Estimating pathogen spread using structured coalescent and birth–death models: A quantitative comparison

Elucidating disease spread between subpopulations is crucial in guiding effective disease control efforts. Genomic epidemiology and phylodynamics have emerged as key principles to estimate such spread from pathogen phylogenies derived from molecular data. Two well-established structured phylodynamic methodologies - based on the coalescent and the birth-death model - are frequently employed to estimate viral spread between populations. Nonetheless, these methodologies operate under distinct assumptions whose impact on the accuracy of migration rate inference is yet to be thoroughly investigated. In this manuscript, we present a simulation study, contrasting the inferential outcomes of the structured coalescent model with constant population size and the multitype birth-death model with a constant rate. We explore this comparison across a range of migration rates in endemic diseases and epidemic outbreaks. The results of the epidemic outbreak analysis revealed that the birth-death model exhibits a superior ability to retrieve accurate migration rates compared to the coalescent model, regardless of the actual migration rate. Thus, to estimate accurate migration rates, the population dynamics have to be accounted for. On the other hand, for the endemic disease scenario, our investigation demonstrates that both models produce comparable coverage and accuracy of the migration rates, with the coalescent model generating more precise estimates. Regardless of the specific scenario, both models similarly estimated the source location of the disease. This research offers tangible modelling advice for infectious disease analysts, suggesting the use of either model for endemic diseases. For epidemic outbreaks, or scenarios with varying population size, structured phylodynamic models relying on the Kingman coalescent with constant population size should be avoided as they can lead to inaccurate estimates of the migration rate. Instead, coalescent models accounting for varying population size or birth-death models should be favoured. Importantly, our study emphasises the value of directly capturing exponential growth dynamics which could be a useful enhancement for structured coalescent models.