51: Likelihood-based inference of migration surfaces

Music City Center 

In this work, we derive a method for visualizing spatial population structure using inverse instantaneous coalescent rate (IICR) curves. Unlike traditional approaches, such as EEMS, which model genetic variation as a function of migration rates and approximate its expectation using resistance distance, our method introduces a fundamentally different perspective by focusing on the coalescent process. The IICR curve quantifies the rate at which lineages coalesce as a function of time, providing a framework for inferring population structure. Our approach is based on a stepping-stone model and we model the relationship between pairs of samples as independent Markov processes with an extended joint state space that accounts for coalescence. By utilizing efficient procedures to compute the matrix exponential, we derive the distribution of coalescent times and expected IICR curves with high computational efficiency. This enables us to infer migration surfaces and visualize population structure.

migration surface

demographic inference

population genetics 

Section on Statistics in Genomics and Genetics