Calculating functional diversity metrics using neighbor-joining trees

Abstract

The study of functional diversity (FD) provides ways to understand phenomena as complex as community assembly or the dynamics of biodiversity change under multiple pressures. Different frameworks are used to quantify FD, either based on dissimilarity matrices (e.g., Rao entropy, functional dendrograms) or multidimensional spaces (e.g. convex hulls, kernel-density hypervolumes). While the first does not enable the measurement of FD within a richness/divergence/regularity framework, or results in the distortion of the functional space, the latter does not allow for comparisons with phylogenetic diversity (PD) measures and can be extremely sensitive to outliers. We propose the use of neighbor-joining trees (NJ) to represent and quantify functional diversity in a way that combines the strengths of current FD frameworks without many of their weaknesses. Our proposal is also uniquely suited for studies that compare FD with PD, as both share the use of trees (NJ or others) and the same mathematical principles. We test the ability of this novel framework to represent the initial functional distances between species with minimal functional space distortion and sensitivity to outliers. The results using NJ are compared with conventional functional dendrograms, convex hulls, and kernel-density hypervolumes using both simulated and empirical datasets. Using NJ we demonstrate that it is possible to combine much of the flexibility provided by multidimensional spaces with the simplicity of tree-based representations. Moreover, the method is directly comparable with PD measures, and enables quantification of the richness, divergence and regularity of the functional space.

Land-use change interacts with island biogeography to alter bird community assembly

“…We then built a functional dendrogram using a modified version of neighbour-joining clustering [50] based on a Gower dissimilarity distance matrix of the five morphological traits (scaled and centred). This clustering method minimizes functional space distortion [51] and we observed that the functional dendrogram provided a high-quality representation of the distances between species in the Gower dissimilarity distance matrix (0.98, measured by the standardized inverse of mean squared deviation [52], with 1 representing the maximum quality). The functional dendrogram was built using the tree.build function in the ‘BAT’ package [53].…”

“…We then built a functional dendrogram using a modified version of neighbour-joining clustering [50] based on a Gower dissimilarity distance matrix of the five morphological traits (scaled and centred). This clustering method minimizes functional space distortion [51] and we observed that the functional dendrogram provided a high-quality representation of the distances between species in the royalsocietypublishing.org/journal/rspb Proc. R. Soc.…”

Context‐dependent evolution of high trophic position drives functional disparity in subterranean crustaceans

“…The FD of each ecological group was calculated as a sum of the cophenetic distances between species in the same group on a dendrogram inferred from the three functional traits. We constructed dendrograms using Euclidean distance matrix and neighbour‐joining agglomeration algorithms (Cardoso et al, 2022). α ‐FD was calculated for the entire dataset and for each ecological group separately.…”

Components of functional diversity revisited: A new classification and its theoretical and practical implications

“…FDUs as nodes of a minimum spanning tree FDM (Ricotta & Moretti, 2008) Ricotta and Moretti (2008) Unweighted FEve (Villéger et al, 2008) FDUs as terminal nodes of a rooted additive tree Sum of path lengths from all terminal nodes to the root (Cardoso et al, 2022) Mean of path lengths from all terminal nodes to the root (Cardoso et al, 2022) Variance of path lengths from all terminal nodes to the root (Cardoso et al, 2022) FDUS as terminal nodes of an unrooted additive tree Sum of branch lengths (Cardoso et al, 2022) Mean of branch lengths (Cardoso et al, 2022) Variance of branch lengths (Cardoso et al, 2022) cases, a technique does exist logically, but it has not yet been used -these are labeled "not yet used". Below, we first provide some information on FDUs and the functional variables describing them, and then the methods are grouped according to components (columns of Table 2).…”