The CAT model exhibits broadly consistent adequacy across evolutionary timescales

Amino-acid substitution models are central to phylogenomic inference, yet their adequacy (i.e. whether they realistically describe features of real datasets) remains insufficiently tested. Here, we evaluated the adequacy of seven widely used models of amino acid substitution across empirical datasets spanning diverse evolutionary timescales. We focused specifically on the model's ability to capture across-site compositional heterogeneity in empirical data, by evaluating complementary metrics that quantify both site-level diversity and amino-acid frequency spectrum. Of the models we tested, LG+G, representing the site-homogeneous models, always fails to adequately describe the real data. Among site-heterogeneous mixture models, Poisson+CAT+G consistently achieves a close match to empirical data, while other finite-mixture models show intermediate or mixed behavior, with performance varying by datasets and by metric. Taken together, our results highlight that adequacy tests are important for identifying model strengths and limitations in accounting for across-site compositional heterogeneity.