The Lowdown on Linkage Disequilibrium

Abstract

Flowering time varies among Arabidopsis accessions. Some of the genes that contribute to this polygenic trait have been localized using quantitative trait loci (QTL) mapping, eventually leading to the identification of genetic variants that contribute to observed differences in flowering time (El-Assal et al., 2001). Despite this and other similar successes with the positional cloning of QTL, the path from a mapped QTL to a gene underlying trait variation is fraught with obstacles. One obstacle is the lack of fixed genetic differences between parental lines used to create the mapping population. This “diversity hurdle” can be overcome by repeating QTL analyses in many mapping populations (or by mapping variance components in a number of families), but this approach is not feasible for most taxa and phenotypes. Linkage disequilibrium (LD) mapping steps into this void. Unlike traditional linkage mapping, which maps genes using gametic phase disequilibrium created in a single- or multiple-generation cross, LD mapping can rely on segregating variation in natural populations. As a result, LD mapping samples contain many more informative meioses (i.e., all those that have occurred in the history of the sample) than a traditional mapping population. Although not without its own problems (Lander and Schork, 1994), LD mapping holds great promise for fine-mapping genes and variants that contribute to a trait of interest, such as flowering time. Here, we briefly review LD (What is it? How is it measured? What biological and evolutionary factors shape its distribution?), summarize recent studies of LD in plant systems, and relate genomic patterns of LD to mapping genes that underlie variation in complex phenotypic traits. Two SNP Sites Typed from Eight Individuals. Estimates of D, D′, and r 2 (see text) are provided for each data set. (A) Complete LD between the two sites. (B) Randomized data, implying recombination between sites. (C) Unequal marginal frequencies between sites. Unequal frequencies do not imply that recombination has occurred; for example, the C may be a relatively new mutation that occurred on the T background. Because only three of four possible gametic types are found at the two sites, there is no need to invoke recombination to explain the pattern of variation. (D) All four gametic types with the same marginal frequencies as in (C); the four gametic types imply recombination. The metric D is a quantitative measure of allelic association. With respect to Figure 1, D 12=p 1A2G− \(\left(\mathit{p}_{1A}\right)\) \(\left(\mathit{p}_{2G}\right)\) where D 12 is a measure of LD between sites 1 and 2, p 1A2G is the frequency of sequences that contain an A at site 1 and a G at site 2, p 1A is the marginal frequency of allele A at site 1, and p 2G is the marginal frequency of allele G at site 2. Using this formula, D = 0.5 − (0.5)(0.5) = 0.25 for the data in Figure 1A and D= 0.25 − (0.5)(0.5) = 0.00 for the data in Figure 1B. Note that the absolute value of D is symmetric, in that it does not matter which alleles are measured and associated. For example, one can measure the frequency of either A or T at site 1 to calculate D. Here, we demonstrate D on haplotypic data, but D also is estimated routinely from unphased diploid data. D incorporates information about allelic association and allele frequencies. For example, imagine that only one of eight sequences in Figure 1Acontained an A at site 1 and a G at site 2 (with the seven remaining sequences containing a T and a C). Although the two sites are still in complete disequilibrium, the change in frequency of the A and G alleles leads to D = 0.125 − (0.125)(0.125) = 0.109. Because of this frequency dependence, values of D are expected to vary widely over many pairs of SNPs, even when sites are in complete LD. There are two ways to address the dependence of D on marginal allele frequencies. The first is to ignore low-frequency variants, which contribute inordinately to variation in D. Most empirical studies of LD ignore alleles with marginal frequencies of <5 or 10%. The second solution is to use measures of allelic association that are normalized, to some extent, with respect to allele frequencies. The most common normalized measure of D is Lewontin's D′ (Lewontin, 1964). D′ has the desirable property that its absolute value is equal to 1.0 if two SNPs are in complete LD or if there are only three gametic types in the sample (Figure 1). For this reason, D′ has intuitive appeal; with only three gametic types, one need not invoke recombination to explain patterns of variation (Figure 1). A drawback of D′ is that its sampling properties are poorly understood when |D′| < 1.0. A modern alternative to normalization, based on the likelihood of observed LD conditional on allele frequencies, is rapidly gaining acceptance (Hudson, 2001). Another measure that deserves mention is r 2, which is equal to D 2 divided by the product of the allele frequencies at the two loci. Hi