Papaya (Carica papaya L.) S1 family recurrent selection: Opportunities and selection alternatives from the base population

Scientia Horticulturae 260 (2020) 108848

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Papaya (Carica papaya L.) S1 family recurrent selection: Opportunities and selection alternatives from the base population

T

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Renato Santa Catarinaa, , Messias Gonzaga Pereiraa, Julio Cesar Fiorio Vettorazzia, Diego Fernando Marmolejo Cortesb, Tathianne Pastana de Sousa Poltronieria, Alinne Oliveira Nunes Azevedoa, Nádia Fernandes Moreiraa, Daniel Pereira Mirandaa, Ramon de Moraesa, Adriana Azevedo Vimercati Pirovania, Helaine Christine Cancela Ramosa, Marcelo Vivasa, Alexandre Pio Vianaa a

Department of Plant Breeding, Universidade Estadual do Norte Fluminense Darcy Ribeiro - UENF, Av. Alberto Lamego, 2000, 28013-602, Campos dos Goytacazes, RJ, Brazil b Empresa Brasileira de Pesquisa Agropecuária - EMBRAPA, Rua Embrapa s/n, 44380-000, Cruz das Almas, BA, Brazil

A R T I C LE I N FO

A B S T R A C T

Keywords: Papaya breeding Production Fruit quality

The existing genetic variability in papaya crop can be explored in segregating populations, through breeding population methods, such as recurrent selection. The paper aims have been to estimate the repeatability coefficients, and select superior individuals from the base population of papaya recurrent selection. Sixteen traits were evaluated in 224 individuals, in three harvest seasons. The repeatability coefficients were estimated by REML/Blup method. The repeatability coefficient magnitudes were high (r > 0.60) for eleven traits, showing the genetic control and average traits stability along successive seasons. The gains with direct selection was two to three times higher compared with the combined selection index, and the direct selection is more indicated for short-term selection, aiming at the per se lines development. However, for the purposes of long-term individual’s selection, it is important to simultaneously utilize combined and direct selection, thus ensuring the favorable alleles sources to important traits. The current paper, it is shown that if on one side recurrent selection is a longterm strategy, on the other side the same offers opportunities to already select superior.

1. Introduction In the papaya crop it is necessary to expand the genetic basis and explore the existing genetic variability in genus Carica. One of the ways of creating and exploring the genetic variability in this crop is to obtain segregating populations. These populations are formed by crosses or recombination of genotypes, with sources of favorable alleles for the attributes related to resistance to diseases, fruit quality and production. For disease resistance, adaptation and rusticity, landrace varieties can be used as a source of genes to increase the genetic basis of papaya crop (Oliveira et al., 2010). Vivas et al. (2012, 2013a, 2014) in a study with landrace varieties, pointed the progenies STA-02 (2), STA-02 (6), STA04 (5), STA-05 (5), and STA-22 (3) for the constitution of the future populations, with potential for reduction of black-spot and phoma-spot diseases. For fruit yield and quality, elite parents of commercial hybrids can be considered as gene donors in the constitution of segregating

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populations (Pereira et al., 2018, 2019a,b; Luz et al., 2015, 2018a,b). The JS12 and Sekati parents, belong to the Formosa heterotic group, however they are contrasting for agronomic and sensory traits. Sekati parent produces large fruits with excellent pulp firmness and moderate soluble solids content, while the JS12 parent differs from the first to the last two traits, with moderate pulp firmness and high soluble solids content (Cardoso et al., 2014; Cortes et al., 2019). In addition to agronomic traits, Sekati parent has alleles of resistance to phoma-spot, black-spot and powdery mildew (Vivas et al., 2013b). Such segregating populations with genes for diseases, fruit yield and quality, aggregate highly valuable genetic resources and can be explored through different breeding methods, thus contributing to the development of new papaya varieties. Among the breeding methods, the recurrent selection proposed by Hull (1945), which aims at gradually increasing the frequency of favorable alleles for a quantitative trait, through repeated selection cycles, without genetic variability losses in the population. This method is comprised of three stages, the

Corresponding author. E-mail address: [email protected] (R. Santa Catarina).

https://doi.org/10.1016/j.scienta.2019.108848 Received 25 March 2019; Received in revised form 9 August 2019; Accepted 11 September 2019 0304-4238/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Representation of the scheme employed to obtain the UCP-C0 base population of papaya plants. 1 - STA-22(3), 2 - STA-05(5), 3 - STA-17(6), 4 - STA-02(6), 5 STA-04(5).

2. Material and methods

obtaintion, the evaluation and the recombination of progenies, which are cyclically conducted until satisfactory favorable allele frequency levels are achieved in the population (Hallauer et al., 2010). The results reported in the literature have confirmed that the method has been efficiently employed in the breeding of popcorn (Freitas Júnior et al., 2009; Rangel et al., 2011), and passion fruit plant (Silva et al., 2017) populations, among others. In the segregating populations of perennial plants such as papaya, it is usual to estimate parameters that affect those traits that enable characterizing the genotypes throughout time, among which the repeatability coefficient. According to Cruz et al. (2012) the repeatability coefficient of a trait assesses the correlation between the measures found in a same individual, repeated along time or in space, expressing the total proportion of variance in relation to the variations provided by the genotype and to the permanent alterations attributed to the environment. In a papaya plant, knowledge of the repeatability coefficient for the interest traits for the crop enables evaluating the amount of time and workforce deemed necessary so that the selection of genetically superior individuals is performed with the desired accuracy by the researcher (Pinto et al., 2013; Luz et al., 2015). After characterizing the individuals throughout time, the selection of superior individuals becomes more promising and effective when undertaken based on many different important traits for a certain crop, through the use of selection indexes (Smith, 1936). In the papaya plant, the combined selection index enables associating weight to the standardized means of the traits being selected, and efficiently in the combined selection of superior genotypes (Silva et al., 2008; Ramos et al., 2014) Combined selection is more indicated to the development of a cultivar, however when the purpose is to enhance a population, direct selection must also be employed in order to select sources of favorable alleles for specific traits. Thus, the current paper’s purpose has been to estimate the repeatability coefficient and the efficiency gains through the use of m measurements of those traits related to fruit production and quality in 224 individuals from the base population of the S1 family recurrent selection program (UCP-C0), in addition to identifying and selecting superior individuals by utilizing combined and direct selection, and comparing the respective genetic gains and different alternatives for breeding purposes.

2.1. Genetic material A base population from the recurrent selection program using papaya (UCP-C0 – UENF Caliman Population Cycle 0) was evaluated, comprising 224 individuals. In order to obtain the UCP-C0, five half-sib papaya progenies were employed: STA-22(3), STA-05(5), STA-17(6), STA-02(6), and STA-04(5). These progenies are resistant to black-spot disease – Asperisporium caricae (Speg.) Maubl., and to phoma-spot – Stagonosporopsis caricae (Sydow and P. Sydow) Aveskamp, Gruyter and Verkley [=Phoma caricae-papayae (Tar) Punith.] (Vivas et al., 2012, 2013a, 2014), and were employed as female genitors, recombined between each other and with five elite genitors SS-72/12, JS-12, Sekati, UC 36/7 and UC 41/7, genitors of hybrids already registered at the Ministry of Agriculture, Livestock and Food Supply – MAPA (Pereira et al., 2018, 2019a,b). The half-sib progenies were sown in the nursery of company CALIMAN Agrícola S.A., lat 19° 23′ S, long 40° 04′ O and alt 33 m asl, located in Linhares, ES. The climate of the region is classified as type AWi (tropical humid), with rainy summer and dry winter (Alvares et al., 2013). Approximately 30 days after sowing the seedlings were planted in an experimental area, where the fertilization and cultural practices applied in the experiment were the same used to the crop by the Caliman Agrícola S.A., in the commercial plantations. For every half-sib progeny, 10 pits were planted with three seedlings each, totalizing 50 pits, at a 3.6 m distance between the rows and 1.5 m between each pit/plant. 90 days after planting, the plants of dioecious population were submitted to sexing. The male plants were eliminated, remaining only a female plant in each pit, which were employed as female genitors. The pollen donor elite genitors (male genitors) were planted in the seed production area of company CALIMAN Agrícola S.A. It is important to stress that the half-sib progenies were converted into gynoecius-andromonoecius progenies already, when forming the UCPC0 base population. As only female plants of the dioecious population were used, and they received the pollen of hermaphrodite plants, there was the sexual conversion through the replacement of the Y (male) for the Yh (hermaphrodite) sexual chromosome (Ming et al., 2007). In order to pollinate female plants, a mix of pollen from the hermaphrodite plants of five elite genitors was prepared. 50 flowers from hermaphrodite plants of each elite genitor were collected to compose the “mix”, totalizing 250 flowers. The pollen was withdrawn from the 2

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flowers and placed in a 2 ml Eppendorf tube in order to prepare the mix and form the pollen “mix”. After obtaining the pollen “mix”, the floral buds of the female plants were pollinated using a paintbrush (Fig. 1). At the end, equal quantities of seeds from the pollinated fruits were collected, and bulk clustered to form the base population of UCP-C0 papaya. The bulk-clustered seeds were left to germinate in a greenhouse, and after germination the seedlings were acclimatized for approximately 30 days. After acclimatization, the seedlings were planted in the experimental area, at a 1.5 m space between plants along the line, and at 3.6 m between lines. Since each plant corresponds to a different individual, it was not possible to utilize experimental design for the evaluation. Thus, each plant was individually evaluated and the statistical analysis were conducted by utilizing the Selegen REML/Blup software, model 63 (Resende, 2016).

model methodology, through the REML (restricted maximum likelihood) procedure to estimate the genetic variance components and genetic parameters, and the BLUP (best linear unbiased prediction) procedure to estimate the permanent phenotypic values. The genetic evaluation was undertaken by employing the following statistical model: Y = Xm + Wp + e, in which: y is the observation vector; m is the measurement effect vector (assumed as fixed) added to the overall mean; p is the plant permanent effect vector (genotypic effects + permanent environmental effects assumed as random); e is the residual vector (random). This is the basic repeatability model employed for experiments without an experimental design, being appropriate to evaluate UCP-C0. The analysis were conducted utilizing the SelegenREML/Blup software according to (Resende, 2016). The following variance components (individual REML) and genetic parameters associated to repeatability, were estimated: σ2fp: permanent phenotypic variance between plants (genotypic variance + permanent environmental variance between measures; σ2et: temporary environmental variance; σ2f: individual phenotypic variance (σ2fp + σ2et); r:

2.2. Evaluated traits 2.2.1. Traits evaluated in the field trial The traits evaluated in the field trial were: plant height (PH); stem diameter (SD); number of deformed fruits (NDF); fruitless nodes (FN) and number of commercial fruits (NCF). These traits, were evaluated with the digital phenotyping technique’s assistance and according to the methodology described and validated by (Cortes et al., 2017). For that purpose, a Sony DSCHX 300 digital camera was employed, utilizing two full pictures per plant, a picture of side A and another picture of side B of the plant. Each plant was identified with a label attached to the stem to facilitate identification during the image analysis and processing process. In addition to that, a known measurement scale was employed, attached to the soil and close to the stem of the plants that were evaluated. The images were processed and analyzed by employing the ImageJ v1.50c software. The imagens were obtained in 180, 270 and 360 days (summer, autumn, and winter seasons) after planting, or 90 days after anthesis (DAA) in each evaluated season. The plants were marked with a red color wool, to identify the last fruit evaluated on the leaf axil.

individual repeatability ( repeated measurements (

σ 2fp

σ 2p + σ 2et σ 2p 2

σ σ 2fp + et

); rm: repeatability of the mean of m

) ; Acm: accuracy based on the mean of

2

m repeated measurements ( rm ) and MG: overall mean of the experiment. 2.4. Selection of superior genotypes In the current study 30 individuals were selected in combination, by simultaneously considering many traits through the combined selection index (CSI). This index has been proposed and rectified by (Silva et al., 2008) and (Ramos et al., 2014) and associates weights to the standardized means of the traits being selected. For the current study the permanent phenotypic values were employed. The index may be estin mated through the following equation: CSI = ∑t = 1 (fpi x pi) . Where: fpi is the standardized permanent phenotypic value of trait i, and p is the economic weight attributed to the trait i, and it may be either positive or negative according to the direction of the selection. The weights attributed to the 16 traits were: PH (1), SD (5), NCF (100), NDF (-20), FN (-20), FW (1), PROD (100), FF (200), PF (200), SST (200), FL (1), FD (1), OCL (1), OCD (1), PT (70) and VP% (50). Some of those weights were established according to (Silva et al., 2008), while other ones were established based on the agronomic importance of each trait, according to the knowledge held by the breeders from the UENF/CALIMAN papaya breeding program. Since in the study population each plant is a different individual, higher weights (200) were attributed to the traits of greater importance related to fruit quality (FF, PF and SST), which were obtained based on the average number of fruits in each plant. To build the index, the Selegen REML/ BLUP and Microsoft Office Excel 2016 software were employed. For each trait, the permanent phenotypic values were obtained for each individual, and these were standardized utilizing the following (x − x¯) equation: fpi = i σ , where fpi is the standardized phenotypic value; xi is the value for the individual; x¯ is the overall mean of all individuals; σ is the standard deviation of the distribution. After being standardized, the permanent phenotypic values were multiplied by the weights taken from the abovementioned index. Those individuals with the largest total sum of all the traits (final value of the CSI) were the superior individuals. In order to select those 30 superior individuals, the selection differential (Ds = Xs − Xo) was calculated through the difference between the population mean (Xo), estimated through the overall mean of the experiment and the mean value for the selected individuals (Xs). In order to estimate gain by selection (Gs = r x Ds), individual repeatability (r) was employed, which provides the upper limit of the heritability coefficients (Viana and Resende, 2014). It is important to stress that it was not possible to estimate the heritability component for the

2.2.2. Physicochemical traits determinations The physicochemical traits evaluated were: fruit length (FL); fruit diameter (FD); ovarian cavity length (OCL); ovarian cavity diameter (OCD); pulp thickness (PT), and pulp volume percentage (VP%). The traits were evaluated using the methodology described and validated by (Santa-Catarina et al., 2018). For these analysis, all the papaya fruits were collected in the beginning of the fruiting, in the stem and presented the same RST1 ripening stage, where the fruit reaches its maximum physical development and it could be harvested (BarragánIglesias et al., 2018). Firstly, each fruit was weighed on an analytical balance in order to obtain the average fruit weight (FW), then each fruit was cut in half along its longitudinal axis. Half of the fruit was scanned by using an Optico Pro A320 Scanner, in order to obtain the images and perform posterior evaluation of the morphological traits using the ImageJ v1.50c software. The other half of the fruit was employed to measure fruit firmness (FF) and pulp firmness (PF), using an Italy TR digital penetrometer, and the soluble solid content (SST) using an RTD-95 portable digital refractometer, according to the Association of Official Analytical Chemists methodology (AOAC, 1990). The traits FW, FF, PF and SST were not measured using digital phenotyping. The physicochemical evaluation was performed in 270, 360 and 450 days after the planting or 180 DAA in each evaluated season, when the fruits presented the RST1 ripening stage. 2.3. Statistical analysis Considering that in UCP-C0 each plant is a different individual, it was not possible to utilize the experimental design. Thus, the individuals were genetically evaluated by utilizing the linear mixed 3

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Table 1 Variance components (individual REML) and genetic parameters associated to repeatability evaluated through REML for 16 traits evaluated in 224 individual papaya plants. Trait

σ2fp

σ2et

σ2f

r

PH SD NCF FN NDF FW PROD FF PF SST FL FD OCL OCD PT VP%

1136.25 2.53 31.49 8.12 12.50 82160.3 23.54 245.26 163.79 2.54 7.60 1.32 4.56 0.75 0.12 23.96

132.52 0.70 43.33 14.30 12.38 35565.8 49.17 100.31 86.53 1.27 1.64 0.67 1.13 0.45 0.04 17.73

1468.78 3.23 74.82 22.42 24.87 117726.1 72.71 345.57 250.30 3.81 9.24 1.99 5.68 1.20 0.16 41.69

0.91 0.78 0.42 0.36 0.50 0.70 0.32 0.71 0.65 0.67 0.82 0.66 0.80 0.62 0.75 0.57

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.11 0.10 0.07 0.08 0.08 0.10 0.06 0.10 0.09 0.09 0.10 0.09 0.10 0.09 0.10 0.09

rm

Acm

MG

0.97 0.92 0.68 0.63 0.75 0.87 0.59 0.88 0.85 0.86 0.93 0.86 0.92 0.83 0.90 0.80

0.98 0.96 0.83 0.79 0.87 0.93 0.77 0.94 0.92 0.93 0.97 0.93 0.96 0.91 0.95 0.89

226.07 11.22 14.02 8.07 4.81 864.49 11.45 126.14 106.47 10.23 18.29 9.45 13.66 5.13 2.14 77.52

Table 2 Results related to determination (R2), accuracy (Ac) and efficiency (Ef) obtained by conducting m repeated measurements in the UCP-C0 population under Recurrent Selection. Trait

PH

SD

NCF

FN

NDF

σ2fp: permanent phenotypic variance between plants (genotypic variance + environmental variance), permanent between measures.; σ2et: temporary environmental variance.; σ2f: individual phenotypic variance.; r: individual repeatability.; rm: repeatability of the mean of m repeated measurements.; Acm: accuracy based on the mean of m repeated measurements.; MG: overall mean of the experiment.; PH: plant height.; SD: stem diameter.; NCF: number of commercial fruits.; FN: fruitless nodes.; NDF: number of deformed fruits.; FW: average fruit weight; PROD: Production.; FF: fruit firmness.; PF: pulp firmness.; SST: soluble solid content.; FL: fruit length.; FD: fruit diameter.; OCL: ovarian cavity length.; OCD: ovarian cavity diameter.; PT: pulp thickness.; VP%: pulp volume percentage.

FW

PROD

FF

PF

SST

traits evaluated in that population. In addition to CSI, the direct selection (DS) of individuals was also undertaken by ranking the highest permanent phenotypic values for traits PROD, FF and SST in order to compare in which situations we should utilize the CSI and/or DS of the genotypes.

FL

FD

OCL

3. Results OCD

3.1. Variance components and genetic parameters It is observed that the temporary effect variance (σ2et) presented a higher individual phenotypic variance percentage (σ2f) for the traits, number of commercial fruits (NCF), number of fruitless nodes (FN) and production (PROD). The remaining traits presented a phenotypic variance between plants (σ2fp) at a higher percentage of σ2f. These values indicate that the environmental variance is too little in relation to the variance between plants (Table 1). The traits that presented high magnitudes (p > 0.60) for repeatability were PH, SD, FW, FF, PF, SST, FL, FD, OCL, OCD and PT (Table 1). On the other side, the traits NCF, NDF, FN, PROD, and VP% presented intermediary magnitudes (0.30 < p > 0.60) for repeatability. The repeatability coefficient based on the mean (rm) of three measures presented high magnitudes for traits PH, SD, NDF, FW, FF, PF, SST, FL, FD, OCL, OCD, PT, and VP%. The traits PROD, FN and NCF presented an intermediary rm magnitude of 0.59, 0.63 and 0.68, respectively (Table 1). For the mean accuracy parameter, we observed a variation from 0.77 (PROD) to 0.98 (PH), with higher estimates or equal to 0.83 being found for 14 out of the 16 traits evaluated in that population (Table 1). Thus, there is a significant degree of certainty in the inferences and precision and gain in the selection.

PT

VP%

Measurements

2

R Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef R2 Ac Ef

1

2

3

4

5

6

7

8

9

10

0.91 0.95 1.00 0.78 0.89 1.00 0.42 0.65 1.00 0.36 0.60 1.00 0.50 0.71 1.00 0.70 0.84 1.00 0.32 0.57 1.00 0.71 0.84 1.00 0.65 0.81 1.00 0.67 0.82 1.00 0.82 0.91 1.00 0.66 0.81 1.00 0.80 0.90 1.00 0.62 0.79 1.00 0.75 0.87 1.00 0.57 0.76 1.00

0.95 0.98 1.02 0.88 0.94 1.06 0.59 0.77 1.19 0.53 0.73 1.21 0.67 0.82 1.15 0.82 0.91 1.09 0.49 0.70 1.23 0.83 0.91 1.08 0.79 0.89 1.10 0.80 0.89 1.10 0.90 0.95 1.05 0.80 0.89 1.10 0.89 0.94 1.05 0.77 0.88 1.11 0.86 0.93 1.07 0.73 0.85 1.13

0.97 0.98 1.03 0.92 0.96 1.08 0.69 0.83 1.28 0.63 0.79 1.32 0.75 0.87 1.22 0.87 0.93 1.12 0.59 0.77 1.35 0.88 0.94 1.11 0.85 0.92 1.14 0.86 0.93 1.13 0.93 0.97 1.06 0.86 0.93 1.14 0.92 0.96 1.07 0.83 0.91 1.16 0.90 0.95 1.10 0.80 0.90 1.18

0.98 0.99 1.04 0.94 0.97 1.09 0.74 0.86 1.33 0.69 0.83 1.38 0.80 0.90 1.26 0.90 0.95 1.14 0.66 0.81 1.42 0.91 0.95 1.13 0.88 0.94 1.16 0.89 0.94 1.15 0.95 0.97 1.07 0.89 0.94 1.16 0.94 0.97 1.08 0.87 0.93 1.18 0.92 0.96 1.11 0.84 0.92 1.21

0.98 0.99 1.04 0.95 0.97 1.10 0.78 0.89 1.37 0.74 0.86 1.43 0.83 0.91 1.29 0.92 0.96 1.15 0.71 0.84 1.48 0.92 0.96 1.14 0.90 0.95 1.18 0.91 0.95 1.17 0.96 0.98 1.08 0.91 0.95 1.17 0.95 0.98 1.09 0.89 0.94 1.20 0.94 0.97 1.12 0.87 0.93 1.23

0.98 0.99 1.04 0.96 0.98 1.10 0.81 0.90 1.39 0.77 0.88 1.46 0.86 0.93 1.31 0.93 0.97 1.16 0.74 0.86 1.51 0.94 0.97 1.15 0.92 0.96 1.19 0.92 0.96 1.18 0.97 0.98 1.08 0.92 0.96 1.18 0.96 0.98 1.09 0.91 0.95 1.21 0.95 0.97 1.12 0.89 0.94 1.24

0.99 0.99 1.04 0.96 0.98 1.11 0.84 0.91 1.41 0.80 0.89 1.49 0.88 0.94 1.32 0.94 0.97 1.16 0.77 0.88 1.54 0.94 0.97 1.15 0.93 0.96 1.19 0.93 0.97 1.18 0.97 0.98 1.09 0.93 0.97 1.19 0.97 0.98 1.10 0.92 0.96 1.22 0.95 0.98 1.13 0.90 0.95 1.25

0.99 0.99 1.04 0.97 0.98 1.11 0.85 0.92 1.42 0.82 0.91 1.50 0.89 0.94 1.33 0.95 0.97 1.17 0.79 0.89 1.57 0.95 0.98 1.16 0.94 0.97 1.20 0.94 0.97 1.19 0.97 0.99 1.09 0.94 0.97 1.19 0.97 0.98 1.10 0.93 0.96 1.22 0.96 0.98 1.13 0.92 0.96 1.26

0.99 0.99 1.04 0.97 0.99 1.11 0.87 0.93 1.44 0.84 0.91 1.52 0.90 0.95 1.34 0.95 0.98 1.17 0.81 0.90 1.58 0.96 0.98 1.16 0.94 0.97 1.20 0.95 0.97 1.19 0.98 0.99 1.09 0.95 0.97 1.19 0.97 0.99 1.10 0.94 0.97 1.23 0.96 0.98 1.13 0.92 0.96 1.27

0.99 1.00 1.04 0.97 0.99 1.11 0.88 0.94 1.45 0.85 0.92 1.53 0.91 0.95 1.35 0.96 0.98 1.17 0.83 0.91 1.60 0.96 0.98 1.16 0.95 0.97 1.21 0.95 0.98 1.20 0.98 0.99 1.09 0.95 0.98 1.20 0.98 0.99 1.10 0.94 0.97 1.23 0.97 0.98 1.14 0.93 0.96 1.27

PH: plant height.; SD: stem diameter.; NCF: number of commercial fruits.; FN: fruitless nodes.; NDF: number of deformed fruits.; FW: average fruit weight.; PROD: Production.; FF: fruit firmness.; PF: pulp firmness.; SST: soluble solid content.; FL: fruit length.; FD: fruit diameter.; OCL: ovarian cavity length.; OCD: ovarian cavity diameter.; PT: pulp thickness.; VP%: pulp volume percentage.

3.2. Efficiency gain estimates with m measurements Table 2 shows the values related to the estimate for the coefficient of determination (R2), accuracies (Ac), and efficiency gains (Ef) of the selection, that would be obtained by conducting up to 10 measurements in each individual, for the 16 measured traits. We may verify that the utilization of a measurement is enough to estimate the actual value for the individuals for traits PH, FL and OCL, with a reliability above 80%, and a selective accuracy above 90%. For traits SD, FW, FF, PF, SST, FD and PT, two measurements are enough to estimate those traits with reliability and accuracy. As for traits OCD and VP%, at least three measurements are necessary to estimate them with 4

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Table 3 Permanent phenotypic effects (fp), and permanent phenotypic values (u + fp), in six traits of greater importance in papaya breeding for the individuals selected according to the CSI index. N°

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 X0 Xs ds r Gs Gs(%)

Genotype

UCPC015-052 UCPC015-166 UCPC015-209 UCPC015-064 UCPC015-200 UCPC015-184 UCPC015-094 UCPC015-202 UCPC015-061 UCPC015-110 UCPC015-108 UCPC015-144 UCPC015-044 UCPC015-230 UCPC015-041 UCPC015-003 UCPC015-189 UCPC015-186 UCPC015-034 UCPC015-152 UCPC015-143 UCPC015-148 UCPC015-197 UCPC015-167 UCPC015-033 UCPC015-178 UCPC015-162 UCPC015-159 UCPC015-240 UCPC015-142

NCF

FW

PROD

FF

PF

SST

fp

u + fp

fp

u + fp

fp

u + fp

fp

u + fp

Fp

u + fp

fp

u + fp

5.2 18.9 10.3 2.7 9.4 7.7 3.4 7.7 3.4 1.8 8.0 7.7 5.7 10.0 1.4 −1.5 5.7 12.3 4.4 5.5 11.6 −4.8 2.6 −6.2 2.0 1.6 5.7 −4.2 6.2 −6.6

19.3 33.0 24.3 16.8 23.5 21.7 17.4 21.7 17.4 15.8 22.0 21.7 19.7 24.1 15.4 12.5 19.7 26.3 18.4 19.5 25.7 9.2 16.6 7.8 16.1 15.6 19.7 9.8 20.2 7.5 14.0 18.6 4.6 0.42 1.93 13.8

130.7 −50.2 −272.3 267.9 −164.6 −64.3 171.3 33.3 500.7 121.9 −32.2 −296.6 −17.5 −88.1 427.6 447.8 220.8 −97.4 −69.3 17.5 −4.8 589.9 −183.5 782.7 −59.0 −42.8 304.6 5.5 196.4 13.8

995.1 814.3 592.2 1132.3 699.9 800.2 1035.8 897.8 1365.2 986.4 832.3 567.9 847.0 776.4 1292.1 1312.3 1085.3 767.1 795.2 882.0 859.7 1454.4 681.0 1647.2 805.5 821.7 1169.1 870.0 1060.9 878.3 864.5 957.5 93.0 0.70 65.10 7.5

6.6 11.8 2.1 5.2 3.5 4.3 5.3 6.0 10.0 2.8 6.2 0.5 4.9 5.5 5.5 2.0 7.2 7.5 2.1 3.9 7.6 −1.1 −0.3 −0.8 0.9 1.1 8.1 −3.1 7.4 −4.7

18.0 23.3 13.6 16.6 14.9 15.7 16.8 17.4 21.5 14.2 17.6 11.9 16.4 16.9 16.9 13.5 18.6 19.0 13.6 15.3 19.1 10.4 11.1 10.7 12.4 12.6 19.6 8.3 18.9 6.7 11.5 15.4 3.9 0.32 1.25 10.9

31.4 24.9 4.0 10.7 5.0 17.5 14.7 6.5 10.4 28.8 9.8 9.2 10.5 1.9 13.5 10.7 5.7 −6.7 19.4 14.4 2.8 23.9 1.1 22.5 3.7 18.1 8.9 9.8 1.8 18.1

157.5 151.0 130.2 136.9 131.2 143.6 140.8 132.7 136.6 154.9 135.9 135.3 136.7 128.0 139.7 136.9 131.8 119.5 145.5 140.5 129.0 150.1 127.2 148.6 129.9 144.2 135.0 135.9 127.9 144.3 126.1 137.7 11.6 0.71 8.24 6.5

16.3 5.6 11.1 10.1 4.0 7.9 6.9 11.0 20.9 15.1 13.0 5.0 6.2 0.9 1.6 14.0 6.3 0.2 9.9 5.9 4.8 13.8 6.2 16.4 15.9 2.2 5.0 14.7 3.0 3.7

122.7 112.1 117.6 116.6 110.5 114.3 113.4 117.5 127.4 121.6 119.4 111.5 112.6 107.4 108.1 120.5 112.8 106.7 116.3 112.3 111.3 120.3 112.7 122.8 122.3 108.7 111.5 121.1 109.4 110.2 106.5 115.1 8.6 0.65 5.59 5.3

2.4 −0.3 3.8 2.1 2.3 0.3 2.1 0.5 −1.5 −1.5 0.0 2.4 1.6 0.9 0.7 −0.3 0.6 1.6 0.3 0.1 −0.8 −0.4 3.3 −1.5 1.5 −0.5 −0.8 1.7 0.4 3.2

12.6 10.0 14.0 12.3 12.5 10.5 12.3 10.7 8.8 8.7 10.3 12.6 11.8 11.1 11.0 10.0 10.8 11.9 10.5 10.3 9.4 9.8 13.6 8.8 11.7 9.8 9.4 12.0 10.6 13.4 10.2 11.0 0.8 0.67 0.54 5.3

X0: overall mean of the experiment.; Xs: improved means.; NCF: number of commercial fruits.; FW: average fruit weight.; PROD: Production.; FF: fruit firmness.; PF: pulp firmness.; SST: soluble solid content.; UCPC015: UENF CALIMAN Population Cycle 0 (15 = year of the cross).; ds: selection differential.; r: repeatability.; Gs: gain by selection.; Gs(%): gain by selection in percentage terms.

167 stood out from the remaining ones, with a permanent phenotypic value of 1647.2 g. As for the Solo standard, genotype UCPC015-209 stood out from the remaining ones, with a permanent phenotypic value of 592.2 g. We may verify that the mean for the permanent phenotypic values for the selected genotypes amounted to 15.4 kg plant−1 for production, being superior to the overall mean (11.5 kg plant−1). As regards production, genotype UCPC015-166 stood out, with a permanent phenotypic value of 23.3 kg plant−1 (Table 3). By analyzing the traits related to fruit quality, we may verify that for fruit firmness, the mean for the permanent phenotypic values for the selected genotypes amounted to 137.7 N, it being slightly superior to the overall mean (126.1 N). For this trait, genotype UCPC015-052 presented the highest permanent phenotypic value, at 157.5 N. In relation to pulp firmness, the mean for the permanent phenotypic values for the selected genotypes amounted to 115.1 N, it being superior to the overall mean (106.5 N), with genotype UCPC015-061 standing out with a permanent phenotypic value of 127.4 N. On the other side, the mean for the permanent phenotypic values of the genotypes selected for SST amounted to 11.0 °Brix, while the overall mean amounted to 10.2 °Brix, and especially genotype UCPC015-209, which presented a permanent phenotypic value of 14 °Brix (Table 3). It is also important to stress that genotype UCPC015-209 showed traits both for production and quality, this latter being highly important for a crop, especially when production and quality are simultaneously desired. The DS of the 30 superior individuals for each one of the traits

accuracy and reliability. Knowledge of this information is highly important for crop breeding, since it saves time and workforce in order to obtain superior genotypes. For the remaining traits (NCF, FN, NDF and PROD), at least four measurements are necessary to estimate them with reliability and accuracy (Table 2). 3.3. Combined selection in the development of genotypes per se Based on the CSI, 30 superior genotypes (13.4%) were selected for the 16 traits evaluated in the UCP-C0 papaya population under recurrent selection. Table 3 shows the 30 genotypes selected through the index, ordered according to their permanent phenotypic values. That table only provides the results for traits NCF, FW, PROD, FF, PF and SST, which are highly important for papaya breeding program. However, the selection was conducted based on those 16 traits. By analyzing the traits related to production, we may verify that the overall mean for the permanent phenotypic values for the genotypes selected through the index, for trait NCF, amounted to 18.6 fruits, a value superior to the overall mean (14 fruits). Genotype UCPC015-166 stood out from the remaining ones for NCF, with a permanent phenotypic value of 33 commercial fruits. For trait FW, the overall mean of the permanent phenotypic values for the selected genotypes amounted to 957.5 g, superior to the overall mean (864.5 g). For this trait it is necessary to look for both larger fruits (Formosa standard) and smaller fruits (Solo standard). For the Formosa standard, genotype UCPC0155

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Table 4 Permanent phenotypic values (u + fp), in three traits of a papaya plant and for the individuals selected through direct selection. Order

PROD

FF

Selected 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 xs xo ds r Gs Gs(%)

u + fp a

UCPC015-141 UCPC015-183a UCPC015-166 UCPC015-029 UCPC015-061 UCPC015-162 UCPC015-143 UCPC015-186 UCPC015-240 UCPC015-212 UCPC015-189 UCPC015-016 UCPC015-215 UCPC015-052 UCPC015-108 UCPC015-202 UCPC015-041 UCPC015-230 UCPC015-094 UCPC015-120 UCPC015-064 UCPC015-131 UCPC015-223 UCPC015-172 UCPC015-044 UCPC015-055 UCPC015-184 UCPC015-037 UCPC015-241 UCPC015-152

24.8 23.9 23.3 22.8 21.5 19.6 19.1 19.00 18.9 18.8 18.6 18.6 18.0 18.0 17.6 17.5 16.9 16.9 16.8 16.8 16.6 16.6 16.6 16.6 16.4 16.1 15.8 15.7 15.3 15.3 18.3 11.5 6.8 0.32 2.18 19.1

SST

Selected UCPC015-165 UCPC015-052 UCPC015-110 UCPC015-058 UCPC015-111 UCPC015-166 UCPC015-148 UCPC015-167 UCPC015-251 UCPC015-066 UCPC015-122 UCPC015-187 UCPC015-157 UCPC015-034 UCPC015-045 UCPC015-115 UCPC015-142 UCPC015-178 UCPC015-216 UCPC015-184 UCPC015-118 UCPC015-174 UCPC015-243 UCPC015-206 UCPC015-085 UCPC015-087 UCPC015-138 UCPC015-094 UCPC015-176 UCPC015-152

a

u + fp

Selected

u + fp

161.8 157.5 154.9 154.1 151.9 151.0 150.1 148.6 147.7 146.8 146.7 146.4 146.3 145.6 144.7 144.4 144.3 144.2 143.8 143.6 143.0 142.4 142.3 142.2 141.8 141.4 141.3 140.8 140.6 140.5 146.4 126.1 20.3 0.71 14.38 11.4

UCPC015-209 UCPC015-028a UCPC015-197 UCPC015-022 UCPC015-092 UCPC015-142 UCPC015-078 UCPC015-069 UCPC015-144 UCPC015-052 UCPC015-103 UCPC015-104 UCPC015-200 UCPC015-229 UCPC015-062 UCPC015-119 UCPC015-225 UCPC015-045 UCPC015-064 UCPC015-094 UCPC015-046 UCPC015-083 UCPC015-211 UCPC015-097 UCPC015-063 UCPC015-208 UCPC015-159 UCPC015-099 UCPC015-165 UCPC015-186

14.0 13.7 13.6 13.5 13.5 13.4 13.4 13.3 12.6 12.6 12.6 12.6 12.5 12.4 12.4 12.4 12.3 12.3 12.3 12.3 12.2 12.2 12.1 12.1 12.0 12.0 12.0 11.9 11.9 11.9 12.6 10.0 2.6 0.70 1.70 17.2

a Individuals selected through direct selection that are not common to combined selection considering the first three positions.; X0: overall mean of the experiment.; Xs: improved means.; PROD: Production.; FF: fruit firmness.; SST: soluble solid content.; UCPC015: UENF CALIMAN Population Cycle 0 (15 = year of the cross).; ds: selection differential.; r: repeatability.; Gs: gain by selection.; Gs(%): gain by selection in percentage terms.

PROD, FF and SST, by ranking them according to the highest permanent phenotypic values, are presented in Table 4. The estimated genetic gain for trait PROD amounted to 19.1% (6.82 kg plant−1), approximately twice the gain from CSI (10.9%). The genetic gain for FF trait amounted to 11.4% (20.26 N), twice when compared to CSI (6.5%). As for the estimated genetic gain using the DS for SST trait, it amounted to 17.2% (2.6 °Brix), approximately three times higher if compared to the estimated genetic gain using the DS (5.3%) (Table 4). 3.4. Agronomic profile of the effect of combined and direct selection Considering the CSI and DS for the PROD, FF, and SST traits, two individuals (UCPC015-052 and UCPC015-094) have those traits in common (PROD ∩ TSS ∩ FF ∩ CSI), and they are productive with high fruit firmness and soluble solid content (Fig. 2) values. Out of the 30 individuals selected through the CSI, 17 have the PROD trait in common (CSI ∩ PROD), 11 individuals have FF (CSI ∩ FF) in common, and 10 individuals have trait SST (CSI ∩ SST) in common. Thus, out of the 30 individuals selected according to the CSI index, five individuals have traits FF and PROD (CSI ∩ PROD ∩ FF) in common, three individuals have FF and SST (CSI ∩ SST ∩ FF) in common, and four individuals have traits SST and PROD (CSI ∩ SST ∩ PROD) in common. Only two individuals (UCPC015-033 and UCPC015-144) submitted to the CSI do not have traits FF, PROD and SST (Fig. 2) in common. Considering the DS, 17 individuals are just related through trait the

Fig. 2. Venn Diagram for the papaya individuals selected through combined selection and direct selection. FF: fruit firmness.; PROD: productivity.; SST: soluble solid content.; CSI: combined selection index.

FF, 13 through trait PROD and 18 through trait SST. It is important to stress that two individuals (UCPC015-045 and UCPC015165) only have FF and SST (FF ∩ TSS) in common, and they were not selected through 6

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purpose of the selection. In case the individuals are selected to comprise a population, determination values above 0.80, and accuracy values above 0.89 are already deemed adequate (Viana and Resende, 2014). In terms of selective efficiency (Ef) in general, the use of two measurements enabled an Ef increase from 6% for SD to 18% for PV%. By analyzing the Ef values, we may observe that for highly repeatable traits, the selection of superior individuals may be conducted with fewer measurements to achieve the maximum possible determination. On the other side, for those traits with low repeatability, a higher number of measurements is necessary in order to accurately and efficiently select superior individuals in terms of genetic gain. In the repeatability studies, when genotypic values are not available, it is recommended to use permanent phenotypic values to compare individuals, which may be analyzed as expected value or likely future production capacity (Viana and Resende, 2014). Favorable results were found by using the CSI to select the promising genotypes in papaya breeding (Pinto et al., 2013; Ramos et al., 2014; Silva et al., 2008). The selection of 30 superior genotypes shows that population has a high potential for the development of new papaya lines, with higher means for the most important traits for the crop. The selection index was deemed satisfactory when ranking genotypes based on the evaluated traits, not only for the most important traits, but for the remaining traits studied in the current paper as well. The selection gain for the traits related to production, considering a selection pressure of 13.4% amounted to 13.8% for NCF, corresponding to a 1.93 accrual for commercial fruits. For FW, GS amounted to 7.5%, corresponding to a 65.10 g accrual for average fruit weight, and for PROD trait, the GS amounted to 10.9% (1.25 kg plant −1). For those traits related to fruit quality, gain by selection amounted to 6.5% for FF (8.24 N), and 5.3% for PF (5.59 N) and SST (0.54 °Brix), respectively (Table 3). The selected individuals presented higher soluble solids content than the Sekati variety in the same RST1 ripening stage and presenting the potential to development of new genotypes (BarragánIglesias et al., 2018). Characterization studies show that the selected genotypes are superior to the elite parents used in this study as pollen donor for the SST trait. In addition, the selected individuals in the UCPC0 have FW representing the Sekati, JS-12 and SS-72/12 elite parents used, showing the variability for this selectable trait in the papaya breeding program (Cardoso et al., 2014). Although the gains using the DS are higher, the CSI is more indicated to situations whose purpose is to develop a per se lines, in which individuals are selected based on the combination of all the traits being studied, so that the selected individual bears the desired traits both in terms of production and fruit quality. However, if the purpose is to conduct a selection for the purposes of recurrent selection, in addition to the individuals selected through the CSI, we should take into consideration those individuals that are directly superior in terms of a certain trait. Such individuals are sources of favorable alleles and must also be taken into consideration for recurrent selection, during the recombination phase of superior individuals. In study with guava population, the maximization of individual gains was observed with the use of direct selection processes. However, between the indexes used, the Smith (1936) and Hazel (1943) selection index presented the best results for gains in fruit number and fruit weight simultaneously (Paiva et al., 2016). Considering the PROD trait, individuals UCPC015-141 and UCPC015-183 were not selected through the CSI, however in the case of DS, they must be selected as sources of favorable alleles for production. Individuals UCPC015-165 and UCPC015-028 were superior for FF and SST traits, respectively, and were not selected through the CSI (Table 4). Those four individuals must be selected as a source of favorable alleles for PROD, FF, and SST traits. Thus, in the recombination phase in the S1 family recurrent selection, we should select 30 superior individuals considering both the DS and CSI. The results of the DS, demonstrate that although the majority of individuals selected through the CSI have common traits, it is possible

CSI (Fig. 2). 4. Discussion The variance of temporary effect (σ2et) presented a higher percentage of individual phenotypic variance (σ2f) for the number of commercial fruits (NCF), number of fruitless nodes (FN) and production (PROD). According to Viana and Resende (2014), the σ2et accounts for the temporary variation associated to the ephemeral environmental effects manifested in each measurement, as year-on-year climate fluctuations and their interactions with the effects verified in the plant. Estimating individual repeatability coefficient (p) is important in papaya breeding as well as in the breeding of other crops, because of the need to evaluate several crop seasons and to identify superior genotypes for an important trait. The high p values observed to the traits PH, SD, FW, FF, PF, SST, FL, FD, OCL, OCD and PT indicate regularity in the trait repetition between evaluation times. Repeatability coefficient values equal or superior to 0.60 are considered high, indicating that it is possible to predict the actual value for the individuals, with a relatively small number of measurements (Resende, 2002). These results demonstrate high genetic control and high average stability in terms of similar values for the variables throughout the measurements. For the intermediary repeatability, is expected for the traits NCF, NDF, FN, PROD e VP%, because they are highly influenced by the time of the evaluation. Thus, when repeatability is high, an accrual in the number of measurements will lead to a small increase in terms of precision if compared to an individual measured just once, reducing the time and labor expended during the crop seasons. Therefore, the use of repeatability is important to analyze field trials, and can help the breeders to make better decisions in the breeding program (Sanchéz et al., 2017). When we consider an estimated repeatability of 0.75, we may verify that for short-term breeding it is not worth evaluating more than three harvests, while for long-term breeding the ideal selection would be based on just one harvest (Viana and Resende, 2014). For an estimated repeatability of 0.5, the utilization of two harvests also contributes to long-term breeding, while the utilization of two or three harvests only becomes worthwhile for long-term breeding, when the estimated repeatability is equal or inferior to 0.45 and 0.35 (Viana and Resende, 2014). The high magnitude estimates observed to the traits PH, SD, NDF, FW, FF, PF, SST, FL, FD, OCL, OCD, PT and VP% indicate that those traits presented a high regularity in the conducted measurements, and that three measurements for each individual are enough to predict the actual value for the individuals, with a slight gain in terms of accuracy by increasing the number of repeated measurements. In addition to that, those highly repeatable traits improve the phenotyping process, and require lower costs in terms of workforce and time. The repeatability of those traits is influenced by their nature and by the environmental conditions the population is submitted to (Cruz et al., 2014). The traits PROD, FN and NCF presented an intermediary rm magnitude are related to summer infertility, which increases during the hotter months, while the carpellody and pentandry rates increase in the colder months of the year (Damasceno Junior et al., 2008). In addition to papaya, in studies with other crops such as grapes, the estimates of the coefficient of repeatability (rm) turned out to be high for most of the parameters of interest in the table grape breeding program (Sales et al., 2019). The number of measurements is an important information to the crop breeding, since it saves time and workforce in order to obtain superior genotypes. For the remaining traits (NCF, FN, NDF and PROD) at least four measurements are necessary to estimate them with reliability and accuracy (Table 2). With such values, it is possible to predict the efficiency of m measurements in situations in which only one measurement is conducted. The reliability or determination level to be adopted will depend on the 7

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to select sources of favorable alleles for each specific trait when the purpose of the breeding is to select individuals to comprise the recombination phase of recurrent selection. Individuals UCPC015-052 and UCPC015-094, both through the DS and CSI, are promising for papaya breeding, especially the individual UCPC015-052, which stood out in the CSI, being superior to the remaining ones for all the traits jointly evaluated in the UCP-C0 population. The effect of agronomic profile to direct and combined selection indicated that 28 individuals selected through the CSI are similar for the DS for the PROD, FF, and SST traits, and that in addition to the CSI, there are other sources of favorable alleles obtained through the DS that must be taken into consideration depending on the purpose of the papaya breeding.

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5. Conclusion Plant height, stem diameter, average fruit weight, fruit firmness, pulp firmness, soluble solid content, fruit length and diameter, ovarian cavity length and diameter, and pulp thickness traits, presented higher repeatability coefficients, which demonstrates a regularity in the repetition of traits between evaluation times. However, for traits: production, number of commercial fruits, number of deformed fruits, number of fruitless nodes and pulp volume percentage, the repeatability values were low. The CSI facilitated the combined selection of 30 genotypes for the traits of interest for the crop, showing that those genotypes have a high genetic potential for the development of per se lines and/or hybrids. Direct selection enables to identify superior individuals with favorable alleles for specific traits, which were not selected through the CSI, and they must be taken into consideration when the purpose is recurrent selection, especially at individuals’ recombination stage. Recurrent selection, although known as a mid and long-term gain strategy, enables, already in the base generation, to identify agronomically promising individuals that might be selected and advanced through self-fertilization, the same being promising as a source of new lines and as hybrid genitors. Funding This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001 and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [a research fellowship for the first author]. Acknowledgments The authors kindly thank the Universidade Estadual do Norte Fluminense “Darcy Ribeiro” (UENF) and Caliman Agrícola S.A. Company for the support. References AOAC, 1990. Official Methods of Analysis, 13th ed. Association of Official Analytical Chemists, Washington, DC, USA. Alvares, C.A., Stape, J.L., Sentelhas, P.C., Gonçalves, J.L.M., Sparovek, G., 2013. Koppen’s climate classification map for Brazil. Meteorol. Z. 22, 711–728. https://doi.org/10. 1127/0941-2948/2013/0507. Barragán-Iglesias, J., Méndez-Lagunas, L.L., Rodríguez-Ramírez, J., 2018. Ripeness indexes and physicochemical changes of papaya (Carica papaya L. cv. Maradol) during ripening on-tree. Sci. Hortic. 236, 272–278. https://doi.org/10.1016/j.scienta.2017. 12.012. Cardoso, D.L., Luz, L.N., de Macêdo, C.M.P., Gonsalves, L.S.A., Pereira, M.G., 2014. Heterosis in papaya: inter and intragroup analysis. Rev. Bras. Frutic. 36, 610–619. https://doi.org/10.1590/0100-2945-279/13. Cortes, D.F.M., Santa-Catarina, R., Barros, G.B.A., Arêdes, F.A.S., Silveira, S.F., Ferreguetti, G.A., Ramos, H.C.C., Viana, A.P., Pereira, M.G., 2017. Model-assisted phenotyping by digital images in papaya breeding program. Sci. Agric. 74, 294–302. https://doi.org/10.1590/1678-992x-2016-0134.

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parameters and papaya progenies reaction to black-spot disease. Bragantia 71, 235–238. https://doi.org/10.1590/S0006-87052012005000021. Vivas, M., Silveira, S.F., Vivas, J.M.S., Pereira, M.G., 2013a. Prediction of genetic gain and progenies selection of papaya for resistance to black-spot. Trop. Plant Pathol. 38, 142–148. https://doi.org/10.1590/S1982-56762013000200008. Vivas, M., Silveira, S.F., Amaral Júnior, A.T., Cardoso, D.L., Pereira, M.G., 2013b. Inheritance of papaya resistance to fungal disease based on Hayman’s diallel analysis. Bragantia 72, 332–337. https://doi.org/10.1590/brag.2013.047. Vivas, M., Silveira, S.F., Vivas, J.M.S., Viana, A.P., Amaral Júnior, A.T., Pereira, M.G., 2014. Selection of female papaya progenies for resistance to phoma-spot using mixed models. Bragantia 73, 446–450. https://doi.org/10.1590/1678-4499.216.

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