Estimating heritability in plant breeding programs

遗传率被定义为遗传变异和表型变异的比值。它是评价植物育种计划的关键指标。例如，它可以用来计算对选择的响应。因此，在植物育种试验的分析中，遗传力通常被评估。在植物育种中使用的标准方程，例如对选择的响应，假设一个简单的数据结构。具体来说，假设数据遵循一个简单的混合模型，具有正态分布的随机效应，并且数据是平衡的。这些简单的假设在实际的植物育种计划中几乎总是被违背。通常，这些数据是不平衡的。例如，并非所有的基因型都可以在所有环境中进行测试。此外，在个别环境中的试验几乎总是使用某种形式的不完全阻塞。此外，空间分析方法正变得越来越流行。在这些情况下，表型通常是一个调整后的平均值，它不符合遗传力的共同定义所需的假设，因为这些平均值是相关的，它们的方差可能不是恒定的。此外，表型通常是通过最佳线性无偏预测来估计的，例如为了利用系谱或全基因组标记信息，这进一步使遗传力的评估复杂化。进一步的两个问题是，许多性状被评估为计数或序数分数，这不符合正态性假设，并且可能在同一观察单元（地块，植物等）上进行重复测量，在这种情况下需要考虑序列相关性。在这些情况下，如何最好地评估遗传性并不明显。因此，该项目的目标是提出新的方法来估计遗传力，这些方法是专门为不平衡的植物育种数据设计的，并将这些方法与现有的建议进行比较，这些方法都是使用真实的植物育种数据集以及蒙特卡罗模拟。此外，仅限于正态分布数据的现有方法将扩展到(i)非正态数据，特别是可以通过广义线性混合模型（GLMM）建模的计数数据，以及（ii）重复测量数据。

Heritability is defined as the ratio of genetic and phenotypic variance. It is a key quantity for the evaluation of plant breeding programs. For example, it may be used to compute the response to selection. Thus, heritability is routinely assessed in the analysis of plant breeding trials. Standard equations used in plant breeding, such as for the response to selection, assume a simple data structure. Specifically, it is assumed that the data follow a simple mixed model with normally distributed random effects and that the data is balanced. These simple assumptions are almost always violated in real plant breeding programs. Typically, such data are unbalanced. For example, not all genotypes may have been tested in all environments. Moreover, trials in individual environments almost always use some form of incomplete blocking. Also, spatial analysis methods are becoming increasingly popular. In these situations, the phenotype is usually an adjusted mean, which does not meet the assumptions needed for the common definitions of heritability, because these means are correlated and their variance may not be constant. Moreover, the phenotype is often estimated by best linear unbiased prediction, for example in order to exploit pedigree or genome-wide marker information, which further complicates the assessment of heritability.Two further problems are that many traits are assessed as counts or ordinal scores, which do not meet the normality assumption, and that repeated measurements may be taken on the same observational unit (plot, plant etc), in which case serial correlation needs to be taken into account. In these situations, it is not obvious how heritability should best be assessed.The objective of this project is therefore to propose new methods for estimating heritability that are specifically designed for unbalanced plant breeding data and to compare these methods to existing proposals both empirically using real plant breeding data sets as well as Monte Carlo simulation. Moreover, existing approaches that are exclusively restricted to normally distributed data will be extended (i) to non-normal data, in particular to count data that can be modelled by generalized linear mixed models (GLMM), as well as (ii) to repeated measures data.