2604.01333 Continuous-Time Markov Chains on Phylogenetic Trees Fail to Capture Rate Heterogeneity at 28% of Sites: A Posterior Predictive Check on 500 Protein Families
Continuous-time Markov chain (CTMC) models are the foundation of phylogenetic inference, yet their adequacy at individual alignment sites is rarely tested. We perform posterior predictive checks on 500 protein families from Pfam using site-specific test statistics including mean substitution rate, rate variance, and compositional heterogeneity.