When migration leaves a clean trace: Decoupling migration from coalescence in the structured serial coalescent

With the rapid accumulation of population genomic data across space and time, there is an urgent need for demographic inference methods that incorporate explicit time-series modeling, achieve fine spatial resolution, and ensure clear identifiability between migration and coalescence rates. To address this need, we investigate pairwise genealogical processes under the structured serial coalescent, deriving evolution equations for pairwise branch length distributions and related statistics. By classifying the resulting relationships according to their parameter dependencies and computational complexity, we identify a class that is not only computationally tractable but also determined solely by migration rates. Building on this theoretical basis, we propose an inference framework for fine-resolution, time-varying migration rates inference and demonstrate its feasibility through simulation. We further outline how this framework can be extended to the joint estimation of migration and coalescence rates.