Genetic gain via REML / BLUP and selection indices in snap bean

The aim of this study was to compare four selection indexes and REML/BLUP methodology in the evaluation of predicted genetic gains of traits of interest in snap bean breeding program. We evaluated 17 selected lines, in a randomized complete block design, with four replicates, in four environments, Bom Jesus de Itapaboana-RJ, in 2011 and 2012 and Cambuci-RJ, in 2011 and 2013. The evaluated traits were pod and grain productivity, number of pods per plant, number of seeds per pod and weight of 100 seeds. For gain prediction, the employed selection indexes were Pesek & Baker, Smith & Hazel, Mulamba & Mock, Williams and REML/BLUP methodology. Among the tested selection indexes, Mulamba & Mock was the one which showed the best gain distribution considering the tested variables, such as the higher coincidence coefficients in comparison to REML/ BLUP, resulting in 62% of grain productivity and pod productivity per plant. The REML/BLUP methodology permitted to select lines with high relative performances and obtained simultaneous gains for the evaluated traits, being superior in relation to the tested selection indexes for snap bean crop.

Besides the use of selection indexes, mixed model methodology is a trend in plant breeding.These procedures provide additional parameters relevant for the identification of superior genotypes (Maia et al., 2011;Ramalho & Araújo, 2011).Ramalho & Araújo (2011) state the use of mixed models as an appropriate strategy to improve efficiency of autogamous plant breeding, through the identification of progenies or lines with higher genotypic merit.Mendes et al. (2011) used predictions via REML (Restricted Maximum Likelihood Method) and BLUP (Best Linear Unbiased Prediction Method), to identify superior progenies and individuals within segregating populations of common beans.Studies have confirmed the use of mixed models for annual plant breeding in different crops such as soybeans (Pinheiro et al., 2013), cowpea (Barros et al., 2011), common beans (Bertoldo et al., 2009) and popcorn (Freitas et al, 2013).
Although the application of selection indexes has been demonstrated for several crops, in snap beans few studies using this strategy can be found in literature for snap beans.
Given the above, this study aims to compare four kinds of selection indexes and REML/BLUP methodology evaluating the predicted genetic gains of traits of interest in the snap bean breeding program.

MATERIAL AND METHODS
Seventeen snap bean genotypes F 9-10 generation were evaluated, being three controls and the other genotypes were lines from snap bean Breeding Program of Universidade Estadual Norte Fluminense Darcy Ribeiro (UENF).The experiments were installed in two places and in two years: Instituto Federal Fluminense, Campus Bom Jesus de Itabapoana-RJ, in May, 2011and 2012and Campus Cambuci-RJ, in May, 2011and 2013.The experimental design was randomized blocks, with four replicates, being individual plants evaluated within each replicate.The spacing used was 1 m between rows and 50 cm between plants.The experimental plot consisted of 5 m 2 , using 8 central plants and 2 at the end of the plot as border lines.The values are real and obtained per plot of 10 plants and estimated for 1 hectare.
Two seeds were sown per pit, at 2.5 cm depth.Plantlets were thinned ten days after emergence, in order to leave only one plant per pit, in both experiments.
About fifteen days after emergence, plants were staked using wires.During the experiment, cultural and phytosanitary practices were done according to recommendations for the crop.Sprinkler irrigation system was adopted.Ten harvests were carried out lasting approximately 120 days.
The following traits were evaluated individually: pod productivity (t ha -1 ); grain productivity (t ha -1 ); average number of pods per plant; average number of seeds per pod; weight of 100 seeds.
The selection indexes of Smith (1936), Hazel (1943), Williams (1962), Pesek & Baker (1969) and Mulamba & Mock (1978) were tested, in order to select 8 superior lines, with selection intensity of 47%.For statistical analyses, values were assigned by attempts, for five evaluated traits.The software GENES (Cruz, 2013) was used for selection of lines based on the selection indexes.
The software SELEGEN Windows-REML/BLUP was used for statistical analyses (Resende, 2007), statistical model 114 (Evaluation in several locations/several years -Annual crops; Complete block design with triple interaction and stability and adaptability)."Interaction locations and years": y = Xf + Zg + Qa + Ti +Wt + ε, in which y= data vector; f= vector of the effect of combinations repetitionlocation-year (assumed to be fixed) added to the overall average; g= vector of genotypic effects (assumed to be random) a= vector of effects of genotype-year interaction (random); i= vector of the effects of genotype-location interaction; t= triple (genotypelocation-year) interaction (assumed to be random), and ε= vector of errors or residues (random).Capital letters represent the incidence matrixes for these effects.Vector f represents effects of repetitions within locations within years, locations, years and interaction locations x years.
The coincidence coefficient was obtained through the ratio of double coincident lines between two indices and the total of selected lines, in percentage.
The relative performance of each selected line was calculated using the ratio between the new average of improved population and the new average of improved population showing higher genetic value of the 8 selected lines, in percentage.Pod weight and number of pods per plant showed negative gains of -0.03 and -2.78, respectively, using Pesek & Baker index, which is undesirable.Thus, Pesek & Baker index is not recommended for selection, since the main goal is the simultaneous improvement of evaluated traits (Table 1).Similarly, Bárbaro et al. (2007) did not obtain satisfactory results with this index for superior genotype selection in soybean either.

RESULTS AND DISCUSSION
Mulamba & Mock indexes showed best gain distribution among the evaluated variables, making them suitable for genotype selection in this study.This index was recommended in other studies, such as the one which provided the best results for superior genotype selection, as the verified in cowpea (Santos & Araújo, 2001), soybean (Costa et al., 2004) and popcorn (Freitas, 2013) (2005) for oat breeding program.
Table 2 shows the coincidence coefficients for 8 selected lines, for the four indexes and REML/BLUP methodology, for the two traits considered the most important ones for snap bean crop, which are: pod productivity and grain productivity.The values were high, ranging from 50 to 87%.According to Pedrozo et al. (2009), the higher the coincidence coefficient between two selection indices, the greater will be the agreement of selection results between them.Comparing the selection indexes with REML/BLUP methodology, the authors could notice that higher coincidence coefficient of selected lines were obtained using Smith & Hazel index: 0.75% for grain productivity (Table 2).For pod productivity, all indexes showed coincidence coefficient of 62%, except for Pesek & Baker index which was 50%.This result can be explained by the fact that REML/BLUP methodology uses, as solution vector, predicted genotypic effects and selection gain individually, completely excluding the environmental effect.
REML/BLUP methodology showed to be the most appropriate in relation to other selection indexes, selecting lines with high relative performance and promising predicted genetic gains for snap bean crop, probably due to the exclusion of environmental effect (Table 3).For traits pod productivity, grain productivity and number of pods per plant, 5 lines coincided, of the total of 8 selected lines, using REML/ BLUP, validating the efficiency of this methodology in relation to the other index selections.
The relative performance of progeny was high, when selected lines showed estimates higher than 86.60%, both for PV and PG, which is an evidence of selective accuracy of REML/BLUP methodology.Borges et al. (2010) showed that genotypic values are quite close to the new average and viceversa.Thus, the authors can conclude that this methodology was efficient to select progenies with high relative performance.

Table 1 .
Estimates of gains (%) based on the selection of five traits of snap bean lines.Campos dos Goytacazes, UENF, 2016.

Table 2 .
Coincidence coefficients for 8 selected lines using selection indexes and REML/ BLUP methodology, in relation to pod productivity above the diagonal and grain productivity below the diagonal of snap beans.Campos dos Goytacazes, UENF, 2016.

Table 3 .
Ranking and estimates of 8 lines, effects (g), predicted genotypic values (u+g), new average (BLUP) and relative performance (DR), in relation to pod productivity and grain productivity of snap beans.Campos dos Goytacazes, UENF, 2016.