Application of the bayesian-AMMI model in the study of genotypic stability and adaptability in mustard data
Keywords:Interaction; Credibility region; Biplot.
The analysis of data sets from multienvironmental trials is of fundamental importance in the final stages of plant breeding programs. In this context, the Additive Main Effects and Multiplicative Interaction (AMMI) model has become a popular method for evaluating genotype responses in different environments. In the present work, the AMMI model was applied, under the bayesian approach, to a set of data from a randomized block experiment with 12 mustard genotypes (varieties) in 6 different environments. The objective was to analyze genotypic stability and adaptability through the AMMI-2 biplot representation, highlighting differences in this approach in relation to the classical AMMI analysis. The results showed the great flexibility of the bayesian method to incorporate a random effect for genotypes, as well as inference to the biplot through regions of credibility for genotypic and environmental scores that describe the effect of the interaction between genotypes by environments (GEI). The regions of credibility built for main effects and bilinear parameters allowed to identify more productive genotypes and to visualize homogeneous subgroups of genotypes and environments in relation to the effect of GEI. The more productive genotypes were G8 and G10 and only G2 was considered statistically stable.
Box, G. E. P., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. New York: John Wiley.
Chen, M. H., & Shao, Q. M. (1999). Monte Carlo estimation of bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69-92.
Crossa, J., Perez-Elizalde, S., Jarquin, D., Cotes, J. M., Viele, K; Liu, G., & Cornelius, P. L. (2011). Bayesian estimation of the additive main effects and multiplicative interaction model. Crop Science, 51(4), 1458-1469. https://doi.org/10.2135/cropsci2010.06.0343
Denis, J. B., & Gower, J. C. (1994). Asymptotic covariances for parameters of biadditive models. Utilitas Mathematica, v. 46, 193-205.
Duarte, J. B., & Vencovsky, R. (1999). Interação genótipos × ambientes: uma introdução à análise “AMMI”. Ribeirão Preto: Sociedade Brasileira de Genética.
Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal components analysis. Biometrika, 58(3), 453-467.
Heidelberger, P., & Welch, P. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.https://doi.org/10.1287/opre.31.6.1109
Indian Agricultural Statistics Research Institute. IASRI. (2014). Recuperado de http://www.iasri.res.in/design/Analysis%20of%20data/combined_anlysis_rcbd.html
Jarquin, D., Perez-Elizalde, S., Burgueño, J., & Crossa, J. (2016). A hierarchical Bayesian estimation model for multi-environment plant breeding trials in successive years. Crop Science, 56(5), 2260-2276. https://doi.org/10.2135/cropsci2015.08.0475
Júnior, L. A. Y. B., Silva, C. P., Oliveira, L. A., Nuvunga, J. J., Pires, L. P. M., Pinho, R. G. V., & Balestre, M. (2018). AMMI Bayesian Models to Study Stability and Adaptability in Maize. Agronomy Journal, 110(5), 1765-1776. https://doi.org/10.2134/agronj2017.11.0668
Kempton, R. A. (1984). The use of biplots in interpreting variety by environment interactions. Journal of Agricultural Science, 103(1), 123-135. https://doi.org/10.1017/S0021859 600043392
Liu, G. (2001). Bayesian computations for general linear-bilinear models. (Thesis, University of Kentucky).
Oliveira, L. A., Silva, C. P., Nuvunga, J. J., Silva, A. Q., & Balestre, M. (2015). Credible intervals for scores in the AMMI with random effects for genotype. Crop Science, 55(2), 465-476. https://doi.org/10.2135/cropsci2014.05.0369
Oliveira, L. A., Silva, C. P., Teodoro, P. E., Torres, F. E., Corrêa, A. M., & Bhering, L. L. (2017). Performance of Cowpea Genotypes in the Brazilian Midwest Using the Bayesian Additive Main Effects and Multiplicative Interaction Model. Agronomy Journal, 110(1), 147-154. https://doi.org/10.2134/agronj2017.03.0183
Ooms, J. C. L. (2009). The highest posterior density posterior prior for Bayesian model selection. (Master's thesis). https://dspace.library.uu.nl/handle/1874/34234
Perez-Elizalde, S., Jarquin, D., & Crossa, J. (2012). A general Bayesian estimation method of linear–bilinear models applied to plant breeding trials with genotype× environment interaction. Journal of Agricultural, Biological, and Environmental Statistics, 17(1), 15-37. https://doi.org/10.1007/s13253-011-0063-9
R Core Team (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/
Raftery, A. E., & Lewis, S. (1992). How many iterations in the Gibbs sampler? In: Bernardo, J. M. et al. (Ed.), Bayesian statistics, 763-773. Oxford: Oxford University.
Resende, M. D. V., & Duarte, J. B. (2007). Precisão e controle de qualidade em experimentos de avaliação de cultivares. Pesquisa Agropecuária Tropical, 37(3), 182-194. Recuperado de https://www.revistas.ufg.br/pat/article/view/1867.
Silva, C. P., Oliveira, L. A., Nuvunga, J. J., Pamplona, A. K. A., & Balestre, M. (2015). A Bayesian Shrinkage approach for AMMI Models. PLoS One, 10(7), 1-27. https://doi.org/10.1371/journal.pone.0131414
Silva, C. P., Oliveira, L. A., Nuvunga, J. J., Pamplona, A. K. A., & Balestre, M. (2019). Heterogeneity of Variances in the Bayesian AMMI Model for Multienvironment Trial Studies. Crop Science, 59(6), 2455-2472. https://doi.org/10.2135/cropsci2018.10.0641
Smith, A. B., Cullis, B. R., & Thompson, R. (2005). The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches. Journal of Agricultural Science, 143(6), 449-462. https://doi.org/10.1017/S0021859605005587
Smith, B. J. (2007). Boa: An R Package for MCMC Output Convergence Assessment and Posterior Inference. Journal of Statistical Software, 21(11), 1-37.
Viele, K., & Srinivasan, C. (2000). Parsimonious estimation of multiplicative interaction in analysis of variance using Kullback-Leibler information. Journal of Statistical Planning and Inference, 84(1-2), 201-219. https://doi.org/10.1016/S0378-3758(99)00151-2
Yan, W., Glover, K. D., & Kang, M. S. (2010). Comment on “Biplot analysis of Genotype × environment interaction: proceed with caution”, by R.-C. Yang, J. Crossa, PL Cornelius, and J. Burgueño in 2009 49, 1564-1576. Crop Science, 50(4), 1121-1123. https://doi.org/10.2135/cropsci2010.01.0001le
Yang, R. C., Crossa, J., Cornelius, P. L., & Burgueño, J. (2009). Biplot analysis of genotype × environment interaction: proceed with caution. Crop Science, 49(5), 1564-1576. https://doi.org/10.2135/cropsci2008.11.0665
Zobel, R. W., Wright, M. J., & Gauch, H. G. (1988). Statistical analysis of a yield trial. Agronomy Journal, 80(3), 388-393. https://doi.org/10.2134/agronj1988.00021962008 000030002x
How to Cite
Copyright (c) 2020 Alessandra Querino da Silva, Luciano Antonio de Oliveira, Carlos Pereira da Silva, Cristian Tiago Erazo Mendes, Elias Silva de Medeiros, Thelma Sáfadi
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2) Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3) Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.