Applications of population genetics to the search for disease genes

Association mapping can be viewed as an application of population genetics and evolutionary biology to the problem of identifying genes causally connected to phenotypes. However, some population-genetic principles important to the design and analysis of association studies have not been widely understood or have even been generally misunderstood. Some of these principles underlie techniques that can aid in the discovery of genetic variants that influence phenotypes (‘windfalls’), whereas others can interfere with study design or interpretation of results (‘pitfalls’). Here, considering examples involving genetic variant discovery, linkage disequilibrium, power to detect associations, population stratification and genotype imputation, we address misunderstandings in the application of population genetics to association studies, and we illuminate how some surprising results in association contexts can be easily explained when considered from evolutionary and population-genetic perspectives. Through our examples, we argue that population-genetic thinking—which takes a theoretical view of the evolutionary forces that guide the emergence and propagation of genetic variants—substantially informs the design and interpretation of genetic association studies. In particular, population-genetic thinking sheds light on genetic confounding, on the relationships between association signals of typed markers and causal variants, and on the advantages and disadvantages of particular strategies for measuring genetic variation in association studies. K E Y W O R D S : genome-wide association studies; imputation; linkage disequilibrium; population stratification Identification of genetic loci that contribute to phenotypic outcomes is one of the most important missions of genetics. Researchers continue to vigorously seek genetic factors that underlie disease phenotypes and other traits, particularly in humans. Over the last decade, a primary tool in this search has been the association study, which aims to locate disease-susceptibility loci by identifying alleles whose presence in study subjects is statistically associated with the occurrence of disease. Association studies rely on the fact that once disease variants arise, evolutionary processes including mutation, recombination and coalescence of genealogical lineages tend to maintain associations review 254 The Author(s) 2013. Published by Oxford University Press on behalf of the Foundation for Evolution, Medicine, and Public Health. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. between susceptibility alleles and disease status and to disrupt associations between disease status and other alleles. Thus, the utility of association mapping for locating disease loci is grounded in population-genetic phenomena. Association-based identification of disease-susceptibility loci is difficult partly because associations between genotypes and phenotypes are complicated by the evolutionary histories and population-genetic properties of the genomic regions under study. Depending on the specific populations and study designs used, these complications can lead to failures to uncover true causal relationships, attributions of true signals to the wrong markers and detections of spurious associations that are not due to any causal relationship. At the same time, other aspects of evolutionary and population-genetic thinking provide a basis for surprising techniques that enhance the overall program of association mapping. In some cases, difficulties and successes in the application of population genetics to association mapping are widely appreciated and are routinely incorporated in study design and analysis. In other cases, however, mechanisms by which population-genetic processes hinder or aid association studies are counterintuitive or not generally recognized. To facilitate a deeper understanding of association studies and their basis in evolutionary biology and population genetics, this article aims to illuminate some recurring difficulties or misunderstandings (‘pitfalls’) and some unexpected successes (‘windfalls’) in the application of population genetics to association studies. 1. PITFALL: THE MAXIMUM POSSIBLE VALUE OF THE R STATISTIC FOR LINKAGE DISEQUILIBRIUM BETWEEN TWO LOCI IS TYPICALLY NOT 1. INSTEAD, IT IS A FUNCTION OF THE ALLELE FREQUENCIES OF THE LOCI In the 1990s, well before the advent of genome-wide association (GWA) studies, linkage disequilibrium (LD) was increasingly recognized as a potentially valuable tool for genetic mapping [1, 2]. Given that testing every locus in the human genome for disease association was not imminently feasible, the idea of indirect association testing arose, in which a subset of markers carefully chosen to ‘capture’ ungenotyped variation would be examined [3, 4]. These markers would not necessarily be expected to have a direct impact on disease risk; rather, associations between a marker and disease would represent statistical associations arising from LD between genotyped markers and true causal loci. The measurement of LD—a topic that originated in evolutionary modeling [5, 6] and had long been of interest in purely population-genetic studies [7–9]—became fundamental to the dominant paradigm for genetic mapping. Among the LD measures available [1], the squared correlation coefficient r emerged as particularly useful in association mapping because of its simplicity, its interpretation as the square of a correlation, and its relationship to the power to detect association with a marker in LD with a causal variant—but more on that later. As a consequence of this important new role for r, mathematical properties of the r statistic have become directly relevant to association mapping. Some of these properties have not always been understood, potentially leading to confusion in the interpretation of association studies. As a general rule, correlation coefficients lie between 1 and þ1, and the same is true in the LD context for the correlation coefficient r, which measures the correlation between two indicator variables, one for the presence of a specific allele at the first of a pair of biallelic loci and the other for the presence of a specific allele at the second locus. It is tempting to assume that r ranges from 1 to 1 (and thus r ranges from 0 to 1) for any pair of markers with any allele frequencies. This is a misunderstanding. Squared correlations between binary indicator variables, in fact, can only achieve a value of 1 when the variables have equal expectation or when the sum of their expectations is 1. Otherwise, the upper bound is strictly smaller than 1. Consider two loci, one with alleles A and a and the other with alleles B and b, where pA, pa1⁄4 1 pA, pB, and pb1⁄4 1 pB represent the (non-zero) frequencies of alleles A, a, B and b, respectively, and pAB, pAb, paB and pab, respectively, represent the frequencies of haplotypes AB, Ab, aB and ab. Denoting the correlation coefficient between the two loci by r 1⁄4 ðpAB pApBÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pApapBpb p , r1⁄4 1 if and only if pA1⁄4 pB1⁄4 pAB, and r1⁄4 1 if and only if pA1⁄4 pb1⁄4 pAb. In both cases, as a function of pA, pB and pAB, the maximum possible value of r , or r max, equals 1 if and only if the allele frequencies are equal at the two loci (i.e. {pa, pA}1⁄4 {pb, pB}). Without loss of generality, interchanging loci and Windfalls and pitfalls Edge et al. | 255