## The Index of Relative Rarity

The Index of Relative Rarity is a metric quantifying the rarity at the community level. It has been developed to improve the existing methods by integrating the biogeographical concepts of rarity. This rarity metric includes a variable parameter, the rarity cut-off, which makes it adaptable regardless of the considered taxon, spatial scale or geographic area.

The rarity cut-off point is here defined as the threshold of occurrence below which species are considered rare.

The calculation is as follows: we assign a rarity weight to each species as a function of their occurrence, which is obtained from a biodiversity database.

### Rarity weights

The rarity cut-off point is integrated at this step of the calculation: the weight assignation depends upon the chosen rarity cut-off point. The rarity weighting function has been fitted such rare species have a rarity weight that increases exponentially below the rarity cutoff point (see the below figure).  Conversely, above the rarity cut-off point, the weight decreases to reach 0.

The weight assignation function can be adjusted to any chosen rarity cut-off point. In the example below, 5 weight assignation curves have been adjusted to 5 different rarity cut-off points (each rarity cut-off is defined in relation to the maximum occurrence, i.e., the occurrence of the most widespread species).

The weight assignation formula has been developed and compared with classical methods such as the inverse of occurrence (Leroy et al. 2012), and then improved and published in an R package (Leroy et al. 2013).

### Calculation of the Index of Relative Rarity

Once rarity weights have been assigned to each species, the Index of Relative Rarity of an assemblage of species is calculated as the sum of the weights of the assemblage’s species, which is divided by the assemblage’s richness, and then normalized between 0 and 1.

## Integrating multiple scales in the calculation of the Index of Relative Rarity

The flexiblity of the Index of Relative Rarity allowed to integrate multiple spatial scales into a single index. To this end, occurrence data from different databases can be coupled (Leroy et al. 2013).

The relevance of this multiscale approach comes from the use of “scale-dependent” rarity cut-off points, i.e., a rarity cut-off point is adjusted for each considered scale. This original approach allowed to discriminate among different types of rarity inside species assemblages (e.g., species that were rare at all scales vs. species that were rare at a single scale, etc.).

## Multi-taxon Index of Rarity

Similarly, a multi-taxon version of the Index of Relative Rarity has been developed and used to assess the rarity of invertebrate assemblages of subtidal rocky areas of western France. The relevance of this index comes from the use of “taxon-specific” rarity cut-off points.

## The “Rarity” package for R

In order to simplify the application of the Index of Relative Rarity, the “Rarity” package has been developed for R (can be directed download from R). This packages allows calculating quickly rarity weights for species and indices for assemblages of species, and to adjust the parameters according to the user’s choices.

This package simply requires occurrence data to calculate species rarity weights, and presence-absence or abundance data per site/assemblage/community to calculate rarity indices of sites/assemblages/species.