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.