Abstract
FST and kinship are key parameters often estimated in modern population genetics studies in order to quantitatively characterize structure and relatedness. Kinship matrices have also become a fundamental quantity used in genome-wide association studies and heritability estimation. The most frequently-used estimators of FST and kinship are method-of-moments estimators whose accuracies depend strongly on the existence of simple underlying forms of structure, such as the independent subpopulations model of non-overlapping, independently evolving subpopulations. However, modern data sets have revealed that these simple models of structure likely do not hold in many populations, including humans. In this work, we analyze the behavior of these estimators in the presence of arbitrarily-complex population structures, which results in an improved estimation framework specifically designed for arbitrary population structures. After generalizing the definition of FST to arbitrary population structures and establishing a framework for assessing bias and consistency of genome-wide estimators, we calculate the accuracy of existing FST and kinship estimators under arbitrary population structures, characterizing biases and estimation challenges unobserved under their originally-assumed models of structure. We then present our new approach, which consistently estimates kinship and FST when the minimum kinship value in the dataset is estimated consistently. We illustrate our results using simulated genotypes from an admixture model, constructing a one-dimensional geographic scenario that departs nontrivially from the independent subpopulations model. Our simulations reveal the potential for severe biases in estimates of existing approaches that are overcome by our new framework. This work may significantly improve future analyses that rely on accurate kinship and FST estimates.
Highlights
In population genetics studies, one is often interested in characterizing structure, genetic differentiation, and relatedness among individuals
We find that existing FST estimators are downwardly biased, and that existing kinship matrix estimators have related biases that are on average downward and of similar magnitude but vary for every pair of individuals
These insights led us to a new estimation framework for kinship and FST that is practically unbiased for any population structure, as demonstrated by theory and simulations
Summary
One is often interested in characterizing structure, genetic differentiation, and relatedness among individuals. FST is the probability that alleles drawn randomly from a subpopulation are “identical by descent” (IBD) relative to an ancestral population [1, 2]. The kinship coefficient is a measure of relatedness between individuals defined in terms of IBD probabilities, and it is closely related to FST, since the mean kinship of the parents in a subpopulation is the FST of the following generation [1]. There are many likelihood approaches that estimate FST and kinship, but these are limited by assuming independent subpopulations or Normal approximations for FST [3,4,5,6,7,8,9,10,11] or totally outbred individuals for kinship [12, 13]. Non-parametric approaches such as those based on the method of moments are considerably more flexible and computationally tractable [16], so they are the natural choice to study arbitrary population structures
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