Advertisement

Community Ecology

, Volume 9, Issue 1, pp 11–16 | Cite as

Quantifying functional diversity with graph-theoretical measures: advantages and pitfalls

  • C. RicottaEmail author
  • M. Moretti
Open Access
Article
First Online:

Abstract

Recently, a number of measures of functional diversity have been proposed for data on species presences and absences. One of the most fashionable methods uses cluster analysis of species computed from a matrix of functional characters. Functional diversity is then summarized as the sum of branch lengths of the dendrogram (FDD). Like other graph-theoretical measures of functional diversity, FDD is an increasing function of species richness. This makes FDD inadequate for comparative studies if we want to quantify a component of functional diversity that is not directly related to differences in species counts. The aim of this paper is thus to develop a graph-theoretical measure of functional diversity that does not depend of species richness. The edges of the minimum spanning tree, calculated from the pair-wise inter-species dissimilarity matrix based on functional traits, are ranked and then a power law relationship is established with the cumulative distances. We empirically demonstrate that the exponent of this relationship is independent of species richness and is therefore a suitable measure of functional diversity.

Keywords

Clustering Minimum spanning tree Pair-wise species distances 

Abbreviations

FDD

Functional Diversity based on Dendrograms

FDM

Functional Diversity based on Minimum spanning trees

MST

Minimum Spanning Tree

Download to read the full article text

References

  1. Botta-Dukát, Z. 2005. Rao’s quadratic entropy as a measure of functional diversity based on multiple traits. J. Veg. Sci. 16: 533–540.CrossRefGoogle Scholar
  2. da Silva, I.A. and M.A. Batalha. 2006. Taxonomic distinctness and diversity of a hyperseasonal savanna in Central Brazil. Divers. Distrib. 12: 725–730.CrossRefGoogle Scholar
  3. Díaz, S. and M. Cabido. 2001. Vive la difference: plant functional diversity matters to ecosystem processes. Trends Ecol. Evol. 16: 646–650.CrossRefGoogle Scholar
  4. de Bello, F., J. Lepš, S. Lavorel and M. Moretti. 2007. Importance of species abundance for assessment of trait composition: an example based on pollinator communities. Community Ecol. 8: 163–170.CrossRefGoogle Scholar
  5. de Bello, F., J. Lepš and M.T. Sebastià. 2006. Variations in species and functional plant diversity along climatic and grazing gradients. Ecography 29: 801–810.CrossRefGoogle Scholar
  6. Faith, D.P. 1992. Conservation evaluation and phylogenic diversity. Biol. Cons. 61: 1–10.CrossRefGoogle Scholar
  7. Farris, J.S. 1970. Methods for computing Wagner trees. Syst. Zool. 19: 83–92.CrossRefGoogle Scholar
  8. Fonseca, C.R. and G. Ganade. 2001. Species functional redundancy, random exinctions and the stability of ecosystems. J. Ecol. 89: 118–125.CrossRefGoogle Scholar
  9. Gower, J.C. 1971. A general coefficient of similarity and some of its properties. Biometrics 27: 857–874.CrossRefGoogle Scholar
  10. Gower, J.C. and G.J.S. Ross. 1969. Minimum spanning trees and single linkage cluster analysis. Appl. Stat. 18: 54–64.CrossRefGoogle Scholar
  11. Heemsbergen, D.A., M.P. Berg, M. Loreau, J.R. van Hal, J.H. Faber and H.A. Verhoef. 2004. Biodiversity effects on soil processes explained by intraspecific functional dissimilarity. Science 306: 1019.CrossRefGoogle Scholar
  12. Hill, M.O. 1997. An evenness statistic based on the abundance-weighted variance of species proportions. Oikos 79: 413–416.CrossRefGoogle Scholar
  13. Juhász-Nagy, P. 1993. Notes on compositional diversity. Hydrobiologia 249: 173–182.CrossRefGoogle Scholar
  14. Laherrère, J.H. 1996. Distributions de type fractal parabolique dans la Nature. C. R. Acad. Sci. Paris II 322: 535–541.Google Scholar
  15. Laherrère, J.H. and D. Sornette. 1998. Stretched exponential distributions in nature and economy: “Fat tails”’ with characteristic scales. Eur. Phys. J. B 2: 525–539.CrossRefGoogle Scholar
  16. Landini, G. and J.P. Rigaut. 1997. A method for estimating the dimension of asymptotic fractal sets. Bioimaging 5: 65–70.CrossRefGoogle Scholar
  17. Lawton, J.H., S. Naeem, L.J. Thompson, A. Hector and M.J. Crawley. 1998. Biodiversity and ecosystem function: getting the Ecotron experiment in its correct context. Funct. Ecol. 12: 848–852.Google Scholar
  18. Lepš, J., F. de Bello, S. Lavorel and S. Berman. 2006. Quantifying and interpreting functional diversity of natural communities: practical considerations matter. Preslia 78: 481–501.Google Scholar
  19. Loreau, M. and A. Hector. 2001. Partitioning selection and complementarity in biodiversity experiments. Nature 412: 72–76.CrossRefGoogle Scholar
  20. Mandelbrot, B.B. 1983. The Fractal Geometry of Nature. Freeman, San Francisco.CrossRefGoogle Scholar
  21. Mason, N.V.H., D. Mouillot, W.G. Lee and J.B. Wilson. 2005. Functional richness, functional evenness and functional divergence: the primary components of functional diversity. Oikos 111:112–118.CrossRefGoogle Scholar
  22. Moretti, M., P. Duelli, K.M. Obrist. 2006. Biodiversity and resilience of arthropod communities after fire disturbance in temperate forests. Oecologia 149: 312–327.CrossRefGoogle Scholar
  23. Mouillot, D., N.W.H. Mason, O. Dumay and J.B. Wilson. 2005. Functional regularity: a neglected aspect of functional diversity. Oecologia 142: 353–359.CrossRefGoogle Scholar
  24. Mouillot, D. and J.B. Wilson. 2002. Can we tell how a community was constructed? A comparison of five evenness indices for their ability to identify theoretical models of community construction. Theor. Popul. Biol. 61: 141–151.CrossRefGoogle Scholar
  25. Petchey, O.L. and K.J. Gaston. 2002. Functional diversity (FD), species richness and community composition. Ecol. Lett. 5: 402–411.CrossRefGoogle Scholar
  26. Petchey, O.L. and K.J. Gaston. 2006. Functional diversity: back to basics and looking forward. Ecol. Lett. 9: 741–758.CrossRefGoogle Scholar
  27. Podani., J. 1999. Extending Gower’s general coefficient of similarity to ordinal characters. Taxon 48: 331–340.CrossRefGoogle Scholar
  28. Podani. J. 2000. Introduction to the Exploration of Multivariate Biological Data. Backhuys Publishers, Leiden.Google Scholar
  29. Podani, J. 2001. SYN-TAX 2000. Computer Programs for Data Analysis in Ecology and Systematics. User’s Manual. Scientia, Budapest.Google Scholar
  30. Podani, J., P. Csontos, J. Tamás and I. Miklós. 2005. A new multi-variate approach to studying temporal changes of vegetation. Plant. Ecol. 181: 1–16.CrossRefGoogle Scholar
  31. Podani, J. and D. Schmera. 2006. On dendrogram-based measures of functional diversity. Oikos 115: 179–185.CrossRefGoogle Scholar
  32. Ricotta, C. 2004. A parametric diversity measure combining the relative abundances and taxonomic distinctiveness of species. Divers. Distrib. 10: 143–146.CrossRefGoogle Scholar
  33. Ricotta, C. 2005. A note on functional diversity measures. Basic Appl. Ecol. 6: 479–486.CrossRefGoogle Scholar
  34. Ricotta, C. 2007. A semantic taxonomy for diversity measures. Acta Biotheor. 55: 23–33.CrossRefGoogle Scholar
  35. Sherwin, W.B., F. Jabot, R. Rush and M. Rossetto. 2006. Measurement of biological information with applications from genes to landscapes. Mol. Ecol. 15: 2857–2869.CrossRefGoogle Scholar
  36. Solow, A.R. and S. Polasky. 1994. Measuring biological diversity. Environ. Ecol. Stat. 1: 95–107.CrossRefGoogle Scholar
  37. Tilman, D. 2001. Functional diversity. In: S.A. Levin (ed.), Encyclopedia of Biodiversity. Academic Press, San Diego, pp. 109–120.CrossRefGoogle Scholar
  38. Tjørve, E. 2003. Shapes and functions of species-area curves: a review of possible models. J. Biogeogr. 30: 827–835.CrossRefGoogle Scholar
  39. Von Euler, F. and S. Svensson. 2001. Taxonomic distinctness and species richness as measures of functional structure in bird assemblages. Oecologia 129: 304–311.CrossRefGoogle Scholar
  40. Walker, B., A.P. Kinzig and J. Langridge. 1999. Plant attribute diversity, resilience, and ecosystem function: the nature and significance of dominant and minor species. Ecosystems 2: 95–113.CrossRefGoogle Scholar
  41. Weitzman, M.L. 1992. On diversity. Quart. J. Econ. 107: 363–405.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest 2008

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 Plant BiologyUniversity of Rome “La Sapienza”RomeItaly
  2. 2.Swiss Federal Research Institute WSLResearch Unit Ecosystem BoundariesBellinzonaSwitzerland

Personalised recommendations