Benjamin Teo | Searcharxiv

arXiv2025

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

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.

q-bio.PE↗

arXiv2024

Leveraging graphical model techniques to study evolution on phylogenetic networks

The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture. Computing the likelihood of data observed at the leaves is costly as the size and complexity of the phylogeny grows. Efficient algorithms exist for trees, but cannot be applied to networks. We show that a vast array of models for trait evolution along phylogenetic networks can be reformulated as graphical models, for which efficient belief propagation algorithms exist. We provide a brief review of belief propagation on general graphical models, then focus on linear Gaussian models for continuous traits. We show how belief propagation techniques can be applied for exact or approximate (but more scalable) likelihood and gradient calculations, and prove novel results for efficient parameter inference of some models. We highlight the possible fruitful interactions between graphical models and phylogenetic methods. For example, approximate likelihood approaches have the potential to greatly reduce computational costs for phylogenies with reticulations.

q-bio.PE↗