ammi_indexes function

AMMI-based stability indexes

• ammi_indexes() computes several AMMI-based stability statistics. See Details for a detailed overview.
• AMMI_indexes() use ammi_indexes() instead.

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.

Returns

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

Details

First, let's define some symbols: \mjseqn N' is the number of significant interation principal component axis (IPCs) that were retained in the AMMI model via F tests); \mjseqn \lambda _n is the singular value for th IPC and correspondingly \mjseqn \lambda _n^2 its eigen value; \mjseqn \gamma _in

is the eigenvector value for ith genotype; \mjseqn \delta _jn is the eigenvector value for the th environment. \mjseqn PC_1, \mjseqn PC_2, and \mjseqn PC_n are the scores of 1st, 2nd, and nth IPC; respectively; \mjseqn \theta _1, \mjseqn \theta _2, and \mjseqn \theta _n are percentage sum of squares explained by the 1st, 2nd, and nth IPC, respectively.

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• AMMI Based Stability Parameter (ASTAB) (Rao and Prabhakaran 2005). \mjsdeqn ASTAB = \sum _n=1^N'\lambda _n\gamma _in^2
• AMMI Stability Index (ASI) (Jambhulkar et al. 2017) \mjsdeqn ASI = \sqrt \left [ PC_1^2 \times \theta _1^2 \right ]+\left [ PC_2^2 \times \theta _2^2 \right ]
• AMMI-stability value (ASV) (Purchase et al., 2000). \mjsdeqn ASV_i=\sqrt \frac SS_IPCA1SS_IPCA2(\mathrm IPC \mathrm A 1)^2+(\mathrm IPCA 2)^2
• Sum Across Environments of Absolute Value of GEI Modelled by AMMI (AVAMGE) (Zali et al. 2012) \mjsdeqn AV_(AMGE) = \sum _j=1^E \sum _n=1^N' \left |\lambda _n\gamma _in \delta _jn \right |
• Annicchiarico's D Parameter values (Da) (Annicchiarico 1997) \mjsdeqn D_a = \sqrt \sum _n=1^N'(\lambda _n\gamma _in)^2
• Zhang's D Parameter (Dz) (Zhang et al. 1998) \mjsdeqn D_z = \sqrt \sum _n=1^N'\gamma _in^2
• Sums of the Averages of the Squared Eigenvector Values (EV) (Zobel 1994) \mjsdeqn EV = \sum _n=1^N'\frac \gamma _in^2N'
• Stability Measure Based on Fitted AMMI Model (FA) (Raju 2002) \mjsdeqn FA = \sum _n=1^N'\lambda _n^2\gamma _in^2
• Modified AMMI Stability Index (MASI) (Ajay et al. 2018) \mjsdeqn MASI = \sqrt \sum _n=1^N' PC_n^2 \times \theta _n^2
• Modified AMMI Stability Value (MASV) (Ajay et al. 2019) \mjsdeqn MASV = \sqrt \sum _n=1^N'-1\left (\frac SSIPC_nSSIPC_n+1 \right ) \times (PC_n)^2 + \left (PC_N'\right )^2
• Sums of the Absolute Value of the IPC Scores (SIPC) (Sneller et al. 1997) \mjsdeqn SIPC = \sum _n=1^N' | \lambda _n^0.5\gamma _in|
• Absolute Value of the Relative Contribution of IPCs to the Interaction (Za) (Zali et al. 2012) \mjsdeqn Za = \sum _i=1^N' | \theta _n\gamma _in |
• Weighted average of absolute scores (WAAS) (Olivoto et al. 2019) \mjsdeqn WAAS_i = \sum _k = 1^p |IPCA_ik \times \theta _k/ \sum _k = 1^p\theta _k

For all the statistics, simultaneous selection indexes (SSI) are also computed by summation of the ranks of the stability and mean performance, Y_R, (Farshadfar, 2008).

Examples

library(metan)
model <-
  performs_ammi(data_ge,
                env = ENV,
                gen = GEN,
                rep = REP,
                resp = c(GY, HM))
model_indexes <- ammi_indexes(model)

# Alternatively (and more intuitively) using %>%
# If resp is not declared, all traits are analyzed
res_ind <- data_ge %>%
           performs_ammi(ENV, GEN, REP, verbose = FALSE) %>%
           ammi_indexes()

rbind_fill_id(res_ind, .id = "TRAIT")

References

Ajay BC, Aravind J, Abdul Fiyaz R, Bera SK, Kumar N, Gangadhar K, Kona P (2018). “Modified AMMI Stability Index (MASI) for stability analysis.” ICAR-DGR Newsletter, 18, 4–5.

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. https://www.isgpb.org/article/rectification-of-modified-ammi-stability-value-masv.

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53–62. tools:::Rd_expr_doi("10.1023/A:1002954824178")

Farshadfar E (2008) Incorporation of AMMI stability value and grain yield in a single non-parametric index (GSI) in bread wheat. Pakistan J Biol Sci 11:1791–1796. tools:::Rd_expr_doi("10.3923/pjbs.2008.1791.1796")

Jambhulkar NN, Rath NC, Bose LK, Subudhi HN, Biswajit M, Lipi D, Meher J (2017). “Stability analysis for grain yield in rice in demonstrations conducted during rabi season in India.” Oryza, 54(2), 236–240. tools:::Rd_expr_doi("10.5958/2249-5266.2017.00030.3")

Olivoto T, LUcio ADC, Silva JAG, et al (2019) Mean Performance and Stability in Multi-Environment Trials I: Combining Features of AMMI and BLUP Techniques. Agron J 111:2949–2960. tools:::Rd_expr_doi("10.2134/agronj2019.03.0220")

Raju BMK (2002). “A study on AMMI model and its biplots.” Journal of the Indian Society of Agricultural Statistics, 55(3), 297–322.

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.

Sneller CH, Kilgore-Norquest L, Dombek D (1997). “Repeatability of yield stability statistics in soybean.” Crop Science, 37(2), 383–390. tools:::Rd_expr_doi("10.2135/cropsci1997.0011183X003700020013x")

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.

Zhang Z, Lu C, Xiang Z (1998). “Analysis of variety stability based on AMMI model.” Acta Agronomica Sinica, 24(3), 304–309. http://zwxb.chinacrops.org/EN/Y1998/V24/I03/304.

Zobel RW (1994). “Stress resistance and root systems.” In Proceedings of the Workshop on Adaptation of Plants to Soil Stress. 1-4 August, 1993. INTSORMIL Publication 94-2, 80–99. Institute of Agriculture and Natural Resources, University of Nebraska-Lincoln.

Author(s)

Tiago Olivoto tiagoolivoto@gmail.com