Quantifying functional diversity with graph-theoretical measures: advantages and pitfalls
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.
KeywordsClustering Minimum spanning tree Pair-wise species distances
Functional Diversity based on Dendrograms
Functional Diversity based on Minimum spanning trees
Minimum Spanning Tree
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