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AMMI stability value and yield stability index

Source: R/stab_asv.R
stab_asv.Rd

stab_asv() computes the AMMI stability value (ASV) of Purchase et al. (2000), which combines the genotype scores of the first two AMMI axes weighted by the share of the interaction each axis explains, and the yield stability index (YSI) of Farshadfar (2008), the sum of the ranks of the ASV and of the mean.

Usage

stab_asv(.data, .y, .rep, .gen, .env)

# Default S3 method
stab_asv(.data, .y, .rep, .gen, .env)

Arguments

.data

a data frame (or data.table) with one row per plot.

.y

response: a column of .data given by name (.y = Yield or .y = "Yield") or a numeric vector of length nrow(.data).

.rep

replicate: not used (kept for compatibility); may be omitted.

.gen

genotype: a column of .data or a vector, as for .y.

.env

environment: a column of .data or a vector, as for .y.

Value

An object of class c("stab_asv", "stab_result", "list") with the component of earlier versions:

ASD

data.table sorted by YSI: Gen, Mean, ASD (the ASV), rMean, rASD, YSI; new columns PC1, PC2 (the scores).

Methods: print(), summary(), plot() (which = c("ranks", "mean")), stab_interpret().

Details

With the AMMI genotype scores \(PC_{i1}\), \(PC_{i2}\) (ammi) and the sums of squares \(SS_1\), \(SS_2\) of the two axes (\(SS_n \propto \lambda_n^2\)), $$ASV_i = \sqrt{\left(\frac{SS_1}{SS_2}PC_{i1}\right)^2 + PC_{i2}^2}, \qquad YSI_i = R(ASV_i) + R(\bar{y}_{i\cdot}),$$ where \(R(ASV_i) = 1\) for the smallest ASV (the most stable genotype) and \(R(\bar{y}_{i\cdot}) = 1\) for the highest mean. The genotype with the smallest YSI is the most desirable. The formula is the one used by agricolae and metan.

Changes from the earlier version. The weight was the ratio of the singular values \(\lambda_1/\lambda_2\) applied to the squared score, instead of the ratio of the sums of squares applied to the score; and the stability values were paired with other genotypes' means unless the data were sorted by genotype.

References

Purchase, J. L., Hatting, H. and van Deventer, C. S. (2000). Genotype x 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.

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), 1791–1796.

See also

stab_masv, stab_dist, ammi, stab_interpret

Other stability analyses: add_anova(), ammi(), ammi_biplot(), er_anova(), ge_effects(), ge_means(), gge_biplot(), indiv_anova(), stab_dist(), stab_eskridge(), stab_fox(), stab_huehn(), stab_kang(), stab_masv(), stab_measures(), stab_par(), stab_reg(), stab_reliability(), stab_superiority()

Author

Muhammad Yaseen (myaseen208@gmail.com), Kent M. Eskridge (keskridge1@unl.edu)

Examples

data(ge_data)
fit <-
  stab_asv(
      .data = ge_data
    , .y    = Yield
    , .rep  = Rep
    , .gen  = Gen
    , .env  = Env
    )
head(fit$ASD)
#>            Gen     Mean       ASD rMean  rASD   YSI        PC1        PC2
#>         <char>    <num>     <num> <int> <int> <int>      <num>      <num>
#> 1:       PR115 4444.273 1.1235033     3     2     5 -0.9031507  0.4057644
#> 2:      V14154 4364.727 2.6556975     5     5    10 -0.1647526 -2.6488118
#> 3:        MSH3 4247.045 1.9014683    12     3    15  1.2330175 -1.2529001
#> 4:      V14168 4342.045 5.6958779     7    12    19  4.7800620 -1.3024826
#> 5:       PR119 4156.727 0.6095297    24     1    25  0.1556221 -0.5821833
#> 6: LOCAL CHECK 4280.136 7.7084442     9    19    28  1.6384767 -7.4704480
plot(x = fit, which = c("ranks", "mean")[1])