Improved Phylogenetic Posterior Estimation through Regularised Conditional Clade Distributions

Bayesian phylogenetic inference uses Markov chain Monte Carlo sampling to estimate the posterior distribution of phylogenetic trees. However, the complex geometry of treespace makes these distributions difficult to characterise. Traditional approaches often summarise posterior samples into a single point estimate, discarding much of the information contained in the full distribution. Conditional clade distributions (CCDs) address this by providing a tractable model of the full tree distribution, but existing parameterisations exhibit complementary strengths. We introduce a new family of models called regularised conditional clade distributions (regCCD), which apply regularisation to balance sample fidelity against overfitting, thereby combining the strengths of existing parameterisations. We show that regCCD outperforms existing models in capturing the posterior distribution and provides better point estimates than its underlying model. Furthermore, we provide an efficient procedure for selecting the optimal regularisation parameter for a given posterior tree set. Finally, we demonstrate the application of regCCD in assessing whether different phylogenetic models or data produce statistically distinguishable tree distributions.