Measures for differentially weighted, raw abundance data

The calculation of this asymmetric metric transforms a matrix of quantitative values into a matrix of conditional probabilities (i.e. the quotient of a given value in a cell and either the row or column totals). A weighted Euclidean distance measure is then computed based on the values in the rows (or columns in R mode analysis) of the conditional probability matrix. Weights, which are the reciprocal of the variable (column) totals from the raw data matrix, serve to reduce the influence of the highest values measured.

This asymmetric distance is similar to the χ2 metric, however, the weighted Euclidean distances are multiplied by the total of all values in the raw data matrix. This converts the weights in the Euclidean distances to probabilities rather than column totals. This is the measure used in correspondence analysis and related analyses.

This asymmetric distance is similar to the χ2 metric. While no weights are applied, the square roots of conditional probabilities are used as variance-stabilising data transformations. This distance measure performs well in linear ordination. Variables with few non-zero counts (such as rare species) are given lower weights.