Index | Expression | Description |
---|---|---|
CWM | CWM_{x} = ∑ p_{i}x_{i} | CWMx is the CWM for the trait x, p_{i} is the relative abundance of species i in the community, and x_{i} is the trait value for the species i. |
RaoQ | \( \mathrm{RaoQ}=\sum \limits_{i=1}^S\sum \limits_{j=1}^S{d}_{ij}{p}_i{p}_j \) | p_{i} and p_{j} are the relative abundances of species i and j, and the d_{ij} values are the dissimilarities between species i and j in the community. |
FRic | \( \left({Kx}_{a_1}+\left(1-K\right){x}_{b_1},{Kx}_{a_2}+\left(1-K\right){x}_{b_2},\dots, {Kx}_{a_T}+\left(1-K\right){x}_{b_T}\ \right)\ \mathrm{for}\ 0\le K\le 1 \) | a and b are species inside the convex hull volume, whose coordinates, i.e., trait values, are (x_{a1}, x_{a2}, ..., x_{aT}) and (x_{b1}, x_{b2}, ..., x_{bT}), respectively. |
FEve |
\( \mathrm{FEev}=\frac{\sum \limits_{l=1}^{S-1}\min \left({\mathrm{PEW}}_l,\frac{1}{S-1}\right)-\frac{1}{S-1}}{1-\frac{1}{S-1}} \) with \( {\mathrm{PEW}}_l=\frac{{\mathrm{EW}}_l}{\sum \limits_{l=1}^{S-1}{\mathrm{EW}}_l} \) and \( {\mathrm{EW}}_l=\frac{\mathrm{dist}\left(i,j\right)}{w_i+{w}_j} \) | EW is weighted evenness; dist(i, j) is the Euclidean distance between species i and j, the species involved is branch l, and w_{i} is the relative abundance of species i. PEW is the partial weighted evenness; S is number of species. |
FDis |
\( \mathrm{FDis}=\frac{\sum {a}_j{z}_j}{\sum {a}_j} \) and \( \mathbf{c}=\left[{c}_i\right]=\frac{\sum {a}_j{x}_{ij}}{\sum {a}_j} \) | a_{j} is the abundance of species j and z_{j} is the distance of species j to the weighted centroid c, where c is the weighted centroid in the i-dimensional space, and x_{ij} the attribute of species j for trait i. |
FDiv |
\( \mathrm{FDiv}=\frac{2}{\pi}\arctan (5V) \) with V = ∑ p_{i}(lnx_{i} − ln x)^{2} and \( {p}_i=\frac{a_i}{\sum {a}_i} \) | 5 is a scaling factor used to define the index over a range of 0–1, and V is the weighted variance of trait x. Inx_{i} is the trait value for the species i; a_{i} is the relative abundance of species i in the community. |