  Distance based algorithms are a common technique in the construction of
phylogenetic trees from taxonomic sequence data. The first step in the
implementation of these algorithms is the calculation of a pairwise distance
matrix to give a measure of the evolutionary change between any pair of the
extant taxa. A standard technique is to use the log det formula to construct
pairwise distances from aligned sequence data. We review a distance measure
valid for the most general models, and show how the log det formula can be used
as an estimator thereof. We then show that the foundation upon which the log
det formula is constructed can be generalized to produce a previously unknown
estimator which improves the consistency of the distance matrices constructed
from the log det formula. This distance estimator provides a consistent
technique for constructing quartets from phylogenetic sequence data under the
assumption of the most general Markov model of sequence evolution.
