When migration leaves a clean trace: Decoupling migration from coalescence in the Structured Serial Coalescent

Abstract

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 high spatial scalability, 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 identities according to their parameter dependencies and computational complexity, we identify a class that is not only computationally tractable but also determined exclusively by migration rates. Building on this theoretical basis, we propose a scalable framework for inferring time-varying migration rates and demonstrate its feasibility through simulation. We further outline how this framework can be extended to the joint estimation of migration and coalescence rates.