfocati (Fuzzy set Theory). Braun-Blanquetia 16: 121–226.Google Scholar

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© Akadémiai Kiadó, Budapest 2013

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Life SciencesUniversity of TriesteItaly
  2. 2.Department of Sciences and Biological TechnologyUniversity of SalentoLecceItaly

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