Maximum likelihood estimation of linkage disequilibrium in half-sib families

Abstract

Maximum likelihood methods for the estimation of linkage disequilibrium between biallelic DNA-markers in half-sib families (half-sib method) are developed for single and multifamily situations. Monte Carlo computer simulations were carried out for a variety of scenarios regarding sire genotypes, linkage disequilibrium, recombination fraction, family size, and number of families. A double heterozygote sire was simulated with recombination fraction of 0.00, linkage disequilibrium among dams of δ=0.10, and alleles at both markers segregating at intermediate frequencies for a family size of 500. The average estimates of δ were 0.17, 0.25, and 0.10 for Excoffier and Slatkin (1995), maternal informative haplotypes, and the half-sib method, respectively. A multifamily EM algorithm was tested at intermediate frequencies by computer simulation. The range of the absolute difference between estimated and simulated δ was between 0.000 and 0.008. A cattle half-sib family was genotyped with the Illumina 50K BeadChip. There were 314,730 SNP pairs for which the sire was a homo-heterozygote with average estimates of r2 of 0.115, 0.067, and 0.111 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. There were 208,872 SNP pairs for which the sire was double heterozygote with average estimates of r2 across the genome of 0.100, 0.267, and 0.925 for half-sib, Excoffier and Slatkin (1995), and maternal informative haplotypes methods, respectively. Genome analyses for all possible sire genotypes with 829,042 tests showed that ignoring half-sib family structure leads to upward biased estimates of linkage disequilibrium. Published inferences on population structure and evolution of cattle should be revisited after accommodating existing half-sib family structure in the estimation of linkage disequilibrium.

Figure 1

Bias in the estimation of LD using the Excoffier and Slatkin (1995) algorithm in a half-sib family from a double heterozygote sire. (A) $f_T=0.5$, $f_M=0.5$, (B) $f_T=0.4$, $f_M=0.1$

Figure 2

Bias in the estimation of LD using maternal haplotypes in a half-sib family from a double heterozygote sire. (A) $f_T=0.5$, $f_M=0.5$, (B) $f_T=0.4$, $f_M=0.1$.

Figure 3

Q-Q plots of likelihood-ratio test using the multi-half EM algorithm on 10⁶ replicates. Quantiles LRT are the quantiles from simulated data for c = 0 and under the null hypothesis (δ = 0).

Figure 4

Average values of estimates r² across the genome using half-sib (HS), Excoffier and Slatkin (ES), and maternal informative haplotypes (MIH) methods for maximum distances between SNPs of 10, 20, 30, 40, and 50 Mb.