McIntosh Index

A dominance index based on the Euclidean distance from the origin.

Usage

mcintosh(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 McIntosh index is defined as: $$\frac{X_T - \sqrt{\sum_{i = 1}^{n} (X_i)^2}}{X_T - \sqrt{X_T}}$$

Where:

• \(n\) : The number of features.

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

• \(X_T\) : Total of all counts.

Base R Equivalent:

x <- ex_counts[1,]
(sum(x) - sqrt(sum(x^2))) / (sum(x) - sqrt(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

McIntosh, R. P. (1967). An index of diversity and the relation of certain concepts to diversity. Ecology, 48(3), 392-404. doi:10.2307/1932674

See also

alpha_div(), vignette('adiv')

Other Dominance metrics: berger()

Examples

    mcintosh(ex_counts)
#>      Saliva        Gums        Nose       Stool 
#> 0.315000947 0.103044944 0.413637580 0.006771808