Application of the bayesian-AMMI model in the study of genotypic stability and adaptability in mustard data

Authors

DOI:

https://doi.org/10.33448/rsd-v9i9.7023

Keywords:

Interaction; Credibility region; Biplot.

Abstract

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.

Author Biography

Alessandra Querino da Silva, Universidade Federal da Grande Dourados

Doutora e Mestre em Estatística e Experimentação Agropecuária pela Universidade Federal de Lavras (UFLA). Licenciada em Matemática e também Bacharel em Estatística pela Universidade Estadual Paulista “Júlio Mesquita Filho” (UNESP).

Docente da Faculdade de Ciências Exatas e Tecnologia (FACET) da Universidade Federal da Grande Dourados (UFGD).

 

 

References

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

Published

14/08/2020

How to Cite

Silva, A. Q. da, Oliveira, L. A. de, Silva, C. P. da, Mendes, C. T. E., Medeiros, E. S. de, & Sáfadi, T. (2020). Application of the bayesian-AMMI model in the study of genotypic stability and adaptability in mustard data. Research, Society and Development, 9(9), e166997023. https://doi.org/10.33448/rsd-v9i9.7023

Issue

Section

Agrarian and Biological Sciences