Chao1

Chao1 alpha diversity metric.

A non-parametric estimator of the number of unobserved species in a sample. The Chao1 index estimates total species richness based on the number of species that occur only once (singletons) and twice (doubletons) in the sample.

Usage

chao1(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

Prerequisite: all counts are whole numbers.

In the formulas below, x is a single column (sample) from counts. $n$ is the total number of non-zero OTUs, $a$ is the number of singletons, and $b$ is the number of doubletons.

$$D = \displaystyle n + \frac{a^{2}}{2b}$$

  x <- c(1, 0, 3, 2, 6)
  sum(x>0) + (sum(x==1) ^ 2) / (2 * sum(x==2))
  #>  4.5

Note that when $x$ does not have any singletons or doubletons ($a = 0, b = 0$), the result will be NaN. When $x$ has singletons but no doubletons ($a > 0, b = 0$), the result will be Inf.

References

Chao A 1984. Non-parametric estimation of the number of classes in a population. Scandinavian Journal of Statistics, 11:265-270.

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
    
    # Chao1 diversity values
    chao1(ex_counts)
#> Saliva   Gums   Nose  Stool 
#>    4.5    Inf    6.0    Inf 
    
    # Low diversity
    chao1(c(100, 1, 1, 1, 1)) # Inf
#> [1] Inf
    
    # High diversity
    chao1(c(20, 20, 20, 20, 20)) # NaN
#> [1] NaN
    
    # Low richness
    chao1(1:3) # 3.5
#> [1] 3.5
    
    # High richness
    chao1(1:100) # 100.5
#> [1] 100.5