UMR GenPhySE, INRA, Castanet-Tolosan 31320, France.
Instituto Nacional de Investigación Agropecuaria (INIA), 11100 Montevideo, Uruguay.
J Dairy Sci. 2020 Apr;103(4):3363-3367. doi: 10.3168/jds.2019-17750. Epub 2020 Feb 11.
The genomic measure of inbreeding is closer to the actual inbreeding than the pedigree-based measure. However, it cannot be computed for ungenotyped animals. An estimate of genomic inbreeding comes from the diagonal of matrix H used in single-step methods. This matrix projects genomic relationships to all ungenotyped members of the pedigree. The diagonal element of H gives an estimate of the genomic inbreeding coefficient. However, so far no computational methods are available to compute the diagonal of H. Here we propose 3 exact methods to compute this diagonal. The first uses an already-existing algorithm to compute, for each ungenotyped individual, products of the form Hx to obtain the corresponding diagonal element of H. The second method computes, for each ungenotyped individual, a term that can be written as a quadratic form involving pedigree and genomic relationships. For both methods, the computational burden is linear in the number of ungenotyped animals. The last method reorders the computations of the second method so that they become linear in the number of genotyped animals, which is usually much smaller. We tested the methods in 3 small data sets (with ~2,000 genotyped animals and 30,000-500,000 animals in pedigree) and in a large simulated population (with 1,220,000 animals in pedigree and 36,000 genotyped animals). Tests resulted in satisfactory computing times (<10 min in the largest example using 10 parallel threads). Computing times were much shorter for the third method, as expected. Using these methods, estimates of genomic inbreeding in ungenotyped animals can be obtained on a regular basis.
遗传交配系数的基因组度量比基于系谱的度量更接近实际的近交程度。然而，对于未基因型动物，无法计算其遗传交配系数。基因组近交系数的估计值来自于单步方法中使用的矩阵 H 的对角线。该矩阵将基因组关系投影到系谱中所有未基因型个体上。H 的对角元素给出了基因组近交系数的估计值。然而，到目前为止，还没有计算 H 对角线的计算方法。在这里，我们提出了 3 种精确的方法来计算这个对角线。第一种方法使用现有的算法，为每个未基因型个体计算形式为 Hx 的乘积，以获得 H 的相应对角元素。第二种方法为每个未基因型个体计算一个可以表示为涉及系谱和基因组关系的二次形式的项。对于这两种方法，计算负担都与未基因型个体的数量呈线性关系。最后一种方法重新安排了第二种方法的计算，使它们与基因型个体的数量呈线性关系，而基因型个体的数量通常要小得多。我们在 3 个小数据集（约 2000 个基因型个体和 300000-500000 个系谱个体）和一个大型模拟种群（1220000 个系谱个体和 36000 个基因型个体）中测试了这些方法。测试结果表明，计算时间令人满意（在使用 10 个并行线程的最大示例中，计算时间不到 10 分钟）。正如预期的那样，第三种方法的计算时间要短得多。使用这些方法，可以定期获得未基因型动物的基因组近交系数估计值。
