Li-Wu-Luo Method

In this method (Li et al 1985), each site in a codon is allocated to 0-fold, 2-fold or 4-fold degenerate categories. For computing distances, all 0-fold and two-thirds of the 2-fold sites are considered nonsynonymous, whereas one-third of the 2-fold and all of the 4-fold sites are considered synonymous. The observed transitional and transversional differences between codons then are partitioned into those occurring at 0-fold, 2-fold and 4-fold degenerate sites. Based on this information, the following quantities can be estimated.

Synonymous distance

This is the number of synonymous substitutions per synonymous site.

Nonsynonymous distance

This is the number of nonsynonymous substitutions per nonsynonymous site.

 Substitutions at the 4-fold degenerate sites

This is the number of substitutions per 4-fold degenerate site; it is useful for measuring the rate of neutral evolution.

 Substitutions at the 0-fold degenerate sites

This is the number of substitutions per 0-fold degenerate site; it is useful for measuring the rate of amino acid sequence evolution.

 Number of 4-fold degenerate sites

This is the estimate of the number of 4-fold degenerate sites, computed by averaging the number of 4-fold degenerate sites in the two sequences, compared.

 Number of 0-fold degenerate sites

This is the estimate of the number of 0-fold degenerate sites, computed by averaging the number of 0-fold degenerate sites in the two sequences, compared.

Difference between synonymous and nonsynonymous distances

This computes the differences between the synonymous and nonsynonymous distances. These statistics are useful for conducting tests of selection.

The formulas for computing these quantities are:

Here,

are the number of 0-fold, 2-fold and 4-fold degenerate sites, respectively.

, and

, where

, , ,

Pi and Qi are the proportions of i-fold degenerate sites that show transitional and transversional differences, respectively.

,

See also Nei and Kumar (2000), page 62.