A distance‐based framework for measuring functional diversity from multiple traits

TLDR

A recently proposed framework for measuring functional diversity from multiple traits has been limited to quantitative traits without missing values and to situations with more species than traits, though an extension to other trait types was suggested. This note aims to extend the framework to handle any distance or dissimilarity measure, any number of traits, and any trait type, including quantitative, semi‑quantitative, and qualitative. The authors present a highly flexible distance‑based framework that measures different facets of functional diversity in multidimensional trait space using any distance or dissimilarity measure, introduces the functional dispersion (FDis) index—a weighted mean absolute deviation analogue of Rao’s entropy—and provides the FD R package for implementation. The new approach permits missing trait values and trait weighting, and for unweighted presence–absence data, the FDis index can be used to formally test differences in functional diversity.

Abstract

A new framework for measuring functional diversity (FD) from multiple traits has recently been proposed. This framework was mostly limited to quantitative traits without missing values and to situations in which there are more species than traits, although the authors had suggested a way to extend their framework to other trait types. The main purpose of this note is to further develop this suggestion. We describe a highly flexible distance‐based framework to measure different facets of FD in multidimensional trait space from any distance or dissimilarity measure, any number of traits, and from different trait types (i.e., quantitative, semi‐quantitative, and qualitative). This new approach allows for missing trait values and the weighting of individual traits. We also present a new multidimensional FD index, called functional dispersion (FDis), which is closely related to Rao's quadratic entropy. FDis is the multivariate analogue of the weighted mean absolute deviation (MAD), in which the weights are species relative abundances. For unweighted presence–absence data, FDis can be used for a formal statistical test of differences in FD. We provide the “FD” R language package to easily implement our distance‐based FD framework.