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Andrew L Hipp, Jocelyn C Hall, Kenneth J Sytsma, Congruence Versus Phylogenetic Accuracy: Revisiting the Incongruence Length Difference Test, Systematic Biology, Volume 53, Issue 1, February 2004, Pages 81–89, https://doi.org/10.1080/10635150490264752
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Phylogenies inferred from independent data partitions usually differ from one another in topology despite the fact that they are drawn from the same set of organisms (Rodrigo et al., 1993). Some topological differences are due to sampling error or to the use of inappropriate phylogenetic models. These types of topological incongruence do not have their origin in genealogical discordance, i.e., differences between phylogenies underlying the respective data partitions (Baum et al., 1998). Incongruence that is not due to genealogical discordance can often be addressed by modifying the model used in phylogenetic reconstruction (Cunningham, 1997b), and combining data is an appropriate way of dealing with random topological differences that are attributable to sampling error. However, other topological differences, e.g., those arising from lineage sorting (Maddison, 1997; Avise, 2000) and hybridization (Dumolin-Lapègue et al., 1997; Rieseberg, 1997; McKinnon et al., 1999; Avise, 2000), reflect genealogical discordance between the data partitions.
Most systematists consider data partitions to be combinable if and only if they are not strongly incongruent with one another (Sytsma, 1990; Bull et al., 1993; Huelsenbeck et al., 1996; Baum et al., 1998; Johnson and Soltis, 1998; Thornton and DeSalle, 2000; Yoder et al., 2001; Barker and Lutzoni, 2002; Buckley et al., 2002). Systematists who follow this prior agreement or conditional combination approach to analyzing multiple data partitions (Bull et al., 1993; Huelsenbeck et al., 1996; Johnson and Soltis, 1998) evaluate incongruence using tests such as the incongruence length difference (ILD) test (Farris et al., 1994, 1995) or other tests of taxonomic congruence (Templeton, 1983; Kishino and Hasegawa, 1989; Larson, 1994; Shimodaira and Hasegawa, 1999) before deciding whether the partitions should be analyzed in combination. Data that exhibit strong incongruence are then analyzed separately or under assumptions that minimize incongruence (Cunningham, 1997b).
