Direct calculation of a tree length using a distance matrix

Comparative studies of tree-building methods have shown minimum evolution to be in general an accurate criterion fur selecting a true tree. To improve the use of this criterion, this paper proposes a method for rapidly and directly calculating a length of a dichotomous tree without having to resort to branch length calculations. This direct calculation (DC) method applies to the complete final topology, giving equal importance to each branch after a dichotomy. According to this method, the tree length S-DC is S-DC = Sigma(i)Sigma(j)(D-ij/2B(ij)) = (Sigma(i<j)Sigma D(ij)2(Bmax-Bij))/2B(max-1) where D-ij is the observed distance between taxa i and j, B-ij is the number of branches connecting i and j, Bmax is the greatest B-ij in the tree, and the powers of two are due to the dichotomy of the tree. This tree length expression may be used as a rapid method for selecting the shortest tree from a set of hypothetical or subobtimal trees.