Selecting the number of multiplicative terms in AMMI and GGE models

在多种环境下进行的一系列品种和植物育种试验，即所谓的多环境试验（MET），是开发和推广新作物品种的基础。MET的一个显著特征是存在基因型-环境相互作用，这使得最佳品种的选择变得复杂。因此，仔细建模和相互作用的研究对于育种计划的成功至关重要。基因型-环境相互作用的乘法项模型，如加性主效应和乘法相互作用（AMMI）模型和基因型和基因型-环境（GGE）模型通常用于分析MET数据。这些模型的流行源于其多种用途，如描绘大环境以培育地方适应性品种，以及获得可视化显示（如双标图）以研究基因型-环境互作模式。使用这些模型的一个关键问题是要拟合的乘法项的数目的选择。如果拟合的项太少，则得到的基因型-环境平均值的估计是有偏差的，而拟合的项太多则会导致效率低下的估计，从而导致方差膨胀。到目前为止，已经提出了几个程序的模型选择问题，包括显着性测试和交叉验证程序。但是，经验经验还没有确定一个单一的最佳策略来确定乘法项的数量，到目前为止提出的每一个程序都有一些缺点。拟议项目的目的是开发新的方法来选择AMMI和GGE模型中的乘法项的数量，并评估和比较这些经验的竞争方法，使用德国植物育种和品种测试计划的MET数据以及Monte Carlo模拟。

Series of variety and plant breeding trials conducted at multiple environments, so-called multi-environment trials (MET), are the basis for the development and dissemination of new crop varieties. A salient feature of MET is the presence of genotype-environment interaction, and this complicates the selection of the best varieties. Careful modelling and study of the interaction is therefore of utmost importance for the success of breeding programs. Models with multiplicative terms for genotype-environment interaction such as the Additive Main effects and Multiplicative Interaction (AMMI) model and the Genotype and Genotype-Environment (GGE) model are commonly used for analysing MET data. Their popularity stems from the multiple uses of the model fits, such as the delineation of mega-environments for breeding locally adapted varieties and the facility to obtain visual displays such as the biplot which allow studying the genotype-environment interaction pattern.A key problem in the use of these models is the choice of the number of multiplicative terms to be fitted. If too few terms are fitted, the resulting estimates of genotype-environment means are biased, whereas fitting too many terms leads to inefficient estimates suffering from inflated variance. Several procedures have been proposed so far for the model selection problem, including significance tests and cross-validation procedures. But empirical experience has not yet identified a single best strategy to determine the number of multiplicative terms, and each of the procedures proposed so far has some drawbacks.The purpose of the proposed project is to develop new methods to select the number of multiplicative terms in AMMI and GGE models and to evaluate and compare these empirically to contending approaches, using MET data from German plant breeding and variety testing programs as well as Monte Carlo simulation.