Average values of a dissimilarity measure not requiring sequence alignment are twice the averages of conventional mismatch counts requiring sequence alignment for a variety of computer-generated model systems

Summary A measure of sequence similarity,d _t, not requiring prior sequence alignment gave correct results for a variety of computer-generated model sequences without and with gaps for all degrees of substitution,s. Measured was the squared Euclidean distance between vectors of counts of t-tuplets of characters in the two sequences. In models without gaps and without Needleman-Wunsch alignment, averaged was very closely equal to twice average conventional mismatch counts,m. In these models one of each of the conditions on the Jukes-Cantor model was violated in turn: (1) both descendant lineages receive the same number of substitutions, (2) all sites are equally likely to be substituted, (3) all different replacement characters are equally likely to be chosen, and (4) all original characters are equally likely to be substituted. In Jukes-Cantor models with gaps Needleman-Wunsch alignment was necessarily performed, a procedure that generally produced incorrect values ofm. For these models averaged was found to be very closely equal to twice the averagem estimated from the known value ofs using the inverted Jukes-Cantor formula.