Linkage disequilibrium (LD) is commonly measured based on the squared coefficient of correlation $$\left({r}^{2}\right)$$ 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. 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. 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. 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.

中文翻译：

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从杂交种群的基因型与单倍型估计的连锁不平衡的比较

连锁不平衡 (LD) 通常基于单倍型携带的两个基因座处的等位基因之间的相关平方系数 $$\left({r}^{2}\right)$$ 来测量。当两个基因座的等位基因频率和近交系数对于亲本系相同时，LD 也可以估计为两个基因座的非定相基因型剂量之间的 $${r}^{2}$$。在这里，我们调查了是否可以使用基因型数据估计杂交种群 (F1) 的 $${r}^{2}$$。杂交（F1）的亲本系可以是纯种或杂交。我们首先表明 F1 杂交种群的近交系数是负的，并且基因座之间的大小通常不同。然后，我们证明了从非阶段性基因型数据计算的预期 $${r}^{2}$$ 预期与从 F1 杂交种群的单倍型数据计算的 $${r}^{2}$$ 相同，无论两个位点的近交系数。最后，我们研究了随机模拟中使用非相位基因型与单倍型数据估计的 $${r}^{2}$$ 的偏差和精度。我们的研究结果表明，对于等位基因频率、样本量（900、1800 和 2700）和 LD 水平的不同组合，基于单倍型和非定相基因型数据的 $${r}^{2}$$ 估计值都是无偏的。一般来说，对于任何等位基因频率组合和所考虑的 $${r}^{2}$$ 值场景，以及对于估计 $${r}^{2}$$ 的两种方法，估计的精度都会提高，并且估计的偏差随着样本量的增加而减少，表明两个估计量是一致的。对于给定的场景，使用单倍型数据的 $${r}^{2}$$ 估计比使用单倍型数据更精确且偏差更小。随着样本量的增加，使用单倍型数据和未定相基因型数据的 $${r}^{2}$$ 估计之间的精度和偏差差异减小。我们的理论推导表明，基于 F1 杂交种中未定相基因型和单倍型的基因座之间的 LD 估计具有相同的预期。根据我们的模拟结果，我们得出结论，可以从未定相的基因型数据中准确估计 F1 杂交种群的 LD。该结果也适用于其他杂交（F2、F3、Fn、BC1、BC2 和 BCn），只要来自两个亲本系的（选定的）个体随机交配。