Measuring Inconsistency in Phylogenetic Trees

Abstract

Listen

Translate article

Suppose that we seek a treeTgiving the phylogenetic relationships among the species in a setS. A common method selects for such a tree a maximum parsimony tree using the genome of the species inS. Suppose thatKis a proper subset ofS. ThenTinduces a treeUwhich gives the same relationships among the species inKbut omits the species ofSwhich are not inK. Unfortunately, whenTis a maximum parsimony tree for the species inS, thenUneed not be a maximum parsimony tree for the species inK. This phenomenon exhibits an inconsistency in the criterion of maximum parsimony—maximum parsimony trees for different groups of species may be “inconsistent”. It implies that the addition of a new species scan change relationships already “established” for prior species if the trees are obtained by the criterion of maximum parsimony. The phenomenon occurs both in artificial examples and with real data.An alternative method for generating phylogenetic trees seeks to minimize such inconsistencies. For each groupJconsisting of four of the species, we find a treeT(J) describing the relationship only among the four species inJ, for example by the use of maximum parsimony on those four species alone. In favorable cases one may combine all the treesT(J) into a single treeTthat is consistent with all the treesT(J). If such a treeTexists, then it is unique, and there is a computationally efficient algorithm for finding the treeT. In unfavorable bases such a treeTdoes not exist, but there may still be a tree containing only “mild” inconsistencies with the treesT(J). A numerical measure is given for the inconsistencyI(T) of a treeTin terms of the treelengths of the various trees with setJof leaves in comparison with the treeT. We may then seek a “minimally inconsistent treeT” that minimizes the inconsistencyI(T). We describe procedures which find a treeTwith low inconsistencyI(T). Examples are provided using both artificial strings and data from the complete mitochondrial DNA sequences for 16 species. In particular, minimally inconsistent trees are identified for the 16 species. The definition permits a proof that the trees are in fact minimally inconsistent. The criterion can be applied in both a relative and an absolute sense.