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, 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

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

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.

Annicchiarico P (1997). “Joint regression vs AMMI analysis of genotype-environment interactions for cereals in Italy.” Euphytica, 94(1), 53--62. doi: 10.1023/A:1002954824178 , https://link.springer.com/article/10.1023/A:1002954824178.

Purchase JL (1997). Parametric Analysis to Describe Genotype × Environment Interaction and Yield Stability in Winter Wheat. PhD thesis, University of the Orange Free State. http://scholar.ufs.ac.za:8080/xmlui/handle/11660/1966.

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

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.

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. doi: 10.1080/02571862.2000.10634878 .

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.

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. http://eprints.icrisat.ac.in/id/eprint/7173.

Jambhulkar NN, Bose LK, Singh ON (2014). “AMMI stability index for stability analysis.” In Mohapatra T (ed.), CRRI Newsletter, January-March 2014, volume 35 number 1, 15. Central Rice Research Institute, Cuttack, Orissa. http://www.crri.nic.in/CRRI_newsletter/crnl_jan_mar_14_web.pdf.

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. http://www.envirobiotechjournals.com/article_abstract.php?aid=6346&iid=200&jid=3.

Jambhulkar NN, Rath NC, Bose LK, Subudhi H, 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. doi: 10.5958/2249-5266.2017.00030.3 .

See also

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

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 -8.659740e-15 3.3801820 0.0232206231 4.7855876 2.9592568
#> 2    104.22 31.28887  1.110223e-15 1.4627695 0.0175897578 3.8328358 2.2591593
#> 3    121.31 30.10174  4.440892e-16 2.2937918 0.0342010876 4.0446758 3.3872806
#> 4    141.28 39.75624  1.021405e-14 4.4672401 0.0529036285 5.1867706 4.3846248
#> 5    157.26 36.95181  2.220446e-15 3.2923168 0.0965635719 7.6459224 5.4846596
#> 6     163.9 21.41747 -1.243450e-14 4.4269636 0.0236900961 4.4977055 2.6263670
#> 7    221.19 22.98480 -4.440892e-15 1.8014494 0.0127574566 2.1905344 2.0218098
#> 8    233.11 28.66655  2.275957e-15 1.0582263 0.0211138628 3.1794345 2.1624442
#> 9     235.6 38.63477  5.773160e-15 3.7647078 0.0723274691 8.4913020 4.8273551
#> 10    241.2 26.34039 -5.329071e-15 1.6774241 0.0153823821 2.0338659 2.0056410
#> 11    255.7 30.58975 -3.774758e-15 3.3289736 0.0317506280 4.7013868 3.6075128
#> 12   314.12 28.17335  5.773160e-15 2.9170536 0.0170302467 3.1376678 2.4584089
#> 13    317.6 35.32583  2.220446e-15 2.1874274 0.0136347120 2.3345492 1.8698826
#> 14   319.20 38.75767  1.731948e-14 6.7164864 0.0855988994 8.6398087 5.9590451
#> 15   320.16 26.34808 -6.217249e-15 3.3208950 0.0180662044 3.8822326 2.7040109
#> 16   342.15 26.01336 -2.442491e-15 2.9219360 0.0225156118 3.6438425 2.9755899
#> 17    346.2 23.84175 -1.110223e-14 5.1827747 0.0459434537 5.3987165 3.9525017
#> 18   351.26 36.11581  1.021405e-14 2.9786832 0.0639652186 5.4005468 4.5622439
#> 19   364.21 34.05974  1.415534e-15 0.7236998 0.0018299284 1.4047546 0.7526264
#> 20    402.7 27.47748 -3.885781e-16 0.2801470 0.0001339385 0.3537818 0.2284995
#> 21    405.2 28.98663 -1.088019e-14 3.9832546 0.0229492190 4.1095727 2.7952381
#> 22   406.12 32.68323  3.108624e-15 2.5631734 0.0264692745 5.3218165 2.8834753
#> 23    427.7 36.19020  1.110223e-16 1.1467970 0.0135698145 2.4124676 2.0049278
#> 24    450.3 36.19602  6.439294e-15 3.1430174 0.0216161656 4.6608954 2.8200387
#> 25    506.2 33.26623 -5.773160e-15 0.7511331 0.0318266934 1.9330143 2.2178470
#> 26  Canchan 27.00126  9.325873e-15 3.0975884 0.0461305761 3.6665608 3.5328212
#> 27  Desiree 16.15569 -1.132427e-14 7.7833445 0.0901534938 9.0626072 5.8073242
#> 28    Unica 39.10400  5.329071e-15 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     28.0      43     37       42       39
#> 2    104.22 31.28887     28.0      19     21       25       22
#> 3    121.31 30.10174     29.0      25     34       29       33
#> 4    141.28 39.75624     27.5      26     23       21       23
#> 5    157.26 36.95181     22.5      22     33       29       31
#> 6     163.9 21.41747     28.0      51     42       43       38
#> 7    221.19 22.98480     35.0      34     29       31       32
#> 8    233.11 28.66655     36.0      21     27       26       24
#> 9     235.6 38.63477     26.5      25     28       29       28
#> 10    241.2 26.34039     30.0      29     28       26       27
#> 11    255.7 30.58975     24.0      33     31       32       34
#> 12   314.12 28.17335     40.5      30     25       26       28
#> 13    317.6 35.32583     26.5      18     14       15       12
#> 14   319.20 38.75767     31.0      30     29       30       31
#> 15   320.16 26.34808     27.0      39     30       34       33
#> 16   342.15 26.01336     35.0      37     36       34       41
#> 17    346.2 23.84175     28.0      51     45       47       46
#> 18   351.26 36.11581     34.5      22     31       31       31
#> 19   364.21 34.05974     26.0      12     12       12       12
#> 20    402.7 27.47748     31.0      20     20       20       20
#> 21    405.2 28.98663     20.0      39     29       31       29
#> 22   406.12 32.68323     32.0      23     28       33       27
#> 23    427.7 36.19020     20.0      12     11       14       11
#> 24    450.3 36.19602     30.0      22     17       23       20
#> 25    506.2 33.26623     18.0      14     29       14       19
#> 26  Canchan 27.00126     45.0      35     41       31       39
#> 27  Desiree 16.15569     30.0      56     55       56       55
#> 28    Unica 39.10400     23.0      24     27       28       27
#> 
#> $`SP Correlation`
#>        AMGE    ASV     EV   MASV   SIPC
#> AMGE 1.00**   <NA>   <NA>   <NA>   <NA>
#> ASV   -0.03 1.00**   <NA>   <NA>   <NA>
#> EV     0.31 0.70** 1.00**   <NA>   <NA>
#> MASV   0.21 0.81** 0.90** 1.00**   <NA>
#> SIPC   0.28 0.81** 0.96** 0.94** 1.00**
#> 
#> $`SSI Correlation`
#>        AMGE    ASV     EV   MASV   SIPC
#> AMGE 1.00**   <NA>   <NA>   <NA>   <NA>
#> ASV    0.20 1.00**   <NA>   <NA>   <NA>
#> EV     0.24 0.84** 1.00**   <NA>   <NA>
#> MASV   0.23 0.92** 0.90** 1.00**   <NA>
#> SIPC   0.32 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        -0.03 1.00**   <NA>   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> EV          0.31 0.70** 1.00**   <NA>   <NA>     <NA>    <NA>   <NA>     <NA>
#> MASV        0.21 0.81** 0.90** 1.00**   <NA>     <NA>    <NA>   <NA>     <NA>
#> SIPC        0.28 0.81** 0.96** 0.94** 1.00**     <NA>    <NA>   <NA>     <NA>
#> AMGE_SSI    0.34   0.03  -0.08  -0.10  -0.03   1.00**    <NA>   <NA>     <NA>
#> ASV_SSI  -0.56** 0.71**   0.21   0.35   0.34     0.20  1.00**   <NA>     <NA>
#> EV_SSI    -0.42* 0.64** 0.48**  0.47* 0.53**     0.24  0.84** 1.00**     <NA>
#> MASV_SSI  -0.46* 0.73**  0.40* 0.54** 0.51**     0.23  0.92** 0.90**   1.00**
#> SIPC_SSI  -0.38* 0.70**  0.45* 0.50** 0.54**     0.32  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`
#>