EM-AMMI之區域試驗資料缺值估計

Abstract

區域試驗施行於品系產量試驗之後，其目的為確保品系之產量與農藝性狀在不同環境下皆能具有良好表現，於不同地區或不同季節進行多重複的產量及農藝性狀評估，以討論基因型與環境交感對於作物產量或農藝性狀的穩定性及適應性影響。AMMI (Additive Main Effect and Multiplicative Interaction) 模式利用奇異值分解將交感項拆解成數個主成分之奇異值、品系或環境特徵向量以及殘差項，進行區域試驗資料的穩定性分析。然而AMMI模式奇異值分解的不允許基因型與環境組合的平均產量有缺值的情形，但多年度多重地區之區域試驗資料通常高度不均衡，限制育種家探討跨年度間基因型與環境的交感。 本研究利用EM-AMMI (Expectation-Maximization-Additive Main Effect and Multiplicative Interaction) 方式進行缺值估計，模擬結果顯示，當缺值比例小於50%時，EM-AMMI應採用第一主成分進行缺值估計，但當缺值比例超過50%時，則EM-AMMI應採用前三主成分進行缺值估計。本研究亦應用EM-AMMI於毛豆區域試驗資料之缺值估計，希望藉由適當缺值估計法提供完整的區域試驗資料，幫助育種家了解完詳之基因型與環境交感的資訊。

The purpose of regional trials is to confirm yield and agronomic traits of lines have stable and good performance in different environments. Some statistical methods were proposed to explain the patterns of genotype and environment interactions in the regional trial data. Particularly, Additive Main Effect and Multiplicative Interaction (AMMI) model uses singular decomposition value (SVD) to decompose genotype by environment interaction into the singular values, the genotype eigenvectors, and the environment eigenvectors to carry out the stability analysis on the tested genotype. However, a major limitation of AMMI model is that SVD requires a complete two-way table of genotype and environment mean yields. A typical multi-year or multi-location regional trial data is usually highly unbalanced so that the investigation of genotype by environment interaction across years is restricted. In this study we impute missing values by expectation-maximization-additive main effect and multiplicative interaction (EM-AMMI) method. The results of simulated data suggest to conduct EM-AMMI using one principal component to impute the missing values when the proportions of the missing values is less than 50%; when the proportion of missing values is more than 50%, we suggest to perform EM-AMMI using first three principal components. We also imputed the missing values of vegetable soybean regional trial data by EM-AMMI. In conclusion, providing a complete regional trial data by appropriate EM-AMMI can help the plant breeders to better understand of genotype by environment interaction.