Linkage disequilibrium in humans: models and data

Abstract

In this review, we describe recent empirical and theoretical work on the extent of linkage disequilibrium (LD) in the human genome, comparing the predictions of simple population-genetic models to available data. Several studies report significant LD over distances longer than those predicted by standard models, whereas some data from short, intergenic regions show less LD than would be expected. The apparent discrepancies between theory and data present a challenge-both to modelers and to human geneticists-to identify which important features are missing from our understanding of the biological processes that give rise to LD. Salient features may include demographic complications such as recent admixture, as well as genetic factors such as local variation in recombination rates, gene conversion, and the potential segregation of inversions. We also outline some implications that the emerging patterns of LD have for association-mapping strategies. In particular, we discuss what marker densities might be necessary for genomewide association scans.

Figure 1

Simulated decay of , as a function of genetic distance, for five independent replicates for each of four demographic models. Each plot shows the results for one sample of 400 chromosomes simulated under a particular demographic model of population history. On the X-axis is the genetic distance, in centimorgans, separating pairs of markers; at the genome average recombination rate of ≈1 cM/Mb, this is equivalent to distances in megabases. Each plot shows all pairwise comparisons for 40 biallelic markers, chosen randomly from the available markers whose minor-allele frequencies were ⩾.2. Points above the horizontal lines are in significant LD at the .05 level; for a sample size of 400, this corresponds to a value of r=.098 (see the “Models and Measures of LD” section). The first column shows results for a panmictic population of constant size N_e=10⁴; the second column shows results for the model of population growth considered by Kruglyak and described in the “Model Predictions” section; and the third and fourth columns show results for a simple model of population structure. In the third column, all individuals are drawn from the same subpopulation; in the last column they are drawn equally from both subpopulations. We used the symmetric two-island migration model (Wright 1951), with N_e=5,000 for each deme, and migration rates of one individual per deme per generation.

Figure 2

Decay of expected value of , as a function of genetic distance, for different growth models (sample size of 100 chromosomes). From top to bottom, the four models are as follows: constant population size of N_e=10⁴ (unbroken line); population-growth onset 500 generations ago—that is, 10⁴ years ago, under the assumption that there are 20 years per generation (dotted line); population-growth onset 5,000 generations ago (short-dashed line); and the model used by Kruglyak (see the “Model Predictions” section) (long-dashed line). In two growth models (dotted line and short-dashed line), the current population was fixed at 10⁵. Except in the Kruglyak model, the parameters were chosen to match the amount of genetic diversity seen in humans (see text). In each of 10⁴ simulations, 10 SNPs with a minor-allele frequency ⩾.2 were chosen.

Figure 3

Plots of , as a function of physical distance (in kb), for SNP data from five regions (Dunning et al. ; Taillon-Miller et al. ; Abecasis et al. 2001). On each plot, points above the unbroken line are in significant LD at the .05 level, and points above the dotted line correspond to what Kruglyak has called “useful LD”; these lines are set at r=.316, the equivalent of r²=.1.

Figure 4

Simulated decay of (+) and (♦), as a function of genetic distance. These data correspond to one realization from figure 1 (first column, second row), simulated under a model of constant population size (i.e., N_e=10⁴) and random mating.