Orthogonal Estimates of Variances for Additive, Dominance, and Epistatic Effects in Populations
Orthogonal Estimates of Variances for Additive, Dominance, and Epistatic Effects in Populations
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DOI：
10.1534/genetics.116.199406
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发表时间：
2017-07-01
期刊：
影响因子：
3.3
通讯作者：
Varona, Luis
中科院分区：
文献类型：
--
作者：
Vitezica, Zulma G.;Legarra, Andres;Varona, Luis
基于多标记的基因组预测方法在复杂性状的预测和分析中具有潜在的非加性效应。然而，大多数发展假设哈迪-温伯格均衡（HWE）。基因组选择的统计方法，在一般情况下解释显性和上位性，而不假设HWE（例如，杂交或纯合系）。我们的方法扩展了自然和正交相互作用（NOIA）方法，该方法基于基因型（非等位基因）频率构建发病率矩阵，以包括基因组评估背景下任意数量的相互作用位点的全基因组上位性。这导致方差的正交划分，否则这是不必要的。我们还提出了分区的方差作为一个函数的基因型值和频率以下Cockerham的正交对比方法。然后，我们证明了第一次，即使不是在HWE，多位点NOIA方法是等价的，以构建上位基因组关系矩阵的高阶相互作用，使用阿达玛产品的添加剂和显性基因组正交关系。然而，需要基于关系矩阵的迹线的标准化。我们说明这些结果与两个模拟的F-1（而不是在HWE）人口，无论是在连锁平衡（LE），或在连锁不平衡（LD）和发散选择，和纯生物显性成对上位性。在LE情况下，使用NOIA基因组关系获得了正确和正交的方差估计值，但如果假设HWE构建关系，则无法获得。对于LD模拟，由于F1与HWE的偏差较小，因此差异较小。错误地假设HWE来建立基因组关系和估计方差分量产生有偏估计，膨胀总遗传方差，并且估计不是经验正交的。建立基因组关系的NOIA方法，再加上使用Hadamard产品的上位性条款，允许获得正确的估计，无论是在HWE或不在HWE的人口，并扩展到任何顺序的上位性相互作用。
Genomic prediction methods based on multiple markers have potential to include nonadditive effects in prediction and analysis of complex traits. However, most developments assume a Hardy-Weinberg equilibrium (HWE). Statistical approaches for genomic selection that account for dominance and epistasis in a general context, without assuming HWE (e.g., crosses or homozygous lines), are therefore needed. Our method expands the natural and orthogonal interactions (NOIA) approach, which builds incidence matrices based on genotypic (not allelic) frequencies, to include genome-wide epistasis for an arbitrary number of interacting loci in a genomic evaluation context. This results in an orthogonal partition of the variances, which is not warranted otherwise. We also present the partition of variance as a function of genotypic values and frequencies following Cockerham's orthogonal contrast approach. Then we prove for the first time that, even not in HWE, the multiple-loci NOIA method is equivalent to construct epistatic genomic relationship matrices for higher-order interactions using Hadamard products of additive and dominant genomic orthogonal relationships. A standardization based on the trace of the relationship matrices is, however, needed. We illustrate these results with two simulated F-1 (not in HWE) populations, either in linkage equilibrium (LE), or in linkage disequilibrium (LD) and divergent selection, and pure biological dominant pairwise epistasis. In the LE case, correct and orthogonal estimates of variances were obtained using NOIA genomic relationships but not if relationships were constructed assuming HWE. For the LD simulation, differences were smaller, due to the smaller deviation of the F1 from HWE. Wrongly assuming HWE to build genomic relationships and estimate variance components yields biased estimates, inflates the total genetic variance, and the estimates are not empirically orthogonal. The NOIA method to build genomic relationships, coupled with the use of Hadamard products for epistatic terms, allows the obtaining of correct estimates in populations either in HWE or not in HWE, and extends to any order of epistatic interactions.