Can three incongruence tests predict when data should be combined?

Advocates of conditional combination have argued that testing for incongruence between data partitions is an important step in data exploration. Unless the partitions have had distinct histories, as in horizontal gene transfer, incongruence means that one or more data support the wrong phylogeny. This study examines the relationship between incongruence and phylogenetic accuracy using three tests of incongruence. These tests were applied to pairs of mitochondrial DNA data partitions from two well-corroborated vertebrate phylogenies. Of the three tests, the most useful was the incongruence length difference test (ILD, also called the partition homogeneity test). This test distinguished between cases in which combining the data generally improved phylogenetic accuracy (P > 0.01) and cases in which accuracy of the combined data suffered relative to the individual partitions (P < 0.001). In contrast, in several cases, the Templeton and Rodrigo tests detected highly significant incongruence (P < 0.001) even though combining the incongruent partitions actually increased phylogenetic accuracy. All three tests identified cases in which improving the reconstruction model would improve the phylogenetic accuracy of the individual partitions.