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Convert asymmetric pairwise matrix to reciprocally symmetrical matrix

Source: R/pairwise_matrices.R
pairwise_ratios.Rd

This function produces a "pairwise ratio matrix" that can be used in tests about asymmetric flows among nodes in a data set (e.g. the "asymmetry" and "diversity" hypotheses; Kling and Ackerly (2021)). The input data set can be an asymmetric matrix with entries representing directed edge weights (e.g. directional flows of wind or genes connecting each pair of populations or "nodes"), or it can be a vector of node attributes (e.g. properties of a site or population, such as genetic diversity). The result is a matrix that represents each pair's relative asymmetry, removing information about their absolute magnitudes.

Usage

pairwise_ratios(x, log = TRUE)

Arguments

x

Either a square matrix with entries representing directional edge weights between pairs of nodes, or a numeric vector with a value for each node.

log

Should ratios be log-transformed? Default is TRUE, since this generates a symmetrical frequency distribution desirable for most analyses.

Value

A square matrix the same size as x, with ones in the diagonal (zeros if log = TRUE) and reciprocal values in the upper and lower triangles. The diagonal is set regardless of the diagonal of x, which for a matrix of flows is typically zero. A pair with zero flow in one direction gives a ratio of 0 or Inf (-Inf or Inf if logged), and a pair with no flow in either direction gives NaN. If x is a matrix, the output represents the ratios of above-diagonal to below-diagonal values in x. If x is a vector, the output represents the ratios of every pairwise combination of x values; e.g. a matrix in which the value of cell [2, 4] equals x[2] / x[4].

References

Kling and Ackerly (2021). Global wind patterns shape genetic differentiation, asymmetric gene flow, and genetic diversity in trees. Proceedings of the National Academy of Sciences 118: e2017317118. doi:10.1073/pnas.2017317118

Examples

# directional flows among three sites, from row to column
x <- matrix(c(0, 2, 6,
              4, 0, 1,
              2, 3, 0), 3, byrow = TRUE)
pairwise_ratios(x)
#>            [,1]       [,2]      [,3]
#> [1,]  0.0000000 -0.6931472  1.098612
#> [2,]  0.6931472  0.0000000 -1.098612
#> [3,] -1.0986123  1.0986123  0.000000

# ratios of a site attribute, such as genetic diversity
pairwise_ratios(c(0.2, 0.4, 0.8))
#>           [,1]       [,2]       [,3]
#> [1,] 0.0000000 -0.6931472 -1.3862944
#> [2,] 0.6931472  0.0000000 -0.6931472
#> [3,] 1.3862944  0.6931472  0.0000000