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），是开发和推广作物新品种的基础。MET的一个显著特征是基因型-环境相互作用的存在，这使最佳品种的选择复杂化。因此，对这种相互作用进行仔细的建模和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，如可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。它们的流行源于模型拟合的多种用途，例如为培育本地适应品种划定大环境，以及获得视觉显示的设施，例如允许研究基因型-环境相互作用模式的双标图。使用这些模型的一个关键问题是选择拟合的乘法项的数量。如果拟合的项太少，对基因型-环境均值的估计就会有偏差，而拟合的项太多，则会导致因方差膨胀而导致的估计效率低下。到目前为止，已经提出了几种方法来解决模型选择问题，包括显著性检验和交叉验证程序。但是，经验经验还没有确定确定乘法项数量的单一最佳策略，而且迄今为止提出的每种方法都有一些缺点。该项目的目的是开发新的方法来选择AMMI和GGE模型中乘法项的数量，并利用来自德国植物育种和品种测试项目以及蒙特卡罗模拟的MET数据，对这些方法进行评估和经验比较。

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.