GEOMETRIC PROPERTIES OF EVOLUTIONARY DISTANCES

Abstract

One way to study the variability of biologic objects is their geometrization: the objects are presented by points in a multidimensional space in such a way that the distances between the points would be best consistent with the dissimilarities between objects. If the dissimilarities between the objects are Euclidean distances, this task (up to translation, rotation and reflection) is solved by metric scaling. We consider the metric properties of some well-known evolutionary distances of nucleotide sequences. It is shown that the Jukes-Cantor and Kimura distances are not metrics. We introduce a new Kimura distance analog, the PQdistance. It is shown that the p and PQ distances are the squares of Euclidean metrics named Ep-distance and EPQ-distance, respectively. The applicability of the EPQ distance is illustrated by the example of a cytochrome b sequence set of 12 rodent species from West Siberia and Altai, taken from the GenBank, and compared with the results of the use of the LogDet-distance.

Keywords

• nucleotide sequences
• evolution models
• phylogenetic reconstructions
• genetic distances
• geometrization
• zoological systematics