Full-Support Conditional Clade Distribution for Bayesian Tree Topology Testing

Abstract

Bayesian phylogenetic inference uses Markov chain Monte Carlo sampling to estimate the posterior distribution of phylogenetic trees. However, the complex geometry of tree space makes these distributions difficult to characterise. Conditional clade distributions (CCDs) address this by providing a tractable model of posterior tree distributions, but existing parameterisations do not provide full support over tree space and exhibit complementary strengths. We introduce a new family of models, called K-depth regularised conditional clade distributions (KRegCCD), which apply regularisation to balance sample fidelity against overfitting, thereby combining the strengths of existing parameterisations. KRegCCD achieves full support by extending the model to unexplored regions of tree space through a structured modelling of unseen clades. We show that KRegCCD outperforms existing models in posterior estimation while maintaining comparable point estimates. We further introduce an efficient cross-validation procedure for optimising regularisation parameters for individual posterior tree sets. Finally, we demonstrate that KRegCCD enables Bayesian tree topology testing by allowing candidate topologies to be evaluated against posterior tree distributions through their credible levels.