Selection index via REML / BLUP for identifying superior banana genotypes in the central region of Goiás state , Brazil

Submetted on April 12 , 2018 and accepted on January 31 , 2019. This work is part of the Breeding Musa Project of Embrapa Universidade Federal de Viçosa, Departamento de Fitotecnia, Viçosa, Minas Gerais, Brazil. gabriellaqueirozalmeida@hotmail.com Universidade Federal de Goiás, Escola de Agronomia, Goiânia, Goiás, Brazil. juholiveira13@hotmail.com Embrapa Floresta, Colombo, Paraná, Brazil. marcos.deon@gmail.com Embrapa Produtos e Mercado, Sinop, Mato Grosso, Brazil. joaomeneguci@embrapa.br Embrapa Arroz e Feijão, Santo Antônio de Goiás, Goiás, Brazil. glays.matos@embrapa.br *Corresponding author:gabriellaqueirozalmeida@hotmail.com Selection index via REML/BLUP for identifying superior banana genotypes in the central region of Goiás state, Brazil 1


INTRODUTION
Bananas are one of the most consumed fruits in the world.They are cultivated in more than 150 countries.Bananas are the sixth most important global food product (FAO, 2016).Brazil is a major banana producer.It holds the fifth place in world production (FAOSTAT, 2017), with an estimated production of 6,962,134 tons, which covers an estimated area of 516,980 hectares (IBGE, 2017).
Relatively few banana cultivars have been transferred from their Southeast Asia origin.This has resulted in a diversity decline of these plants, as they were taken from Asia to Africa and ultimately to the Americas.Thus, several banana trees genetic breeding programs have been created to expand their genetic base, mainly due to their susceptibility to diseases such as Black Sigatoka and Panama (Martin et al. 2016).Among them, we highlight the Brazilian Program for Banana Genetic Breeding, which is coordinated by Embrapa Mandioca and Fruticultura and was founded in 1976.This program aims the development of banana cultivars of the Prata, and Maçã types, which would be resistant to the main diseases of the crop (Weber et al., 2017).As a result of this program, different cultivars were made available to farmers (Weber et al., 2017), Castricini et al. 2017).
Genotypes of the breeding program need to be characterized and evaluated in different production soil, and climate conditions (Silva et al. 2016), which is relevant for evaluating agronomic characteristics, and for allowing the identification of promising cultivars for inclusion in breeding programs or technical indication to producers.Thus, several studies have been carried out on different soils and climates (Silva et al., 2006and 2016, Pimentel et al., 2010, Marques et al. 2011, Borges et al., 2011and 2014, Ribeiro et al., 2012, Mendonça et al., 2013).
The aim of this study was to evaluate the performance of 23 banana genotypes from the Cavendish, Prata, Prata-Anã, Pacovan, Mysore and Maçã groups during three production cycles.In addition, it aimed to evaluate the agronomic and productive characters of resistant cultivars and the incidence of main diseases which are harmful to the banana trees, in the climatic conditions of the central region of Goiás, Brazil.

MATERIAL AND METHODS
The experiment was carried out at Embrapa Products and Markets Unit, located in Goiânia (Goiás state, Brazil).The period between flowering (2008) and the third production cycle (2010) was evaluated.in 2009, and 1240mm, and 65% ARH in 2010(Evaporimetric Station, 2015).
The micro propagated seedlings from Embrapa Cassava and Tropical Fruit (Table 1) were transplanted to the field, in a previously prepared area, with a spacing of 2.5 x 3.0 m.Organic fertilization was carried out with 10 liters of tanned bovine manure and phosphate fertilization (single superphosphate) with 40 g of P 2 O 5 per pit in the planting.Thirty days after the initial plating, nitrogen and potassium fertilization (20-00-20) with 45 g of N and 45 g of K 2 O per plant was carried out.The management practices carried out during the three production cycles were: complementary irrigation, weed control, pest control, removal of dry leaves, elimination of shoots (leaving only two) at the time of flowering, and elimination of the heart and pseudo stems cut after harvest.
The genotypes were arranged in a completely randomized design, with 23 treatments with replicates varying from 3 to 18 clones according to the availability of seedlings.Since the date are unbalanced, the components of variance were estimated using the mixed model methodology, which uses REML/BLUP (Restricted Maximum Likelihood/Best Linear Unbiased Prediction) method.Considering the model, y = Xm + Zg + Ti + y, where y is the data vector, m is the vector of measurements effects (assumed as fixed) added to the general mean, g is the genotypic effects vector (assumed as random), i is the interaction effects vector (genotypes x measurements), and e is the error vector (assumed as random), the uppercase letters represent the incidence matrices for these effects (Resende, 2002).For this analysis, Model 55 of Selegen software, which is a repeatability model, was used (Resende, 2016).
The following characters were evaluated: plant mortality (M); days from planting to flowering (DPF); number of living leaves in flowering (NLF); number of shoots (NS), which was counted at the moment of flowering; height of the plant in centimeter (HP), which was also measured at the moment of flowering with the aid of a flexible steel tape measure, positioned at ground level and measuring up to the leaf rosette (insertion point of the peduncle in the pseudo stems); circumference of the pseudo stems in centimeter (CPC), which was measured with a tape measure at 20 cm above ground level; mass of the bunch in kilos (MB); mass of the hands in kilos (MH); average weight of the fruits in grams (AWF), by weighing the second hand and the penultimate hand; number of hands (NH); number of fruits (NF); length (LF), and average diameter (DF) of the fruits in centimeters located at the center of the hands that were weighed, these measurements were made with the aid of an analog pachymeter; days from flowering to harvest (DFH); number of living leaves (NLH) at harvest time.
In order to identify the superior genotypes for each evaluated character, it was considered: the predicted mean genotypic values (u + g + gem), which refers to the average genotype value over several years and capitalize an average interaction which comprises the three years of the evaluation; the heritability of genotype averages (broad sense); the genotypic values prediction accuracy (accuracy in genotype selection), based on the three years of measurements and the repeatability coefficient.
With the purpose of suggesting the best genotypes to be grown in the central region of Goiás state, considering all the characters, the multitrait selection index (model 101 of Selegen software) was used.Two alternative approaches were applied (Resende, 2002), the Active index, in which the character weights are given, and the Medium Rank index, adapted from Mulamba & Mock, in which the genotypic values are classified for each character and the average of the rankings of each genotype for all characters is presented as the final result.For the calculation of the indices, the NLL and NF characters were considered null because they did not present a significant genotypic variance, for M, DPF, HP and, DFH the lowest predicted genotypic values were considered, and the for the remaining characters, the highest predicted genotypic values were taken into account.The accuracy was used as weights in the Active index because it represents the reliability of the characters for selecting the best genotypes.

RESULTS AND DISCUSSION
A significant variance was observed among the evaluated genotypes for most of the characters, except for NLF and NS, therefore, they did not enter the multitrait selection index because they were not able to differentiate the genotypes.For the interaction (years x genotype), no significant variance was detected for NS and DFH characters (Table 2), which demonstrates that, for these characters, a single measurement would be sufficient.Arantes et al. (2017), did a similar study and also found significant differences among treatments and cycles, with the exception of the flowering period.
All the characters presented low heritability, which indicates that they are quantitative and very influenced by the environment (Table 3).Considering a repeatability greater than 40% and accuracy greater than 60%, it is possible to identify, through the average genotypic value (Table 3), the superior genotypes for each character that presented significant variance among the treatments.
The Maçã (4), Bucanero ( 16), and FHIA-17 (20) genotypes demonstrated the highest mortality rate, while the Calypso (7), Pacovan (18), and Garantida (19) genotypes presented the lowest mortality rate.The avarage number of days from planting to flowering (DPF) ranged from 448.3 to 618.4, with the YB42-07 (17) genotype being the latest and the Maçã (4) genotype the earliest (Table 2).These characters presented a low repeatability, but with selective accuracy above 50% and 60% respectively.Based on predicted genetic values, the genotypes with the lowest mortality rates were Pacovan (18), Garantida (19), and Calipso, which shows that they were the least affected by the pests and diseases of the region.The FHIA-02, PA42-44 (13), and FHIA-18 (10) genotypes presented higher precocity of flowering (Table 3).The precocity of flowering is an important characteristic because it reduces the exposure time to pathogens, and is able to increase the number of living leaves at the floral differentiation stage, and to favor a greater amount of female flowers during the inflorescence, which results in clusters with greater number of fruits (Robinson & Galán Saúco, 2010).Arantes et al. (2017) found the FHIA-18 and Pacovan cultivars were the earliest at the flowering stage and the FHIA-23 and FHIA-17 cultivars were the latest.
In the evaluation of plant height (Table 2), the Grande Naine (15) genotype demonstrated the lowest mean (HP = 262.2cm), followed by FHIA-02 (23) and Calipso (7).The highest observed averages were of the Garantida (HP = 413.7 cm), Vitória (11), and Japira (9) genotypes.Similarly, Arantes et al. (2017) found that the highest cultivars in all cycles were the Japira, Pacovan-Ken, and JV42-135 genotypes, and the shortest ones were the Grande Naine and Caipira genotypes.On the other hand, Nomura et al. (2016) found, in the Ribeira Valley, high pseudo stems height values (> 4.5 m) in the Caipira cultivar, which is considered a substitute for Maçã cultivar.According to Santos et al. (2006), the ideal height range for commercial bananas, is between 2.0 and 3.5 m.
The height of the plant influences planting spacing and density, and consequently, the productivity Furthermore, it is an important feature in genotypes selection, since high cultivars are not desirable because they are of difficult harvest, the breaking of the pseudo stem, and the tipping over of plants (Santos et al., 2006).These are recurrent problems in the Pacovan genotype and their descendants (Azevedo et al., 2010).Thus, smaller sizes such as those found, based on the genotypic values (Table 3), for the Grande Naine (15), , and FHIA-02 (23) genotypes, are the most desirable, especially in strong winds regions, since they benefit productivity avoiding damages to the bunches.
The FHIA-17 (20) genotype showed the highest pseudo stems circumference mean (CPC = 79.19 cm), while Caipira (12) genotype showed the lowest mean (CPC = 52.90cm) (Table 2).Arantes et al. (2017) and Nomura et al. (2016) also found low pseudo stems circumference values for the Caipira cultivar.The pseudo stems circumference is related to the vigor of the plant.The more vigorous the plant, the greater its ability to support the bunches and the lower is the susceptibility to tipping (Silva et al., 2011).In view of this, FHIA-17, Bucanero ( 16) and PV79-34 ( 14) are the most appropriate agronomically sized genotypes (Table 3).
At harvesting period, the highest number of living leaves (NLH) was observed in the PA42-44 (13) genotype and the lowest number in the Vitória (11) genotype.
Differently from what was related by Arantes et al. (2017), who found the Prata-Anã cultivar to have the highest number of living leaves and the Garantida cultivar the lowest number of living leaves at the time of harvest.The size of the fruits is positively correlated with the number of living leaves present until harvesting time (Oliveira et al. 2013).In this study, it was possible to observe this because the genotype with the highest number of living leaves, PA42-44 (13), was one with the highest fruit weight mean, length, and diameter (Table 2).
The banana yield was correlated with the characters of the bunches, and the FHIA-17 (20) genotype showed the highest mean (MB = 28.60 kg and MH = 10.87 kg), while Tropical (22) presented the lowest mean (MB = 26.33 kg and MH = 10.05 kg).The mass of the bunch is an important factor in banana productivity, but it cannot be solely considered for genotype selection, since other characters also influence this selection, such as the characters related directly to the fruit, such as size, weight, and shape.In this way, and based on the genotypic values (Table 3), we were able to highlight the following genotypes: Bucanero, FHIA-17, and Grande Naine, with the heavier bunches; Bucanero, FHIA-17, and Grande Naine, with the heavier hands; Thap Maeo (6), FHIA-17, and FHIA-02, with the highest number of Rev. Ceres, Viçosa, v. 66, n.1, p. 026-033, jan/fev, 2019   hands; Thap Maeo, FHIA-17, and Caipira (12), with the highest number of fruits; FHIA-01 (3), Bucanero, and Grande Naine, with the highest average fruit weight; Bucanero, Grande Naine, and Calipso (7), with the largest length of the fruits.The two methodologies for calculating the multitrait selection index (Table 4) presented the same four first genotypes, however they presented different gain values due to the difference between the methodologies.Since in the Active index it is necessary for assigning weight (precision between 0 and 1) for each character, which reduces the percentage of the gain; in the index of Medium Rank selection it is not necessary to attribute weight to the characters, which increases gains percentage.Regardless of the gain presented by the two methodologies, the FHIA-17, Grande Naine, Bucanero, and FHIA-02 genotypes, in this order, proved to be the most productive and with the most desired agronomic characters.The Bucanero cultivar was also recommended by Lédo et al. (2018) based on physical-chemical characters of the fruits of thirteen banana genotypes, to be cultivated in coastal flat regions.The Grande Naine cultivar has shown great performance according to Patel et al. (2018), who reports a constant increase in banana production and productivity in India, due to the adoption of this variety and other Cavendish clones.According to Nomura et al. (2017), the FHIA-17 cultivar has great potential for introduction into the Brazilian production system for showing characteristics similar to the Grand Naine cultivar.According to Weber et al. (2017) the FHIA 02 cultivar shows an adequate profile and high yield potential, which can be an alternative to the traditional Prata subgroup.
The FHIA-17, Grande Naine, Bucanero, and FHIA-02 genotypes are the most promising for the central region of Goiás and they can adapt well to other regions of similar climate.
The indexes used (Medium Rank and Active) are concordant with the selection of the first four genotypes.However, they are discordant with the magnitude of the expected gain.
; M -mortality; DPF -days from planting to flowering; HP -height of the plant; CPC -circumference of the pseudo stems ; NLF -number of living leaves in flowering; NS -number of suckers produced; DFH -days from flowering to harvest; NLH -number of living leaves at harvest time.; MB -mass of the bunch; MH -mass of the hands; NP -number of the hands; NF -number of fruits; AWF -average weight of the fruits; LF -length of the fruits; DF -diameter of the fruits.estimative of genotypic variance; -estimative of the variance of the interaction between years and genotypes; -estimative of residual variance.Statistical significance: '***' 0.001 '**' 0.01 '*' 0.05.Selection index via REML/BLUP for identifying superior banana genotypes in the central region... Rev. Ceres, Viçosa, v. 66, n.1, p. 026-033, jan/fev, 2019 Table 3: Predicted genotypic values of 23 banana genotypes for each characteristic evaluated in the three production cycles and estimates of genetic parameters Genótipo Temperatures ranged from 16 °C to 31 °C in 2008, from 17 °C to 30 °C in 2009, and from 17 °C to 31 °C in 2010, with annual rainfall of 1726 mm and average relative humidity (ARH) of 74% in 2008, 1577 mm and 70% ARH

Table 1 :
Genotypes evaluated from Embrapa Mandioca and fruticulture Tropical

Table 2 :
Means and variance components of 23 banana genotypes estimated by the mixed model methodology mortality; DPF -days from planting to flowering; HP -height of the plant; CPC -circumference of the pseudo stems ; NLF -number of living leaves in flowering; NS -number of suckers produced; DFH -days from flowering to harvest; NLH -number of living leaves at harvest time.; MB -mass of the bunch; MH -mass of the hands; NP -number of the hands; NFr -number of fruits; AWF -average weight of the fruits; LF -length of the fruits; DF -diameter of the fruits; h 2 a -heritability of averages; r -repeatability; Ac -accuracy in genotype selection). M

Table 4 :
Medium Rank selection index (left) and Active selection index (right) of 23 banana genotypes evaluated