Abstract
Two new optimality indices are developed for selecting subsets of trees from a set of most parsimonious trees. The optimal character compatibility index (OCCI) quantifies, for each most parsimonious tree, the proportion of characters that are postulated to have changed only once. The tree(s) with the highest OCCI value is (are) selected. The optimum parsimonious likelihood index (OPLI) selects the tree(s), from a set of most parsimonious trees, that is (are) most likely to give the observed data under certain assumptions. In simulation trials, both the OCCI and OPLI are highly efficient at retrieving the closest approximation to the true tree.

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