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).