ranki {rYWAASB} | R Documentation |
The values and ranks of genotypes
Description
ranki()
function ranks the genotypes (or entries) based on
a new index utilizing the given trait and "WAASB" index to
simultaneous select the top-ranked ones. This can be compared
with WAASBY index of Olivoto (2019). We suggest users handle
the missing data in inputs before considering analyses,
due rank codes dose not implement a widespread algorithm
to do this task.
WAASB(Weighted Average of Absolute Scores), Computes
the Weighted Average of Absolute Scores (Olivoto et al.,
2019) for quantifying the stability of g genotypes
conducted in e environments using linear mixed-effect models.
Usage
ranki(datap, lowt = FALSE)
Arguments
datap |
The data set |
lowt |
A parameter indicating whether lower rates of the trait is preferred or not. For grain yield e.g. Upper values is preferred. For plant height lower values e.g. is preferred. |
Details
According to Olivoto et al. (2019a), WAASB(The weighted average of absolute scores) is computed considering all Interaction Principal Component Axis (IPCA) from the Singular Value Decomposition (SVD) of the matrix of genotype-environment interaction (GEI) effects generated by a linear mixed-effect model, 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 score of the ith genotype in the kth Interaction Principal Component Axis (IPCA); and \(EP_k\) is the explained variance of the kth IPCA for k = 1,2,..,p, considering \(p=min(g-1; e-1)\).
Further, \(WAASBY_i\) is a superiority or simultaneous selection index allowing weighting between mean performance and stability \[ WAASBY_i=\frac{\left({rY}_i\times\theta_Y\right)+ \left({rW}_i\times\theta_s\right)}{\theta_Y+\theta_s} \] , where \(WAASBY_i\) 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, rescaling and mathematics notations see (Olivoto et al., 2019).
Finally, \(rYWAASB_i\) index is the sum of the ranks (or in fact the rank of sum of ranks of the trait and WAASB index) as follows: (\(rY_i\)) and WAASB index (\(rWAASB_i\)) for each individual:
\[ rYWAASB_i = {rY_i} + {rWAASB_i}\]or: = \[rank{{rY_i} + {rWAASB_i}}\].
The input format of table of data(NA free), here maize data, should be as follows:
GEN | Y | WAASB | WAASBY |
Dracma | 262.22 | 0.81 | 81.6 |
DKC6630 | 284.04 | 2.20 | 88.5 |
NS770 | 243.48 | 0.33 | 71.4 |
... |
Value
Returns a data frame showing numerical rankings
Author(s)
Ali Arminian abeyran@gmail.com
References
Olivoto, T., Lúcio, A., DC, da Silva, J.A.G., Sari, B.G. and Diel, M. 2019. Mean performance and stability in multi-environment trials II: Selection based on multiple traits. Agronomy Journal, 111(6):2961-2969.
Olivoto, T., & Lúcio, A.D.C.2020. metan: An R package for multi‐environment trial analysis. Methods in Ecology and Evolution, 11(6), 783-789.
Kang, M.S. 1988. “A Rank-Sum Method for Selecting High-Yielding, Stable Corn Genotypes.” Cereal Research Communications 16: 113–15.
Examples
# 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)
# Case 2: In this case, the lower values of the given trait are preferred.
# For instance days to maturity (dm) and plant height are traits where their
# lower values are preferred.
data(dm)
ranki(dm, lowt = TRUE)