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.

Abbreviations

FDD:

Functional Diversity based on Dendrograms

FDM:

Functional Diversity based on Minimum spanning trees

MST:

Minimum Spanning Tree

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Correspondence to C. Ricotta.

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Ricotta, C., Moretti, M. Quantifying functional diversity with graph-theoretical measures: advantages and pitfalls. COMMUNITY ECOLOGY 9, 11–16 (2008). https://doi.org/10.1556/ComEc.9.2008.1.2

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Keywords

  • Clustering
  • Minimum spanning tree
  • Pair-wise species distances