Brillouin Index

A diversity index derived from information theory, appropriate for fully censused communities.

Usage

brillouin(counts, margin = 1L, cpus = n_cpus())

Arguments

counts

A numeric matrix of count data (samples \(\times\) features). Typically contains absolute abundances (integer counts), though proportions are also accepted.

margin

The margin containing samples. 1 if samples are rows, 2 if samples are columns. Ignored when counts is a special object class (e.g. phyloseq). Default: 1

cpus

How many parallel processing threads should be used. The default, n_cpus(), will use all logical CPU cores.

Details

The Brillouin index is defined as: $$\frac{\ln{[(\sum_{i = 1}^{n} X_i)!]} - \sum_{i = 1}^{n} \ln{(X_i!)}}{\sum_{i = 1}^{n} X_i}$$

Where:

• \(n\) : The number of features.

• \(X_i\) : Integer count of the \(i\)-th feature.

Base R Equivalent:

x <- ex_counts[1,]
# note: lgamma(x + 1) == log(x!)
(lgamma(sum(x) + 1) - sum(lgamma(x + 1))) / sum(x)

Input Types

The counts parameter is designed to accept a simple numeric matrix, but seamlessly supports objects from the following biological data packages:

• phyloseq

• rbiom

• SummarizedExperiment

• TreeSummarizedExperiment

For large datasets, standard matrix operations may be slow. See vignette('performance') for details on using optimized formats (e.g. sparse matrices) and parallel processing.

References

Brillouin, L. (1956). Science and information theory. Academic Press.

See also

alpha_div(), vignette('adiv')

Other Diversity metrics: fisher(), inv_simpson(), shannon(), simpson()

Examples

    brillouin(ex_counts)
#>     Saliva       Gums       Nose      Stool 
#> 0.72541640 0.35924823 1.13029903 0.04175076