Abordagem bayesiana para avaliação da adaptabilidade e estabilidade de genótipos de alfafa

Abstract

Resumo -O objetivo deste trabalho foi propor uma abordagem bayesiana do método de Eberhart & Russell para avaliar a adaptabilidade e da estabilidade fenotípica de genótipos de alfafa (Medicago sativa), bem como avaliar a eficiência da utilização de distribuições a priori informativas e pouco informativas. Foram utilizados dados de um experimento em blocos ao acaso, no qual se avaliou a produção de massa de matéria seca de 92 genótipos. A metodologia bayesiana proposta foi implementada no programa livre R por meio da função MCMCregress do pacote MCMCpack. Para representar as distribuições a priori pouco informativas, utilizaram-se distribuições de probabilidade com grande variância; e, para representar distribuições a priori informativas, adotou-se o conceito de meta-análise, que se caracteriza pela utilização de informações provenientes de trabalhos anteriores. A comparação entre as distribuições a priori foi realizada por meio do fator de Bayes, com a função BayesFactor do pacote MCMCpack, que indicou a priori informativa como a mais adequada nas condições deste estudo.Termos para indexação: Medicago sativa, fator de Bayes, priori informativa, interação genótipo x ambiente, MCMC. Bayesian approach for the evaluation of adaptability and stability of alfalfa genotypesAbstract -The objective of this work was to propose a Bayesian approach for the Eberhart & Russell method to evaluate the phenotypic adaptability and stability of alfafa (Medicago sativa) genotypes, as well as to evaluate the efficiency of the use of prior informative and noninformative distributions. Data from a randomized block design experiment evaluating the forage dry weight of 92 genotypes were used. The Bayesian methodology proposed was implemented in the free software R by the MCMCregress function of the MCMCpack package. To represent the noninformative prior distributions, a probability distribution with high variance was used; and, to represent the informative prior, a meta-analysis concept was adopted, characterized by the use of information provided by previous studies. The comparison between the prior distributions was done using the Bayes Factor, with the BayesFactor function of the MCMCpack package, which indicated that an informative prior is more appropriate under the conditions of this study.

Adaptability and phenotypic stability of common bean genotypes through Bayesian inference

“…For the Bayesian analysis, we considered all genotypes that were evaluated in Corrêa et al (2009), which were used as references for the specification of a priori distributions (Table 2). With the Bayesian approach, we considered the following statistical model, developed by Nascimento et al (2011): where each Y ij observation was assumed to have the following distribution:…”

“…For example, we obtained a sample of the joint a posteriori distribution using the Markov chain and Monte Carlo (MCMC) method, which was used to determine the moments associated with the marginal distributions of interest (Cassela and George, 1992). In this study, the analyses were performed using R software (R Development Core Team, 2015) with codes developed by Nascimento et al (2011), and the joint distribution sample was obtained using the MCMC regression function of the MCMC package.…”

“…To evaluate the influence of a priori information when estimating the adaptability and stability parameters, we utilized two different models: informative a priori distributions and minimally informative a priori distributions (Nascimento et al, 2011). In Model 1, the informative a priori information was derived from the application of meta-analysis techniques, which were characterized using information from the study by Corrêa et al (2009).…”

“…Nascimento et al (2011) formulated a Bayesian approach using the Eberhart and Russell (1966) method to evaluate GE interaction, and concluded that the selection of genotypes in different environments was most accurate when a priori information was used. It is a robust statistical procedure with many possible applications, but its use in plant genetic improvement is still limited (Teodoro et al, 2015).…”

Pattern analysis of multi-environment trials in common bean genotypes

“…Beyond traditional statistical methods used to evaluate, study and interpret the G x E is realized on the analysis of variance from the interaction (WRICKE, 1965); in the simple linear regression (EBERTHART; RUSSELL, 1966) and linear bissegmented regression (CRUZ et al, 1989) Watson et al (1966), GGE Biplot Analysis (genotype main effect + genotype environment interaction) which was developed by Yan (2001), Artificial Neural Networks (NASCIMENTO et al, 2013;TEODORO et al, 2015a) and Bayesian perspective (NASCIMENTO et al, 2011;TEODORO et al, 2015b;BARROSO et al, 2016).…”