MASV.AMMI {ammistability}

Modified AMMI Stability Value

Description

MASV.AMMI computes the Modified AMMI Stability Value (MASV) (Zali et al. 2012; Ajay et al. 2019) (Please see Note) from a modified formula of AMMI Stability Value (ASV) (Purchase 1997). This formula calculates AMMI stability value considering all significant interaction principal components (IPCs) in the AMMI model. Using MASV, the Simultaneous Selection Index for Yield and Stability (SSI) is also calculated according to the argument ssi.method.

Usage

MASV.AMMI(model, n, alpha = 0.05, ssi.method = c("farshadfar", "rao"), a = 1)

Arguments

model

The AMMI model (An object of class AMMI generated by AMMI).

n

The number of principal components to be considered for computation. The default value is the number of significant IPCs.

alpha

Type I error probability (Significance level) to be considered to identify the number of significant IPCs.

ssi.method

The method for the computation of simultaneous selection index. Either "farshadfar" or "rao" (See SSI).

a

The ratio of the weights given to the stability components for computation of SSI when method = "rao" (See SSI).

Details

The Modified AMMI Stability Value (\(MASV\)) (Ajay et al. 2019) is computed as follows:

\[MASV = \sqrt{\sum_{n=1}^{N'-1}\left (\frac{SSIPC_{n}}{SSIPC_{n+1}} \times PC_{n} \right )^2 + \left (PC_{N'} \right )^2}\]

Where, \(SSIPC_{1}\), \(SSIPC_{2}\), \(\cdots\), \(SSIPC_{n}\) are the sum of squares of the 1st, 2nd, ..., and \(n\)th IPC; and \(PC_{1}\), \(PC_{2}\), \(\cdots\), \(PC_{n}\) are the scores of 1st, 2nd, ..., and \(n\)th IPC.

Value

A data frame with the following columns:

MASV

The MASV values.

SSI

The computed values of simultaneous selection index for yield and stability.

rMASV

The ranks of MASV values.

rY

The ranks of the mean yield of genotypes.

means

The mean yield of the genotypes.

The names of the genotypes are indicated as the row names of the data frame.

Note

In Zali et al. (2012), the formula for both AMMI stability value (ASV) was found to be erroneous, when compared with the original publications (Purchase 1997; Purchase et al. 1999; Purchase et al. 2000).

ASV (Zali et al. 2012) \[ASV = \sqrt{\left ( \frac{SSIPC_{1}}{SSIPC_{2}} \right ) \times (PC_{1})^2 + \left (PC_{2} \right )^2}\]

ASV (Purchase 1997; Purchase et al. 1999; Purchase et al. 2000) \[ASV = \sqrt{\left (\frac{SSIPC_{1}}{SSIPC_{2}} \times PC_{1} \right )^2 + \left (PC_{2} \right )^2}\]

The authors believe that the proposed Modified AMMI stability value (MASV) in Zali et al. (2012) is also erroneous and have implemented the corrected one in MASV.AMMI (Ajay et al. 2019).

MASV (Zali et al. 2012) \[MASV = \sqrt{\sum_{n=1}^{N'-1}\left ( \frac{SSIPC_{n}}{SSIPC_{n+1}} \right ) \times (PC_{n})^2 + \left (PC_{N'} \right )^2}\]

References

Ajay BC, Aravind J, Fiyaz RA, Kumar N, Lal C, Gangadhar K, Kona P, Dagla MC, Bera SK (2019). “Rectification of modified AMMI stability value (MASV).” Indian Journal of Genetics and Plant Breeding (The), 79, 726–731.

Purchase JL (1997). Parametric analysis to describe genotype × environment interaction and yield stability in winter wheat. Ph.D. Thesis, University of the Orange Free State.

Purchase JL, Hatting H, van Deventer CS (1999). “The use of the AMMI model and AMMI stability value to describe genotype x environment interaction and yield stability in winter wheat (Triticum aestivum L.).” In Proceedings of the Tenth Regional Wheat Workshop for Eastern, Central and Southern Africa, 14-18 September 1998. University of Stellenbosch, South Africa.

Purchase JL, Hatting H, van Deventer CS (2000). “Genotype × environment interaction of winter wheat (Triticum aestivum L.) in South Africa: II. Stability analysis of yield performance.” South African Journal of Plant and Soil, 17(3), 101–107.

Zali H, Farshadfar E, Sabaghpour SH, Karimizadeh R (2012). “Evaluation of genotype × environment interaction in chickpea using measures of stability from AMMI model.” Annals of Biological Research, 3(7), 3126–3136.

See Also

AMMI, index.AMMI, SSI

Examples

library(agricolae)
data(plrv)

# AMMI model
model <- with(plrv, AMMI(Locality, Genotype, Rep, Yield, console = FALSE))

# ANOVA
model$ANOVA

# IPC F test
model$analysis

# Mean yield and IPC scores
model$biplot

# G*E matrix (deviations from mean)
array(model$genXenv, dim(model$genXenv), dimnames(model$genXenv))

# With default n (N') and default ssi.method (farshadfar)
MASV.AMMI(model)

# With n = 4 and default ssi.method (farshadfar)
MASV.AMMI(model, n = 4)

# With default n (N') and ssi.method = "rao"
MASV.AMMI(model, ssi.method = "rao")

# Changing the ratio of weights for Rao's SSI
MASV.AMMI(model, ssi.method = "rao", a = 0.43)