stability: Genotype-by-Environment Interaction and Yield Stability Analysis
Source:R/stability-package.R
stability-package.Rdstability analyses multi-environment trials of plant breeding, laid out in randomized complete blocks in every environment, to find genotypes that are high-yielding and stable: analyses of variance, regression on the environment index, variance-based and rank-based stability statistics, AMMI and GGE biplots, and a plain-language interpretation of every result.
Details
Functions, in the order of an analysis:
ge_means,ge_effects: tables of means, rankings and interaction effects.indiv_anova,add_anova: analysis of variance in each environment and combined.er_anova,stab_reg: Eberhart and Russell's analysis; Finlay and Wilkinson's regression.stab_measures,stab_par,stab_kang,stab_fox: variance, ecovalence, stability variance, Kang's yield-stability statistic and rank-sum, Fox's top third.stab_eskridge,stab_reliability,stab_superiority,stab_huehn: safety-first indices, reliability index, superiority measure, nonparametric statistics.ammi,ammi_biplot,stab_asv,stab_masv,stab_dist: AMMI analysis, biplots and AMMI-based stability values.gge_biplot: GGE biplot with the which-won-where, mean-stability and discrimination views.stab_interpret: the interpretation of any of these results.
Every analysis keeps the names, arguments and result components of the earlier versions and returns the result
with a class and the methods print, summary, plot and as.data.table; see
stab-methods. Utilities: stab_theme, stab_save, stab_notation,
stab_reference.
Data. ge_data: 60 wheat genotypes in 11 environments.
Vignettes. Start with vignette("stability_01_getting_started", package = "stability");
browseVignettes("stability") lists all of them, each as HTML and as PDF.
Notation
Scalars are upper-case letters in normal face, indices lower-case italic, vectors lower-case bold and matrices
upper-case bold. The full table is stab_notation().
| \(G\), \(E\), \(B\) | numbers of genotypes, environments and replicates |
| \(i\), \(j\), \(k\) | genotype, environment, replicate |
| \(\mathbf{Y}\), \(\bar{y}_{ij}\) | table of means, mean of genotype \(i\) in environment \(j\) |
| \(\bar{y}_{i\cdot}\), \(\bar{y}_{\cdot j}\), \(\bar{y}\) | genotype, environment and grand means |
| \(\mathbf{Z}\), \(z_{ij}\) | interaction effects |
| \(I_j\) | environment index \(\bar{y}_{\cdot j} - \bar{y}\) |
| \(s^2\), \(f_e\) | pooled error mean square of the plots and its degrees of freedom |
| \(\beta_i\), \(S^2_{d_i}\) | regression slope and deviation variance |
| \(W_i\), \(\sigma^2_i\) | ecovalence and stability variance |
| \(\lambda_n\) | singular values of the interaction (AMMI) or of G + GE (GGE) |
References
Becker, H. C. and Leon, J. (1988). Stability analysis in plant breeding. Plant Breeding, 101(1), 1–23.
Kang, M. S. (2002). Quantitative Genetics, Genomics and Plant Breeding. CABI Publishing, Wallingford.
Singh, R. K. and Chaudhary, B. D. (2004). Biometrical Methods in Quantitative Genetic Analysis. Kalyani Publishers, New Delhi.
Yan, W. and Kang, M. S. (2003). GGE Biplot Analysis: A Graphical Tool for Breeders, Geneticists, and Agronomists. CRC Press, Boca Raton.
Author
Muhammad Yaseen (myaseen208@gmail.com), Kent M. Eskridge (keskridge1@unl.edu)