Towards a consensus for calculating dendrogram‐based functional diversity indices

Abstract

The widely used FD index of functional diversity is based on the construction of a dendrogram. This index has been the subject of a strong debate concerning the choice of the distance and the clustering method to be used, since the method chosen may greatly affect the FD values obtained. Much of this debate has been centred around which method of dendrogram construction gives a faithful representation of species distribution in multidimensional functional trait space. From artificially generated datasets varying in species richness and correlations between traits, we test whether any single combination of clustering method(s) and distance consistently produces a dendrogram that most closely corresponds to the matrix of functional distances between pairs of species studied. We also test the ability of consensus trees, which incorporate features common to a range of different dendrograms, to summarize distance matrices. Our results show that no combination of clustering method(s) and distance constantly outperforms the others due to the complexity of interactions between correlations of traits, species richness, distance measures and clustering methods. Furthermore, the construction of a consensus tree from a range of dendrograms is often the best solution. Consequently, we recommend testing all combinations of distances and clustering methods (including consensus trees), then selecting the most reliable tree (with the lowest dissimilarity) to estimate FD value. Furthermore we suggest that any index that requires the construction of functional dendrograms potentially benefits from this new approach.

Improving plant functional groups for dynamic models of biodiversity: at the crossroads between functional and community ecology

“…This issue is usually tackled using a clustering algorithm, for instance agglomerative hierarchical clustering based on a distance matrix (Herault, 2007, Mouchet et al, 2008, Pillar, 1999. If the plant traits are continuous, categorical and/or ordinal, the appropriate measure is the Gower distance, which mixes categorical and quantitative traits (Pavoine et al, 2005, Podani & Schmera, 2006.…”

“…where H is plant height (squared-transformed), L light class, D dispersal class (exponentially-transformed), P palatability class, O climatic overlap (Schoener's D metric) and N t the number of classes for trait t. We used the Unweighted Pair Group Method with Arithmetic Mean clustering algorithm (UPGMA, Kaufman & Rousseeuw, 1990), as it has been shown to distort the distance matrix less than other methods (Mouchet et al, 2008). We used the Dunn index, the R-squared (Halkidi et al, 2001), the index of Calinski & Harabasz (Calinski & Harabasz, 1974) and the average silhouette (Kaufman & Rousseeuw, 1990) to choose the number of groups.…”

Assessing the spatial variation of functional diversity estimates based on dendrograms in phytoplankton communities

“…These indices can be based on distance matrices (e.g., FAD, Walker et al 1999;MFAD, Heemsbergen et al 2004;Rao (Rao 1982;Botta-Dukát 2005), functional dendrograms (e.g., FD, Petchey & Gaston 2002;MPD and MNTD, Webb 2000) or the volume occupied in multidimensional functional space (e.g., FRic, FDiv, FEve, Villéger et al 2008;FDis, Laliberté & Legendre 2010), or they may consider intraspecific variability (TOP and TED, Fontana et al 2016) and gaps in one-dimensional and multidimensional functional space (e.g., FRls and FRlm, Schleuter et al 2010). While some of the most commonly used indices are based on dendrograms (e.g., Hidasi-Neto et al 2012;Carvalho & Tejerina-Garro 2014;Rodríguez & Ojeda 2014), they remain the subject of numerous discussions regarding methodological aspects inherent in their construction (Podani & Schmera 2006;Petchey & Gaston 2007;Podani & Schmera 2007;Mouchet et al 2008).…”

“…While previous studies have compared the performance of different functional diversity indices (e.g., Petchey et al 2004;Schmera et al 2009;Teresa & Casatti 2017), none of these studies were dedicated exclusively to indices based on dendrograms, despite their increased use and occurrence in the scientific literature (for the use of FD see Mouchet et al 2008;. Similarly, there are ample discussions on their methodological issues (Podani & Schmera 2006;Petchey & Gaston 2007), although there is still no general consensus (Mouchet et al 2008).…”

“…Similarly, there are ample discussions on their methodological issues (Podani & Schmera 2006;Petchey & Gaston 2007), although there is still no general consensus (Mouchet et al 2008). ;…”