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 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
A stacked data.frame containing species' names and their
restrictedness value in the Ri column, similar to what
uniqueness() returns.
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.