The effect that genotyping errors have on the robustness of common linkage-disequilibrium measures

Abstract

The rapid development of a dense single-nucleotide-polymorphism marker map has stimulated numerous studies attempting to characterize the magnitude and distribution of background linkage disequilibrium (LD) within and between human populations. Although genotyping errors are an inherent problem in all LD studies, there have been few systematic investigations documenting their consequences on estimates of background LD. Therefore, we derived simple deterministic formulas to investigate the effect that genotyping errors have on four commonly used LD measures-D', r, Q, and d-in studies of background LD. We have found that genotyping error rates as small as 3% can have serious affects on these LD measures, depending on the allele frequencies and the assumed error model. Furthermore, we compared the robustness of D', r, Q, and d, in the presence of genotyping errors. In general, Q and d are more robust than D' and r, although exceptions do exist. Finally, through stochastic simulations, we illustrate how genotyping errors can lead to erroneous inferences when measures of LD between two samples are compared.

Figure 1

Symbolic and mathematical representations of error models used in analyses. The genotyping-error rates at loci 1 and 2 are denoted as μ and ν, respectively. Panels A and B correspond to the SEM and the DEM, respectively.

Figure 2

The effect that genotyping errors have on FT values, as a function of genotyping-error rate. In panel A, the haplotype frequencies are P_AB=.3, P_Ab=.3, P_aB=.1, and P_ab=.3; in panel B, the haplotype frequencies are P_AB=.1, P_Ab=.4, P_aB=.3, and P_ab=.2. Note that, in panel B, the lines corresponding to r and Q for the SEM are nearly superimposable.

Figure 3

Comparison of the robustness of D′, r, Q, and d. The ratio of FT values is plotted versus P_AB. The curves correspond to the ratios d/r (blue), r/D^′ (green), r/Q (orange), Q/d (red), Q/D^′ (black), and D^′/d (brown). In panel A, the haplotype frequencies are P_Ab=P_aB=0 and P_ab=1-P_AB. In panel B, the haplotype frequencies are P_Ab=P_aB=.25 and P_ab=.5-P_AB. The genotyping-error rate was set at 5%.

Figure 4

Distribution of the difference, in absolute value of D′, between two simulated samples, in the presence of genotyping errors. In panel A, the allele frequencies are P_A=P_B=.5; in panel B, the allele frequencies are P_A=P_B=.8. For both panels, the value of in the absence of genotyping errors is 0. Note that as the error rates increase the distribution begins to shift away from the expected difference of 0.