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).

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: $$AS{V_i} = {\left[ {{{\left[ {\frac{{r\mathop \lambda \nolimits_1^2 }}{{r\mathop \lambda \nolimits_2^2 }} \times (\mathop \lambda \nolimits_1^{0.5} {a_{i1}}{t_{j1}})} \right]}^2} + {{(\mathop \lambda \nolimits_2^{0.5} {a_{i2}}{t_{j2}})}^2}} \right]^{0.5}}$$

where \(r\) is the number of replications included in the analysis,

The SIPC index is computed as follows: $$SIP{C_i} = \sum\nolimits_{k = 1}^P {\left| {\mathop {|\lambda }\nolimits_k^{0.5} {a_{ik}}} \right|}$$

where \(P\) is the number of IPCA retained via F-tests.

The EV index is computed as follows: $$E{V_i} = \sum\nolimits_{k = 1}^P {\mathop a\nolimits_{ik}^2 } /P$$

The ZA index is computed as follows: $$Z{a_i} = \sum\nolimits_{k = 1}^P {{\theta _k}{a_{ik}}} $$

where \(\theta _k\) is the percentage sum of squares explained by the kth IPCA.

$$ WAAS_i = \sum_{k = 1}^{p} |IPCA_{ik} \times EP_k|/ \sum_{k = 1}^{p}EP_k$$

where \(WAAS_i\) is the weighted average of absolute scores of the ith genotype; \(PCA_{ik}\) is the score of the ith genotype in the kth IPCA; and \(EP_k\) 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

Author

Tiago Olivoto tiagoolivoto@gmail.com

Examples

# \donttest{ 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()
#> variable GY #> --------------------------------------------------------------------------- #> AMMI analysis table #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) Proportion Accumulated #> ENV 13 279.574 21.5057 62.33 0.00e+00 . . #> REP(ENV) 28 9.662 0.3451 3.57 3.59e-08 . . #> GEN 9 12.995 1.4439 14.93 2.19e-19 . . #> GEN:ENV 117 31.220 0.2668 2.76 1.01e-11 . . #> PC1 21 10.749 0.5119 5.29 0.00e+00 34.4 34.4 #> PC2 19 9.924 0.5223 5.40 0.00e+00 31.8 66.2 #> PC3 17 4.039 0.2376 2.46 1.40e-03 12.9 79.2 #> PC4 15 3.074 0.2049 2.12 9.60e-03 9.8 89 #> PC5 13 1.446 0.1113 1.15 3.18e-01 4.6 93.6 #> PC6 11 0.932 0.0848 0.88 5.61e-01 3 96.6 #> PC7 9 0.567 0.0630 0.65 7.53e-01 1.8 98.4 #> PC8 7 0.362 0.0518 0.54 8.04e-01 1.2 99.6 #> PC9 5 0.126 0.0252 0.26 9.34e-01 0.4 100 #> Residuals 252 24.367 0.0967 NA NA . . #> Total 536 389.036 0.7258 NA NA <NA> <NA> #> --------------------------------------------------------------------------- #> #> variable HM #> --------------------------------------------------------------------------- #> AMMI analysis table #> --------------------------------------------------------------------------- #> Source Df Sum Sq Mean Sq F value Pr(>F) Proportion Accumulated #> ENV 13 5710.32 439.255 57.22 1.11e-16 . . #> REP(ENV) 28 214.93 7.676 2.70 2.20e-05 . . #> GEN 9 269.81 29.979 10.56 7.41e-14 . . #> GEN:ENV 117 1100.73 9.408 3.31 1.06e-15 . . #> PC1 21 381.13 18.149 6.39 0.00e+00 34.6 34.6 #> PC2 19 319.43 16.812 5.92 0.00e+00 29 63.6 #> PC3 17 114.26 6.721 2.37 2.10e-03 10.4 74 #> PC4 15 81.96 5.464 1.92 2.18e-02 7.4 81.5 #> PC5 13 68.11 5.240 1.84 3.77e-02 6.2 87.7 #> PC6 11 59.07 5.370 1.89 4.10e-02 5.4 93 #> PC7 9 46.69 5.188 1.83 6.33e-02 4.2 97.3 #> PC8 7 26.65 3.808 1.34 2.32e-01 2.4 99.7 #> PC9 5 3.41 0.682 0.24 9.45e-01 0.3 100 #> Residuals 252 715.69 2.840 NA NA . . #> Total 536 9112.21 17.000 NA NA <NA> <NA> #> --------------------------------------------------------------------------- #> #> All variables with significant (p < 0.05) genotype-vs-environment interaction #> Done!
# }