2018/11/07 by Younhun Kim, Frederic Koehler, Kim, Younhun +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #FOS: Biological sciences #FOS: Mathematics #Genetic diversity and population structure #Populations and Evolution (q-bio.PE) #Quantitative Methods (q-bio.QM) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1811.03177
openalex publication_date 2018/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure -- the history of multiple subpopulations that merge, split and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.