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META-R (multi-environment trial analysis in R) is a suite of R scripts linked by a graphical user interface (GUI) designed in Java language. The objective of META-R is to accurately analyze multi-environment plant breeding trials (METs) by fitting mixed and fixed linear models from experimental designs such as the randomized complete block design (RCBD) and the alpha-lattice/lattice designs. META-R simultaneously estimates the best linear and unbiased estimators (BLUEs) and the best linear and unbiased predictors (BLUPs). Additionally, it computes the variance-covariance parameters, as well as some statistical and genetic parameters such as the least significant difference (LSD) at 5% significance, the coefficient of variation in percentage (CV), the genetic variance, and the broad-sense heritability. These parameters are very important in the selection of top performing genotypes in plant breeding. META-R also computes the phenotypic and genetic correlations among environments and between traits, as well as their statistical significance. The genetic correlations between environments or traits can be visualized in a biplot graph or a tree diagram (dendrogram). Genetic correlations are very important for identifying environments with similar behavior or making indirect selection and identifying the most highly associated traits. META-R performs multi-environment analyses by using the residual maximum likelihood (REML) method; these analyses can be done by environment, across environments by grouping factors (stress conditions, nitrogen content, etc.) and across environments; the analyses across environments can be done with a pre-defined degree of heritability.
Alvarado et al. (Sat,) studied this question.