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The geometric mean length, a new statistic to describe the distribution of character steps on a tree

The geometric mean length (GML) is proposed as a new statistic aimed at describing the evenness of character changes on a tree for a given set of character optimizations. It is the geometric mean of the number of steps on each branch of the tree, varying between a maximum value when all branch lengths are equal, and a minimum value when all branches but one have only one character step. It can be scaled according to its theoretical maximum value, thus indicating a relative GML that allows a comparison of the evenness of character steps between different tree topologies.