rYWAASB (version 0.3)

ranki: 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)

Value

Returns a data frame showing numerical rankings

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.

Author

Ali Arminian

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 = _k = 1^p |IPCA_ik EP_k|/ _k = 1^pEP_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=(rY_i_Y)+ (rW_i_s)_Y+_s

, where WAASBY_i is the superiority index for genotype i that weights between mean performance and stability; _Y and _s are the weights for mean performance and stability, respectively; rY_i and rW_i are the rescaled values for mean performance 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: = rankrY_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

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.
# \donttest{
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.
# \donttest{
data(dm)
ranki(dm, lowt = TRUE)
# }