Exact Limits of Inference in Coalescent Models

TL;DR

This paper derives exact probability limits for correctly inferring population size histories from coalescent data, informing optimal experimental design in population genetics.

Contribution

It provides precise formulas for the probability of correctly distinguishing population histories based on coalescent times, advancing understanding of inference limits.

Findings

Exact expressions for inference accuracy in coalescent models

Implications for optimal data collection in population genetics

Application to human population history analysis

Abstract

Recovery of population size history from molecular sequence data is an important problem in population genetics. Inference commonly relies on a coalescent model linking the population size history to genealogies. The high computational cost of estimating parameters from these models usually compels researchers to select a subset of the available data or to rely on non-sufficient summary statistics for statistical inference. 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 individuals, loci, and the sampling times. The results are applied to human population history. This work has significant implications for optimal design when the inferential goal is to test scientific hypotheses about population size trajectories in coalescent models with and without recombination.