Linkage analysis of a complex disease through use of admixed populations

Abstract

Linkage disequilibrium arising from the recent admixture of genetically distinct populations can be potentially useful in mapping genes for complex diseases. McKeigue has proposed a method that conditions on parental admixture to detect linkage. We show that this method tests for linkage only under specific assumptions, such as equal admixture in the parental generation and admixture that occurs in a single generation. In practice, these assumptions are unlikely to hold for natural populations, resulting in an inflation of the type I error rate when testing for linkage by this method. In this article, we generalize McKeigue's approach of testing for linkage to allow two different admixture models: (1) intermixture admixture and (2) continuous gene flow. We calculate the sample size required for a genomewide search by this method under different disease models: multiplicative, additive, recessive, and dominant. Our results show that the sample size required to obtain 90% power to detect a putative mutant allele at a genomewide significance level of 5% can usually be achieved in practice if informative markers are available at a density of 2 cM.

Figure 1

Two admixture models used in the calculation of ancestral probability. Left panel, IA model. Right panel, CGF model.

Figure 2

IA model. Number of cases required for 90% power to detect linkage at a significance level of .001 at different population risk ratios and recombination fractions between marker and disease loci under four genetic models: multiplicative, additive, recessive (with the low-risk allele in the low-risk population), and dominant (with the high-risk allele in the high-risk population). Upper panels, Total contributions of the parental populations X and Y are 50%/50% (λ=1.0). Lower panels, Total contributions of parental populations X and Y are 74%/26% (λ=0.52). Samples are drawn from the 10th generation.

Figure 3

CGF model. Number of cases required for 90% power to detect linkage at a significance level of .001 at different population risk ratios and recombination fractions between marker and disease loci under four genetic models: multiplicative, additive, recessive (with the low-risk allele in the low-risk population), and dominant (with the high-risk allele in the high-risk population). Upper panels, Total contributions of parental populations X and Y are 50%/50% (λ=1). Lower panels, total contributions of parental population X and Y are 74%/26% (λ=0.06). Samples are drawn from the 10th generation.

Figure 4

Number of cases required for 90% power to detect linkage at a genomewide significance level of .05, when 3,000 markers are evenly placed along the genome, under four genetic models: multiplicative, additive, recessive (with the low-risk allele in the low-risk population), and dominant (with the high-risk allele in the high-risk population). The population has been admixed for 10 generations, according to the CGF model. Total contributions of parental populations X and Y are 74%/26% (λ=0.06). Left, X has a higher population risk than Y; the curve for the dominant model does not appear because the number is >2,500. Right, Y has a higher population risk than X. Samples are drawn from the 10th generation.

Figure 5

Type I error rate when we test linkage by testing r=1 under four genetic models: multiplicative, additive, recessive (with the low-risk allele in the low-risk population), and dominant (with the high-risk allele in the high-risk population). Total contributions of the parental populations X and Y are 74%/26%. Left, IA model. Right, CGF model. Two hundred fifty cases are drawn from the 10th generation.

Figure 6

Histograms of estimated ancestral proportions (Π) across the markers; 1,000 markers on 1,000 individuals were generated. A, Data simulated using the IA model at a marker density of 1 marker/cM. B, Data simulated using the CGF model at a marker density of 1 marker/cM. C, Data simulated using the IA model at a marker density of 1 marker/5cM. D, Data simulated using the CGF model at a marker density of 1 marker/5 cM.

Figure 7

Comparisons of a person’s estimated and true ancestral proportion; 1,000 markers were generated on 1,000 individuals. A–D, Known ancestral allele frequencies. E–H, Ancestral allele frequencies estimated by STRUCTURE. A and E, Data simulated using the IA model at a marker density of 1 marker/cM. B and F, Data simulated using the CGF model at a marker density of 1 marker/cM. C and G, Data simulated using the IA model at a marker density of 1 marker/5 cM. D and H, Data simulated using the CGF model at a marker density of 1 marker/5 cM.