Exact Limits of Inference in Coalescent Models
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Recovery of population size history from sequence data and testing of hypotheses about features of population size history are important problems in population genetics. Inference commonly relies on a coalescent-based model linking the population size history to genealogies. We consider the problem of recovering the true population size history from two possible alternatives on the basis of coalescent time data. We give exact expressions for the probability of selecting the correct alternative in a variety of biologically interesting cases as a function of the separation between the alternative size histories, the number of genealogies and loci sampled, and the sampling times. The results are applied to human population history. As coalescent times are inferred from sequence data rather than directly observed, the inferential limits we give can be viewed as optimistic.
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