Fisher's Alpha

A parametric diversity index assuming species abundances follow a log-series distribution.

Usage

fisher(counts, digits = 3L, 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.
digits: Precision of the returned values, in number of decimal places. E.g. the default digits=3 could return 6.392.
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

Fisher's Alpha ($\alpha$) is the parameter in the equation: $$\frac{n}{\alpha} = \ln{\left(1 + \frac{X_T}{\alpha}\right)}$$

Where:

$n$ : The number of features.
$X_T$ : Total of all counts (sequencing depth).

The value of $\alpha$ is solved for iteratively.

Parameter: digits

The precision (number of decimal places) to use when solving the equation.

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

Fisher, R. A., Corbet, A. S., & Williams, C. B. (1943). The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12, 42-58. doi:10.2307/1411

Examples

    fisher(ex_counts)
#> Saliva   Gums   Nose  Stool 
#>  0.635  0.700  0.847  0.744