Selection of snap bean F 2 progenies for production using the REML / BLUP methodology

Este trabalho objetivou selecionar progenies F2 de feijao-vagem para caracteres relacionados a producao de vagens e graos atraves do procedimento REML/BLUP. O experimento foi conduzido na area experimental do Instituto Federal Fluminense (IFF), localizado no municipio de Bom Jesus do Itabapoana-RJ. Foram semeadas linhas de 55 genotipos, entre eles, 42 progenies F2 oriundas de cruzamentos dialelicos, alem dos 13 parentais, utilizados como testemunhas. Cada linha foi composta por 24 plantas, sem repeticoes e o espacamento utilizado foi de 1,0x0,5 m. As plantas foram colhidas e avaliadas individualmente para as caracteristicas producao de vagens verdes por planta e producao de graos por planta. Foi realizada a selecao entre e dentro de progenies via BLUP utilizando-se o programa Selegen-REML/BLUP. Com base na Maxima Verossimilhanca Restrita (REML), foi possivel estimar os coeficientes de variacao genetico e residual de 19,43% e 33,53%, respectivamente para producao de vagens verdes por planta e producao de graos por planta. Utilizou-se 7,9% de intensidade de selecao, totalizando 100 plantas selecionadas com base no valor genotipico individual. A acuracia estimada para a selecao de progenies foi de 0,5014 para a producao de vagens e 0,5130 para producao de graos, indicando dificuldades na selecao dos caracteres devido a alta influencia ambiental sobre as caracteristicas de producao. Apesar disso, a predicao dos valores geneticos estimados por meio do Melhor Preditor Linear Nao-Viesado (BLUP), apontou os cruzamentos Feltrin x UENF 15-23-4, UENF 7-5-1 x UENF 9-24-2 e Feltrin x UENF 14-3-3 como as progenies mais promissoras, com ganhos de 65,66 g, 61,49g e 57,63 g, respectivamente na producao de vagens verdes e 52,45 g, 46,96 g e 49,29 g, respectivamente na producao de graos. O ganho genetico aditivo predito com a selecao foi de 36,05% na producao de graos, e 33,5% na producao de vagens verdes. Conclui-se que a selecao via BLUP para a producao de vagens e graos possibilitou a predicao e obtencao de ganhos geneticos significativos para o melhoramento do feijao-vagem nas proximas geracoes.


Received on August 21, 2015; accepted on May 11, 2016
industrialized.In Brazil, this vegetable is traditionally produced by family farmers, who still use a small number of cultivars of indeterminate-growth-habit under protected cultivation (Peixoto et al., 2002).
The crop has proven to be promising, among the vegetables which have been grown in Brazil, since it has reached the sixth position in production (CEASA, 2010); especially the Southeastern Region, producing about 37 thousand t/year and the state of Rio de Janeiro which is responsible for about 21% of this amount.Nevertheless, despite being very popular in the North and Northwest of the State, these regions still have low participation in this agricultural crop production due to the unfavorable weather conditions for cultivation (Vilela et al., 2011).
UENF develops a snap-bean breeding program aiming to obtain promising cultivars for productivity of pods for the North and Northwest regions of the State.Silva (2013) characterized genetic diversity of 33 accessions from Active Germplasm Bank of snap bean of UENF using multivariate procedures based on 37 minimum morphological descriptors for snap bean.Then, diallelic crosses were carried out among 12 divergent accessions of the Bank, F 1 generation was evaluated together with parental genotypes based on Griffing's model 2 (1956).Thenceforth, the authors started this research aiming to select F 2 breeding lines with better pod yield under environmental conditions in the North region of the state of Rio de Janeiro, in order to ensure continuity of the breeding program.
Thus, the authors observed that the breeding programs of the species should be implemented to select and obtain genotypes more adapted with quality and production of superior pods in order to be recommended to the producers of these regions (Vilela et al., 2011).The authors believe that superior genotypes should be selected based on, mainly, genetic components, contributing both as subsidy for planning efficient breeding strategies, as well as for identifying the nature of action of the genes involved in controling the traits to be improved.Another benefit of well estimated genetic components, according to Resende (2007b), is the possibility to predict the genotypic values of the selecting individuals, since the prediction procedure of genetic values depends on the identification of the genetic control of traits under selection, especially concerning individual heritability and repeatability parameters.
The authors consider the need of using specific methods when the aim is to estimate genetic parameters and to predict genetic values.According to Resende (2007b), the standard procedure recommended for quantitative and genetic analysis and for selection based on genotypic values is the REML/ BLUP methodology.That means, the authors used the Restricted Maximum Likelihood Method (REML) to estimate the variance components and Best Linear Unbiased Prediction Method (BLUP) to predict genotypic values.The REML/BLUP methodology has been used as a tool associated with progeny selection in several crops like popcorn (Freitas et al., 2013), coffee (Resende et al., 2001;Pereira et al., 2013), sugar cane (Resende & Barbosa, 2006), papaya (Oliveira et al., 2012), common beans (Chiorato et al., 2008) and others.In plant breeding, its use is relatively little, comparing to its use for animal breeding; the reason is because the experiments with plants are generally balanced (Resende, 2007b).
The aim of this work was to select snap bean F 2 progenies for production traits using REML/BLUP methodology.

MATERIAL AND METHODS
The experiment was carried out in the experimental field of Instituto Federal Fluminense, located in the municipality of Bom Jesus de Itbapoana, Northwest of the state of Rio de Janeiro (21º08'S, 41 o 40'W, 88 m altitude).The local climate is Aw, according to Köppen classification, alternating hot and rainy season with dry season and average annual temperature ranging from 22 to 25°C and average annual rainfall from 1200 to 1300 mm.
The genetic material in this work consisted of F 2 population derived from a research carried out by Silva (2013), in which the author aimed to evaluate, through partial diallel 6 x 6, twelve snap bean genotypes (Table 1), chosen from 37 morphologic and agronomic traits, in accordance to the Form of Minimum Morphological Descriptors for Beans (Formulário de Descritores Morfológicos Mínimos de Feijão) (Phaseolus vulgaris), recommended by the National Service of Plant Varieties Protection [Serviço Nacional de Proteção de Cultivares (SNPC)], in order to select the best parents for generating productive populations and for the advancement of generations using SSD method (Single Seed Descent).
The authors evaluated 55 snap bean genotypes; 42 F 2 progenies were obtained from diallelic crosses and 13 parents used as control.Among the parents, three cultivars and 10 lines, from the Snap Bean Breeding Program of Universidade Estadual Norte Fluminense Darcy Ribeiro, were used.
The F 2 plants were arranged in the experimental field without the establishment of experimental plots, being 24 plants of each of F 2 progenies properly arranged and spaced with their parents.Each plant was arranged in spacing of 1.0x0.5 m.
Sowing was carried out at a depth of 2.5 cm, with two seeds per pit.During the experiment, cultural and phytosanitary practices were carried out according to the recommendations for the crop, according to Filgueira (2008), as well as sprinkler irrigation.
The progenies were evalutated in relation to pod and grain production traits, considering the weight of pods per plant (PVP), only the weight of green pods per plant, in grams, was considered (PGP).Analyses were carried out using the individual value of the plants of each progeny.
The authors used individual analyses referring to the values per plant for the two traits used for selection.The authors used the program SELEGEN -REML/ BLUP (Restricted Maximum Likelihood -the Best Linear Unbiased Estimation) for estimation and prediction of genetic values.BLUP was the procedure adopted by the program for predicting the genetic values, using variance estimates obtained through REML method, presented by Resende (2007b).Variables were analyzed according to the following model (Resende, 2007b): y = Xr + Za + e Where y, r, a, and e are individual data vectors, repetition effects (fixed), individual additive genetic effects (random), respectively; X and Z are incidence matrices for repetition effects and for individual additive genetic effects, respectively.
Random effects were assumed to be uncorrelated and to be normally distributed.

RESULTS AND DISCUSSION
The traits grain production per plant (PGP) and pod production per plant (PVP) showed genetic variance of 465.69 and 792.08, respectively (Table 2).Estimate of genetic variance (s g 2 ) among the progenies, when presenting positive values and different from zero, shows variability among progenies due to genotype and, consequently, the possibility of selecting superior breeding lines for each trait evaluated.Therefore, these values reflect considerable genetic variability or difference among genotypes to be used for selection, mainly for pod production, since this is the most economically relevant trait for the crop.
The authors highlight that the phenotypic variation should be composed, most part, of variations from genotype of the selection candidates, contributing to higher heritability of the selected character.From broad-sense heritability anlysis (h 2 a ) for PGP and PVP traits, the authors observed values around 0.2632 for grain production and 0.2514 for pod production.These values show that 26.32% and 25.14% of the variation for traits PGP and PVP, respectively, are due to genetic causes.Heritability values for the traits showed to be seriously influenced by the high environmental variance obtained; this fact hinders the successful selection based on these traits.However, even being considered of low magnitude, these values are relevant in order to improve these traits, since they are polygenic traits, any gain for such traits should be considered.
Heritability values for PGP and PVP showed to be superior to the estimated by Coelho et al. (2002), which obtained  Broad-sense heritability values can show great variation; factors like progenies of different origins and different levels of environmental influence on traits may be crucial in order to obtain better estimates for this parameter (Pereira et al., 2013).Thus, the authors highlight that heritability is not an immutable trait, being not only a property of the characteristic, but also a property of population and environmental conditions in which the population was submitted (Cruz, 2005).
Heritability based on progeny average is determined considering the number of replications and plants evaluated per plot in the experient (Chiorato et al., 2008).In this work, heritability based on the progeny average for PGP and PVP maintained the same broad-sense heritability estimates.This fact occurred in order to estimate genetic parameters, the authors used only data at level of plants within progenies and consequently, without replications, being discarded the progeny averages.
Selective accuracy estimated for PGP showed an average of 0.513, whereas for PVP the average was 0.501; these values reflect dificulties for selecting based on these traits.According to Resende & Duarte (2007), selective accuracy can range from 0 to 1, classified very high (Ac prog ≥0.90), high (0.70≤Ac prog ≤ 0.90), moderate (0.50≤Ac prog ≤0.70), and low (Ac prog <0.50).The authors observed levels of accuracy for two traits within Selective accuracy is associated to precision and represents correlation between the predicted genetic values and true genetic values of the candidate for selection.This reliability factor is a function of the coefficient of genotypic determination associated with the trait evaluated, which corresponds to the heritability coefficient, in a intrapopulation selection process (Resende & Duarte, 2007).
The traits PGP and PVP showed values close to CV g (%) (20.491 and 19.434, respectively), which indicate relative magnitude of changes of a character due to genetic action, being directly proporcional to genetic variance and allowing the breeder a better notion of genetic variability and, consequently, advances that can be obtained through the selection of a particular trait.These values for CV g show that the selection of better progenies will allow a significant increase of the population genetic value for the traits evaluated.
Another important parameter to define the best breeding strategy for each trait is the coefficient of relative variation (CV r ) or variance índex (I v ), as this is the ratio between CV g and CV e .Therefore, this coefficient is not influenced by the average of the trait.According to Vencovsky (1987), when this ratio is close to or above 1, a favorable situation of selection for a particular trait is characterized.Based on this parameter, the traits PGP and PVP can provide acceptable genetic gains, since the magnitude of the CV r was 0.597 and 0.579, respectively.These values show a higher proportion of genetic variation in relation to the environmental influence, favoring selection process.
The authors highlight the importance of reporting the main advantages of using the mixed model methodology (REML/BLUP) in the simultaneous estimation of genetic parameters and  et al. (2011).In this research, line UENF 7-10-1 showed to be the most productive for the trait under environmental conditions in the North region of Rio de Janeiro State.
The progenies 14,12,24,26,27,16,25,19,21 and 36 stood out among others (Table 3), since they showed greater genetic gains for PGP and will certainly contribute to further advances for the trait.From these progenies, the authors highlight that four of them are from line UENF 7-6-1 and three are from the just mentioned UENF 7-5-1.Ten progenies showing greater gains for PGP showed average genetic gain in the next generation of 40.876 g/ plant; this value can vary according to the selection pressure to be exercised in the line selection.
Table 3 presents the top-ranked genotypes, which showed greater gains and higher new averages.The progeny 14, from the cross Feltrin x UENF 15-23-4, showed to be superior than the others, with a gain of 52.455 g/plant in relation to the population average if selected, thus providing a new average of 157.769 g/plant for PGP.Genotypes 46, 40, 49 and 54 obtained lower PGP in this study, with gains ranging from 2.215 to 0 g/plant.These genotypes, if selected, provided new population averages between 107.439 to 105.314 g/plant.Among them, the authors notice only one progeny, from the cross UENF 7-10-1 x UENF 14-3-3, and three parental lines used as controls, UENF 7-14-1, UENF 7-3-1 and UENF 15-23-4.4), the authors noticed a high degree of correspondence between progenies with the best performance for this trait and the best-ranked progenies for PGP, for the interdependence between both traits evaluated.Progenies 14,24,12,26,27,36,25,22,19 and 16 stood out for green pod production in this study; when selected, these progenies will provide predicted average genetic gain for the next generation population of 50.642 g/ plant for this trait.
Once again, progeny 14, from the cross of the commercial variety Feltrin x UENF 15-23-4, stood out reaching the best productive performance for PVP and, consequently, the greatest predicted genetic gain of 65.664 g/plant, obtaining a new predicted average of 210.478 g/ plant.Francelino et al. (2011) carried out selections among promising snap bean lines aiming to release improved material for producers from the North and Northwest regions of the State and showed line UENF 15-23-4 among the most productive lines both for grain production and green pod production in the region.
The lowest PVP were obtained by genotypes 1, 7, 49 and 54, showing predicted average gain of only 1.574 g/plant.Among these genotypes, two progenies and two parental lines are presented, UENF 7-3-1 and UENF 15-23-4.Although UENF 15-23-4 is one of the parents from which the line with the greatest PVP derived, the performance of the line itself was not satisfactory under the conditions of this study.
For an efficient selection of superior genotypes, Chiorato et al. (2008) state that this selection should be based both on variance components and on average components and for a considerable genetic gain, the genotypes with the highest averages and the greatest genetic variability should be selected.Based on criteria such as the greatest importance to good productive performance of green pods per plant, as well the greatest genetic variability for PVP, the authors concluded that the use of priority ranking and prediction of values for this trait becomes more feasible.This methodology aims to potentiate genetic gain by selecting the best plants within these selected progenies.

Selection within progenies
Evaluating the traits in plants, the authors verified estimates for each plant or individual.Then, not only the selection among progenies was carried out but also the increase of gains in the population for the next generation, through the selection of ten best plants of each selected progeny, could be obtained.
Analysis of genetic parameters, showed in Table 2, allowed to verify that although in smaller proportions in relation to environmental variance, the authors noticed genetic variability in the population for both traits, with significant values which can be used through selection.
The selection of the most productive plant was carried out based on predicted genetic values of each individual.According to Resende (2007b), REML/BLUP methodology provides ordering potential genotypes for selection exploiting all the genotypic variation among and within progenies, considering each variable analyzed separately, though.Due to the different ordering of progenies by BLUP for selection among progenies for evaluated traits, the authors noticed that priorizing the most relevant trait for the snap bean crop aiming subsequent selection within progenies (among progenies).
At this stage, 10 individuals of each progeny were selected, totalizing 100 plants in order to generate F 3 generation, allowing selection intensity about 7.9%.
The average of genotypic values of each progeny selected after selection of the best plants, general advances obtained through selection process carried out in this study, including genetic gains in relation to average of the original population from the selection among and within progenies and their performance in relation to the commercial controls are presented in Table 5.
Selecting plants with best productive performance for pods and grains, new predicted averages for progenies were obtained, especially for plants from the cross Feltrin x UENF 15-23-4, which obtained new averages ranking from 242.643 g to 219.729 g for PVP, production value above all commercial Selection of snap bean F 2 progenies for production using the REML/BLUP methodology Table 5.Average predicted genetic value (µ+g) of the selected plants within progenies for the grain yield per plant (PGP) and pods production per plant (PVP) traits.Campos dos Goytacazes, UENF, 2015.
From this percentage, 29.48% of the gains for PGP resulted from selection among progenies and 6.57% due to individual selection within progenies.For PVP, selection among progenies provided 27.38% of gains and individual selection within progenies resulted in 6.12%, showing that most of variability present in population is among the different progenies evaluated.
Obtaining superior progenies and plants, from these crosses both for pod and grain production, was possible in low heritability conditions of traits, which makes REML/BLUP methodology an effective tool to obtain genetic gains in snap bean breeding program of UENF.

CMB
Sousa et al.

Table 2 .
Genetic parameters estimated for grain yield per plant (PGP) and pod production per plant (PVP) and the general mean of the progenies.Campos dos Goytacazes, UENF, 2014.

Table 3 .
Prediction of genetic effects, predicted genetic gain and new mean of the improved population for the trait grain yield per plant in snap beans F 2 progeny evaluated at Bom Jesus do Itabapoana, Rio de Janeiro State, Brazil.Campos dos Goytacazes, UENF, 2015.

Table 3 . continuation Table 4 .
Selection of snap bean F 2 progenies for production using the REML/BLUP methodology Prediction of genetic effects, predicted genetic gain and new mean of the improved population for the trait pods production per plant in snap beans F 2 progeny evaluated at Bom Jesus do Itabapoana, Rio de Janeiro State, Brazil.Campos dos Goytacazes, UENF, 2015.