Noise and incongruence: interpreting results of the incongruence length difference test

Incongruence between data sets is an important concept in molecular phylogenetics and is commonly measured by the incongruence length difference (ILD) test (J. S. Farris et al., Cladistics 10, 315-319). The ILD test has been used to infer specific evolutionary events and to determine whether to combine data sets for phylogenetic analysis. However, the interpretation in the literature of the test's results varies because authors have conflicting expectations of the effect that noise will have. Using simulations we demonstrate that noise can by itself generate highly significant results in the ILD test and demonstrate why this is the case. To clarify the interpretation of test results, we suggest an additional procedure in which the result is compared against a frequency distribution generated from completely shuffled data. As examples, we apply this approach to two previous studies that have reported incongruence.