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；SNPs)作为预测变量被纳入统计模型，以达到改进动物基因组评估的目的。这导致更准确地估计尚未表型的动物的育种值，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，效应大小也是一个相关参数。特别是，就像今天可用的高维SNP数据一样，致病变异可以精确地定位到基因组上的特定碱基对。由于维度灾变，效果估计的精度只能用耗时的计算方法来近似；它不是以解析公式给出的。由于估计的精确度影响显著性检验的结果，因此可靠地识别原因变量是复杂的。该项目旨在从理论上确定SNP效应估计的标准误差以及检验其重要性的能力，特别是在SNP数量超过个体数量的情况下。本项目中开发的理论将通过公开的模拟和经验数据进行验证。此外，当计划新的实验时，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目标人群中进行任何基因组评估之前确定最低所需样本量。目标人群可能包括半同胞家庭和/或全同胞家庭。由于目标个体的基因分型数据通常不是先验的，我们将采用可以从父母基因组信息中推断出的基因类型的理论分布。最优育种设计的标准将通过考虑必须由实验者规定的特定性状参数和特定于种群的参数来得出SNPs的理论分布。最终目标是提供对实际应用有用的实验设计，在这些实验设计中，可以阐明所选性状的遗传结构。

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.