AMMI_indexes: AMMI-based stability indexes

Description

This function computes the following AMMI-based stability indexes: ASV, AMMI stability value (Purchase et al., 2000); SIPC, sums of the absolute value of the IPCA scores (Sneller et al. 1997); EV, averages of the squared eigenvector values (Sneller et al. 1997); and Za, absolute value of the relative contribution of IPCAs to the interaction (Zali et al. 2012), and WAAS, weighted average of absolute scores (Olivoto et al. 2019).

Usage

AMMI_indexes(.data, order.y = NULL, level = 0.95)

Arguments

.data

An object of class waas or performs_ammi

order.y

A vector of the same length of x used to order the response variable. Each element of the vector must be one of the 'h' or 'l'. If 'h' is used, the response variable will be ordered from maximum to minimum. If 'l' is used then the response variable will be ordered from minimum to maximum. Use a comma-separated vector of names. For example, order.y = c("h, h, l, h, l").

level

The confidence level. Defaults to 0.95.

Value

A list where each element contains the result AMMI-based stability indexes for one variable.

Details

The ASV index is computed as follows: $A S V_{i} = {[{[\frac{r λ_{1}^{2}}{r λ_{2}^{2}} \times (λ_{1}^{0.5} a_{i 1} t_{j 1})]}^{2} + {(λ_{2}^{0.5} a_{i 2} t_{j 2})}^{2}]}^{0.5}$

where $r$ is the number of replications included in the analysis,

The SIPC index is computed as follows: $S I P C_{i} = \sum_{k = 1}^{P} | {| λ}_{k}^{0.5} a_{i k} |$

where $P$ is the number of IPCA retained via F-tests.

The EV index is computed as follows: $E V_{i} = \sum_{k = 1}^{P} a_{i k}^{2} / P$

The ZA index is computed as follows: $Z a_{i} = \sum_{k = 1}^{P} θ_{k} a_{i k}$

where $θ_{k}$ is the percentage sum of squares explained by the kth IPCA.

$W A A S_{i} = \sum_{k = 1}^{p} | I P C A_{i k} \times E P_{k} | / \sum_{k = 1}^{p} E P_{k}$

where $W A A S_{i}$ is the weighted average of absolute scores of the ith genotype; $P C A_{i k}$ is the score of the ith genotype in the kth IPCA; and $E P_{k}$ is the explained variance of the *k*th IPCA for k = 1,2,..,p, considering p the number of significant PCAs.

Five simultaneous selection indexes (ssi) are also computed by summation of the ranks of the ASV, SIPC, EV and Za indexes and the ranks of the mean yields (Farshadfar, 2008), which results in ssiASV, ssiSIPC, ssiEV, ssiZa, and ssiWAAS, respectively.

References

Purchase, J.L., H. Hatting, and C.S. van Deventer. 2000. Genotype vs environment interaction of winter wheat (Triticum aestivum L.) in South Africa: II. Stability analysis of yield performance. South African J. Plant Soil 17:101-107. doi:10.1080/02571862.2000.10634878

Sneller, C.H., L. Kilgore-Norquest, and D. Dombek. 1997. Repeatability of Yield Stability Statistics in Soybean. Crop Sci. 37:383-390. doi:10.2135/cropsci1997.0011183X003700020013x

Zali, H., E. Farshadfar, S.H. Sabaghpour, and R. Karimizadeh. 2012. Evaluation of genotype vs environment interaction in chickpea using measures of stability from AMMI model. Ann. Biol. Res. 3:3126-3136.

Olivoto, T., A.D.C. L\'ucio, J.A.G. da silva, V.S. Marchioro, V.Q. de Souza, and E. Jost. 2019a. Mean performance and stability in multi-environment trials I: Combining features of AMMI and BLUP techniques. Agron. J. 111:2949-2960. doi:10.2134/agronj2019.03.0220

Examples

Run this code

# NOT RUN {
library(metan)
model <- waas(data_ge,
              env = ENV,
              gen = GEN,
              rep = REP,
              resp = c(GY, HM),
              verbose = FALSE)
model_indexes <- AMMI_indexes(model)


# Alternatively (and more intuitively) using %>%
res_ind <- data_ge %>%
           waas(ENV, GEN, REP, c(GY, HM)) %>%
           AMMI_indexes()
# }
# NOT RUN {
# }

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