Computes functional distinctiveness from a site-species matrix (containing presence-absence or relative abundances) of species with provided functional distance matrix considering only species within a given range in the functional space. Basically species are cutoff when their dissimilarity is above the input threshold. The sites-species matrix should have sites in rows and species in columns, similar to vegan package defaults.
distinctiveness_alt(pres_matrix, dist_matrix, given_range)a site-species matrix (presence-absence or relative abundances), with sites in rows and species in columns
a species functional distance matrix
a numeric indicating the dissimilarity range at which the the other species are considered maximally dissimilar
a similar matrix from provided pres_matrix with Distinctiveness
values in lieu of presences or relative abundances, species absent from
communities will have an NA value (see Note section)
The Functional Distinctiveness of a species is the average functional distance from a species to all the other in the given community. It is computed as such: $$ D_i(T) = \frac{ \sum\limits_{j = 1 ~,j \neq i ~}^S \left[ \frac{d_{ij}}{T} + \theta(d_{ij} - T) \left(1 - \frac{d_{ij}}{T} \right) \right] }{ S - 1 } $$ with \(D_i\) the functional distinctiveness of species \(i\), \(N\) the total number of species in the community and \(d_{ij}\) the functional distance between species \(i\) and species \(j\). \(T\) is the chosen maximal range considered. The function \(\theta(d_ij - T)\) is an indicator function that returns 1 when \(d_{ij} \geq T\) and 0 when \(d_{ij} < T\). IMPORTANT NOTE: in order to get functional rarity indices between 0 and 1, the distance metric has to be scaled between 0 and 1.
Absent species should be coded by 0 or NA in input matrices.
When a species is alone in its community the functional distinctiveness
cannot be computed (denominator = 0 in formula), and its value is assigned
as NaN.
For speed and memory efficiency sparse matrices can be used as input of
the function using as(pres_matrix, "dgCMatrix") from the
Matrix package.
(see vignette("sparse_matrices", package = "funrar"))