Exact Indices, Criteria to Select from Minimum Length Trees

Abstract

Abstract—Modifications of the consistency, retention and rescaled consistency indices are introduced. These apply to particular transformations of a character state rather than all of the transformations of a character. For example, if one observes relatively many losses in a character state over a suite of minimum length trees, a low weight is applied to the transformation to a loss; however, these observations infer nothing on the probability of the character state being gained independently. If the same character state shows few or no convergent gains on the suite of minimum length cladograms, then gains receive a relatively high weight. Conversely, if for a particular character state, convergent gains are common and losses rare, the transformation to a loss is given a higher weight than the transformation to a gain. For multistate characters, each possible transformation is weighted independently. Three indices are proposed, i.e. the exact consistently index, the exact retention index and the exact rescaled consistency index. The consistency index is modified to deal with characters with unknown entries. The methods outlined not only select (or generate) preferred tree topologies but they also choose character optimizations, even for trees of identical topology.