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GGE biplot

Source: R/gge_biplot.R
gge_biplot.Rd

gge_biplot() draws the GGE biplot (Yan et al. 2000) of a multi-environment trial: the first two principal components of the genotype main effect plus the genotype-by-environment interaction (G + GE). Besides the basic biplot it draws the three views used for decisions: which won where (the polygon of the vertex genotypes and the sectors that group environments into mega-environments), mean against stability (the average environment coordination, ATC) and discriminativeness against representativeness of the environments.

Usage

gge_biplot(.data, .y, .rep, .gen, .env, .which = "basic", .svp = "genotype")

# Default S3 method
gge_biplot(.data, .y, .rep, .gen, .env, .which = "basic", .svp = "genotype")

Arguments

.data

a data frame (or data.table) with one row per plot.

.y

response: a column of .data given by name (.y = Yield or .y = "Yield") or a numeric vector of length nrow(.data).

.rep

replicate: as for .y; optional (the biplot does not depend on it).

.gen

genotype: a column of .data or a vector, as for .y.

.env

environment: a column of .data or a vector, as for .y.

.which

"basic" (default, the plot of earlier versions), "which-won-where", "mean-stability" or "discrimination".

.svp

singular value partition: "genotype" (default, as in earlier versions), "symmetric" or "environment".

Value

A ggplot with the attribute "gge": a list with gen and env (data.tables of scores, with means), percent (of the G + GE sum of squares on the two components), winners (data.table: environment and winning genotype), vertex (vertex genotypes), atc (data.table: genotypes ranked on the AEA with their instability), envs (data.table: vector length and angle with the AEA of every environment), svp, which, meta (response, numbers of genotypes and environments, grand mean).

Details

With the table of means centred on the environment means, \(\mathbf{X} = (\bar{y}_{ij} - \bar{y}_{\cdot j})\), and its singular value decomposition \(\mathbf{X} = \mathbf{U}\mathbf{D}\mathbf{V}^{\top}\), the genotype and environment scores of the first two components are \(\mathbf{U}\mathbf{D}^{P}\) and \(\mathbf{V}\mathbf{D}^{1-P}\): \(P = 1\) genotype-focused scaling (.svp = "genotype"; distances between genotypes; the scaling for mean against stability), \(P = 0.5\) symmetric (the usual scaling for which won where), \(P = 0\) environment-focused (lengths of and angles between environment vectors; the scaling for discriminativeness and representativeness). The inner products of genotype and environment points, and hence the winner of every environment and the ranking of genotypes on the average environment axis, are the same for every scaling; the polygon, the instability of genotypes and the lengths and angles of environment vectors are not. The vignette The GGE biplot: every view with every scaling draws and interprets all twelve combinations.

Which won where: the convex hull of the genotype points is drawn with lines from the origin perpendicular to its sides; they divide the plane into sectors, and the vertex genotype of a sector yields best in the environments that fall in it (Yan and Tinker 2006). The winner of every environment is also computed directly as the genotype with the largest two-component fitted value.

Mean against stability: the average environment axis (AEA) passes through the origin and the mean of the environment scores; the projection of a genotype on it ranks the means, the distance from it measures instability.

Discriminativeness and representativeness: the length of an environment vector measures how well it separates genotypes; a small angle with the AEA marks a representative environment.

Change from the earlier version. The function returns, as before, a ggplot; the data of the biplot (scores, percentages, winners, ATC ranking, environment vectors) are now attached as the attribute "gge", which stab_interpret() uses.

References

Yan, W., Hunt, L. A., Sheng, Q. and Szlavnics, Z. (2000). Cultivar evaluation and mega-environment investigation based on the GGE biplot. Crop Science, 40(3), 597–605. doi:10.2135/cropsci2000.403597x

Yan, W. and Kang, M. S. (2003). GGE Biplot Analysis: A Graphical Tool for Breeders, Geneticists, and Agronomists. CRC Press, Boca Raton.

Yan, W. and Tinker, N. A. (2006). Biplot analysis of multi-environment trial data: principles and applications. Canadian Journal of Plant Science, 86(3), 623–645. doi:10.4141/P05-169

See also

ammi_biplot, stab_interpret

Other stability analyses: add_anova(), ammi(), ammi_biplot(), er_anova(), ge_effects(), ge_means(), indiv_anova(), stab_asv(), stab_dist(), stab_eskridge(), stab_fox(), stab_huehn(), stab_kang(), stab_masv(), stab_measures(), stab_par(), stab_reg(), stab_reliability(), stab_superiority()

Author

Muhammad Yaseen (myaseen208@gmail.com), Kent M. Eskridge (keskridge1@unl.edu)

Examples

data(ge_data)
p <-
  gge_biplot(
      .data  = ge_data
    , .y     = Yield
    , .rep   = Rep
    , .gen   = Gen
    , .env   = Env
    , .which = c("basic", "which-won-where", "mean-stability", "discrimination")[2]
    , .svp   = c("genotype", "symmetric", "environment")[2]
    )
p

attr(x = p, which = "gge")$winners
#>              Env       Winner
#>           <char>       <char>
#>  1:          FSD FAISALABAD08
#>  2:         FSDR        DN126
#>  3:        Okara        DN126
#>  4:     Sargodha       V14170
#>  5:   Gujranwala         IVII
#>  6:     KotNaina       V14170
#>  7:          KSK       SD1013
#>  8:     Khanewal       V14170
#>  9:      Sahiwal       V14170
#> 10:      Bhakkar       V14170
#> 11: Bahawalnagar       V14170
stab_interpret(
    x             = p
  , higher_better = TRUE
  , top           = 5L
  )
#> GGE biplot: which won where
#> 
#> The biplot shows 45.1% of G + GE; 5 winning genotype(s) divide the
#> environments into 5 sector(s) with environments.
#> 
#> Findings:
#> - Which won where (from the two-component fit, the same for every scaling):
#>   FAISALABAD08 wins in FSD; DN126 wins in FSDR and Okara; V14170 wins in
#>   Sargodha, KotNaina, Khanewal, Sahiwal, Bhakkar and Bahawalnagar; IVII wins
#>   in Gujranwala; SD1013 wins in KSK.
#> - Vertex genotypes of the polygon: DN126, V14170, V13348, KT325, SD1013,
#>   IVII, FAISALABAD08 and 12B.2511; they are the most responsive genotypes,
#>   best or poorest in some environments.
#> - Vertex genotypes whose sectors hold no environment (they win nowhere and
#>   are among the poorest in some environments): V13348, KT325 and 12B.2511.
#> - Genotypes near the origin respond little to the environments: 9496, AUR0810
#>   and TWS12464; they are neither winners nor losers.
#> 
#> Recommendations:
#> - More than one sector holds environments: consider a separate recommendation
#>   for each group (mega-environment), once the grouping recurs over years.
#> - Recommend FAISALABAD08 for FSD.
#> - Recommend DN126 for FSDR and Okara.
#> - Recommend V14170 for Sargodha, KotNaina, Khanewal, Sahiwal, Bhakkar and
#>   Bahawalnagar.
#> - Recommend IVII for Gujranwala.
#> - Recommend SD1013 for KSK.
#> 
#> Cautions:
#> - The two components hold less than 60% of G + GE; conclusions from the
#>   biplot are tentative.
#> - Mega-environments must be repeatable across years before they guide
#>   recommendations.