The effect of evenly spaced constant sites on the distribution of the random division of a molecular sequence

A modified Sherman statistic can be used to test whether the differences between two aligned sequences are distributed at random along the sequences, or whether they are clustered, which suggests anomalies of evolution such as partial gene recombination or functional constraints. The presence of evenly spaced constant sites (such as constancy at the second codon position in genes coding for proteins) lowers the statistic and makes the significance less than it should be.

The magnitude of the constant-site effect is shown by simulation to depend mainly on the proportion of differences between two sequences and on the number of constant sites that are added after each variable site. This latter number can be estimated from the variance of sites in a sequence matrix at the first, second and third codon positions, to obtain a ratio that corrects the statistic. When expressed as standard errors, the uncorrected results are too low (typically half to one unit when almost all the variation is at the third codon position). Correction raises the standard errors to levels close to expectation. If the data show no marked ternary periodicity, the correction is very small. The method is illustrated with biological data that show close to random behaviour, and with data that exhibit strong clustering.

The software is available from the author and has also been placed on the EMBL file server (Software@embl-ebi.ac.uk).

phas1@le.ac.uk