Bayesian Stability Analysis of Genotype by Environment Interaction (GEI)

Performs the general Bayesian estimation method of linear-bilinear models for genotype x environment interaction of Perez-Elizalde, Jarquin and Crossa (2012) : the additive main effects and multiplicative interaction (AMMI) model and the sites regression (SREG, GGE) model, with the data of an earlier trial as the prior (conjugate normal and von Mises-Fisher priors weighted by its replicates) or with vague priors; a compiled Gibbs sampler; posterior summaries with highest posterior density intervals; convergence diagnostics; biplots with highest posterior density regions; DIC and WAIC; a plain-language interpretation of every result; and a built-in 'shiny' application. For Bayesian stability analysis in general (regression and variance models, stability indices, probabilities of superior performance), see the package 'bayesstability'.

baystability: Bayesian Stability Analysis of Genotype by Environment

Interaction (GEI)

Overview

baystability fits the linear-bilinear models of multi-environment trials, AMMI and SREG (GGE), by the general Bayesian method of Perez-Elizalde, Jarquin and Crossa (2012). The data of an earlier trial with the same genotypes and environments can be the prior: its cell means, effects and singular value decomposition give conjugate normal and von Mises-Fisher priors, weighted by its replicates. Every parameter has a posterior distribution, and the biplot carries highest posterior density (HPD) regions.

• bayes_ammi(): the Gibbs sampler (compiled), with .prior_data (an earlier trial as prior), .model = "AMMI" or "SREG", the number of terms, chains, burn-in and a seed; summaries with HPD intervals, diagnostics, DIC and WAIC;
• bayes_gge(): the SREG (GGE) model, the same as bayes_ammi(.model = "SREG");
• bayes_ammi_biplot(), bayes_gge_biplot(): the biplots with HPD regions;
• bys_compare(): WAIC and DIC of several fits; bys_interpret(): a plain-language interpretation; bys_cite(): the references of a result;
• bys_ls_means(), bys_ls_ge_effects(), bys_ls_ammi() and the other bys_ls_ functions: the tables and the least-squares AMMI (the names of version 0.2.0 still work, with a deprecation warning);
• bys_app(): all of this in a web browser, without code.

Version 1.0.0 replaces the sampler of version 0.2.0. That version read the earlier trial from objects in the workspace, never sampled the singular values and returned a precision computed from a residual that was never updated (see NEWS). The new sampler reproduces the 38 linear effects of Table B.1 of the paper to within 0.03 posterior standard deviations. It adds exact two-column moves, without which the genotype scores of a fit with all terms cannot move.

For Bayesian stability analysis in general (Finlay-Wilkinson, Eberhart-Russell and Shukla models, stability indices, probabilities of superior performance), see bayesstability. For the Bayesian AMMI model of Crossa et al. (2011), see bayesammi.

Installation

install.packages("baystability")

Quick start

library(baystability)
data(cultivo2008)
data(cultivo2009)
fm <-
  bayes_ammi(
      .data       = cultivo2009
    , .y          = y
    , .gen        = entry
    , .env        = site
    , .rep        = rep
    , .nIter      = 3000
    , .prior_data = cultivo2008
    , .n0         = NULL
    , .model      = "AMMI"
    , .k          = NULL
    , .burnin     = 1000
    , .thin       = 1
    , .chains     = 2
    , .priors     = bys_priors(
          mu_mean     = 0
        , mu_var      = 1e+8
        , tau_mean    = 0
        , tau_var     = 1e+8
        , delta_mean  = 0
        , delta_var   = 1e+8
        , lambda_mean = 0
        , lambda_var  = 1e+8
        , nu          = 1
        , s2          = NULL
        )
    , .level      = 0.95
    , .seed       = 2012
    , .align      = TRUE
    , .waic       = TRUE
    )
fm$summary[block %in% c("mu", "sigma2", "lambda")][1:5]

   parameter  block label axis        mean           sd        mc_se
1:        mu     mu         NA    3848.226     30.84317    0.3981837
2:    sigma2 sigma2         NA 1705532.341 102595.88335 1441.5652227
3: lambda[1] lambda          1    3661.031    396.46664    9.1043484
4: lambda[2] lambda          2    3281.938    351.22780    8.8038961
5: lambda[3] lambda          3    2824.031    315.66069    8.8833684
         lower       upper      ess     rhat
1:    3787.723    3909.102 6000.000 1.000438
2: 1500321.098 1902118.289 5065.138 1.000096
3:    2889.820    4423.813 1896.337 1.003106
4:    2591.935    3960.180 1591.578 1.004796
5:    2213.368    3459.256 1262.658 1.003067

bp <-
  bayes_ammi_biplot(
      fit           = fm
    , burnin        = 0
    , thin          = 1
    , pb            = c(0.10, 0.05)
    , plot_stable   = FALSE
    , plot_unstable = TRUE
    , ncolors       = 5
    , .which        = "both"
    , .grid         = 100
    )
bp$biplot

Learn more

• Vignettes: browseVignettes("baystability"), starting with baystability_01_getting_started.
• The application: bys_app().
• References of the methods behind a result: bys_cite()

Citation

Yaseen M, Jarquin D, Perez-Elizalde S, Burgueno J, Crossa J (2026).
_baystability: Bayesian Stability Analysis of Genotype by Environment
Interaction (GEI)_. R package version 1.0.0 (first released 2018),
<https://CRAN.R-project.org/package=baystability>.

BibTeX:

@Manual{baystability,
  title = {{baystability}: Bayesian Stability Analysis of Genotype by Environment Interaction ({GEI})},
  author = {Muhammad Yaseen and Diego Jarquin and Sergio Perez-Elizalde and Juan Burgueno and Jose Crossa},
  year = {2026},
  note = {R package version 1.0.0 (first released 2018)},
  url = {https://CRAN.R-project.org/package=baystability},
}

Please also cite the methods you use: citation("baystability") lists them with the package, and bys_cite(x) gives the references of a single result.