Functional diversity metrics
Three functional metrics based on Villéger et al. (2008) and Mouillot et
al. (2013) were selected: functional evenness (FEve), functional
divergence (FDiv), and functional specialization (FSpe). These metrics
were obtained by plotting all traits jointly in functional space and
measuring the positions within this space in relation to the species
abundances and trait distributions within it. FEve measures the changes
in abundance distributions within the functional space based on a
Minimum spanning tree (MST). FDiv measures the changes in distance to
the mean abundance (center) in relation to species abundances, i.e. if
species with high abundance have a greater distance than the overall
mean, divergence will be higher. FSpe measures abundance of generalist
or specialist species by measuring the mean distance from the rest of
the species pool in the functional space (Cornwell et al. 2006; Villéger
et al. 2008; Mouillot et al. 2013). Functional richness (FRic) was not
selected because it is highly correlated with taxonomic richness
(Botta-Dukat & Czúcz, 2016). A fourth metric of functionality, Rao’s
quadratic entropy (RaoQ), was obtained with the “FD” package in R
(Laliberté et al. 2015). The index follows the formula:
\begin{equation}
RaoQ=\sum_{I=L}^{S-1}{}\sum_{J=I+1}^{s}{}d_{\text{ij}}p_{i}p_{i}\nonumber \\
\end{equation}Where pi iis considered as S -species community
characterized by the relative abundance vector p = (p 1,p 2,…, p s) such that\(\sum_{i=1}^{S}\text{pi}=1\), and dij is the difference
between the i-th and j-th species (dij = djiand dii = 0). RaoQ measures changes in the sum of weighted
abundances of pairwise functions between species. It combines the
information provided by FRic and FDiv and is suitable for detecting
trait convergence and divergence. The higher the measure, the higher the
dissimilarity and abundances of traits within the habitat (Botta-Dukat
& Czúcz, 2016). To obtain all previously mentioned indices of
functional diversity, all numerical variables were standardized to zero
mean and unit standard deviation to reduce the relative influence of
variables in different orders of magnitude prior to analysis. To examine
the overall differences between individual traits, we also obtained CWM
using the “FD”’ package in R (Laliberté et al. 2015).