SSI {ammistability}

Simultaneous Selection Indices for Yield and Stability

Description

SSI computes the Simultaneous Selection Index for Yield and Stability (SSI) according to the methods specified in the argument method.

Usage

SSI(y, sp, gen, method = c("farshadfar", "rao"), a = 1)

Arguments

y

A numeric vector of the mean yield/performance of genotypes.

sp

A numeric vector of the stability parameter/index of the genotypes.

gen

A character vector of the names of the genotypes.

method

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

a

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

Details

The SSI according to Rao and Prabhakaran (2005) (\(I_{i}\)) is computed as follows:

\[I_{i} = \frac{\overline{Y}_{i}}{\overline{Y}_{..}} + \alpha \frac{\frac{1}{SP_{i}}}{\frac{1}{T}\sum_{i=1}^{T}\frac{1}{SP_{i}}}\]

Where \(SP_{i}\) is the stability measure of the \(i\)th genotype under AMMI procedure; \(\overline{Y}_{i}\) is mean performance of \(i\)th genotype; \(\overline{Y}_{..}\) is the overall mean; \(T\) is the number of genotypes under test and \(\alpha\) is the ratio of the weights given to the stability components (\(w_{2}\)) and yield (\(w_{1}\)) with a restriction that \(w_{1} + w_{2} = 1\). The weights can be specified as required.

\(\alpha\)	\(w_{1}\)	\(w_{2}\)
1.00	0.5	0.5
0.67	0.6	0.4
0.43	0.7	0.3
0.25	0.8	0.2

The SSI proposed by Farshadfar (2008) is called the Genotype stability index (\(GSI\)) or Yield stability index (\(YSI\)) (Farshadfar et al. 2011) and is computed by summation of the ranks of the stability index/parameter and the ranks of the mean yields.

\[GSI = YSI = R_{SP} + R_{Y}\]

Where, \(R_{SP}\) is the stability parameter/index rank of the genotype and \(R_{Y}\) is the mean yield rank of the genotype.

Value

A data frame with the following columns:

SP

The stability parameter values.

SSI

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

rSP

The ranks of the stability parameter.

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.

References

Farshadfar E (2008). “Incorporation of AMMI stability value and grain yield in a single non-parametric index (GSI) in bread wheat.” Pakistan Journal of biological sciences, 11(14), 1791.

Farshadfar E, Mahmodi N, Yaghotipoor A (2011). “AMMI stability value and simultaneous estimation of yield and yield stability in bread wheat (Triticum aestivum L.).” Australian Journal of Crop Science, 5(13), 1837–1844.

Rao AR, Prabhakaran VT (2005). “Use of AMMI in simultaneous selection of genotypes for yield and stability.” Journal of the Indian Society of Agricultural Statistics, 59, 76–82.

See Also

AMGE.AMMI, ASI.AMMI, ASTAB.AMMI, AVAMGE.AMMI, DA.AMMI, DZ.AMMI, EV.AMMI, FA.AMMI, MASV.AMMI, SIPC.AMMI, ZA.AMMI

Examples

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

yield <- aggregate(model$means$Yield, by= list(model$means$GEN),
               FUN=mean, na.rm=TRUE)[,2]
stab <- DZ.AMMI(model)$DZ
genotypes <- rownames(DZ.AMMI(model))

# With default ssi.method (farshadfar)
SSI(y = yield, sp = stab, gen = genotypes)

# With  ssi.method = "rao"
SSI(y = yield, sp = stab, gen = genotypes, method = "rao")

# Changing the ratio of weights for Rao's SSI
SSI(y = yield, sp = stab, gen = genotypes, method = "rao", a = 0.43)