SUMMARY: In Bayesian phylogenetic and phylodynamic studies, it is common to summarize the posterior distribution of trees with a time-calibrated summary phylogeny. While the maximum clade credibility (MCC) tree is often used for this purpose, we here show that a novel summary tree method-the highest independent posterior subtree reconstruction, or (HIPSTR)-contains consistently higher supported clades over MCC. We also provide faster computational routines for estimating both summary trees in an updated version of TreeAnnotator X, an open-source software program that summarizes the information from a sample of trees and returns many helpful statistics such as individual clade credibilities contained in the summary tree. RESULTS: HIPSTR and MCC reconstructions on two Ebola virus and two SARS-CoV-2 datasets show that HIPSTR yields summary trees that consistently contain clades with higher support compared to MCC trees. The MCC trees regularly fail to include several clades with very high posterior probability (≥0.95) as well as a large number of clades with moderate to high posterior probability (≥50%), whereas HIPSTR-in particular its majority-rule extension MrHIPSTR-achieves near-perfect performance in this respect. HIPSTR and MrHIPSTR also exhibit favourable computational performance over MCC in TreeAnnotator X. Comparison to the recent CCD0-MAP algorithm yielded mixed results and requires a more in-depth investigation in follow-up studies. AVAILABILITY AND IMPLEMENTATION: TreeAnnotator X is available as part of the BEAST X (v10.5.0) software package, available at https://github.com/beast-dev/beast-mcmc/releases, and on Zenodo (DOI: https://doi.org/10.5281/zenodo.4895234).

GFlowNets are a promising alternative to MCMC sampling for discrete compositional random variables. Training GFlowNets requires repeated evaluations of the unnormalized target distribution, or reward function. However, for large-scale posterior sampling, this may be prohibitive since it incurs traversing the data several times. Moreover, if the data are distributed across clients, employing standard GFlowNets leads to intensive client-server communication. To alleviate both these issues, we propose embarrassingly parallel GFlowNet (EP-GFlowNet). EP-GFlowNet is a provably correct divide-and-conquer method to sample from product distributions of the form $R(\cdot) \propto R_1(\cdot) ... R_N(\cdot)$ — e.g., in parallel or federated Bayes, where each $R_n$ is a local posterior defined on a data partition. First, in parallel, we train a local GFlowNet targeting each $R_n$ and send the resulting models to the server. Then, the server learns a global GFlowNet by enforcing our newly proposed aggregating balance condition, requiring a single communication step. Importantly, EP-GFlowNets can also be applied to multi-objective optimization and model reuse. Our experiments illustrate the effectiveness of EP-GFlowNets on multiple tasks, including parallel Bayesian phylogenetics, multi-objective multiset and sequence generation, and federated Bayesian structure learning.

Coalescent theory combined with statistical modeling allows us to estimate effective population size fluctuations from molecular sequences of individuals sampled from a population of interest. When sequences are sampled serially through time and the distribution of the sampling times depends on the effective population size, explicit statistical modeling of sampling times improves population size estimation. Previous work assumed that the genealogy relating sampled sequences is known and modeled sampling times as an inhomogeneous Poisson process with log-intensity equal to a linear function of the log-transformed effective population size. We improve this approach in two ways. First, we extend the method to allow for joint Bayesian estimation of the genealogy, effective population size trajectory, and other model parameters. Next, we improve the sampling time model by incorporating additional sources of information in the form of time-varying covariates. We validate our new modeling framework using a simulation study and apply our new methodology to analyses of population dynamics of seasonal influenza and to the recent Ebola virus outbreak in West Africa.