Selecting the number of multiplicative terms in AMMI and GGE models

在多个环境中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-环境互作，这使得选择最好的品种变得复杂。因此，对相互作用的仔细建模和研究对于育种计划的成功至关重要。用加性主效应和乘性互作(AMMI)模型和GGE(GGE)模型等具有乘性项的基因型-环境互作模型常用于分析MET数据。它们的流行源于模型拟合的多种用途，例如为培育当地适应的品种描绘大环境，以及获得视觉显示的便利，例如可以研究基因-环境相互作用模式的双曲线图。使用这些模型的一个关键问题是选择要拟合的乘性项的数量。如果拟合项太少，由此得到的对基因-环境平均值的估计是有偏差的，而拟合项太多则会导致低效估计受到夸大方差的影响。到目前为止，已经为模型选择问题提出了几种程序，包括显著性检验和交叉验证程序。本研究的目的是开发一种新的方法来选择AMMI和GGE模型中的乘性项数，并使用来自德国植物育种和品种测试项目的MET数据以及蒙特卡洛模拟对这些方法进行经验评估和比较。

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.