Comparison of linkage disequilibrium estimated from genotypes versus haplotypes for crossbred populations

Background Linkage disequilibrium (LD) is commonly measured based on the squared coefficient of correlation (r^2) between the alleles at two loci that are carried by haplotypes. LD can also be estimated as the r^2 between unphased genotype dosage at two loci when the allele frequencies and inbreeding coefficients at both loci are identical for the parental lines. Here, we investigated whether r^2 for a crossbred population (F1) can be estimated using genotype data. The parental lines of the crossbred (F1) can be purebred or crossbred. Methods We approached this by first showing that inbreeding coefficients for an F1 crossbred population are negative, and typically differ in size between loci. Then, we proved that the expected r^2 computed from unphased genotype data is expected to be identical to the r^2 computed from haplotype data for an F1 crossbred population, regardless of the inbreeding coefficients at the two loci. Finally, we investigated the bias and precision of the r^2 estimated using unphased genotype versus haplotype data in stochastic simulation. Results Our findings show that estimates of r^2 based on haplotype and unphased genotype data are both unbiased for different combinations of allele frequencies, sample sizes (900, 1800, and 2700), and levels of LD. In general, for any allele frequency combination and r^2 value scenarios considered, and for both methods to estimate r^2 , the precision of the estimates increased, and the bias of the estimates decreased as sample size increased, indicating that both estimators are consistent. For a given scenario, the r^2 estimates using haplotype data were more precise and less biased using haplotype data than using unphased genotype data. As sample size increased, the difference in precision and biasedness between the r^2 estimates using haplotype data and unphased genotype data decreased. Conclusions Our theoretical derivations showed that estimates of LD between loci based on unphased genotypes and haplotypes in F1 crossbreds have identical expectations. Based on our simulation results, we conclude that the LD for an F1 crossbred population can be accurately estimated from unphased genotype data. The results also apply for other crosses (F2, F3, Fn, BC1, BC2, and BCn), as long as (selected) individuals from the two parental lines mate randomly.