Nothing
Simultaneous Selection by Trait and WAASB Index"
In rYWAASB: Simultaneous Selection by Trait and WAASB Index
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
out.width = '70%'
)
1-Introduction
I dedicate this package to my colleague, Professor Dr. Manjit S. Kang, a great biostatistician and quantitative geneticist, who passed away recently and has devoted his life to PLANT BREEDING science and has provided me with invaluable supports!.
Stability analysis is crucial in plant breeding to select superior genotypes that perform consistently across different environments. Several models and methods have been developed for this purpose, including Additive Main Effect and Multiplicative Interaction (AMMI), Weighted Average of Absolute Scores (WAASB), and Genotype plus Genotype-Environment (GGE) interactions in multi-environmental trials (MET) [@mishra2024; @sakata2021; @pour2022; @danakumara2023]. These analyses help breeders identify genotypes with stable performance and adaptability under varying conditions, leading to optimal yield stability and successful crop production. Utilizing these stability analysis tools, breeders can navigate the complexities of genotype-environment interactions and select genotypes that consistently excel across different locations and seasons, ensuring the development of resilient and high-performing plant varieties [@swarup2014].
The WAASB and WAASBY objects
By combining the strengths of AMMI for assessing stability and BLUP for prediction accuracy, breeders can effectively select genotypes that consistently perform well across different environmental conditions. This is crucial for developing sustainable agricultural systems and improving food security. To estimate the stability index of genotypes in multi-environment trials (METs), the WAASB index (weighted average of the absolute values obtained from the singular value decomposition of the BLUP matrix for the genotype by environment interaction effects, generated by a linear mixed-effects model) is calculated using the formula provided by [@olivoto2019]. They suggest that the function *waasb()* computes the Weighted Average of the Absolute Scores considering all possible IPCA from the Singular Value Decomposition of the BLUPs for genotype-vs-environment interaction effects obtained by an Linear Mixed-effect Model [@olivoto2019]
, as follows:
$$ WAASB_i = \sum_{k = 1}^{p} |IPCA_{ik} \times EP_k|/ \sum_{k = 1}^{p}EP_k $$
where $WAASB_i$ is the weighted average of absolute scores of the ith genotype; $IPCA_{ik}$ is the scores of the ith genotype in the kth IPCA; and $EP_k$ is the explained variance of the kth PCA for $k = 1,2,..,p$, $p = min(g-1; e-1)$.
Further, WAABSY is a superiority or simultaneous selection index allowing weighting between mean performance and stability [@olivoto2019]:
$$ WAASBY_i=\frac{\left({rY}_i\times\theta_Y\right)+\left({rW}_i\times\theta_s\right)}{\theta_Y+\theta_s} $$
where WAASBYi is the superiority index for genotype \it{i} that weights between mean performance and stability; $\theta_Y$ and $\theta_s$ are the weights for mean performance and stability, respectively; {rY}_i and {rW}_i are the rescaled values for mean performance $\bar{Y_i}$ and stability $W_i$, respectively of the genotype i. For the details of calculations, rescalling and mathematics notations see [@olivoto2019].
In this package, my new index (rYWAASB) gives results which can be compared with WAASBY index provided by Olivoto et al. [@olivoto2019].
For working with rYWAASB package, firstly, if the metan or rYWAASB packages are not already installed, they should be installed on the system. The analysis requires the following packages to be installed:
if(!require('rYWAASB')){
install.packages('rYWAASB') # call the package
}
library('rYWAASB')
The analyses requires the following R packages:
## For graphical displays
library(metan)
library(ggplot2)
library(graphics)
library(factoextra)
library(FactoMineR)
The codes provided below form the metan package, allow you to access the WAASB index values, rankings, and other information for genotypes (or entries) in general.
waasb_model <-
waasb(data_ge,
env = ENV,
gen = GEN,
rep = REP,
resp = everything(),
random = "gen", #Default
verbose = TRUE) #Default
data <- waasb_model$GY$model
print(data)
The output generated by the waasb() function is very similar to that generated by the waas() function. The main difference is that the singular value decomposition is based on the BLUP for GEI effects matrix. For more information, refer to [@olivoto2019].
Several indexes have been developed to identify genotypes that exhibit both high performance and stability in plant breeding programs. One example is the kangranksum index, which was developed by Kang [@kang1988]. This index combines yield and stability ranks based on the Shukla stability index. Olivoto [@olivoto2019], on the other hand, created the WAASBY index by assigning weights to yield and stability. Our rYWAASB index can be compared to these earlier indexes, as it follows a similar computational approach. However, our index (rYWAASB) is a powerful tool, because it incorporates a trait and WAASB rankings in the process.
2- How to apply the package
First, let's examine the Y*WAASB biplot generated by the metan package. This will allow us to compare the results of the rYWAASB package with the Y*WAASB biplot. In the Y*WAASB or GY*WAASB biplot proposed by [@olivoto2019] (Fig. 1), the quadrants illustrate the stability and trait patterns (specifically, the grain yield of oat genotypes in the data_ge dataset) as follows:
- Quadrant I: This quadrant consists of unstable genotypes or environments that have high discrimination ability but productivity below the grand mean.
- Quadrant II: This quadrant includes unstable genotypes with productivity above the grand mean.
- Quadrant III: This quadrant comprises low productive but stable genotypes.
- Quadrant IV: This quadrant contains productive and broadly adapted genotypes.
plot_scores(waasb_model, type = 3)
Fig. 1: Y*WAASB biplot of metan package built-in oat data
In this section, we will utilize the built-in data maize to generate ranking scores for different genotypes, along with their corresponding plots. For further details, please refer to the ?maize documentation. It is also possible to use other datasets as long as they contain the following columns: genotype, trait, and WAASB index for genotypes. To understand how the HTML tables were created, please refer to the Rendering engine section.
data(maize)
head(maize)
Applying the rYWAASB package. Ranking table:
We recommend that users address (handle/overcome/substitute) any missing data in their inputs before proceeding with analyses. This is because the rank codes do not incorporate a comprehensive algorithm to handle this task.
Case 1. Higher trait values are preferred. For instance grain yield in cereals is a trait which its higher values are preferred and ranking is performed from the higher to lower values i.e. 1st, 2nd, 3rd etc in maize dataset.
data(maize)
ranki(maize) # or: ranki(maize, lowt = FALSE)
In the table above, the genotype with the lowest rank (Dracma) is considered the best due to its high grain yield and low WAASB score.
Case 2.
In this case, the lower values of the given trait are preferred. For instance days to maturity and plant height are traits where their lower values are preferred.
data(dm)
ranki(dm, lowt = TRUE)
Drawing the first plot bar_plot1:
case 1. maize dataset:
data(maize)
bar_plot1(maize) # or: bar_plot1(maize, lowt = FALSE)
case 2. dm dataset:
data(dm)
bar_plot1(dm, lowt = TRUE)
Fig.2. The first barplot of the rYWASSB package
Drawing the second plot bar_plot2:
data(maize)
bar_plot2(maize) # or: bar_plot2(maize, lowt = FALSE, verbose = FALSE)
Fig.3. The second barplot of the rYWASSB package
Performing PCA and textual and graphical representations (scree plot and PCA-dependent biplots (3 plots))
case 1. For grain yield data:
data(maize)
PCA_biplot(maize) # or: PCA_biplot(maize, lowt = FALSE)
Figs.4-6. The PCA biplot with loadings for compare genotypes
Case 2. For days to maturity data:
data(dm)
PCA_biplot(dm, lowt = TRUE)
Figs.7-9. The PCA biplot with loadings for compare genotypes
Designing the cluster analysis on data and define the optimum number of clusters uning The Average Silhouette Method. The details of this method is given in the description and details parts of the function nbclust(). For running the cluster analysis by menas of shipunov package (courtesy of late professor Alexy Shipunov) act as:
data(maize)
maize <- as.data.frame(maize)
row.names(maize) <- maize[, 1]
maize[, 1] = NULL
GEN <- row.names(maize)
maize <- scale(maize)
nbclust(maize, verbose = FALSE)
# Perform bootstrap or jackknife clustering by shipunov package.
# The examples should be run in the console manually due to
# problems occurs in the ORPHANED package "shipunov".
#
# library(shipunov) # recalling the shipunov package
# 1- Bootstrap clustering:
# data.jb <- Jclust(maize,
# method.d = "euclidean",
# method.c = "average", n.cl = 2,
# bootstrap = TRUE)
#
# plot.Jclust(data.jb, top=TRUE, lab.pos=1,
# lab.offset=1, lab.col=2, lab.font=2)
# Fence(data.jb$hclust, GEN)
#
# data.jb <- Jclust(maize,
# method.d = "euclidean",
# method.c = "ward.D", n.cl = 2,
# bootstrap = TRUE)
#
# plot.Jclust(data.jb, top=TRUE, lab.pos=1,
# lab.offset=1, lab.col=2, lab.font=2)
# Fence(data.jb$hclust, GEN)
#
#
# if(verbose = TRUE):
# cat("\nnumber of iterations:\n", data.jb$iter, "\n")
#
# For "bootstrap":
# data.jb$mat <- as.matrix((data.jb$mat))
# cat("\nmatrix of results:\n", data.jb$mat, "\n")
# cat("clustering info, by eucledean distance measure:\n")
# print(data.jb$hclust)
# cat("groups:\n", data.jb$gr, "\n")
# cat("\nsupport values:\n", data.jb$supp, "\n")
# cat("\nnumber of clusters used:\n", data.jb$n.cl, "\n")
#
# 2- Jackknife clustering:
# data.jb <- Bclust(maize,
# method.d = "euclidean", method.c = "average",
# bootstrap = FALSE)
# plot(data.jb)
#
# data.jb <- Bclust(maize,
# method.d = "euclidean", method.c = "ward.D",
# bootstrap = FALSE)
# plot(data.jb)
#
# if(verbose = TRUE):
# For"jackknife":
# cat("Consensus:\n", data.jb$consensus, "\n")
# cat("Vlaues:\n", data.jb$values, "\n")
Figures 10-12 Cluster analysis by 1000 bootstrap iterations and determine optimum N clusters using The Average Silhouette algorithm.
References
Try the rYWAASB package in your browser
Any scripts or data that you put into this service are public.
rYWAASB documentation built on June 10, 2025, 9:12 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
knitr::opts_chunk$set( collapse = TRUE, comment = "#>", out.width = '70%' )
1-Introduction
I dedicate this package to my colleague, Professor Dr. Manjit S. Kang, a great biostatistician and quantitative geneticist, who passed away recently and has devoted his life to PLANT BREEDING science and has provided me with invaluable supports!.
Stability analysis is crucial in plant breeding to select superior genotypes that perform consistently across different environments. Several models and methods have been developed for this purpose, including Additive Main Effect and Multiplicative Interaction (AMMI), Weighted Average of Absolute Scores (WAASB), and Genotype plus Genotype-Environment (GGE) interactions in multi-environmental trials (MET) [@mishra2024; @sakata2021; @pour2022; @danakumara2023]. These analyses help breeders identify genotypes with stable performance and adaptability under varying conditions, leading to optimal yield stability and successful crop production. Utilizing these stability analysis tools, breeders can navigate the complexities of genotype-environment interactions and select genotypes that consistently excel across different locations and seasons, ensuring the development of resilient and high-performing plant varieties [@swarup2014].
The WAASB and WAASBY objects
By combining the strengths of AMMI for assessing stability and BLUP for prediction accuracy, breeders can effectively select genotypes that consistently perform well across different environmental conditions. This is crucial for developing sustainable agricultural systems and improving food security. To estimate the stability index of genotypes in multi-environment trials (METs), the WAASB index (weighted average of the absolute values obtained from the singular value decomposition of the BLUP matrix for the genotype by environment interaction effects, generated by a linear mixed-effects model) is calculated using the formula provided by [@olivoto2019]. They suggest that the function *waasb()* computes the Weighted Average of the Absolute Scores considering all possible IPCA from the Singular Value Decomposition of the BLUPs for genotype-vs-environment interaction effects obtained by an Linear Mixed-effect Model [@olivoto2019]
, as follows:
$$ WAASB_i = \sum_{k = 1}^{p} |IPCA_{ik} \times EP_k|/ \sum_{k = 1}^{p}EP_k $$
where $WAASB_i$ is the weighted average of absolute scores of the ith genotype; $IPCA_{ik}$ is the scores of the ith genotype in the kth IPCA; and $EP_k$ is the explained variance of the kth PCA for $k = 1,2,..,p$, $p = min(g-1; e-1)$.
Further, WAABSY is a superiority or simultaneous selection index allowing weighting between mean performance and stability [@olivoto2019]:
$$ WAASBY_i=\frac{\left({rY}_i\times\theta_Y\right)+\left({rW}_i\times\theta_s\right)}{\theta_Y+\theta_s} $$ where WAASBYi is the superiority index for genotype \it{i} that weights between mean performance and stability; $\theta_Y$ and $\theta_s$ are the weights for mean performance and stability, respectively; {rY}_i and {rW}_i are the rescaled values for mean performance $\bar{Y_i}$ and stability $W_i$, respectively of the genotype i. For the details of calculations, rescalling and mathematics notations see [@olivoto2019].
In this package, my new index (rYWAASB) gives results which can be compared with WAASBY index provided by Olivoto et al. [@olivoto2019].
For working with rYWAASB package, firstly, if the metan or rYWAASB packages are not already installed, they should be installed on the system. The analysis requires the following packages to be installed:
if(!require('rYWAASB')){ install.packages('rYWAASB') # call the package } library('rYWAASB')
The analyses requires the following R packages:
## For graphical displays library(metan) library(ggplot2) library(graphics) library(factoextra) library(FactoMineR)
The codes provided below form the metan package, allow you to access the WAASB index values, rankings, and other information for genotypes (or entries) in general.
waasb_model <- waasb(data_ge, env = ENV, gen = GEN, rep = REP, resp = everything(), random = "gen", #Default verbose = TRUE) #Default data <- waasb_model$GY$model print(data)
The output generated by the waasb() function is very similar to that generated by the waas() function. The main difference is that the singular value decomposition is based on the BLUP for GEI effects matrix. For more information, refer to [@olivoto2019].
Several indexes have been developed to identify genotypes that exhibit both high performance and stability in plant breeding programs. One example is the kangranksum index, which was developed by Kang [@kang1988]. This index combines yield and stability ranks based on the Shukla stability index. Olivoto [@olivoto2019], on the other hand, created the WAASBY index by assigning weights to yield and stability. Our rYWAASB index can be compared to these earlier indexes, as it follows a similar computational approach. However, our index (rYWAASB) is a powerful tool, because it incorporates a trait and WAASB rankings in the process.
2- How to apply the package
First, let's examine the Y*WAASB biplot generated by the metan package. This will allow us to compare the results of the rYWAASB package with the Y*WAASB biplot. In the Y*WAASB or GY*WAASB biplot proposed by [@olivoto2019] (Fig. 1), the quadrants illustrate the stability and trait patterns (specifically, the grain yield of oat genotypes in the data_ge dataset) as follows:
- Quadrant I: This quadrant consists of unstable genotypes or environments that have high discrimination ability but productivity below the grand mean.
- Quadrant II: This quadrant includes unstable genotypes with productivity above the grand mean.
- Quadrant III: This quadrant comprises low productive but stable genotypes.
- Quadrant IV: This quadrant contains productive and broadly adapted genotypes.
plot_scores(waasb_model, type = 3)
Fig. 1: Y*WAASB biplot of metan package built-in oat data
In this section, we will utilize the built-in data maize to generate ranking scores for different genotypes, along with their corresponding plots. For further details, please refer to the ?maize documentation. It is also possible to use other datasets as long as they contain the following columns: genotype, trait, and WAASB index for genotypes. To understand how the HTML tables were created, please refer to the Rendering engine section.
data(maize) head(maize)
Applying the rYWAASB package. Ranking table:
We recommend that users address (handle/overcome/substitute) any missing data in their inputs before proceeding with analyses. This is because the rank codes do not incorporate a comprehensive algorithm to handle this task.
Case 1. Higher trait values are preferred. For instance grain yield in cereals is a trait which its higher values are preferred and ranking is performed from the higher to lower values i.e. 1st, 2nd, 3rd etc in maize dataset.
data(maize) ranki(maize) # or: ranki(maize, lowt = FALSE)
In the table above, the genotype with the lowest rank (Dracma) is considered the best due to its high grain yield and low WAASB score.
Case 2. In this case, the lower values of the given trait are preferred. For instance days to maturity and plant height are traits where their lower values are preferred.
data(dm) ranki(dm, lowt = TRUE)
Drawing the first plot bar_plot1:
case 1. maize dataset:
data(maize) bar_plot1(maize) # or: bar_plot1(maize, lowt = FALSE)
case 2. dm dataset:
data(dm) bar_plot1(dm, lowt = TRUE)
Fig.2. The first barplot of the rYWASSB package
Drawing the second plot bar_plot2:
data(maize) bar_plot2(maize) # or: bar_plot2(maize, lowt = FALSE, verbose = FALSE)
Fig.3. The second barplot of the rYWASSB package
Performing PCA and textual and graphical representations (scree plot and PCA-dependent biplots (3 plots))
case 1. For grain yield data:
data(maize) PCA_biplot(maize) # or: PCA_biplot(maize, lowt = FALSE)
Figs.4-6. The PCA biplot with loadings for compare genotypes
Case 2. For days to maturity data:
data(dm) PCA_biplot(dm, lowt = TRUE)
Figs.7-9. The PCA biplot with loadings for compare genotypes
Designing the cluster analysis on data and define the optimum number of clusters uning The Average Silhouette Method. The details of this method is given in the description and details parts of the function nbclust(). For running the cluster analysis by menas of shipunov package (courtesy of late professor Alexy Shipunov) act as:
data(maize) maize <- as.data.frame(maize) row.names(maize) <- maize[, 1] maize[, 1] = NULL GEN <- row.names(maize) maize <- scale(maize) nbclust(maize, verbose = FALSE) # Perform bootstrap or jackknife clustering by shipunov package. # The examples should be run in the console manually due to # problems occurs in the ORPHANED package "shipunov". # # library(shipunov) # recalling the shipunov package # 1- Bootstrap clustering: # data.jb <- Jclust(maize, # method.d = "euclidean", # method.c = "average", n.cl = 2, # bootstrap = TRUE) # # plot.Jclust(data.jb, top=TRUE, lab.pos=1, # lab.offset=1, lab.col=2, lab.font=2) # Fence(data.jb$hclust, GEN) # # data.jb <- Jclust(maize, # method.d = "euclidean", # method.c = "ward.D", n.cl = 2, # bootstrap = TRUE) # # plot.Jclust(data.jb, top=TRUE, lab.pos=1, # lab.offset=1, lab.col=2, lab.font=2) # Fence(data.jb$hclust, GEN) # # # if(verbose = TRUE): # cat("\nnumber of iterations:\n", data.jb$iter, "\n") # # For "bootstrap": # data.jb$mat <- as.matrix((data.jb$mat)) # cat("\nmatrix of results:\n", data.jb$mat, "\n") # cat("clustering info, by eucledean distance measure:\n") # print(data.jb$hclust) # cat("groups:\n", data.jb$gr, "\n") # cat("\nsupport values:\n", data.jb$supp, "\n") # cat("\nnumber of clusters used:\n", data.jb$n.cl, "\n") # # 2- Jackknife clustering: # data.jb <- Bclust(maize, # method.d = "euclidean", method.c = "average", # bootstrap = FALSE) # plot(data.jb) # # data.jb <- Bclust(maize, # method.d = "euclidean", method.c = "ward.D", # bootstrap = FALSE) # plot(data.jb) # # if(verbose = TRUE): # For"jackknife": # cat("Consensus:\n", data.jb$consensus, "\n") # cat("Vlaues:\n", data.jb$values, "\n")
Figures 10-12 Cluster analysis by 1000 bootstrap iterations and determine optimum N clusters using The Average Silhouette algorithm.
References
Try the rYWAASB package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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