Adapting cluster graphs for inference of continuous trait evolution on phylogenetic networks

TL;DR

This paper explores how adapting cluster graphs and loopy belief propagation can improve the efficiency of likelihood inference for continuous trait evolution on complex phylogenetic networks, balancing accuracy and computational cost.

Contribution

It introduces a simulation-based analysis of cluster size effects on inference accuracy and runtime, and proves equivalence of estimation methods for a specific model.

Findings

Optimal cluster size balances accuracy and efficiency.

Loopy belief propagation offers a practical alternative to exact inference.

Proven equivalence of likelihood and energy-based estimates for Brownian motion.

Abstract

Dynamic programming approaches have long been applied to fit models of univariate and multivariate trait evolution on phylogenetic trees for discrete and continuous traits, and more recently adapted to phylogenetic networks with reticulation. We previously showed that various trait evolution models on a network can be readily cast as probabilistic graphical models, so that likelihood-based estimation can proceed efficiently via belief propagation on an associated clique tree. Even so, exact likelihood inference can grow computationally prohibitive for large complex networks. Loopy belief propagation can similarly be applied to these settings, using non-tree cluster graphs to optimize a factored energy approximation to the log-likelihood, and may provide a more practical trade-off between estimation accuracy and runtime. However, the influence of cluster graph structure on this trade-off is not precisely understood. We conduct a simulation study using the Julia package PhyloGaussianBeliefProp to investigate how varying maximum cluster size affects this trade-off for Gaussian trait evolution models on networks. We discuss recommended choices for maximum cluster size, and prove the equivalence of likelihood-based and factored-energy-based parameter estimates for the homogeneous Brownian motion model.