Simpson

Simpson alpha diversity metric.

Gauges the uniformity of species within a community. A Simpson index of 0 indicates that one or a few high abundance OTUs dominate the community, which is indicative of low diversity.

Usage

simpson(counts, cpus = n_cpus())

Arguments

counts

An OTU abundance matrix where each column is a sample, and each row is an OTU. Any object coercible with as.matrix() can be given here, as well as phyloseq, rbiom, SummarizedExperiment, and TreeSummarizedExperiment objects.

cpus

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

Value

A numeric vector.

Calculation

Pre-transformation: drop all OTUs with zero abundance.

In the formulas below, \(x\) is a single column (sample) from counts. \(p\) are the relative abundances.

$$p_{i} = \displaystyle \frac{x_i}{\sum x}$$ $$D = \displaystyle 1 - \sum_{i = 1}^{n} p_{i}\times\ln(p_{i})$$

  x <- c(4, 0, 3, 2, 6)[-2]
  p <- x / sum(x)
  1 - sum(p * log(p))
  #>  2.309526

References

Simpson EH 1949. Measurement of diversity. Nature, 163. doi:10.1038/163688a0

See also

Other alpha_diversity: chao1(), faith(), inv_simpson(), shannon()

Examples

    # Example counts matrix
    ex_counts
#>                   Saliva Gums Nose Stool
#> Streptococcus        162  793   22     1
#> Bacteroides            2    4    2   611
#> Corynebacterium        0    0  498     1
#> Haemophilus          180   87    2     1
#> Propionibacterium      1    1  251     0
#> Staphylococcus         0    1  236     1
    
    # Simpson diversity values
    simpson(ex_counts)
#>     Saliva       Gums       Nose      Stool 
#> 0.50725478 0.18924937 0.64075388 0.01295525 
    
    # Low diversity
    simpson(c(100, 1, 1, 1, 1)) # 0.075
#> [1] 0.07507396
    
    # High diversity
    simpson(c(20, 20, 20, 20, 20)) # 0.8
#> [1] 0.8
    
    # Low richness
    simpson(1:3) # 0.61
#> [1] 0.6111111
    
    # High richness
    simpson(1:100) # 0.99
#> [1] 0.9867327