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Morisita dissimilarity

Source: R/beta_div.r
morisita.Rd

A measure of overlap between samples that is independent of sample size. Requires integer counts.

Usage

morisita(counts, margin = 1L, pairs = NULL, 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

pairs

Which combinations of samples should distances be calculated for? The default value (NULL) calculates all-vs-all. Provide a numeric or logical vector specifying positions in the distance matrix to calculate. See examples.

cpus

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

Details

The Morisita dissimilarity is defined as: $$1 - \frac{2\sum_{i=1}^{n}X_{i}Y_{i}}{\left(\frac{\sum_{i=1}^{n}X_i(X_i - 1)}{X_T(X_T - 1)} + \frac{\sum_{i=1}^{n}Y_i(Y_i - 1)}{Y_T(Y_T - 1)}\right)X_{T}Y_{T}}$$

Where:

  • \(X_i\), \(Y_i\) : Absolute counts of the \(i\)-th feature.

  • \(X_T\), \(Y_T\) : Total counts in each sample. \(X_T = \sum_{i=1}^{n} X_i\).

  • \(n\) : The number of features.

Base R Equivalent:

x <- ex_counts[1,]
y <- ex_counts[2,]
simpson_x <- sum(x * (x - 1)) / (sum(x) * (sum(x) - 1))
simpson_y <- sum(y * (y - 1)) / (sum(y) * (sum(y) - 1))
1 - ((2 * sum(x * y)) / ((simpson_x + simpson_y) * sum(x) * sum(y)))

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

Morisita, M. (1959). Measuring of interspecific association and similarity between communities. Memoirs of the Faculty of Science, Kyushu University, Series E (Biology), 3, 65-80.

See also

beta_div(), vignette('bdiv'), vignette('bdiv_guide')

Other Abundance metrics: aitchison(), bhattacharyya(), bray(), canberra(), chebyshev(), chord(), clark(), divergence(), euclidean(), gower(), hellinger(), horn(), jensen(), jsd(), lorentzian(), manhattan(), matusita(), minkowski(), motyka(), psym_chisq(), soergel(), squared_chisq(), squared_chord(), squared_euclidean(), topsoe(), wave_hedges()

Examples

    morisita(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.2755642                    
#> Nose  0.9718049 0.9654050          
#> Stool 0.9900273 0.9932106 0.9952669