Calculating functional diversity metrics using neighbor-joining trees

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), each with their own strengths and limits. Frameworks based on dissimilarity matrices either do not enable the measurement of all components of FD (i.e. richness, divergence, and regularity), or result in the distortion of the functional space. Frameworks based on multidimensional spaces do not allow for comparisons with phylogenetic diversity (PD) measures and can be sensitive to outliers.

We propose the use of neighbor-joining trees (NJ) to represent and quantify FD in a way that combines the strengths of current frameworks without many of their weaknesses. Importantly, our approach is 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 taxonomic diversity (TD) and PD measures, and enables quantification of the richness, divergence and regularity of the functional space.