How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population Histories. Reconstruction of population histories is a central problem in population genetics. Existing coalescentbased 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 informationtheoretic 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.

An Application of Random Walk Resampling to Phylogenetic HMM Inference and Learning Statistical resampling methods are widely used for confidence interval placement and as a data perturbation technique for statistical inference and learning. An important assumption of popular resampling methods such as the standard bootstrap is that input observations are identically and independently distributed (i.i.d.). However, within the area of computational biology and bioinformatics, many different factors can contribute to intrasequence dependence, such as recombination and other evolutionary processes governing sequence evolution. The SEquential RESampling (xe2x80x9cSERESxe2x80x9d) framework was previously proposed to relax the simplifying assumption of i.i.d. input observations. SERES resampling takes the form of random walks on an input of either aligned or unaligned biomolecular sequences. This study introduces the first application of SERES random walks on aligned sequence inputs and is also the first to demonstrate the utility of SERES as a data perturbation technique to yield improved statistical estimates. We focus on the classical problem of recombinationaware local genealogical inference. We show in a simulation study that coupling SERES resampling and reestimation with recHMM, a hidden Markov modelbased method, produces local genealogical inferences with consistent and often large improvements in terms of topological accuracy. We further evaluate method performance using an empirical HIV genome sequence dataset.