Modelling among-site compositional heterogeneity resolves ant backbone phylogeny: A reply to Boudinot & Lieberman (2025)

Understanding the early evolution of ants has been hindered by conflicting phylogenetic hypotheses and methodological inconsistencies across studies. In Cai (2024), I reanalyzed both Sanger-sequencing and genome-scale datasets of ants using rigorous model comparison and methods that account for among-site compositional heterogeneity to identify the sources of phylogenetic conflict. The results showed that the 11-loci datasets in Borowiec et al. (2019) failed to resolve deep ant relationships and could not determine the position of Martialis heureka. Analyses of the genome-scale data further revealed that the placement of key lineages depends strongly on model fit. Bayesian cross-validation and posterior predictive assessments demonstrated that the infinite mixture CAT-GTR+G4 model substantially outperforms empirical finite mixture models, providing robust support for the Leptanillinae-sister hypothesis. Criticisms by Boudinot & Lieberman (2025) regarding the study design, model choice, and convergence assessments stem from misinterpretations of the analytical framework. The matrices in Cai (2024) were explicitly designed to test model performance under controlled subsampling and filtering schemes, and all analyses showed consistent results across datasets. The findings reaffirm that accurately modelling among-site compositional heterogeneity is essential for resolving the backbone phylogeny of ants, and that under the best-fitting models, Martialis heureka occupies a well-supported position as sister to all non-leptanilline ants.