Population parameters and selection of kale genotypes using Bayesian inference in a multi-trait linear model

Acta Scientiarum http://www.uem.br/acta ISSN printed: 1679-9275 ISSN on-line: 1807-8621 Doi: 10.4025/actasciagron.v39i1.30856 Population parameters and selection of kale genotypes using Bayesian inference in a multi-trait linear model Alcinei Mistico Azevedo1*, Valter Carvalho de Andrade Júnior2, Albertir Aparecido dos Santos2, Aderbal Soares de Sousa Júnior2, Altino Júnior Mendes Oliveira2 and Marcos Aurélio Miranda Ferreira2 1 Universidade Federal de Minas Gerais, Campus Regional de Montes Claros, Avenida Universitária, 1000, 39404-547, Montes Claros, Minas Gerais, Brazil. 2Universidade Federal dos Vales Jequitinhonha e Mucuri, Diamantina, Minas Gerais, Brazil. *Author for correspondence. E-mail: ABSTRACT. Variance components must be obtained to estimate genetic parameters and predict breeding values. This information can be obtained through Bayesian inference. When multiple traits are evaluated, Bayesian inference can be used in multi-trait models. The objective of this study was to obtain estimates of genetic parameters, gains with selection, and genetic correlations among traits. Likewise, we aim to predict the genetic values and select the best kale genotypes using the Bayesian approach in a multi-trait linear model. The following traits were evaluated: stem diameter, plant height, number of shoots, number of marketable leaves and fresh weight of leaves using Bayesian inference in 22 kale genotypes. The experiment consisted of a randomized block design with three replications and four plants per plot. Genetic effects predominated over environmental effects. The highest correlation estimates were found between the fresh weight of leaves and stem diameter and between the plant height and number of marketable leaves. The following commercial cultivars and genotypes are recommended for cultivation and to integrate into breeding programs: UFLA 11, UFLA 5, UFLA 6, UFVJM 3 and UFVJM 19. The estimates of the gain with selection indicate the potential for improvement of the studied population. Keywords: Brassica oleracea L. var. acephala DC., genetic parameters, crop breeding, statistical modeling, correlations. Parâmetros populacionais e seleção de genótipos de couve por inferência bayesiana em modelo linear multicaracterístico RESUMO. Para selecionar genitores em programas de melhoramento deve-se obter os componentes de variância para estimar parâmetros genéticos e predizer valores genéticos, os quais podem ser obtidos vantajosamente pela inferência bayesiana. Quando várias características são avaliadas a inferência bayesiana pode ser utilizada em modelos multicaracterísticos. Objetivou-se obter estimativas de parâmetros genéticos, ganhos de seleção, conhecer as correlações genéticas entre as características, predizer valores genéticos e selecionar melhores genótipos de couve utilizando a abordagem bayesiana em modelo linear multicaracterístico. Foram avaliados o diâmetro do caule, altura da planta, número de brotações, número de folhas comercializáveis e massa fresca de folhas por inferência bayesiana em 22 genótipos de couve. Foi utilizado o delineamento em blocos casualizados com três repetições e quatro plantas por parcela. Verificou-se a predominância dos efeitos genéticos sobre os ambientais. As maiores estimativas de correlação foram encontradas entre a matéria fresca de folhas e as características diâmetro do caule, altura de plantas e número de folhas comercializáveis. Além das testemunhas comerciais, são indicados para o cultivo e para integrar programas de melhoramento os genótipos UFLA 11, UFLA 5, UFLA 6, UFVJM 3 e UFVJM 19. As estimativas do ganho de seleção indicaram o potencial de melhoramento para a população estudada. Palavras Chave: Brassica oleracea L. var. acephala DC., parâmetros genéticos, melhoramento genético, modelagem estatística, correlações. Introduction Kale (Brassica oleracea L. var. acephala DC.) is an annual or biennial vegetable that belongs to the Brassicaceae family. Due to its new uses in culinary dishes and recent discoveries about its nutraceutical properties, the kale consumption has gradually Acta Scientiarum. Agronomy increased (Moreno, Carvajal, Lopez-Berenguer, & Garcia-Viguera, 2006; Vilar, Cartea, & Padilla, 2008; Soengas, Sotelo, Cartea, & Velasco, 2011). The aim of a kale-breeding program is the facilitation of cultural practices and the increase in the yield per area. Thus, there is a growing interest in selecting plants with a lower height, lower number of shoots, Maringá, v. 39, n. 1, p. 25-31, Jan.-Mar., 2017 26 higher stem diameter, and higher number of leaves (Azevedo et al., 2012). To define strategies for breeding programs, it is necessary to estimate variance components, predict breeding values and obtain estimates of genetic parameters (Gonçalves-Vidigal, Mora, Bignotto, Munhoz, & Souza, 2008; Oliveira, Santana, Oliveira, & Santos, 2014). The variance components are unknown and are usually estimated by the method of moments, maximum likelihood (ML), or restricted maximum likelihood (REML). Generally, two or more traits are simultaneously evaluated in studies with kale. In this case, the multi-traits models can be applied, which allow the improvement of the predictions (Viana, Sobreira, Resende, & Faria, 2010) and the determination of associations among traits. In this case, Bayesian inference can be advantageously used because it enables the calculation of the densities of the marginal posterior distributions and the credibility intervals of the variance components, breeding values and genetic parameters, such as heritability, coefficient of genotypic variation, coefficient of residual variation, relative variation index and genotypic correlation (Waldmann & Ericsson, 2006). Thus, the objective of this work was to use the Bayesian approach considering a multi-trait linear model to obtain estimates of the genetic parameters, assess the genetic correlation between traits, predict breeding values, and select the best kale genotypes available in the germplasm bank of the UFVJM (Federal University of the Valleys Jequitinhonha and Mucuri). Azevedo et al. alto", from the Feltrin® company (COM-1); "couve manteiga", from the Vidasul baby® company (COM2), and "couve de folha manteiga Geórgia", from the Horticeres® company (COM-3). On June 7th, 2013, shoots were collected for seedling formation. These shoots were three to four centimeters in height and had two leaflets. After collection, the shoots were planted in trays with 72 cells filled with a commercial substrate. These trays were kept in a greenhouse for 30 days for better rooting. On July 7th, 2013, the seedlings were transplanted into 2.50 m wide and 0.30 m high beds, spaced at 1 m between rows and 0.50 m between plants. Fertilization was carried out according to the recommendations available for the crop. In each plant, the number of shoots (when they were removed), number of marketable leaves and fresh weight of marketable leaves were evaluated. These (...truncated)