The role of the theoretical covariance between SNPs in the design of experiments in genomic evaluations

在动物育种中，分子数据（例如，单核苷酸多态性；SNPs）被纳入统计模型作为预测变量，以达到改进的动物基因组评估。这可以更精确地估计尚未表型的动物的育种价值，这对育种目的很重要，并使一些性状的遗传结构得以阐明。不仅基因组上的位置是一个相关参数，而且效应大小也是一个相关参数。特别是，与今天可用的高维SNP数据一样，致病变异可以精确定位到基因组上的特定碱基对。由于维数的限制，效应估计的精度只能用耗时的计算方法来逼近；它不是用解析公式给出的。由于估计的精度会影响显著性检验的结果，因此病因变异的可靠识别是复杂的。该项目旨在从理论上确定snp效应估计的标准误差和检验其显著性的能力，特别是在snp数量超过个体数量的情况下。在这个项目中发展的理论将通过公开的模拟和经验数据进行验证。此外，在计划新的实验时，必须瞄准足够大的功率来测试SNP效应。因此，在第二阶段，该项目将调查如何在对目标人群进行任何基因组评估之前确定所需的最小样本量。目标人群可能由同父异母和/或全同胞家庭组成。由于目标个体的基因型数据通常是不可先验的，我们将采用可以从亲代基因组信息推断出的基因型理论分布。最佳育种设计的标准将考虑性状特异性参数和种群特异性参数，这些参数必须由实验者规定，而种群特异性参数是推导SNPs理论分布的依据。最终目标是提供对实际应用有用的实验设计，从而阐明选定性状的遗传结构。

In animal breeding, molecular data (e.g., single nucleotide polymorphisms; SNPs) are incorporated as predictor variables in statistical models to reach an improved genomic evaluation of animals. This leads to more precisely estimated breeding values of not-yet phenotyped animals, which is important for breeding purposes, and enables the genetic architecture of some traits to be elucidated. Not only is the position on the genome a relevant parameter but so too is the effect size. Particularly, as with the high-dimensional SNP data that are available today, a causative variant can be pinpointed to a specific base pair on the genome. Due to the curse of dimensionality, the precision of effect estimates can only be approximated with time-consuming computational methods; it is not given in an analytical formula. As precision of estimates influences the outcome of testing for significance, the reliable identification of causative variants is complicated. The project aims to theoretically determine the standard error of SNP-effect estimates and the power of testing their significance, particularly for situations where the number of SNPs exceeds the number of individuals. The theory developed in this project will be validated with simulated and empirical data that are publicly available. Furthermore, when planning new experiments, it is essential to aim at a sufficiently large power to test the SNP effects. Thus, at a second stage, the project will investigate how a minimum required sample size can be determined prior to any genomic evaluation in a target population. The target population may consist of a mixture of half- and/or full-sib families. As genotypic data of target individuals are typically not available a-priori, we will employ the theoretical distribution of genotypes which can be inferred from parental genome information. Criteria for an optimal breeding design will be concluded by taking into account the trait-specific parameters, which have to be stipulated by the experimenter, and population-specific parameters, from which the theoretical distribution of SNPs is derived. The ultimate goal is to provide experimental designs useful for practical applications in which the genetic architecture of selected traits can be elucidated.