Table 3.

List of measures with n being the number of observations, d the total number of dimensions, k any specific row in the matrix, Centroid being their mean and σ ² their variance. Γ is the Gamma distribution and λ_i the eigenvalue of each dimension and q_i and p_i are any pairs of coordinates

Name	Definition	Captures	Source	Notes
Average Euclidean distance from centroid	$\frac{\sqrt{{\sum }_i^n{(k_n-{\text{Centroid}}_k)}^2}}{d}$	Size	Laliberté and Legendre (2010)	The functional dispersion (FDis – without abundance)
Sum of variances	${\sum }_i^d{\sigma }^2{k}_i$	Size	Foote (1992)	Common measure used in palaeobiology (Ciampaglio et al., 2001; Wills, 2001)
Sum of ranges	${\sum }_i^d\text{||max}\left(d_i\right)-min\left(d_i\right)||$	Size	Foote (1992)	More sensitive to outliers than the sum of variances
Ellipsoid volume	$\frac{{\pi }^{d/2}}{\mathrm{\Gamma }\left(\frac{d}{2}+1\right)}\prod _i^d\left({\lambda }_i^{0.5}\right)$	Size	Donohue et al. (2013)	Less sensitive to outliers than the convex hull hypervolume (Blonder, 2018; Díaz et al., 2016)
Minimum spanning tree average distance	$\frac{\sum \left(\text{branch}\text{length}\right)}{n-1}$	Density	Sedgewick (1990)	Similar to the unscaled functional evenness (Villéger et al., 2008)
Minimum spanning tree distances evenness	$\frac{\sum min\left(\frac{\text{branch}\text{length}}{\sum \text{branch}\text{length}}\right)-\frac{1}{n-1}}{1-\frac{1}{n-1}}$	Density	Villéger et al. (2008)	The functional evenness without weighted abundance (FEve; Villéger et al., 2008)
Average nearest neighbor distance	$\sqrt{{\sum }_i^{n}min{(q_i-p_i)}^2})\times \frac{1}{n}$	Density	Foote (1992)	The density of pairs of observations
Average displacement	$\frac{\sqrt{{\sum }_i^n{(k_n)}^2}}{\sqrt{{\sum }_i^n{(k_n-{\text{Centroid}}_k)}^2}}$	Position	This paper	The ratio between the observations' position from their centroid and the center of the trait space (coordinates: 0, 0, 0,…). A value of 1 indicates that the observations' centroid is the center of the trait space