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 for 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)/2(B(ij))) = (sigma(i<j) sigma D(ij)2(Bmax-B(ij)))/2(Bmax)(-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.