Testing adequacy for DNA substitution models

Testing model adequacy is important before a DNA substitution model is chosen for phylogenetic inference. Using a mis-specified model can negatively impact phylogenetic inference, for example, the maximum likelihood method can be inconsistent when the DNA sequences are generated under a tree topology which is in the Felsentein Zone and analyzed with a mis-specified or inadequate model. However, model adequacy testing in phylogenetics is underdeveloped.

Here we develop a simple, general, powerful and robust model test based on Pearson's goodness-of-fit test and binning of site patterns. We demonstrate through simulation that this test is robust in its high power to reject the inadequate models for a large range of different ways of binning site patterns while the Type I error is controlled well. In the real data analysis we discovered many cases where models chosen by another method can be rejected by this new test, in particular, our proposed test rejects the most complex DNA model (GTR+I+ Γ) while the Goldman-Cox test fails to reject the commonly used simple models.

Model adequacy testing and bootstrap should be used together to assess reliability of conclusions after model selection and model fitting have already been applied to choose the model and fit it. The new goodness-of-fit test proposed in this paper is a simple and powerful model adequacy testing method serving such a regular model checking purpose. We caution against deriving strong conclusions from analyses based on inadequate models. At a minimum, those results derived from inadequate models can now be readly flagged using the new test, and reported as such.