Quantifying functional diversity with graph-theoretical measures: advantages and pitfalls
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 distancesAbbreviations
- FDD
Functional Diversity based on Dendrograms
- FDM
Functional Diversity based on Minimum spanning trees
- MST
Minimum Spanning Tree
References
- 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
- 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
- Díaz, S. and M. Cabido. 2001. Vive la difference: plant functional diversity matters to ecosystem processes. Trends Ecol. Evol. 16: 646–650.CrossRefGoogle Scholar
- 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
- 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
- Faith, D.P. 1992. Conservation evaluation and phylogenic diversity. Biol. Cons. 61: 1–10.CrossRefGoogle Scholar
- Farris, J.S. 1970. Methods for computing Wagner trees. Syst. Zool. 19: 83–92.CrossRefGoogle Scholar
- Fonseca, C.R. and G. Ganade. 2001. Species functional redundancy, random exinctions and the stability of ecosystems. J. Ecol. 89: 118–125.CrossRefGoogle Scholar
- Gower, J.C. 1971. A general coefficient of similarity and some of its properties. Biometrics 27: 857–874.CrossRefGoogle Scholar
- Gower, J.C. and G.J.S. Ross. 1969. Minimum spanning trees and single linkage cluster analysis. Appl. Stat. 18: 54–64.CrossRefGoogle Scholar
- 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
- Hill, M.O. 1997. An evenness statistic based on the abundance-weighted variance of species proportions. Oikos 79: 413–416.CrossRefGoogle Scholar
- Juhász-Nagy, P. 1993. Notes on compositional diversity. Hydrobiologia 249: 173–182.CrossRefGoogle Scholar
- Laherrère, J.H. 1996. Distributions de type fractal parabolique dans la Nature. C. R. Acad. Sci. Paris II 322: 535–541.Google Scholar
- 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
- Landini, G. and J.P. Rigaut. 1997. A method for estimating the dimension of asymptotic fractal sets. Bioimaging 5: 65–70.CrossRefGoogle Scholar
- 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
- 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
- Loreau, M. and A. Hector. 2001. Partitioning selection and complementarity in biodiversity experiments. Nature 412: 72–76.CrossRefGoogle Scholar
- Mandelbrot, B.B. 1983. The Fractal Geometry of Nature. Freeman, San Francisco.CrossRefGoogle Scholar
- 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
- 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
- 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
- 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
- Petchey, O.L. and K.J. Gaston. 2002. Functional diversity (FD), species richness and community composition. Ecol. Lett. 5: 402–411.CrossRefGoogle Scholar
- Petchey, O.L. and K.J. Gaston. 2006. Functional diversity: back to basics and looking forward. Ecol. Lett. 9: 741–758.CrossRefGoogle Scholar
- Podani., J. 1999. Extending Gower’s general coefficient of similarity to ordinal characters. Taxon 48: 331–340.CrossRefGoogle Scholar
- Podani. J. 2000. Introduction to the Exploration of Multivariate Biological Data. Backhuys Publishers, Leiden.Google Scholar
- Podani, J. 2001. SYN-TAX 2000. Computer Programs for Data Analysis in Ecology and Systematics. User’s Manual. Scientia, Budapest.Google Scholar
- 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
- Podani, J. and D. Schmera. 2006. On dendrogram-based measures of functional diversity. Oikos 115: 179–185.CrossRefGoogle Scholar
- Ricotta, C. 2004. A parametric diversity measure combining the relative abundances and taxonomic distinctiveness of species. Divers. Distrib. 10: 143–146.CrossRefGoogle Scholar
- Ricotta, C. 2005. A note on functional diversity measures. Basic Appl. Ecol. 6: 479–486.CrossRefGoogle Scholar
- Ricotta, C. 2007. A semantic taxonomy for diversity measures. Acta Biotheor. 55: 23–33.CrossRefGoogle Scholar
- 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
- Solow, A.R. and S. Polasky. 1994. Measuring biological diversity. Environ. Ecol. Stat. 1: 95–107.CrossRefGoogle Scholar
- Tilman, D. 2001. Functional diversity. In: S.A. Levin (ed.), Encyclopedia of Biodiversity. Academic Press, San Diego, pp. 109–120.CrossRefGoogle Scholar
- Tjørve, E. 2003. Shapes and functions of species-area curves: a review of possible models. J. Biogeogr. 30: 827–835.CrossRefGoogle Scholar
- 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
- 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
- Weitzman, M.L. 1992. On diversity. Quart. J. Econ. 107: 363–405.CrossRefGoogle Scholar
Copyright information
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.