Direct Calculation of a Tree Length Using a Distance Matrix

Abstract.

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 =∑ _i ∑ _j (D _ij /2^Bij) = (∑ _i<j ∑D _ij 2^Bmax−Bij)/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.