Parallel algorithms for phylogenetic inference under a structured coalescent approximation.

While advances in molecular epidemiology and computational modeling have enhanced our capacity to track pathogen evolution, the accurate reconstruction of spatiotemporal transmission dynamics remains essential for developing epidemic preparedness frameworks and implementing outbreak response measures. Structured coalescent models offer a phylogeographic framework by restricting lineage coalescence events to geographically proximate host populations. Although the Bayesian structured coalescent approximation (BASTA) provides a tractable approach, contemporary phylogeographic analyses involving dozens of geographic localities and hundreds to thousands of viral genomes substantially exceed the computational capacity of existing implementations. The BASTA likelihood scales cubically with deme count and quadratically with sequence count due to matrix exponentiation and pairwise coalescent probability calculations. Here, we introduce a comprehensive algorithmic restructuring of the structured coalescent likelihood that eliminates redundancies, optimizes memory access, and exposes parallelization opportunities. Our approach reorganizes computations along three dimensions: (i) independent calculation of deme-transition probability matrices across time intervals; (ii) simultaneous evaluation of partial likelihood vectors within temporal slices; and (iii) concurrent aggregation of coalescent probabilities. Algorithmic restructuring cuts average coalescent likelihood computation by 7-8 fold, and parallelization further boosts performance to 10-26 fold, enabling joint phylogeographic analyses of dengue virus across 10 South American countries and H5N1 avian influenza across 20 Eurasian regions to finish in a fraction of prior time. This computational efficiency also enables comparison between backward-in-time structured coalescent approximations and forward-in-time phylogeographic methods, revealing that the former provides appropriately conservative posterior estimates, particularly at intermediate phylogenetic depths. We integrate our implementation into the popular BEAST X and BEAGLE software packages, with an accompanying interface in BEAUti X to easily set up the analyses, providing researchers with an accessible and scalable tool for real-time phylogeographic surveillance of rapidly evolving pathogens.