Canberra

Canberra beta diversity metric.

Usage

canberra(counts, weighted = TRUE, pairs = NULL, 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.

weighted

If TRUE, the algorithm takes relative abundances into account. If FALSE, only presence/absence is considered.

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.

Value

A dist object.

Calculation

In the formulas below, x and y are two columns (samples) from counts. n is the number of rows (OTUs) in counts.

OTUs must be removed if they are absent from both samples.

$$D = \displaystyle \frac{1}{n}\sum_{i = 1}^{n} \frac{|x_i - y_i|}{x_i + y_i}$$

  x <- c(4, 0, 3, 0, 6)[-4]
  y <- c(0, 8, 0, 0, 5)[-4]
  sum(abs(x-y) / (x+y)) / length(x)
  #>  0.7727273

References

Lance, Godfrey LN, Williams WT 1967. A general theory of classificatory sorting strategies II. Clustering systems. The computer journal, 10(3). doi:10.1093/comjnl/10.3.271

See also

Other beta_diversity: bray_curtis(), euclidean(), generalized_unifrac(), gower(), jaccard(), kulczynski(), manhattan(), unweighted_unifrac(), variance_adjusted_unifrac(), weighted_normalized_unifrac(), weighted_unifrac()

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
    
    # Gower weighted distance matrix
    canberra(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.4684762                    
#> Nose  0.7884925 0.8696711          
#> Stool 0.9950258 0.8269576 0.8712341
    
    # Gower unweighted distance matrix
    canberra(ex_counts, weighted = FALSE)
#>          Saliva      Gums      Nose
#> Gums  0.2000000                    
#> Nose  0.3333333 0.1666667          
#> Stool 0.5000000 0.3333333 0.1666667
    
    # Only calculate distances for A vs all.
    canberra(ex_counts, pairs = 1:3)
#>          Saliva      Gums      Nose
#> Gums  0.4684762                    
#> Nose  0.7884925        NA          
#> Stool 0.9950258        NA        NA