The structured coalescent allows inferring migration patterns between viral sub-populations from genetic sequence data. However, these analyses typically assume that no genetic recombination process impacted the sequence evolution of pathogens. For segmented viruses, such as influenza, that can undergo reassortment this assumption is broken. Reassortment reshuffles the segments of different parent lineages upon a coinfection event, which means that the shared history of viruses has to be represented by a network instead of a tree. Therefore, full genome analyses of such viruses is complex or even impossible. While this problem has been addressed for unstructured populations, it is still impossible to account for population structure, such as induced by different host populations, while also accounting for reassortment% at the same time. We address this by extending the structured coalescent to account for reassortment and present a framework for investigating possible ties between reassortment and migration (host jump) events. This method can accurately estimate sub-population dependent effective populations sizes, reassortment and migration rates from simulated data. Additionally, we apply the new model to avian influenza A/H5N1 sequences, sampled from two avian host types, Anseriformes and Galliformes. We contrast our results with a structured coalescent without reassortment inference, which assumes independently evolving segments. This reveals that taking into account segment reassortment and using sequencing data from several viral segments for joint phylodynamic inference leads to different estimates for effective population sizes, migration and clock rates. This new model is implemented as the Structured Coalescent with Reassortment (SCoRe) package for BEAST 2.5 and is available at https://github.com/jugne/SCORE.
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