Estimation of Missing Values Affects Important Aspects of GGE Biplot Analysis

Abstract

RESEARCHT he presence of genotype-by-environment interaction (GEI) is common in multi-environment trials in wheat (Triticum aestivum L.) and other crops; it leads to changes in the performance of cultivars in different environments. A GEI demands that trials be conducted at multiple locations for several years to obtain reliable data for the possible release of a new cultivar.Trials conducted across several years and locations increase the possibility of obtaining datasets with unbalanced or incomplete data. This can occur because of planned or unplanned actions by the breeder. The planned actions might be the removal of genotypes that did not perform well in a given year, introducing new genotypes developed by the breeding program and the introduction of newly released cultivars. On the other hand, unplanned actions, which are unrelated to the breeder, might be attributable to human or environmental causes (Yan, 2013).There are three primary strategies for analyzing unbalanced or incomplete datasets. The first strategy consists in the removal of genotypes or environments with missing values. The second ABSTRACT Multi-environment trials often yield unbalanced datasets, thus necessitating the estimation of missing values. It is unknown whether this estimation affects the graphic characteristics of genotype plus genotype-by-environment interaction (GGE) biplots. Therefore, our objectives were to investigate the effects of different percentages of missing values on the number of significant principal components (pCs) and on mega environments, "winner" (highest-performing) genotypes, and the amount of variation explained by the pCs. Two complete sets of two-way data from wheat (Triticum aestivum L.) were used. The first set consisted of the original data (Data1, from which we created scenarios with 0, 30, and 60% missing data. For the second dataset (Data2), we removed 50% data from the original dataset, estimated missing values to make it a new complete dataset, and created scenarios like those for Data1. Missing values were estimated via expectation-maximization-GGE (EM-GGE) and EM-additive main effects and multiplicative interaction (EM-AMMI) methods. The percentage of variation explained by the pCs was affected by the percentage of missing data; a large percentage of missing values considerably increased the amount of variation explained by pC 1 and pC 2 and reduced the complexity of the genotype-by-environment interaction because two pCs accounted for more than 80% of the variation, instead of the three pCs that were required to explain the variation in the original dataset. The EM-GGE estimation method was able to maintain the original conformation of the 'which-won-where' biplot when £30% of estimated data were used. The EM-GGE was superior to the EM-AMMI method for estimating missing data. The estimation of more than 30% of the data should be avoided because it can lead to significant changes in mega environment conformation and the identification of "winner" genotypes.

Mega‐environment identification for soybean (Glycine max) breeding and production in Brazilian Midwest region

“…Missing values frequently occur in MET, because genotypes and locations are replaced constantly. However, when less than 30% of data are missing, there are no significant changes in the conformation of the biplots or impairment in the quality of the obtained information (Woyann et al, ).…”

“…However, Yan et al () list several points regarding the quality of GGE analysis (for more information, consult Yan et al, ). Moreover, when less than 30% of data are missing, biplots do not suffer strongly noise in the analysis, and the GGE methodology is adequate to perform analysis of unbalanced data from MET (Woyann et al, ).…”

Research Article Genetic and phenotypic multi-character approach applied to multivariate models for wheat industrial quality analysis

“…The GGE method combines the effects attributed to the genotypes tested and those of the G x E interaction (Yan et al, 2000). It allows the identification of the genotype with high performance being efficient in a certain growing environment, in the same way, allows the formation of mega-environments (Woyann et al, 2016). The multivariate model used was based on:…”

“…There are many factors influencing wheat production dynamics, among them, the intrinsic genetic characteristics of each genotype, the edaphoclimatic attributes of growing environment, and the aspects related to genotype x environment interaction (G X E) (Woyann et al, 2016). Therefore, a detailed study is necessary to estimate what cause the phenotypic variation in the character of interest, as well to define macro-environments, phenotypic stability and genotype-specific adaptability to favorable or unfavorable environments (Szareski et al, 2017).…”

The Possibility of Applying the EM-PCA Procedure to Lake Water

“…While the classic PCA taking multiple dimensions of data analysis is quite often used, the analysis of the main components for missing data (EM-PCA) is a little bit different [37][38][39]. EM-PCA begins with the initialization of the missing data by quoting the average values in the corresponding rows and columns, and then their iterations in such a way to substitute missing data with values predicted (estimated) by the PCA [40].…”