Computes geographical restrictedness from a site-species matrix.
Geographical restrictedness is an index related to the extent of a species
in a given dataset, it is close to 1 when the species is present in only a
single site of the dataset (restricted) and close to 0 when the species is
present at all sites. It estimates the geographical extent of a species in a
dataset. See Details section to have details on the formula used for
the computation. The sites-species matrix should have sites
in rows and species in columns, similar to vegan package
defaults.
restrictedness(pres_matrix, relative = FALSE)A stacked data.frame containing species' names and their
restrictedness value in the Ri column, similar to what
uniqueness() returns.
a site-species matrix, with species in rows and sites in columns, containing presence-absence, relative abundances or abundances values
a logical (default = FALSE), indicating if restrictedness should be computed relative to restrictedness from a species occupying a single site
Geographical Restrictedness aims to measure the regional extent of a species
in funrar it is computed the simplest way possible: a ratio of the
number of sites where a species is present over the total number of sites in
the dataset. We take this ratio off 1 to have a index between 0 and 1 that
represents how restricted a species is:
$$
R_i = 1 - \frac{N_i}{N_tot},
$$
where \(R_i\) is the geographical restrictedness value, \(N_i\) the total
number of sites where species \(i\) occur and \(N_tot\) the total number
of sites in the dataset.
When relative = TRUE, restrictedness is computed relatively to the
restrictedness of a species present in a single site:
$$
R_i = \frac{R_i}{R_one}
$$
$$
R_i = \frac{1 - \frac{K_i}{K_tot}}{1 - \frac{1}{K_tot}}
$$
$$
R_i = \frac{K_tot - K_i}{K_tot - 1}
$$
Other approaches can be used to measure the geographical extent
(convex hulls, occupancy models, etc.) but for the sake of simplicity only
the counting method is implemented in funrar.
data("aravo", package = "ade4")
# Site-species matrix
mat = as.matrix(aravo$spe)
ri = restrictedness(mat)
head(ri)
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