CAT-Posterior Mean Site Frequencies improves phylogenetic modeling under Maximum Likelihood and resolves Tardigrada as the sister of Arthropoda plus Onychophora

Tardigrada, the water bears, are microscopic animals with walking appendages that are members of Ecdysozoa, the clade of molting animals that also includes Nematoda (round worms), Nematomorpha (horsehair worms), Priapulida (penis worms), Kinorhyncha (mud dragons), Loricifera (loricated animals), Arthropoda (insects, spiders, centipedes, crustaceans, and their allies), and Onychophora (velvet worms). The phylogenetic relationships within Ecdysozoa are still unclear, with analyses of molecular and morphological data yielding incongruent results. Accounting for across-site compositional heterogeneity using mixture models that partition sites in frequency categories, CATegories (CAT)-based models, has been shown to improve fit in Bayesian analyses. However, CAT-based models such as CAT-Poisson or CAT-GTR (where CAT is combined with a General Time Reversible matrix to account for replacement rate heterogeneity) have proven difficult to implement in maximum likelihood. Here, we use CAT-posterior mean site frequencies (CAT-PMSF), a new method to export dataset-specific mixture models (CAT-Poisson and CAT-GTR) parameterized using Bayesian methods to maximum likelihood software. We developed new maximum likelihood-based model adequacy tests using parametric bootstrap and show that CAT-PMSF describes across-site compositional heterogeneity better than other across-site compositionally heterogeneous models currently implemented in maximum likelihood software. CAT-PMSF suggests that tardigrades are members of Panarthropoda, a lineage also including Arthropoda and Onychophora. Within Panarthropoda, our results favor Tardigrada as sister to Onychophora plus Arthropoda (the Lobopodia hypothesis). Our results illustrate the power of CAT-PMSF to model across-site compositionally heterogeneous datasets in the maximum likelihood framework and clarify the relationships between the Tardigrada and the Ecdysozoa.