{"doi":"10.1093/sysbio/syad039","title":"Scalable Bayesian Divergence Time Estimation With Ratio Transformations","abstract":"Divergence time estimation is crucial to provide temporal signals for dating biologically important events from species divergence to viral transmissions in space and time. With the advent of high-throughput sequencing, recent Bayesian phylogenetic studies have analyzed hundreds to thousands of sequences. Such large-scale analyses challenge divergence time reconstruction by requiring inference on highly correlated internal node heights that often become computationally infeasible. To overcome this limitation, we explore a ratio transformation that maps the original $N-1$ internal node heights into a space of one height parameter and $N-2$ ratio parameters. To make the analyses scalable, we develop a collection of linear-time algorithms to compute the gradient and Jacobian-associated terms of the log-likelihood with respect to these ratios. We then apply Hamiltonian Monte Carlo sampling with the ratio transform in a Bayesian framework to learn the divergence times in 4 pathogenic viruses (West Nile virus, rabies virus, Lassa virus, and Ebola virus) and the coralline red algae. Our method both resolves a mixing issue in the West Nile virus example and improves inference efficiency by at least 5-fold for the Lassa and rabies virus examples as well as for the algae example. Our method now also makes it computationally feasible to incorporate mixed-effects molecular clock models for the Ebola virus example, confirms the findings from the original study, and reveals clearer multimodal distributions of the divergence times of some clades of interest.","journal":"Systematic Biology","year":2023,"id":346376,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":12,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9524,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2023-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":267681,"name":"Alexander A. Fisher","orcid":"0000-0002-8381-6587","position":1,"is_corresponding":false},{"id":108755,"name":"Shuo Su","orcid":"0000-0003-0187-1185","position":2,"is_corresponding":false},{"id":787977,"name":"Jeffrey L. Thorne","orcid":"0000-0003-3779-5743","position":3,"is_corresponding":false},{"id":1086751,"name":"Barney Potter","orcid":"0000-0001-9476-149X","position":4,"is_corresponding":false},{"id":36828,"name":"Philippe Lemey","orcid":"0000-0003-2826-5353","position":5,"is_corresponding":false},{"id":88111,"name":"Guy Baele","orcid":"0000-0002-1915-7732","position":6,"is_corresponding":false},{"id":32104,"name":"Marc A. Suchard","orcid":"0000-0001-9818-479X","position":7,"is_corresponding":false},{"id":108749,"name":"Xiang Ji","orcid":"0000-0002-7243-0865","position":0,"is_corresponding":true}],"reference_count":52,"raw_metadata":null,"created_at":"2026-07-19T01:11:48.317335Z","pmid":"37458991","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}