Shannon

Shannon alpha diversity metric.

The index considers both the number of different OTUs (richness) and how evenly the observations are distributed among those OTUs (evenness).

Usage

shannon(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. $p_i$ is the proportion of the $i$-th OTU in the total community.

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

  x <- c(4, 0, 3, 2, 6)[-2]
  p <- x / sum(x)
  -sum(p * log(p))
  #>  1.309526

References

Shannon CE, Weaver W 1949. The Mathematical Theory of Communication. University of Illinois Press.

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
    
    # Shannon diversity values
    shannon(ex_counts)
#>     Saliva       Gums       Nose      Stool 
#> 0.74119910 0.36684449 1.14222899 0.04824952 
    
    # Low diversity
    shannon(c(100, 1, 1, 1, 1)) # 0.22
#> [1] 0.2163426
    
    # High diversity
    shannon(c(20, 20, 20, 20, 20)) # 1.61
#> [1] 1.609438
    
    # Low richness
    shannon(1:3) # 1.01
#> [1] 1.011404
    
    # High richness
    shannon(1:100) # 4.42
#> [1] 4.416898