Livestock Improvement Corporation, Private Bag 3016, Hamilton 3240, New Zealand.
J Anim Sci. 2023 Jan 3;101. doi: 10.1093/jas/skac272.
For a few decades, animal models (AMs) in the form of best linear unbiased prediction (BLUP) have been used for the genetic evaluation of animals. An equation system is set in the order of all the effects in the model, including all the animals in the pedigree. Solving these large equation systems has been a challenge. Reduced AM (RAM) was introduced in 1980, which allowed setting up equations for parents instead of all animals. That greatly reduced the number of equations to be solved. The RAM is followed by a back-solving step, in which progenies' breeding values are obtained conditional on parental breeding values. Initially, pedigree information was utilized to model genetic relationships between animals. With the availability of genomic information, genomic BLUP (GBLUP), single-step GBLUP (ssGBLUP), and single-step marker models were developed. Single-step methods utilize pedigree and genomic information for simultaneous genetic evaluation of genotyped and nongenotyped animals. There has been a shortage of studies on RAM development for genetic evaluation models utilizing genomic information. This study extended the concept of RAM from BLUP to the single-step methods. Using example data, three RAMs were described for ssGBLUP. The order of animal equations was reduced from the total number of animals to (1) genotyped animals and nongenotyped parents, (2) genotyped animals and nongenotyped phenotyped animals, and (3) genotyped animals and nongenotyped parents of phenotyped nongenotyped nonparents. Solutions for the remaining animals are obtained following a back-solving step. All the RAMs produced identical results to the full ssGBLUP. Advances in computational hardware have alleviated many computational limitations, but, on the other hand, the size of data is growing rapidly by the number of animals, traits, phenotypes, genotypes, and genotype density. There is an opportunity for a RAM comeback for the single-step methods to reduce the computational demands by reducing the number of equations.
几十年来，动物模型（AMs）一直以最佳线性无偏预测（BLUP）的形式用于动物的遗传评估。在模型的所有效应的顺序中设置一个方程组，包括系谱中的所有动物。解决这些大型方程组一直是一个挑战。1980 年引入了简化动物模型（RAM），它允许为父母而不是所有动物设置方程。这大大减少了要解决的方程组的数量。RAM 后面是一个反向求解步骤，其中后代的育种值是根据父母的育种值获得的。最初，系谱信息用于模拟动物之间的遗传关系。随着基因组信息的可用性，开发了基因组 BLUP（GBLUP）、一步 GBLUP（ssGBLUP）和单步标记模型。单步方法利用系谱和基因组信息对已基因型和未基因型动物进行同时遗传评估。利用基因组信息开发遗传评估模型的 RAM 发展研究一直不足。本研究将 RAM 的概念从 BLUP 扩展到单步方法。使用示例数据，描述了三种用于 ssGBLUP 的 RAM。动物方程的顺序从动物总数减少到（1）基因型动物和未基因型父母，（2）基因型动物和未基因型表型动物，和（3）基因型动物和未基因型表型非亲本父母。通过反向求解步骤获得剩余动物的解。所有的 RAM 都产生了与完整的 ssGBLUP 相同的结果。计算硬件的进步缓解了许多计算限制，但另一方面，数据的大小正在迅速增长，包括动物数量、性状、表型、基因型和基因型密度。单步方法的 RAM 可能会重新出现，通过减少方程组的数量来降低计算需求。
