Kulczynski

Kulczynski beta diversity metric.

Usage

kulczynski(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.

$$t = \displaystyle \sum_{i = 1}^{n} min(x_i,y_i)$$ $$D = \displaystyle 1 - 0.5(\frac{t}{\sum_{i = 1}^{n} x_i} + \frac{t}{\sum_{i = 1}^{n} y_i})$$

  x <- c(4, 0, 3, 2, 6)
  y <- c(0, 8, 0, 0, 5)
  t <- sum(pmin(x,y))
  1 - (t/sum(x) + t/sum(y)) / 2
  #>  0.6410256

References

Kulcynski S 1927. Die Pflanzenassoziationen der Pieninen. Bulletin International de l'Academie Polonaise des Sciences et des Lettres. Classe des Sciences Mathematiques et Naturelles.

See also

Other beta_diversity: bray_curtis(), canberra(), euclidean(), generalized_unifrac(), gower(), jaccard(), 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
    
    # Kulczynski weighted distance matrix
    kulczynski(ex_counts)
#>          Saliva      Gums      Nose
#> Gums  0.4925704                    
#> Nose  0.9475164 0.9703510          
#> Stool 0.9909509 0.9903586 0.9921546
    
    # Kulczynski unweighted distance matrix
    kulczynski(ex_counts, weighted = FALSE)
#>           Saliva       Gums       Nose
#> Gums  0.10000000                      
#> Nose  0.16666667 0.08333333           
#> Stool 0.32500000 0.20000000 0.08333333
    
    # Only calculate distances for A vs all.
    kulczynski(ex_counts, pairs = 1:3)
#>          Saliva      Gums      Nose
#> Gums  0.4925704                    
#> Nose  0.9475164        NA          
#> Stool 0.9909509        NA        NA