Multi-environmental analysis (MET) of a simulated dataset using metan pakage

Introduction

Multi-environment trials (MET) are crucial steps in plant breeding programs that aim at increasing crop productivity to ensure global food security. The analysis of MET data requires the combination of several approaches including data manipulation, visualization and modelling. As new methods are proposed, analysing MET data correctly and completely remains a challenge, often intractable with existing tools.

In 50 years (1967–2017) the world average of cereal yields has increased by 64%, from 1.68 to 2.76 tons/ha. In the same period, the total production of cereals has raised from 1.305 × 109 to 3.6 × 109 tons, an increase of 175%, while the cultivated area increased by only 7.9% in the same period (FAOSTAT, 2019). These unparallel increases have been possible due to the improved cultivation techniques in combination with superior cultivars. For maize, for example, 50% of the increase in yield was due to breeding (Duvick, 2005). Plant breeding programs have been developing new cultivars for adaptation to new locations, management practices or growing conditions, in a clear and crucial example of exploitation of genotype-versus-environment interaction (GEI).

The breeders’ desire to modelling the GEI appropriately has led to the development of the so-called stability analyses, which includes ANOVA-based methods (Annicchiarico, 1992; Shukla, 1972; Wricke, 1965; Yates & Cochran, 1938); regression-based methods (Eberhart & Russell, 1966); nonparametric methods (Fox, Skovmand, Thompson, Braun, & Cormier, 1990; Huehn, 1979; Lin & Binns, 1988; Thennarasu, 1995) and some methods that combines different statistical techniques, such as the additive main effect and multiplicative interaction (AMMI; Gauch, 2013) and genotype plus genotype-versus-environment interaction (GGE; Yan & Kang, 2003). Then, it is no surprise that scientific production related to multi-environment trial analysis has been growing fast in the recent decades. A bibliometric survey in the SCOPUS database revealed that in the last half-century (1969–2019) 6,590 documents were published in 902 sources (journals, books, etc.) by 19,351 authors. In this period, the number of publications has been increased on average by 11.22% per year but were in the last 10 years the largest amount (~64%) of the documents that were published (see Appendix S1, item 1 for more details).

Linear mixed-effect models (LMM) has been more frequently used to analyse MET data. For example, between 2013 and 2015, the larger number of papers proposing methods to deal with GEI were related to the best linear unbiased prediction (BLUP) in LMMs (Eeuwijk, Bustos-Korts, & Malosetti, 2016). Recent advances in this field showed that BLUP is more predictively accurate than AMMI and that the main advantages of these methods can be combined to help researchers to select or recommend stable and high productive genotypes (Olivoto, Lúcio, Silva, Marchioro, et al., 2019). Thus, the rapid spread of these methods to users around the world can be facilitated if these procedures are implemented in specific software.

In most cases, analysing MET data involves manual checking of the data subset(s) to identify possible outliers, using some biometrical model to explore the relationships between traits(or groups of traits), computing a within-environment ANOVA, computing a joint-ANOVA, and, in case of a significant GEI, applying some stability method to explore it. While a spreadsheet program (e.g. Microsoft Excel) may be used to perform a visual check for outliers, an integrated development environment (IDE, e.g. R, SAS or Matlab) is often required to process the complex matrix operations required in some stability methods. IDEs, however, require a certain degree of expertise to use and have steep learning curves, which sometimes prevents that a coding layman implements certain methods. In this sense, R (R Core Team, 2019) packages have been making easier the life of hundreds of thousands of researchers by providing freely collections of functions developed by the community.

Some open-source R software packages that are designed—or are suitable—for analysing MET data are available. The stability package (https://CRAN.R-project.org/package=stability) contains a collection of functions to perform stability analysis. The ammistability package (https://CRAN.R-project.org/package=ammistability) computes multiple AMMI-based stability parameters. The gge (https://CRAN.R-project.org/package=gge) and GGEBiplots (https://CRAN.R-project.org/package=GGEBiplots) packages may be used to produce a GGE biplot. The R packages agricolae (https://CRAN.R-project.org/package=agricolae) and plantbreeding (http://plantbreeding.r-forge.r-project.org/), while not specifically coded for MET analysis provide useful functions for computing parametric and nonparametric stability statistics. Although useful, these packages do not offer options to perform a complete analysis of MET data, i.e. to provide tools for all steps of the analysis (check, manipulation, analysis and visualization of data). For example, GGEBiplots requires as input data a two-way table containing genotype by environment means with genotypes in rows and environments in columns, but doesn’t provide any function to create quickly such table from data that often is in a ‘long’ format in R. In addition, several studies often compare different stability methods (e.g. Bornhofen et al., 2017; Freiria et al., 2018; Scapim et al., 2010; Shahbazi, 2019; Teodoro et al., 2019; Woyann et al., 2018). This requires a range of different packages to be used, making the coding tedious and difficult to follow. Thus, it seems to be value the creation of an R package that presents an easy workflow, incorporates the most used stability statistics, recently proposed stability methods (Olivoto, Lúcio, Silva, Marchioro, et al., 2019; Olivoto, Lúcio, Silva, Sari, Lúcio, Silva, Sari, & Diel, 2019), options for cross-validation procedures (Piepho, 1994) and BLUP-based stability statistics (Colombari Filho et al., 2013). These features are frequently used but are not yet implemented in any other R package for MET analysis.

Here, we describe the metan (multi-environment trial analysis) package, an open-source R package designed to provide an efficient and reproducible workflow for the analysis of MET data. Our main aim in this paper was to describe the features of metan and how this collection of functions can be useful for an intuitive and complete analysis of MET data.

Here we describe the metan R package, a collection of functions that implement a workflow-based approach to (a) check, manipulate and summarize typical MET data; (b) analyse individual environments using both fixed and mixed-effect models; (c) compute parametric and nonparametric stability statistics; (d) implement biometrical models widely used in MET analysis and (e) plot typical MET data quickly.

## [1] 10165.55

Scree plot of eigenvalues

Quality of variables representation

Variables contribution to dimension 1

Variables contribution to dimension 2

Variables contribution to both dimensions

Variables loading plot

PCA Bi-plot

## Too few points to calculate an ellipse
## Too few points to calculate an ellipse

Plot of PCA loading

## Scree, Biplot and PCA loading plots on one grid

## Too few points to calculate an ellipse
## Too few points to calculate an ellipse

Pearson’s correlation heatmap for all genotypes

Simulated dataset to matcht the first 3 columns acorsi.grayleafspot of Dataset.

gen	env	rep	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
G01	LD	R1	39	96	20.15	12.33	23.81	77.27	366.37	1059.37
G01	LD	R2	56	81	21.02	25.52	64.30	75.92	689.44	371.22
G01	CM	R1	52	98	19.36	21.83	37.39	95.97	367.19	852.29
G01	CM	R2	32	81	12.35	26.56	12.11	57.07	947.09	472.65
G01	PG	R1	32	95	20.99	14.35	43.39	73.09	580.27	683.20
G01	PG	R2	51	84	16.44	27.72	57.75	33.50	244.82	145.33

Dataset summary and Variables visualisation

## # A tibble: 11 × 10
##    Variable Class   Missing Levels Valid_n    Min Median    Max Outlier Text 
##    <chr>    <chr>   <chr>   <chr>    <int>  <dbl>  <dbl>  <dbl>   <dbl> <lgl>
##  1 gen      factor  No      36         648  NA      NA     NA        NA NA   
##  2 env      factor  No      9          648  NA      NA     NA        NA NA   
##  3 rep      factor  No      2          648  NA      NA     NA        NA NA   
##  4 DTF      numeric No      -          648  25      40     56         0 NA   
##  5 DTM      numeric No      -          648  78      97    118         0 NA   
##  6 PL       numeric No      -          648  10.5    17.6   24.7       0 NA   
##  7 NSP      numeric No      -          648   8.73   18.4   28.7       0 NA   
##  8 NPP      numeric No      -          648   5.68   34.5   65.9       0 NA   
##  9 GYP      numeric No      -          648   7.8    62.9  115.        0 NA   
## 10 GYR      numeric No      -          648  82.3   615.  1069.        0 NA   
## 11 TW       numeric No      -          648 100.    586.  1098.        0 NA

## No issues detected while inspecting data.

Variable	Class	Missing	Levels	Valid_n	Min	Median	Max	Outlier	Text
gen	factor	No	36	648	NA	NA	NA	NA	NA
env	factor	No	9	648	NA	NA	NA	NA	NA
rep	factor	No	2	648	NA	NA	NA	NA	NA
DTF	numeric	No	-	648	25.00	40.00	56.00	0	NA
DTM	numeric	No	-	648	78.00	97.00	118.00	0	NA
PL	numeric	No	-	648	10.51	17.62	24.71	0	NA
NSP	numeric	No	-	648	8.73	18.44	28.66	0	NA
NPP	numeric	No	-	648	5.68	34.50	65.93	0	NA
GYP	numeric	No	-	648	7.80	62.92	114.60	0	NA
GYR	numeric	No	-	648	82.34	615.48	1068.70	0	NA
TW	numeric	No	-	648	100.41	586.17	1098.45	0	NA

Individual ANOVA

ENV	MEAN	DFG	MSG	FCG	PFG	DFB	MSB	FCB	PFB	DFE	MSE	CV	h2	AS
CM	619.7935	35	95181.72	1.8723541	0.0338195	1	73549.5481	1.4468198	0.2371129	35	50835.32	36.37775	0.4659130	0.6825782
GO	608.9446	35	109523.41	1.7939301	0.0441434	1	732.3602	0.0119956	0.9134120	35	61052.22	40.57635	0.4425647	0.6652553
GS	588.2103	35	105603.53	1.3067705	0.2163269	1	78455.5272	0.9708328	0.3312353	35	80812.61	48.32890	0.2347547	0.4845149
JT	609.8557	35	101362.11	1.2613538	0.2478824	1	63167.0196	0.7860527	0.3813481	35	80359.78	46.48280	0.2072010	0.4551934
LD	620.1714	35	62451.63	0.5641662	0.9525368	1	8447.4002	0.0763109	0.7839852	35	110697.22	53.64838	-0.7725274	0.0000000
PG	575.5801	35	57365.09	0.4918532	0.9804392	1	1039.6040	0.0089137	0.9253202	35	116630.51	59.33354	-1.0331268	0.0000000

GE Plot (heatmap)

## Evaluating trait DTF |=====                                      | 12% 00:00:00 
Evaluating trait DTM |===========                                | 25% 00:00:00 
Evaluating trait PL |================                            | 38% 00:00:00 
Evaluating trait NSP |======================                     | 50% 00:00:00 
Evaluating trait NPP |===========================                | 62% 00:00:00 
Evaluating trait GYP |================================           | 75% 00:00:01 
Evaluating trait GYR |======================================     | 88% 00:00:01 
Evaluating trait TW |============================================| 100% 00:00:01 

## Method: REML/BLUP

## Random effects: GEN

## Fixed effects: REP

## Denominador DF: Satterthwaite's method

## ---------------------------------------------------------------------------
## P-values for Likelihood Ratio Test of the analyzed traits
## ---------------------------------------------------------------------------
##     model DTF DTM PL    NSP NPP   GYP    GYR TW
##  Complete  NA  NA NA     NA  NA    NA     NA NA
##  Genotype   1   1  1 0.0908   1 0.266 0.0375  1
## ---------------------------------------------------------------------------
## Variables with nonsignificant Genotype effect
## DTF DTM PL NSP NPP GYP TW 
## ---------------------------------------------------------------------------

GE Plot (line)

Genotypes seems to show higher values in the second replication.

Winning genotypes by Environment and Trait

ENV	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
CM	G28	G17	G05	G01	G35	G25	G09	G06
GO	G28	G06	G36	G17	G19	G21	G29	G26
GS	G24	G09	G29	G07	G36	G03	G05	G22
JT	G09	G15	G18	G35	G15	G09	G08	G36
LD	G26	G34	G07	G09	G29	G29	G21	G15
PG	G05	G30	G29	G12	G01	G31	G04	G33

Genotype ranking by Environment and Trait

ENV	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
CM	G28	G17	G05	G01	G35	G25	G09	G06
CM	G17	G31	G22	G17	G05	G02	G36	G11
CM	G10	G12	G15	G14	G34	G33	G30	G05
CM	G13	G35	G03	G03	G23	G04	G04	G09
CM	G22	G20	G02	G34	G09	G15	G33	G18
CM	G06	G29	G14	G26	G30	G24	G22	G23

ANOVA for DTF trait

Source	Df	Sum Sq	Mean Sq	F value	Pr(>F)
ENV	8.00000	748.1327	93.51659	1.0817645	0.3755126
REP(ENV)	9.00000	865.3194	96.14660	1.1121876	0.3535028
GEN	35.00000	2449.4244	69.98355	0.8095433	0.7721416
GEN:ENV	280.00000	21910.8673	78.25310	0.9052022	0.8032908
Residuals	315.00000	27231.1806	86.44819	NA	NA
CV(%)	22.68342	NA	NA	NA	NA

Classification of evironment favourability

## Evaluating trait TW |============================================| 100% 00:00:02 

ENV	Y	index	class
CM	619.7935	22.994707	favorable
GO	608.9446	12.145818	favorable
GS	588.2103	-8.588488	unfavorable
JT	609.8557	13.056929	favorable
LD	620.1714	23.372623	favorable
PG	575.5801	-21.218626	unfavorable

Plot showing Favourability of Environments (TW)

Ecovalence with regards to TW

## Evaluating trait TW |============================================| 100% 00:00:02 

## Variable TW 
## ---------------------------------------------------------------------------
## Genotypic confidence index
## ---------------------------------------------------------------------------
## # A tibble: 36 × 13
##    GEN       CM      GO     GS     JT      LD     PG     PL     PM      SP
##    <chr>  <dbl>   <dbl>  <dbl>  <dbl>   <dbl>  <dbl>  <dbl>  <dbl>   <dbl>
##  1 G01    156.   144.    186.  -127.   209.    -47.7 -288.   -56.8 -176.  
##  2 G02    107.   -47.3   182.    98.0  -59.6  -167.  -194.   131.   -50.7 
##  3 G03    -71.1 -131.    339.    71.5 -230.    123.  -315.   295.   -81.5 
##  4 G04   -104.    96.7   101.  -197.    24.5   202.    99.4 -239.    16.6 
##  5 G05    305.     2.39  -49.8   51.5   50.6  -133.    46.1   43.2 -316.  
##  6 G06    381.  -378.    -15.8  -34.1 -135.    290.   -68.9 -134.    95.1 
##  7 G07   -118.  -241.   -106.  -217.   277.    229.   185.   -61.9   54.5 
##  8 G08    184.   263.   -325.  -213.    30.5    71.6 -332.   182.   140.  
##  9 G09    271.    70.1  -234.   212.    -2.37   95.0  156.  -162.  -405.  
## 10 G10   -295.    77.6    76.6 -266.   124.    313.   -85.1   60.4   -6.37
## # ℹ 26 more rows
## # ℹ 3 more variables: Ecoval <dbl>, Ecov_perc <dbl>, rank <dbl>

GEN CM GO GS JT LD PG PL PM SP Ecoval Ecov_perc rank G01 156.28585 143.584738 185.999043 -126.62637 208.732932 -47.705818 -287.755957 -56.7708179 -175.743596 516858.5 2.0510323 10 G02 106.74140 -47.284707 182.389599 98.03918 -59.576512 -166.915262 -193.945401 131.2897377 -50.738040 290686.9 1.1535231 4 G03 -71.13304 -131.374151 339.005154 71.53474 -230.485957 123.175293 -314.734846 295.4652932 -81.452485 807298.0 3.2035737 21 G04 -104.49082 96.693071 101.022376 -196.66304 24.506265 201.947515 99.412376 -239.0474846 16.619738 355671.7 1.4114001 7 G05 304.54252 2.386404 -49.819290 51.54029 50.564599 -132.784151 46.075710 43.1758488 -315.681929 443441.6 1.7596947 9 G06 380.88252 -378.183596 -15.844290 -34.14471 -134.740401 289.955849 -68.939290 -134.0741512 95.088071 847021.7 3.3612079 25 G07 -118.27137 -241.227485 -106.148179 -217.27360 276.555710 228.986960 184.786821 -61.9180401 54.509182 601046.8 2.3851142 14 G08 183.83863 262.547515 -324.963179 -213.42860 30.510710 71.576960 -332.228179 181.7769599 140.369182 846113.5 3.3576042 24 G09 270.90529 70.079182 -233.906512 211.55307 -2.367624 95.038627 156.433488 -162.4163735 -405.319151 803879.6 3.1900087 20 G10 -294.61026 77.628626 76.602932 -266.31748 124.416821 313.393071 -85.092068 60.3530710 -6.374707 588465.9 2.3351898 13 G11 273.94585 260.794738 -379.395957 216.80863 20.547932 55.444182 1.034043 -234.1408179 -215.038596 877136.7 3.4807124 27 G12 70.06474 127.173626 -166.092068 125.97252 -54.378179 -7.626929 11.892932 79.3530710 -186.359707 217442.6 0.8628702 2 G13 74.15918 -156.506929 -231.242624 69.63696 -386.608735 226.872515 532.262376 -0.3124846 -128.260262 1178015.9 4.6746812 36 G14 -97.61137 -463.477485 336.836821 243.09640 -28.754290 130.086960 -11.128179 -6.0930401 -102.955818 850809.1 3.3762374 26 G15 -174.16637 47.552515 -59.913179 28.87140 398.410710 -231.458040 -26.428179 231.0569599 -213.925818 698344.5 2.7712173 18 G16 -26.16471 142.689182 -18.381512 -296.30693 -131.732623 29.018626 79.918488 166.5286265 54.430849 328915.0 1.3052224 6 G17 -272.52415 -114.640262 -409.760957 247.10363 -240.662068 161.209182 283.794043 39.1641821 306.316404 1152370.6 4.5729139 35 G18 286.06029 -136.515818 -335.821512 240.77807 137.057377 -161.246374 31.568488 -313.6163735 251.735849 957450.2 3.7994176 29 G19 -47.07582 -309.921929 61.012377 -263.74304 109.766265 -34.267485 65.652377 203.5725154 215.004738 553505.1 2.1964560 12 G20 335.26085 -94.880262 -193.740957 -131.68637 -75.202068 72.359182 75.084043 52.0741821 -39.268596 394123.0 1.5639853 8 G21 -394.07860 -112.609707 151.849599 -64.41082 56.458488 -257.790262 152.054599 386.2447377 82.281960 887810.5 3.5230687 28 G22 -186.06860 -400.424707 450.224599 118.43418 -108.376512 -100.660262 44.879599 -137.7252623 319.716960 1113539.3 4.4188208 33 G23 355.18029 -124.130818 -12.381512 -253.30693 88.462377 -67.846373 36.543488 -236.0713735 213.550849 641954.0 2.5474448 17 G24 227.84585 319.539738 1.109043 -174.84637 -154.647068 52.054182 -246.515957 -156.9458179 132.406404 628301.6 2.4932681 16 G25 -36.87637 161.917515 164.766821 134.61140 -110.599290 -55.998040 99.451821 -185.6030401 -171.670818 324047.0 1.2859048 5 G26 45.91529 417.574182 -235.321512 -275.17693 -121.932624 -148.526374 -44.671512 153.5886265 208.550849 827162.2 3.2824001 22 G27 168.00474 -59.856373 79.827932 206.77752 234.421821 -187.501929 -106.272068 -296.2969290 -39.104707 543326.4 2.1560639 11 G28 -189.22082 -352.616929 368.017377 115.08196 247.121265 -279.372485 32.167377 -198.0674846 256.889738 1108399.1 4.3984234 32 G29 -343.33026 240.403627 -119.027068 212.93252 106.616821 -178.976929 -74.342068 -168.7319290 324.455293 835691.2 3.3162456 23 G30 -337.40360 383.875293 -46.840401 364.95418 -57.146512 54.999738 -382.020401 118.9297377 -99.348040 1145663.2 4.5462971 34 G31 -167.65748 56.756404 343.350710 27.62529 196.509599 -209.319151 6.660710 8.2008488 -262.126929 602471.7 2.3907685 15 G32 91.70196 221.965849 -94.239846 -127.54026 -4.600957 15.290293 71.515154 -7.3347068 -166.757485 232114.0 0.9210902 3 G33 -118.78082 223.918071 -22.577624 -30.64304 -160.158735 250.607515 226.052377 -412.3024846 43.884738 754341.5 2.9934283 19 G34 -14.00415 90.844738 -61.635957 -57.79137 -93.422068 -2.540818 115.184043 111.7341821 -88.368596 115765.5 0.4593884 1 G35 -239.66526 69.208626 172.097932 -453.25248 -73.498179 18.413071 -127.107068 321.8780710 311.925293 1040169.8 4.1276711 30 G36 -98.20137 -293.482485 102.941821 397.80640 -81.769290 -119.893040 -51.243179 423.0819599 -279.240818 1090565.3 4.3276538 31

Shukla stability statistics for TW

## Evaluating trait TW |============================================| 100% 00:00:03 

GEN Y ShuklaVar rMean rShukaVar ssiShukaVar G01 483.1894 32880.344 35 10 45 G02 508.6639 17913.107 33 4 37 G03 626.6133 52100.606 9 21 30 G04 510.7361 22213.572 32 7 39 G05 591.6528 28021.877 21 9 30 G06 602.6828 54729.380 18 25 43 G07 602.8317 38451.633 17 14 31 G08 568.9267 54669.283 28 24 52 G09 615.2450 51874.390 14 20 34 G10 610.7956 37619.074 15 13 28 G11 665.9944 56722.287 6 27 33 G12 677.3256 13066.058 5 2 7 G13 480.1361 76633.408 36 36 72 G14 626.2117 54980.019 10 26 36 G15 585.8967 44890.450 24 18 42 G16 589.8200 20442.909 23 6 29 G17 590.4494 74936.295 22 35 57 G18 598.5450 62037.147 20 29 49 G19 681.8261 35305.491 4 12 16 G20 490.1544 24758.146 34 8 42 G21 641.3589 57428.639 8 28 36 G22 605.8039 72366.573 16 33 49 G23 527.9550 41158.726 31 17 48 G24 575.7144 40255.254 25 16 41 G25 620.5367 20120.760 12 5 17 G26 598.8800 53415.148 19 22 41 G27 691.2856 34631.896 1 11 12 G28 571.4961 72026.418 26 32 58 G29 540.5206 53979.569 30 23 53 G30 569.0239 74492.422 27 34 61 G31 616.8628 38545.927 13 15 28 G32 681.8683 14036.959 3 3 6 G33 685.6811 48596.135 2 19 21 G34 562.9194 6337.428 29 1 30 G35 626.0456 67511.241 11 30 41 G36 661.1067 70846.235 7 31 38

Regression model estimates for TW

## Evaluating trait TW |============================================| 100% 00:00:07 

GEN	b0	b1	t(b1=1)	pval_t	s2di	F(s2di=0)	pval_f	RMSE	R2
G01	483.1894	2.5516184	0.53731624	0.59142854	-6259.5080	0.8490509	0.5474145	165.48150	0.1161143
G02	508.6639	-0.1021069	-0.38165308	0.70297603	-21567.2013	0.4799033	0.8490057	124.41119	0.0003720
G03	626.6133	-5.5654479	-2.27357566	0.02366428	-14425.3132	0.6521311	0.7125144	145.02740	0.4486370
G04	510.7361	2.1367022	0.39363324	0.69411814	-16980.4520	0.5905135	0.7636134	138.00586	0.1169584
G05	591.6528	2.9167532	0.66376027	0.50732926	-12403.2325	0.7008939	0.6713189	150.35184	0.1721447
G06	602.6828	1.2706668	0.09373032	0.92538297	18981.8313	1.4577501	0.1817780	216.83238	0.0186213
G07	602.8317	0.8800724	-0.04153020	0.96689953	1454.0267	1.0350641	0.4063401	182.71164	0.0126570
G08	568.9267	-0.2711152	-0.44017964	0.66010889	17821.1942	1.4297611	0.1925504	214.74069	0.0008799
G09	615.2450	4.8728814	1.34115584	0.18083606	5296.8898	1.1277354	0.3452403	190.71559	0.2650888
G10	610.7956	-2.5931804	-1.24429705	0.21431531	-8606.3008	0.7924576	0.5940745	159.87134	0.1269214
G11	665.9944	6.4464221	1.88606367	0.06020619	112.0488	1.0027021	0.4292213	179.83265	0.4152043
G12	677.3256	1.1011063	0.03501252	0.97209193	-25943.3214	0.3743724	0.9169608	109.88401	0.0525649
G13	480.1361	-0.2053035	-0.41738945	0.67667791	41644.2832	2.0042590	0.0542018	254.24915	0.0003601
G14	626.2117	-1.2211199	-0.76916063	0.44237429	15799.7472	1.3810136	0.2125889	211.04816	0.0181615
G15	585.8967	0.6748456	-0.11259905	0.91042016	8338.9705	1.2010957	0.3016774	196.82099	0.0064537
G16	589.8200	-1.8900649	-1.00081232	0.31768573	-23907.3260	0.4234708	0.8874174	116.86765	0.1262698
G17	590.4494	-0.7054675	-0.59059328	0.55521645	38778.2365	1.9351438	0.0636452	249.82691	0.0043866
G18	598.5450	8.1383888	2.47198170	0.01396475	-9277.8389	0.7762633	0.6076275	158.22938	0.5937776
G19	681.8261	-2.0979851	-1.07281384	0.28417583	-8749.6446	0.7890008	0.5969613	159.52227	0.0872327
G20	490.1544	1.2127665	0.07367979	0.94131195	-13348.1870	0.6781062	0.6906125	147.88750	0.0358265
G21	641.3589	-4.0288958	-1.74147679	0.08257626	3981.5424	1.0960156	0.3653993	188.01433	0.2023710
G22	605.8039	0.3586878	-0.22208259	0.82439350	37778.6721	1.9110391	0.0672823	248.26608	0.0011520
G23	527.9550	5.1515112	1.43764369	0.15152782	-7857.5561	0.8105137	0.5790571	161.68241	0.3593522
G24	575.7144	2.6922907	0.58603022	0.55827486	1376.5373	1.0331954	0.4076401	182.54664	0.1072910
G25	620.5367	3.1635065	0.74920948	0.45429007	-21646.6632	0.4779870	0.8503783	124.16256	0.2639943
G26	598.8800	0.3052403	-0.24059117	0.81002850	17272.4359	1.4165277	0.1978275	213.74459	0.0011255
G27	691.2856	6.9353787	2.05538644	0.04066582	-27685.0600	0.3323701	0.9389058	103.53652	0.7125771
G28	571.4961	3.6309196	0.91107185	0.36295418	32786.5058	1.7906522	0.0884821	240.31906	0.1120021
G29	540.5206	3.8684470	0.99332618	0.32131344	12379.4095	1.2985316	0.2503792	204.64864	0.1648780
G30	569.0239	-1.2153563	-0.76716475	0.44355818	36878.9191	1.8893414	0.0707195	246.85267	0.0132163
G31	616.8628	1.4623708	0.16011628	0.87289211	1414.1479	1.0341024	0.4070088	182.62674	0.0342156
G32	681.8683	1.8568428	0.29671958	0.76687616	-25409.6629	0.3872417	0.9096033	111.75672	0.1323449
G33	685.6811	4.1189621	1.08007806	0.28093369	5503.1664	1.1327098	0.3421511	191.13575	0.2041989
G34	562.9194	-0.3404259	-0.46418155	0.64283831	-34475.1099	0.1686269	0.9912117	73.74727	0.0116366
G35	626.0456	-5.4803635	-2.24411143	0.02551942	2996.9262	1.0722714	0.3810069	185.96660	0.3242561
G36	661.1067	-4.0295487	-1.74170289	0.08253660	18459.3619	1.4451507	0.1865625	215.89330	0.1614134

Regression plot for TW trait

plot(reg_model)

Factor Analysis (FA) plot for TW trait

## Warning: ggrepel: 5 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps

Plot of explained variance by each PC for TW trait

Plot showing CV for each environment

Anova fot TW trait

## variable TW 
## ---------------------------------------------------------------------------
## AMMI analysis table
## ---------------------------------------------------------------------------
##     Source  Df   Sum Sq Mean Sq F value Pr(>F) Proportion Accumulated
##        ENV   8   358041   44755   1.196 0.3947         NA          NA
##   REP(ENV)   9   336710   37412   0.451 0.9062         NA          NA
##        GEN  35  2123026   60658   0.731 0.8688         NA          NA
##    GEN:ENV 280 25199919   90000   1.085 0.2401         NA          NA
##        PC1  42  5920582  140966   1.700 0.0063       23.5        23.5
##        PC2  40  4464626  111616   1.350 0.0850       17.7        41.2
##        PC3  38  3900661  102649   1.240 0.1654       15.5        56.7
##        PC4  36  3155772   87660   1.060 0.3815       12.5        69.2
##        PC5  34  2798200   82300   0.990 0.4883       11.1        80.3
##        PC6  32  2025169   63287   0.760 0.8248        8.0        88.4
##        PC7  30  1844578   61486   0.740 0.8394        7.3        95.7
##        PC8  28  1090332   38940   0.470 0.9908        4.3       100.0
##  Residuals 315 26124634   82935      NA     NA         NA          NA
##      Total 927 79342249   85590      NA     NA         NA          NA
## ---------------------------------------------------------------------------
## 
## ------------------------------------------------------------
## Variables with nonsignificant GxE interaction
## TW 
## ------------------------------------------------------------
## Done!

Source	Df	Sum Sq	Mean Sq	F value	Pr(>F)	Proportion	Accumulated
ENV	8	358040.6	44755.07	1.1962673	0.3946646	NA	NA
REP(ENV)	9	336710.4	37412.27	0.4511016	0.9061622	NA	NA
GEN	35	2123025.8	60657.88	0.7313875	0.8687849	NA	NA
GEN:ENV	280	25199919.2	89999.71	1.0851792	0.2401222	NA	NA
PC1	42	5920581.6	140966.23	1.7000000	0.0063000	23.5	23.5
PC2	40	4464625.6	111615.64	1.3500000	0.0850000	17.7	41.2
PC3	38	3900660.6	102648.96	1.2400000	0.1654000	15.5	56.7
PC4	36	3155772.0	87660.33	1.0600000	0.3815000	12.5	69.2
PC5	34	2798200.0	82300.00	0.9900000	0.4883000	11.1	80.3
PC6	32	2025169.5	63286.55	0.7600000	0.8248000	8.0	88.4
PC7	30	1844577.8	61485.93	0.7400000	0.8394000	7.3	95.7
PC8	28	1090332.2	38940.43	0.4700000	0.9908000	4.3	100.0
Residuals	315	26124634.1	82935.35	NA	NA	NA	NA
Total	927	79342249.4	85590.34	NA	NA	NA	NA

PCA values TW trait

PC	Df	Sum Sq	Mean Sq	F value	Pr(>F)	Proportion	Accumulated
PC1	42	5920582	140966.23	1.70	0.0063	23.5	23.5
PC2	40	4464626	111615.64	1.35	0.0850	17.7	41.2
PC3	38	3900661	102648.96	1.24	0.1654	15.5	56.7
PC4	36	3155772	87660.33	1.06	0.3815	12.5	69.2
PC5	34	2798200	82300.00	0.99	0.4883	11.1	80.3
PC6	32	2025169	63286.55	0.76	0.8248	8.0	88.4

Fitted model TW trait

type	Code	Y	PC1	PC2	PC3	PC4	PC5	PC6	PC7	PC8
GEN	G01	483.1894	-0.5183478	-3.7969043	6.152771	-10.706029	-3.949483	-3.676603	-1.876482	2.370032
GEN	G02	508.6639	3.6887684	0.0277292	5.632924	-3.136529	-4.048111	1.110091	5.699752	-4.266189
GEN	G03	626.6133	8.5389938	-2.4742045	4.460207	2.612873	-8.635438	-6.561361	10.199000	1.311148
GEN	G04	510.7361	-1.0733219	-1.2247274	-5.407674	-1.604350	2.648156	-9.337538	-5.658264	1.934181
GEN	G05	591.6528	-4.6716350	3.9564299	6.964733	-2.029996	-6.747380	3.215490	-3.756800	-3.690296
GEN	G06	602.6828	-2.8838127	9.2358531	-7.664246	-3.467487	-8.784701	-2.351215	8.265601	5.478665

AMMI stability plot for TW

Predicted values for TW

TRAIT	ENV	GEN	Y	RESIDUAL	Ypred	ResAMMI	YpredAMMI	AMMI0
TW	CM	G01	662.470	156.28585	506.1842	130.17536	636.3595	506.1842
TW	CM	G02	638.400	106.74140	531.6586	-28.80103	502.8576	531.6586
TW	CM	G03	578.475	-71.13304	649.6080	-246.13642	403.4716	649.6080
TW	CM	G04	429.240	-104.49082	533.7308	32.62515	566.3560	533.7308
TW	CM	G05	919.190	304.54252	614.6475	173.84645	788.4939	614.6475
TW	CM	G06	1006.560	380.88252	625.6775	218.74420	844.4217	625.6775

Mean of GxE for TW

ENV	GEN	Y	envPC1	genPC1	nominal
CM	G01	662.470	-20.8552	-0.5183478	493.9997
CM	G02	638.400	-20.8552	3.6887684	431.7339
CM	G03	578.475	-20.8552	8.5389938	448.5309
CM	G04	429.240	-20.8552	-1.0733219	533.1205
CM	G05	919.190	-20.8552	-4.6716350	689.0806
CM	G06	1006.560	-20.8552	-2.8838127	662.8253

A plot of AMMI stability scores for TW trait

AMMI2 Biplot with polygon

Y x WAAS Biplot for TW

WAASB_model for Random effects

## Evaluating trait DTF |=====                                      | 12% 00:00:05 
Evaluating trait DTM |===========                                | 25% 00:00:10 
Evaluating trait PL |================                            | 38% 00:00:15 
Evaluating trait NSP |======================                     | 50% 00:00:20 
Evaluating trait NPP |===========================                | 62% 00:00:25 
Evaluating trait GYP |================================           | 75% 00:00:30 
Evaluating trait GYR |======================================     | 88% 00:00:35 
Evaluating trait TW |============================================| 100% 00:00:40 
## ---------------------------------------------------------------------------
## P-values for Likelihood Ratio Test of the analyzed traits
## ---------------------------------------------------------------------------
##     model DTF DTM PL    NSP   NPP   GYP    GYR    TW
##  COMPLETE  NA  NA NA     NA    NA    NA     NA    NA
##       GEN   1   1  1 0.0788 1.000 0.414 0.0369 1.000
##   GEN:ENV   1   1  1 1.0000 0.621 0.365 1.0000 0.691
## ---------------------------------------------------------------------------
## Variables with nonsignificant GxE interaction
## DTF DTM PL NSP NPP GYP GYR TW 
## ---------------------------------------------------------------------------
## The following traits had p-value for GE interaction = 1
## DTM PL NSP GYR 
## WAASBY value for these traits is based on mean performance only (PctResp)
## ---------------------------------------------------------------------------

The variance components for the random effects for TW

## Class of the model: waasb

## Variable extracted: vcomp

Group	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
GEN	0.00000	0.000	0.00000	0.8944214	0.000000	12.74489	2645.17	0.00
GEN:ENV	0.00000	0.000	0.00000	0.0000000	8.028362	51.15377	0.00	1902.08
Residual	81.89123	127.902	16.16779	32.0866246	280.474581	922.96059	77755.71	82935.35

The genetic parameter in the model for TW

## Class of the model: waasb

## Variable extracted: genpar

Group	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
GEN	0.00000	0.000	0.00000	0.8944214	0.000000	12.74489	2645.17	0.00
GEN:ENV	0.00000	0.000	0.00000	0.0000000	8.028362	51.15377	0.00	1902.08
Residual	81.89123	127.902	16.16779	32.0866246	280.474581	922.96059	77755.71	82935.35

Predicted means for each genotypes for TW

## Class of the model: waasb

## Variable extracted: blupg

GEN	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
G01	40.9892	97.81944	17.6188	19.30042	35.53596	61.85278	618.2667	596.7988
G02	40.9892	97.81944	17.6188	18.38978	35.53596	66.75265	565.3474	596.7988
G03	40.9892	97.81944	17.6188	19.28576	35.53596	63.73311	556.2845	596.7988
G04	40.9892	97.81944	17.6188	17.21742	35.53596	61.20298	619.5210	596.7988
G05	40.9892	97.81944	17.6188	17.82216	35.53596	62.42904	551.1903	596.7988
G06	40.9892	97.81944	17.6188	18.39405	35.53596	63.20998	619.5858	596.7988
G07	40.9892	97.81944	17.6188	19.32233	35.53596	61.28983	600.8283	596.7988
G08	40.9892	97.81944	17.6188	18.56204	35.53596	63.38267	679.6396	596.7988
G09	40.9892	97.81944	17.6188	18.61828	35.53596	62.09058	630.0438	596.7988
G10	40.9892	97.81944	17.6188	17.46838	35.53596	64.17803	602.0183	596.7988
G11	40.9892	97.81944	17.6188	17.50661	35.53596	60.14737	647.1818	596.7988
G12	40.9892	97.81944	17.6188	18.98747	35.53596	61.64932	533.9013	596.7988
G13	40.9892	97.81944	17.6188	18.38403	35.53596	59.42250	605.3372	596.7988
G14	40.9892	97.81944	17.6188	18.93104	35.53596	61.92927	571.1452	596.7988
G15	40.9892	97.81944	17.6188	18.55424	35.53596	62.96579	568.2939	596.7988
G16	40.9892	97.81944	17.6188	18.99731	35.53596	61.90764	592.7733	596.7988
G17	40.9892	97.81944	17.6188	19.20056	35.53596	60.63901	587.3630	596.7988
G18	40.9892	97.81944	17.6188	18.10653	35.53596	61.63124	627.8069	596.7988
G19	40.9892	97.81944	17.6188	18.24611	35.53596	62.06711	615.6935	596.7988
G20	40.9892	97.81944	17.6188	19.11610	35.53596	60.05839	569.1895	596.7988
G21	40.9892	97.81944	17.6188	19.21504	35.53596	60.82887	592.2821	596.7988
G22	40.9892	97.81944	17.6188	18.97039	35.53596	63.50090	610.1813	596.7988
G23	40.9892	97.81944	17.6188	17.63228	35.53596	63.38033	618.2161	596.7988
G24	40.9892	97.81944	17.6188	18.47851	35.53596	60.65781	562.2604	596.7988
G25	40.9892	97.81944	17.6188	18.99007	35.53596	63.81072	626.4021	596.7988
G26	40.9892	97.81944	17.6188	18.83656	35.53596	62.68898	590.4142	596.7988
G27	40.9892	97.81944	17.6188	18.70719	35.53596	61.68091	626.6781	596.7988
G28	40.9892	97.81944	17.6188	18.59767	35.53596	61.81449	570.8576	596.7988
G29	40.9892	97.81944	17.6188	18.26263	35.53596	63.40471	590.0015	596.7988
G30	40.9892	97.81944	17.6188	18.65447	35.53596	63.14111	631.9220	596.7988
G31	40.9892	97.81944	17.6188	18.17409	35.53596	62.14726	627.2883	596.7988
G32	40.9892	97.81944	17.6188	18.49837	35.53596	62.33315	547.2133	596.7988
G33	40.9892	97.81944	17.6188	19.19425	35.53596	62.38506	571.7501	596.7988
G34	40.9892	97.81944	17.6188	18.86793	35.53596	58.70535	606.0953	596.7988
G35	40.9892	97.81944	17.6188	18.49744	35.53596	64.03968	565.6681	596.7988
G36	40.9892	97.81944	17.6188	18.75415	35.53596	63.32192	603.2207	596.7988

Predicted means for each genotype environment combination for TW

## Class of the model: waasb

## Variable extracted: blupge

ENV	GEN	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
CM	G01	40.36111	97.06944	17.58889	19.76704	34.21876	64.56077	585.8479	621.6651
CM	G02	40.36111	97.06944	17.58889	18.85640	34.65087	70.95096	532.9286	620.6095
CM	G03	40.36111	97.06944	17.58889	19.75238	34.83254	66.29988	523.8657	617.9814
CM	G04	40.36111	97.06944	17.58889	17.68404	34.38040	65.39677	587.1022	611.4363
CM	G05	40.36111	97.06944	17.58889	18.28878	35.93310	64.16998	518.7715	632.9242
CM	G06	40.36111	97.06944	17.58889	18.86067	34.20116	62.59587	587.1670	636.7560

BLUP-based stability statistics for TW

## Class of the model: waasb

## Variable extracted: WAASB

GEN	DTF	DTM	PL	NSP	NPP	GYP	GYR	TW
G01	0	NA	NA	NA	0.2695868	0.4270761	NA	0.9562070
G02	0	NA	NA	NA	0.2799436	0.5783926	NA	0.7676005
G03	0	NA	NA	NA	0.2717804	0.6458621	NA	1.1745007
G04	0	NA	NA	NA	0.2599578	0.3954558	NA	0.7933199
G05	0	NA	NA	NA	0.2620333	0.3551057	NA	0.9341366
G06	0	NA	NA	NA	0.3039891	0.4195486	NA	1.1684429
G07	0	NA	NA	NA	0.2265533	0.4381595	NA	0.6917625
G08	0	NA	NA	NA	0.2576913	0.6791135	NA	1.1737995
G09	0	NA	NA	NA	0.3053211	0.8262474	NA	1.2627679
G10	0	NA	NA	NA	0.1796253	0.4284019	NA	0.7600957
G11	0	NA	NA	NA	0.3251487	0.4638800	NA	1.3088633
G12	0	NA	NA	NA	0.2955460	0.3948612	NA	0.7319039
G13	0	NA	NA	NA	0.3063619	0.6481795	NA	1.6645755
G14	0	NA	NA	NA	0.2305216	0.2392062	NA	1.1911121
G15	0	NA	NA	NA	0.2391759	0.4997047	NA	0.9808916
G16	0	NA	NA	NA	0.2202117	0.4427403	NA	0.6980696
G17	0	NA	NA	NA	0.2574044	0.5685601	NA	1.2112311
G18	0	NA	NA	NA	0.2051573	0.4930683	NA	1.3726120
G19	0	NA	NA	NA	0.2601689	0.4038787	NA	0.9741786
G20	0	NA	NA	NA	0.1765342	0.6125393	NA	1.0299161
G21	0	NA	NA	NA	0.4474713	0.8083378	NA	1.2100021
G22	0	NA	NA	NA	0.2219202	0.8334188	NA	1.4299000
G23	0	NA	NA	NA	0.2897713	0.5731086	NA	1.0301319
G24	0	NA	NA	NA	0.3503508	0.4521088	NA	1.0692269
G25	0	NA	NA	NA	0.2756768	0.5607946	NA	0.5874401
G26	0	NA	NA	NA	0.2450095	0.4135830	NA	1.0552992
G27	0	NA	NA	NA	0.3053265	0.3877358	NA	1.0557091
G28	0	NA	NA	NA	0.2874898	0.4944244	NA	1.4685137
G29	0	NA	NA	NA	0.4112468	0.5093441	NA	0.8248561
G30	0	NA	NA	NA	0.2208286	0.5409334	NA	1.2281428
G31	0	NA	NA	NA	0.3109397	0.6500136	NA	0.9694722
G32	0	NA	NA	NA	0.3601010	0.3118052	NA	0.7460982
G33	0	NA	NA	NA	0.3037760	0.3008292	NA	1.0729206
G34	0	NA	NA	NA	0.2802086	0.7495773	NA	0.4369744
G35	0	NA	NA	NA	0.3531763	0.5081832	NA	1.3377268
G36	0	NA	NA	NA	0.2684776	0.5246280	NA	1.5604072

GGE model prdictions for TW

CM GO GS JT LD PG PL PM SP 595.0802 725.8355 541.6196 517.7406 609.5521 576.5280 551.7907 584.7806 615.8514 556.6302 564.6001 668.9390 614.6332 639.3224 555.8905 597.3168 587.7336 623.4617 421.2965 510.6095 818.0190 596.1492 674.8205 516.3473 560.8324 692.1165 677.8584 631.9503 681.7954 535.2176 563.9076 607.8077 583.5148 584.2369 545.5898 597.8728 761.1034 592.6848 474.8466 680.0084 592.9059 612.1884 672.9317 420.2336 538.3986 785.8223 465.9052 527.1912 779.0490 604.8582 610.6047 731.9419 376.1585 521.1161 615.8375 543.8935 629.5322 653.7537 629.7731 570.3335 630.2598 533.9540 597.2802 643.6036 995.0227 342.6769 349.4587 563.1164 606.8071 469.1641 593.0807 609.7804 927.2131 593.3121 330.0914 748.6521 558.1918 656.4936 742.8597 280.0990 468.1022 461.6490 730.2023 655.0607 459.1910 636.7797 541.2528 493.7536 698.2382 672.5804 936.8630 739.8508 236.3650 650.0713 536.4084 668.5092 690.7979 298.7724 471.8956 709.0525 662.6723 479.3335 609.3618 594.3141 602.8285 624.1325 476.9909 564.1998 859.8177 541.3626 418.9277 756.9939 579.2511 635.1861 734.2919 327.4938 493.8439 541.3500 195.7267 897.0384 866.5323 692.2778 528.0455 732.1752 533.1201 610.0977 502.0257 624.0002 681.8114 550.3369 642.6915 545.1678 551.4949 644.7092 649.7748 551.8127 796.3845 538.1446 450.3537 609.0534 569.5448 506.4867 634.2247 637.9640 695.2769 568.5886 546.0985 669.5022 609.8801 593.0940 654.3563 471.4017 564.9737 867.3803 522.5831 423.2905 773.2869 580.2084 635.9910 744.6808 317.6714 489.6322 457.4217 506.0392 789.2789 614.3730 667.9060 525.6794 577.8434 660.7788 662.3174 786.9584 692.4998 394.2440 620.8792 574.0483 625.5111 645.6149 416.6729 532.8186 315.0387 505.9545 913.0938 555.2171 697.6005 487.7318 517.7302 780.9798 722.5973 438.3493 224.9290 969.5648 803.2507 709.8106 502.4800 677.4783 625.4303 655.2779 737.5377 629.6030 473.8312 644.3607 592.8375 608.2879 648.8338 446.8877 550.3613 683.7436 881.1676 374.0902 445.8642 570.1100 610.1658 529.7373 538.3509 586.6636 666.5526 556.6381 578.0264 665.9228 617.4808 584.6694 646.8006 493.4669 576.4929 592.7436 1005.7468 380.6415 320.7986 572.2724 593.9451 443.5714 637.9856 631.8910 706.9246 436.5672 612.8578 766.7765 625.2647 587.6894 709.8530 437.4035 552.9436 447.1572 247.9362 948.5101 790.8061 704.8702 506.3099 672.3850 622.2047 652.7857 546.7789 693.5271 602.4203 520.2723 623.9808 561.5745 543.7643 619.6488 634.5648 517.5355 773.8167 581.0825 451.8983 619.2442 558.9562 500.6528 659.0350 651.2634 472.5070 491.3381 784.7275 630.9393 666.7447 528.7518 589.8476 645.3513 655.1400 691.5750 753.0487 441.8941 538.8192 585.7637 603.9957 582.1270 508.2890 576.4591 746.9336 659.1797 448.4396 627.5612 586.8881 612.6979 641.4722 444.3680 547.9734 632.8879 692.0773 528.4148 557.0990 606.2249 584.4273 580.6941 546.6800 598.0287 296.2703 796.5331 760.1868 343.9729 662.3072 501.4577 398.4831 850.0110 746.1676 511.8846 320.3730 850.0619 767.0112 681.6028 528.2268 671.9772 580.8123 629.2752

Biplot type 2: Mean performance vs. stability (colored by genotype)

Biplot type 2: Mean performance for genotype (colored by genotype)

gge_model2 <- gge(df, env, gen, TW, svp = "genotype")
b3 <- plot(gge_model2,type = 2, col.gen = "#00AFBB", col.env = "#FC4E07", axis_expand = 1.5)
b3

Which-won-where (genotypes and environment are coloured)

Discriminativeness vs. representativeness (genotypes and environment are coloured)

Biplot type 5: Examine an environment (genotypes and environment are coloured)

Biplot type 6: Ranking environments (genotypes and environment are coloured)

Examine a genotype (genotypes and environment are coloured)

Ranking genotypes (genotypes and environment are coloured)

## Warning: Removed 2597 rows containing missing values (`geom_arc()`).

Relationship among environments (environment are coloured)

Plot of genotype stability indices (Interpret type III hypotheses with care)

## Warning: Invalid length in 'mresp'. Setting mresp = h to all the 8 variables.

## Warning: Invalid length in 'wresp'. Setting wresp = 65 to all the 8 variables.

## Evaluating trait DTF |=====                                      | 12% 00:00:05 
Evaluating trait DTM |===========                                | 25% 00:00:10 
Evaluating trait PL |================                            | 38% 00:00:15 
Evaluating trait NSP |======================                     | 50% 00:00:20 
Evaluating trait NPP |===========================                | 62% 00:00:25 
Evaluating trait GYP |================================           | 75% 00:00:29 
Evaluating trait GYR |======================================     | 88% 00:00:34 
Evaluating trait TW |============================================| 100% 00:00:39 

## Method: REML/BLUP

## Random effects: GEN, GEN:ENV

## Fixed effects: ENV, REP(ENV)

## Denominador DF: Satterthwaite's method

## ---------------------------------------------------------------------------
## P-values for Likelihood Ratio Test of the analyzed traits
## ---------------------------------------------------------------------------
##     model DTF DTM PL    NSP   NPP   GYP    GYR    TW
##  COMPLETE  NA  NA NA     NA    NA    NA     NA    NA
##       GEN   1   1  1 0.0788 1.000 0.414 0.0369 1.000
##   GEN:ENV   1   1  1 1.0000 0.621 0.365 1.0000 0.691
## ---------------------------------------------------------------------------
## Variables with nonsignificant GxE interaction
## DTF DTM PL NSP NPP GYP GYR TW 
## ---------------------------------------------------------------------------
## The following traits had p-value for GE interaction = 1
## DTM PL NSP GYR 
## WAASBY value for these traits is based on mean performance only (PctResp)
## ---------------------------------------------------------------------------

## Warning: NA values removed to compute the function. Use 'na.rm = TRUE' to
## suppress this warning.

Estimating the WAAS index

The waas() function computes the Weighted Average of Absolute Scores (Olivoto, Lúcio, Da silva, Marchioro, et al. 2019) considering (i) all principal component axes that were significant (p<0.05 by default); or (ii) declaring a specific number of axes to be used

Ranks of genotypes depending on the number of PCA used to estimate the WAAS (type = 2)

## Ranks considering 0 for GY and 100 for WAASB |                   | 1% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |                   | 1% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |                   | 2% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |                   | 2% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |=                  | 3% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |=                  | 4% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |=                  | 4% 00:00:00 
Ranks considering 0 for GY and 100 for WAASB |=                  | 5% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |=                   | 5% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |=                   | 6% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |=                   | 7% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |=                   | 7% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |==                  | 8% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |==                  | 8% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |==                  | 9% 00:00:00 
Ranks considering 5 for GY and 95 for WAASB |==                  | 10% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |==                 | 10% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |==                 | 11% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |==                 | 11% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |==                 | 12% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |==                 | 12% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |==                 | 13% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |===                | 14% 00:00:00 
Ranks considering 10 for GY and 90 for WAASB |===                | 14% 00:00:00 
Ranks considering 15 for GY and 85 for WAASB |===                | 15% 00:00:00 
Ranks considering 15 for GY and 85 for WAASB |===                | 15% 00:00:00 
Ranks considering 15 for GY and 85 for WAASB |===                | 16% 00:00:01 
Ranks considering 15 for GY and 85 for WAASB |===                | 17% 00:00:01 
Ranks considering 15 for GY and 85 for WAASB |===                | 17% 00:00:01 
Ranks considering 15 for GY and 85 for WAASB |===                | 18% 00:00:01 
Ranks considering 15 for GY and 85 for WAASB |====               | 18% 00:00:01 
Ranks considering 15 for GY and 85 for WAASB |====               | 19% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 20% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 20% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 21% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 21% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 22% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 23% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |====               | 23% 00:00:01 
Ranks considering 20 for GY and 80 for WAASB |=====              | 24% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 24% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 25% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 26% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 26% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 27% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 27% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 28% 00:00:01 
Ranks considering 25 for GY and 75 for WAASB |=====              | 29% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 29% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 30% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 30% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 31% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 32% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 32% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 33% 00:00:01 
Ranks considering 30 for GY and 70 for WAASB |======             | 33% 00:00:01 
Ranks considering 35 for GY and 65 for WAASB |======             | 34% 00:00:01 
Ranks considering 35 for GY and 65 for WAASB |=======            | 35% 00:00:01 
Ranks considering 35 for GY and 65 for WAASB |=======            | 35% 00:00:01 
Ranks considering 35 for GY and 65 for WAASB |=======            | 36% 00:00:02 
Ranks considering 35 for GY and 65 for WAASB |=======            | 36% 00:00:02 
Ranks considering 35 for GY and 65 for WAASB |=======            | 37% 00:00:02 
Ranks considering 35 for GY and 65 for WAASB |=======            | 38% 00:00:02 
Ranks considering 35 for GY and 65 for WAASB |=======            | 38% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |=======            | 39% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |=======            | 39% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |========           | 40% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |========           | 40% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |========           | 41% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |========           | 42% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |========           | 42% 00:00:02 
Ranks considering 40 for GY and 60 for WAASB |========           | 43% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |========           | 43% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |========           | 44% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |========           | 45% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |=========          | 45% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |=========          | 46% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |=========          | 46% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |=========          | 47% 00:00:02 
Ranks considering 45 for GY and 55 for WAASB |=========          | 48% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |=========          | 48% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |=========          | 49% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |=========          | 49% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |==========         | 50% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |==========         | 51% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |==========         | 51% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |==========         | 52% 00:00:02 
Ranks considering 50 for GY and 50 for WAASB |==========         | 52% 00:00:02 
Ranks considering 55 for GY and 45 for WAASB |==========         | 53% 00:00:02 
Ranks considering 55 for GY and 45 for WAASB |==========         | 54% 00:00:02 
Ranks considering 55 for GY and 45 for WAASB |==========         | 54% 00:00:02 
Ranks considering 55 for GY and 45 for WAASB |==========         | 55% 00:00:02 
Ranks considering 55 for GY and 45 for WAASB |===========        | 55% 00:00:03 
Ranks considering 55 for GY and 45 for WAASB |===========        | 56% 00:00:03 
Ranks considering 55 for GY and 45 for WAASB |===========        | 57% 00:00:03 
Ranks considering 55 for GY and 45 for WAASB |===========        | 57% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |===========        | 58% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |===========        | 58% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |===========        | 59% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |===========        | 60% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |===========        | 60% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |============       | 61% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |============       | 61% 00:00:03 
Ranks considering 60 for GY and 40 for WAASB |============       | 62% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |============       | 62% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |============       | 63% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |============       | 64% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |============       | 64% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |============       | 65% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |============       | 65% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |=============      | 66% 00:00:03 
Ranks considering 65 for GY and 35 for WAASB |=============      | 67% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 67% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 68% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 68% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 69% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 70% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 70% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |=============      | 71% 00:00:03 
Ranks considering 70 for GY and 30 for WAASB |==============     | 71% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 72% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 73% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 73% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 74% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 74% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 75% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 76% 00:00:04 
Ranks considering 75 for GY and 25 for WAASB |==============     | 76% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 77% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 77% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 78% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 79% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 79% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 80% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 80% 00:00:04 
Ranks considering 80 for GY and 20 for WAASB |===============    | 81% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |===============    | 82% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 82% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 83% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 83% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 84% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 85% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 85% 00:00:04 
Ranks considering 85 for GY and 15 for WAASB |================   | 86% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |================   | 86% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 87% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 88% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 88% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 89% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 89% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 90% 00:00:04 
Ranks considering 90 for GY and 10 for WAASB |=================  | 90% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |==================  | 91% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |==================  | 92% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |==================  | 92% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |=================== | 93% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |=================== | 93% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |=================== | 94% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |=================== | 95% 00:00:05 
Ranks considering 95 for GY and 5 for WAASB |=================== | 95% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |================== | 96% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |================== | 96% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |================== | 97% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |===================| 98% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |===================| 98% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |===================| 99% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |===================| 99% 00:00:05 
Ranks considering 100 for GY and 0 for WAASB |===================| 100% 00:00:05 

## Warning: Vectorized input to `element_text()` is not officially supported.
## ℹ Results may be unexpected or may change in future versions of ggplot2.

Ranks of genotypes depending on the number of PCA used to estimate the WAAS (type = 2)

## Warning: Vectorized input to `element_text()` is not officially supported.
## ℹ Results may be unexpected or may change in future versions of ggplot2.

Compare two genotypes (genotypes and environments coloured)

Heatmap of stability indices by trait

95% CI plot for Pearsons’s correlation coefficient

Path analysis

## --------------------------------------------------------------------------
## The algorithm has selected a set of 6 predictors with largest VIF = 1.006. 
## Selected predictors: DTF GYR PL NPP GYP DTM 
## A forward stepwise-based selection procedure will fit 4 models.
## --------------------------------------------------------------------------
## Adjusting the model 1 with 5 predictors (25% concluded)
## Adjusting the model 2 with 4 predictors (50% concluded)
## Adjusting the model 3 with 3 predictors (75% concluded)
## Adjusting the model 4 with 2 predictors (100% concluded)
## Done!
## --------------------------------------------------------------------------
## Summary of the adjusted models 
## --------------------------------------------------------------------------
##    Model  AIC Numpred   CN Determinant     R2 Residual maxVIF
##  MODEL_1 9189       5 1.15       0.993 0.0114    0.994      1
##  MODEL_2 9188       4 1.10       0.997 0.0109    0.995      1
##  MODEL_3 9186       3 1.06       0.999 0.0101    0.995      1
##  MODEL_4 9185       2 1.01       1.000 0.0083    0.996      1
## --------------------------------------------------------------------------

Model	AIC	Numpred	CN	Determinant	R2	Residual	maxVIF
MODEL_1	9189.465	5	1.145011	0.9930011	0.0113791	0.9942942	1.004274
MODEL_2	9187.774	4	1.098561	0.9972457	0.0109075	0.9945313	1.002017
MODEL_3	9186.297	3	1.055867	0.9992570	0.0101100	0.9949322	1.000711
MODEL_4	9185.483	2	1.011374	0.9999680	0.0082956	0.9958436	1.000032

Eigenvalues

## Weak multicollinearity. 
## Condition Number: 1.286
## You will probably have path coefficients close to being unbiased.

Eigenvalues	DTF	DTM	PL	NSP	NPP	GYP	GYR
1.1172115	0.2576760	-0.5266012	0.0722500	0.5700519	0.0634110	-0.5186110	0.2305141
1.0532951	0.3263705	-0.2252058	0.3310816	-0.2937862	-0.0948458	-0.2366140	-0.7627957
1.0348677	-0.2543191	-0.0346701	0.6716048	0.2005871	0.6035551	0.2766074	-0.0451785
1.0180412	0.1736781	-0.4349575	-0.4429163	-0.4133937	0.6304649	0.1138276	0.0559995
0.9819359	0.8378637	0.2146473	0.2179340	0.0007212	-0.0179075	0.3527581	0.2822344
0.9261234	-0.0829918	-0.5807921	-0.0552848	0.2070820	-0.3897801	0.6649460	-0.1255861

Correlation heatmap based on path analysis

Variable contribution to DIM 1 for raw dataset

Variable contribution to DIM 2 for raw dataset

Covariance

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

	DTF	DTM	PL	NSP	NPP
DTF	121.542857	-17.9095238	-0.131619	-11.5531905	25.262571
DTM	-17.909524	77.7567460	-5.146294	0.1203492	-43.232952
PL	-0.131619	-5.1462937	21.048368	-8.6689387	4.329168
NSP	-11.553190	0.1203492	-8.668939	41.9212584	-6.870458
NPP	25.262571	-43.2329524	4.329168	-6.8704576	285.817574

Hierrachical clustering dendrogram 1

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

## Warning in sqrt((ms[index[i, 1], 3]/NREP) * (ms[index[i, 2], 3]/NREP)): NaNs
## produced

Hierrachical clustering dendrogram (circular)

## Registered S3 method overwritten by 'dendextend':
##   method       from   
##   text.pvclust pvclust

## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
##   Please report the issue at <https://github.com/kassambara/factoextra/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Hierrachical clustering dendrogram (horizontal)

Qualitative and quantitative visualization 1

Qualitative and quantitative visualization 2