Increased congruence does not necessarily indicate increased phylogenetic accuracy - The behavior of the incongruence length difference test in mixed-model analyses

Comprehensive phylogenetic analyses utilize data from distinct sources, including nuclear, mitochondrial, and plastid molecular sequences and morphology. Such heterogeneous datasets are likely to require distinct models of analysis, given the different histories of mutational biases operating on these characters. The incongruence length difference (ILD) test is increasingly being used to arbitrate between competing models of phylogenetic analysis in cases where multiple data partitions have been collected. Our work suggests that the ILD test is unlikely to be an effective measure of congruence when two datasets differ markedly in size. We show that models that increase the contribution of one data partition over another are likely to increase congruence, as measured by this test. More alarmingly, for many bipartition comparisons, character congruence increases bimodally-either increasing or decreasing the contribution of one data partition will increase congruence-making it impossible to arrive at a single optimally congruent model of analysis.