Understanding population structure in an evolutionary context: population-specific FST and pairwise FST

Populations are shaped by their history. It is crucial to interpret population structure in an evolutionary context. Pairwise FST measures population structure, whereas population-specific FST measures deviation from the ancestral population. To understand the current population structure and a population’s history of range expansion, we propose a representation method that overlays population-specific FST estimates on a sampling location map, and on an unrooted neighbor-joining tree and a multi-dimensional scaling plot inferred from a pairwise FST distance matrix. We examined the usefulness of our procedure using simulations that mimicked population colonization from an ancestral population and by analyzing published human, Atlantic cod, and wild poplar data. Our results demonstrated that population-specific FST values identify the source population and trace the evolutionary history of its derived populations. Conversely, pairwise FST values represent the current population structure. By integrating the results of both estimators, we obtained a new picture of the population structure that incorporates evolutionary history. The generalized least squares estimate of genome-wide population-specific FST indicated that the wild poplar population expanded its distribution to the north, where daylight hours are long in summer, to coastal areas with abundant rainfall, and to the south where summers are dry. Genomic data highlight the power of the bias-corrected moment estimators of FST, whether global, pairwise, or population-specific, that provide unbiased estimates of FST. All FST moment estimators described in this paper have reasonable processing times and are useful in population genomics studies.

An Empirical Study of Moment Estimators for Quantile Approximation

We empirically evaluate lightweight moment estimators for the single-pass quantile approximation problem, including maximum entropy methods and orthogonal series with Fourier, Cosine, Legendre, Chebyshev and Hermite basis functions. We show how to apply stable summation formulas to offset numerical precision issues for higher-order moments, leading to reliable single-pass moment estimators up to order 15. Additionally, we provide an algorithm for GPU-accelerated quantile approximation based on parallel tree reduction. Experiments evaluate the accuracy and runtime of moment estimators against the state-of-the-art KLL quantile estimator on 14,072 real-world datasets drawn from the OpenML database. Our analysis highlights the effectiveness of variants of moment-based quantile approximation for highly space efficient summaries: their average performance using as few as five sample moments can approach the performance of a KLL sketch containing 500 elements. Experiments also illustrate the difficulty of applying the method reliably and showcases which moment-based approximations can be expected to fail or perform poorly.

Understanding population structure in an evolutionary context: population-specific FST and pairwise FST

Populations are shaped by their history. Therefore, it is crucial to interpret population structure in an evolutionary context. Wright’s FST measures current population structure, whereas population-specific FST measures deviation from the ancestral population. To understand current population structure and a population’s history of range expansion, we propose a novel representation method that overlays population-specific FST estimates on an unrooted neighbor-joining tree inferred from a pairwise FST distance matrix and on a map of sampling locations. We examined the usefulness of our procedure by conducting simulations that mimicked population colonization from an ancestral population and analyzing published human, Atlantic cod, and wild poplar genotype data sets. Our results demonstrated that population-specific FST values identify the source population and trace the evolutionary history of its derived populations based on genetic diversity. In contrast, pairwise FST values represent the current population structure. By integrating results of both estimators, we obtained a new picture of current population structure that incorporates evolutionary history. The generalized least squares of genome-wide population-specific FST indicated that the wild poplar population expanded its distribution to the north where it adapted to longer day lengths, to seashores where it adapted to abundant rainfall, and to the south where it adapted to dry summers. Genomic data highlight the power of the bias-corrected moment estimators of FST. All FST moment estimators described in this paper have reasonable CPU times and are useful in population genomics studies. The R codes for our representation method and simulations are available in the Supporting Information.