Estimate multiple AMMI model Stability Parameters

Source: R/ammistability.R

ammistability computes multiple stability parameters from an AMMI model. Further, the corresponding Simultaneous Selection Indices for Yield and Stability (SSI) are also calculated according to the argument ssi.method. From the results, correlation between the computed indices will also be computed. The resulting correlation matrices will be plotted as correlograms. For visual comparisons of ranks of genotypes for different indices, slopegraphs and heatmaps will also be generated by this function.

ammistability(
  model,
  n,
  alpha = 0.05,
  ssi.method = c("farshadfar", "rao"),
  a = 1,
  AMGE = TRUE,
  ASI = TRUE,
  ASV = TRUE,
  ASTAB = TRUE,
  AVAMGE = TRUE,
  DA = TRUE,
  DZ = TRUE,
  EV = TRUE,
  FA = TRUE,
  MASI = TRUE,
  MASV = TRUE,
  SIPC = TRUE,
  ZA = TRUE,
  force.grouping = TRUE,
  line.size = 1,
  line.alpha = 0.5,
  line.col = NULL,
  point.size = 1,
  point.alpha = 0.5,
  point.col = NULL,
  text.size = 2
)

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).

AMGE

If TRUE, computes AMGE (see Details). Default is TRUE.

ASI

If TRUE, computes ASI (see Details). n = 2 will be used in this case. Default is TRUE.

ASV

If TRUE, computes ASV (see Details). n = 2 will be used in this case. Default is TRUE.

ASTAB

If TRUE, computes ASTAB (see Details). Default is TRUE.

AVAMGE

If TRUE, computes AVAMGE (see Details). Default is TRUE.

DA

If TRUE, computes DA (see Details). Default is TRUE.

DZ

If TRUE, computes DZ (see Details). Default is TRUE.

EV

If TRUE, computes EV (see Details). Default is TRUE.

FA

If TRUE, computes FA (see Details). Default is TRUE.

MASI

If TRUE, computes MASI (see Details). Default is TRUE.

MASV

If TRUE, computes MASV (see Details). Default is TRUE.

SIPC

If TRUE, computes SIPC (see Details). Default is TRUE.

ZA

If TRUE, computes ZA (see Details). Default is TRUE.

force.grouping

If TRUE, genotypes will be considered as a grouping variable for plotting the slopegraphs. (Each genotype will be represented by a different colour in the slopegraphs). Default is TRUE.

line.size

Size of lines plotted in the slopegraphs. Must be numeric.

line.alpha

Transparency of lines plotted in the slopegraphs. Must be numeric.

line.col

Default is TRUE. Overrides colouring by force.grouping argument.

point.size

Size of points plotted in the slopegraphs. Must be numeric.

point.alpha

Transparency of points plotted in the slopegraphs. Must be numeric.

point.col

Default is TRUE. Overrides colouring by force.grouping argument.

text.size

Size of text annotations plotted in the slopegraphs. Must be numeric.

Value

A list with the following components:

Details

A data frame indicating the stability parameters computed and the method used for computing the SSI.

Stability Parameters

A data frame of computed stability parameters.

Simultaneous Selection Indices

A data frame of computed SSIs.

SP Correlation

A data frame of correlation between stability parameters.

SSI Correlation

A data frame of correlation between SSIs.

SP and SSI Correlation

A data frame of correlation between stability parameters and SSIs.

SP Correlogram

Correlogram of stability parameters.

SSI Correlogram

Correlogram of SSIs.

SP and SSI Correlogram

Correlogram of stability parameters and SSIs.

SP Slopegraph

Slopegraph of stability parameter ranks.

SSI Slopegraph

Slopegraph of SSI ranks.

SP Heatmap

Heatmap of stability parameter ranks.

SSI Heatmap

Heatmap of SSI ranks.

Details

ammistability computes the following stability parameters from an AMMI model.

Sum Across Environments of GEI Modelled by AMMI (AMGE)

Sneller et al. (1997)

AMMI Stability Index (ASI)

Jambhulkar et al. (2014); Jambhulkar et al. (2015); Jambhulkar et al. (2017)

AMMI Stability Value (ASV)

Purchase (1997); Purchase et al. (1999); Purchase et al. (2000)

AMMI Based Stability Parameter (ASTAB)

Rao and Prabhakaran (2005)

Sum Across Environments of Absolute Value of GEI Modelled by AMMI (AVAMGE)

Zali et al. (2012)

Annicchiarico's D Parameter (DA)

Annicchiarico (1997)

Zhang's D Parameter (DZ)

Zhang et al. (1998)

Averages of the Squared Eigenvector Values (EV)

Zobel (1994)

Stability Measure Based on Fitted AMMI Model (FA)

Raju (2002)

Modified AMMI Stability Index (MASI)

Ajay et al. (2018)

Modified AMMI Stability Value (MASV)

Zali et al. (2012); Ajay et al. (2019)

Sums of the Absolute Value of the IPC Scores (SIPC)

Sneller et al. (1997)

Absolute Value of the Relative Contribution of IPCs to the Interaction (Za)

Zali et al. (2012)

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 (2019). “ammistability: R package for ranking genotypes based on stability parameters derived from AMMI model.” Indian Journal of Genetics and Plant Breeding (The), 79(2), 460--466.

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53--62.

Jambhulkar NN, Bose LK, Pande K, Singh ON (2015). “Genotype by environment interaction and stability analysis in rice genotypes.” Ecology, Environment and Conservation, 21(3), 1427--1430.

Jambhulkar NN, Bose LK, Singh ON (2014). “AMMI stability index for stability analysis.” In Mohapatra T (ed.), CRRI Newsletter, January-March 2014, volume 35(1), 15. Central Rice Research Institute, Cuttack, Orissa.

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.

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.

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.

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.

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.

Examples

library(agricolae)
data(plrv)

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

ammistability(model, AMGE = TRUE, ASI = FALSE, ASV = TRUE, ASTAB = FALSE,
              AVAMGE = FALSE, DA = FALSE, DZ = FALSE, EV = TRUE,
              FA = FALSE, MASI = FALSE, MASV = TRUE, SIPC = TRUE,
              ZA = FALSE)
#> $Details
#> $Details$`Stability parameters estimated`
#> [1] "AMGE" "ASV"  "EV"   "MASV" "SIPC"
#> 
#> $Details$`SSI method`
#> [1] "Farshadfar (2008)"
#> 
#> 
#> $`Stability Parameters`
#>    genotype    means          AMGE       ASV           EV      MASV      SIPC
#> 1    102.18 26.31947  1.598721e-14 3.3801820 0.0232206231 4.7855876 2.9592568
#> 2    104.22 31.28887 -8.881784e-15 1.4627695 0.0175897578 3.8328358 2.2591593
#> 3    121.31 30.10174  1.643130e-14 2.2937918 0.0342010876 4.0446758 3.3872806
#> 4    141.28 39.75624 -4.440892e-15 4.4672401 0.0529036285 5.1867706 4.3846248
#> 5    157.26 36.95181  3.241851e-14 3.2923168 0.0965635719 7.6459224 5.4846596
#> 6     163.9 21.41747  3.108624e-15 4.4269636 0.0236900961 4.4977055 2.6263670
#> 7    221.19 22.98480  8.881784e-15 1.8014494 0.0127574566 2.1905344 2.0218098
#> 8    233.11 28.66655 -1.476597e-14 1.0582263 0.0211138628 3.1794345 2.1624442
#> 9     235.6 38.63477 -2.975398e-14 3.7647078 0.0723274691 8.4913020 4.8273551
#> 10    241.2 26.34039  7.105427e-15 1.6774241 0.0153823821 2.0338659 2.0056410
#> 11    255.7 30.58975 -1.598721e-14 3.3289736 0.0317506280 4.7013868 3.6075128
#> 12   314.12 28.17335 -1.776357e-15 2.9170536 0.0170302467 3.1376678 2.4584089
#> 13    317.6 35.32583  1.776357e-15 2.1874274 0.0136347120 2.3345492 1.8698826
#> 14   319.20 38.75767  8.437695e-15 6.7164864 0.0855988994 8.6398087 5.9590451
#> 15   320.16 26.34808  1.154632e-14 3.3208950 0.0180662044 3.8822326 2.7040109
#> 16   342.15 26.01336 -9.325873e-15 2.9219360 0.0225156118 3.6438425 2.9755899
#> 17    346.2 23.84175 -3.552714e-15 5.1827747 0.0459434537 5.3987165 3.9525017
#> 18   351.26 36.11581  1.110223e-15 2.9786832 0.0639652186 5.4005468 4.5622439
#> 19   364.21 34.05974 -4.940492e-15 0.7236998 0.0018299284 1.4047546 0.7526264
#> 20    402.7 27.47748 -4.163336e-16 0.2801470 0.0001339385 0.3537818 0.2284995
#> 21    405.2 28.98663  8.881784e-16 3.9832546 0.0229492190 4.1095727 2.7952381
#> 22   406.12 32.68323 -1.731948e-14 2.5631734 0.0264692745 5.3218165 2.8834753
#> 23    427.7 36.19020 -2.553513e-15 1.1467970 0.0135698145 2.4124676 2.0049278
#> 24    450.3 36.19602  1.021405e-14 3.1430174 0.0216161656 4.6608954 2.8200387
#> 25    506.2 33.26623  6.439294e-15 0.7511331 0.0318266934 1.9330143 2.2178470
#> 26  Canchan 27.00126 -7.993606e-15 3.0975884 0.0461305761 3.6665608 3.5328212
#> 27  Desiree 16.15569  1.754152e-14 7.7833445 0.0901534938 9.0626072 5.8073242
#> 28    Unica 39.10400 -2.042810e-14 3.8380782 0.0770659860 8.5447632 5.0654615
#> 
#> $`Simultaneous Selection Indices`
#>    genotype    means AMGE_SSI ASV_SSI EV_SSI MASV_SSI SIPC_SSI
#> 1    102.18 26.31947       48      43     37       42       39
#> 2    104.22 31.28887       20      19     21       25       22
#> 3    121.31 30.10174       41      25     34       29       33
#> 4    141.28 39.75624       11      26     23       21       23
#> 5    157.26 36.95181       33      22     33       29       31
#> 6     163.9 21.41747       45      51     42       43       38
#> 7    221.19 22.98480       48      34     29       31       32
#> 8    233.11 28.66655       22      21     27       26       24
#> 9     235.6 38.63477        5      25     28       29       28
#> 10    241.2 26.34039       42      29     28       26       27
#> 11    255.7 30.58975       18      33     31       32       34
#> 12   314.12 28.17335       31      30     25       26       28
#> 13    317.6 35.32583       26      18     14       15       12
#> 14   319.20 38.75767       24      30     29       30       31
#> 15   320.16 26.34808       45      39     30       34       33
#> 16   342.15 26.01336       30      37     36       34       41
#> 17    346.2 23.84175       36      51     45       47       46
#> 18   351.26 36.11581       24      22     31       31       31
#> 19   364.21 34.05974       19      12     12       12       12
#> 20    402.7 27.47748       33      20     20       20       20
#> 21    405.2 28.98663       31      39     29       31       29
#> 22   406.12 32.68323       15      23     28       33       27
#> 23    427.7 36.19020       19      12     11       14       11
#> 24    450.3 36.19602       29      22     17       23       20
#> 25    506.2 33.26623       30      14     29       14       19
#> 26  Canchan 27.00126       28      35     41       31       39
#> 27  Desiree 16.15569       55      56     55       56       55
#> 28    Unica 39.10400        4      24     27       28       27
#> 
#> $`SP Correlation`
#>        AMGE    ASV     EV   MASV   SIPC
#> AMGE 1.00**   <NA>   <NA>   <NA>   <NA>
#> ASV    0.16 1.00**   <NA>   <NA>   <NA>
#> EV     0.12 0.70** 1.00**   <NA>   <NA>
#> MASV  -0.01 0.81** 0.90** 1.00**   <NA>
#> SIPC   0.10 0.81** 0.96** 0.94** 1.00**
#> 
#> $`SSI Correlation`
#>        AMGE    ASV     EV   MASV   SIPC
#> AMGE 1.00**   <NA>   <NA>   <NA>   <NA>
#> ASV  0.61** 1.00**   <NA>   <NA>   <NA>
#> EV   0.53** 0.84** 1.00**   <NA>   <NA>
#> MASV 0.52** 0.92** 0.90** 1.00**   <NA>
#> SIPC 0.53** 0.89** 0.96** 0.95** 1.00**
#> 
#> $`SP and SSI Correlation`
#>            AMGE    ASV     EV   MASV   SIPC AMGE_SSI ASV_SSI EV_SSI MASV_SSI
#> AMGE     1.00**   <NA>   <NA>   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> ASV        0.16 1.00**   <NA>   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> EV         0.12 0.70** 1.00**   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> MASV      -0.01 0.81** 0.90** 1.00**   <NA>     <NA>    <NA>   <NA>     <NA>
#> SIPC       0.10 0.81** 0.96** 0.94** 1.00**     <NA>    <NA>   <NA>     <NA>
#> AMGE_SSI 0.75**   0.17  -0.16  -0.18  -0.12   1.00**    <NA>   <NA>     <NA>
#> ASV_SSI    0.21 0.71**   0.21   0.35   0.34   0.61**  1.00**   <NA>     <NA>
#> EV_SSI     0.23 0.64** 0.48**  0.47* 0.53**   0.53**  0.84** 1.00**     <NA>
#> MASV_SSI   0.18 0.73**  0.40* 0.54** 0.51**   0.52**  0.92** 0.90**   1.00**
#> SIPC_SSI   0.20 0.70**  0.45* 0.50** 0.54**   0.53**  0.89** 0.96**   0.95**
#>          SIPC_SSI
#> AMGE         <NA>
#> ASV          <NA>
#> EV           <NA>
#> MASV         <NA>
#> SIPC         <NA>
#> AMGE_SSI     <NA>
#> ASV_SSI      <NA>
#> EV_SSI       <NA>
#> MASV_SSI     <NA>
#> SIPC_SSI   1.00**
#> 
#> $`SP Correlogram`

#> 
#> $`SSI Correlogram`

#> 
#> $`SP and SSI Correlogram`

#> 
#> $`SP Slopegraph`

#> 
#> $`SSI Slopegraph`

#> 
#> $`SP Heatmap`

#> 
#> $`SSI Heatmap`

#>