Prediction of genetic gains with selection between and within S 2 progenies of papaya using the REML / Blup analysis

The objective of this work was to predict the genetic gains with selection of superior individuals within papaya (Carica papaya) progenies using the REML/Blup analysis. Thirty-six S2 progenies, originated from the Calimosa and Tainung 1 hybrids, and two commercial control checks were evaluated in a randomized complete block design, with four replicates. The following traits were evaluated: heights of plants and first fruit; stem diameter at 12 and 18 months; number of days required for fruiting; number, mass, and average mass of commercial fruit; and number and mass of carpelloid and pentandric fruit. The magnitudes of the genetic parameters indicated that the variability present in most of the characters allows greater genetic gain if the selection is made at the progeny level, and not in individual plants. For selection among progenies, PROT268, PROT-74, PROT-55, and PROT-22 were the most promising, with the greatest genetic gain for the studied characters. In the selection among and within progenies, the prediction of the gains is higher for the increase in the expression of the number of commercial fruit and for the decrease in the expression of pentandric fruit.


Introduction
Papaya cultivars in Brazil are classified into two groups: Solo and Formosa (Dias et al., 2011).In the Solo group, the average weight of papayas ranges from 300 to 650 g, and the predominant cultivars are Golden and Sunrise Solo.The Formosa group is commonly represented by the commercial hybrids Tainung 1 and Calimosa, with average weight ranging from 1,000 to 1,300 g (Dias et al., 2011;Luz et al., 2015).
Although Brazil is the second largest producer of papaya (FAO, 2013), the country is still dependent on the import of seeds of the Formosa group, which considerably raises the production costs (Marin et al., 2006).Despite this, Brazilian breeding programs have contributed to the development of new cultivars that have both superior agronomic and commercial qualities (Dantas et al., 2015).Although in recent years breeding programs have achieved satisfactory results regarding Pesq.agropec.bras., Brasília, v.52, n.12, p.1167-1177, dez.2017 DOI: 10.1590/S0100-204X2017001200005 the introduction of cultivars with high agricultural ability, overcoming current levels of productivity is a great challenge (Silva, 2008).Therefore, it is necessary to investigate the variability of the species, which has a narrow genetic base, in order to obtain, in a single genotype, the maximum phenotypic qualities that are preferred by producers and consumers.
The search for more efficient selection methodologies is one of the most efficient alternatives to achieve these goals.This is because one of the main challenges faced by the breeding programs is low selective accuracy, which negatively impacts genetic gains (Costa et al., 2008).Therefore, the implementation of more refined genetic-statistical procedures, such as the REML/Blup methodology, is a trend in plant breeding (Maia et al., 2011).
Even under conditions of unbalanced experiments, this approach allows the accurate and unbiased prediction of genetic values, providing additional information that is relevant to the identification of superior genotypes (Ramalho & Araújo, 2011).Moreover, the Blup method allows maximizing selective accuracy, which positively impacts the identification of the best individuals and the gains with selection (Rocha et al., 2009).However, the application of this methodology in papaya breeding is still very scarce.In the literature, the use of REML/Blup has been associated with different purposes, including the estimation of genetic parameters in segregating populations, aiming at the selection of papaya individuals for fruit length and weight, total soluble solids and fruit firmness (Oliveira et al., 2012;Pinto et al., 2013), reduction of physiological spots (Pinto et al., 2013), and resistance to phoma spot (Vivas et al., 2014).
The objective of this work was to predict the genetic gains with selection of superior individuals within papaya progenies using the REML/Blup analysis.

Materials and Methods
The experiment was performed at the Curu experimental field of Embrapa Agroindústria Tropical, located in the municipality of Paraipaba, in the northern region of the state of Ceará, Brazil, in the final stretch of the Curu river basin (3°28'47"S, 39°09'47"W, at 31 m altitude).
The genetic material was obtained from selffertilized F 1 plants from the Tainung 1 and Calimosa hybrids, from commercial fields in the extreme south of the state Bahia, also in Brazil.The two resulting S 1 populations, 304 plants of Tainung 1 and 342 of Calimosa, were planted in 2009 and evaluated during the period of 2009 to 2011, but covering only one harvest.In these populations, the best individuals for agronomic and fruit quality traits were selected and self-fertilized, generating the S 2 progenies.The latter were evaluated from May 2013 to October 2014.
On the basis of the selection among and within the S 1 progenies, 36 individuals of greater agronomic and commercial potential were identified.Of these, 17 were derived from the Calimosa and 19 from the Tainung 1 hybrids (Table 1).The S 2 progenies, plus the two hybrids from which they were generated, were evaluated in a randomized complete block design with four replicates.The experimental plot consisted of five plants.The spacing used was 2.5 m between rows and 2.0 m between plants.Three seedlings were used per pit, to guarantee the presence of at least one hermaphrodite plant.Cultural practices and phytosanitary measures were those recommended for the culture, as described by Martins & Costa (2003).
Plant sex was determined by inspection at the beginning of flowering.Then, thinning was conducted leaving only one plant (hermaphrodite) per pit.Side shoots were removed from plants when they were still small.
To assess the S 2 progenies, the main agronomic/ phenological traits, related to plant architecture and productivity, and commercial traits, such as fruit size and mass, were considered.The following phenological traits were evaluated: height of the first fruit (HFF), in centimeters, determined at the establishment of the first fruit; plant height at 12 months (PH12M) and at 18 months (PH18M), expressed in centimeters, by measuring the distance from the soil level, contiguous to the stem base of the plant, up to the insertion of the youngest leaf; stem diameter at 12 months (SDIA12M) and at 18 months (SDIA18M), in centimeters, calculated at 20 cm from the soil level; and days after planting to fruiting (DAPFR), referring to the period from planting to first harvest, which guided the selection of plants with earlier fruiting.
Regarding productivity, the following traits were evaluated: number of commercial fruits per plant (NCF) and mass of these fruits (CFM), as well as mean commercial fruit mass (MCFM), calculated pentandric fruits per plant, respectively.All fruit mass are expressed in grams.
The data were analyzed using mixed models, and the effects were tested using the likelihood ratio test (LRT) for the elaboration of the deviance analysis table.In order to obtain the variance components and estimates of genetic parameters, data were subjected to the deviance analysis, based on the following statistical model: y Xr Za Wp Tb e = + + + + , in which y is the vector of phenotypic averages; r is the vector of progenies and controls (considered as random effects); a is the vector of individual additive genetic effects (assumed to be random); p is the plot-effect vector (random); b is the vector of the block effects (fixed); and e is the vector of errors (random).The incidence matrices for the effects of r, a, p, and b are represented by X, Z, W, and T, respectively.
For a better organization and interpretation of the partial results of the analysis, the progenies identified in Table 1 were numbered by individuals.To number each individual, the digit of the unit corresponds to the number of the plant within the plot, the digit of the ten corresponds to the replicate related to the plot, and the remaining digits are from the number of the progeny.For example, individual 1,421 corresponds to plant one, from the second replicate of progeny 14.All analyses were performed using the Selegen software (Resende, 2002).

Results and Discussion
Progenies differed statistically for 7 of the 12 characters studied (Table 2).This indicates that there is genetic variability among these progenies, which allows to obtain gains from selection.Differences were also observed within the progeny for the PH12M, DAPFR, and MCFM characters, indicating the possibility of obtaining genetic gains not only through selection among progenies, but also within progenies.
Among the populations, where the progenies Calimosa and Tainung 1, and the controls (Table 1) are grouped, there were significant differences for HFF, PH18M, DAPFR, NCF, CFM, and MCFM.However, between the progenies obtained and the controls, the differences were only with respect to NCF and MCFM.These results show the existence of genetic variability not only among the evaluated progenies, but also within them.However, the effect among and using the ratio between NCF and CFM; number of carpelloid fruits per plant (NCARF) and mass of these fruits (CARFM), assessed by counting and weighing carpelloid fruits per plant, respectively; number of pentandric fruits per plant (NPENF) and mass of these fruits (PENFM), obtained by counting and weighing The coefficients of heritability of the progeny ranged from 1.6 to 83.9% for PH12M and HFF, respectively (Table 3).PH12M and HFF were evaluated at entirely different periods, and PH12M was susceptible to a greater environmental effect.However, for the majority of the characters, the coefficients of heritability of the progenies varied from medium to high magnitude, which could lead to the selection of superior progenies with high selective accuracy (Resende & Duarte, 2007).Therefore, the prediction information of the genetic values to be used in the selection process is precise.Additionally, it has a substantial fraction of the additive genetic variance, which tends to facilitate the identification and selection of progenies with proper phenotypes (Pimentel et al., 2014).For selection within progenies, individual heritability in the strict sense was low for all characters.Regarding mass selection, the coefficients of heritability also presented low magnitude.These results indicate the possibility of obtaining individuals with the same or similar behavior in the next generation, and also the prospect of practicing a satisfactory selection of progenies and not individual plants.There is well shown by the low values observed for the selective accuracy when analyzed with these heritabilities.Pinto et al. ( 2013) described individual and average values of heritability for several plant and fruit traits, and found that, for averages, the values were up to seven-fold higher than those of individual heritability.
The selective accuracy reflects the quality of the information of the procedures used in the prediction of genetic values.This measure is associated with Values obtained by the likelihood ratio test (LRT), except for the effect of progeny vs. control, for which the F-values are displayed, tested with 1 and 111 degrees of freedom.ns Nonsignificant.***, **, and *Significant by the chi-square test, at 1, 5, and 10% probability, respectively, with 1 degree of freedom.PH12M, plant height (PH) at 12 months; PH18M, at 18 months; SDIA12M, stem diameter (SD) at 12 months; and SDIA18M, at 18 months; DAPFR, days after planting to fruiting; NCF, number of commercial fruit; CFM, mass of commercial fruit; MCFM, mean commercial fruit mass; NCARF, number of carpelloid fruit; CARFM, carpelloid fruit mass; NPENF, number of pentandric fruit; and PENFM, pentandric fruit mass.
within the progenies was not significant for PH18M, SDIA12M, NCARF, and PENFM, indicating that the genotypes within the same progeny or among the progenies evaluated had the same performance.Therefore, it is not feasible to obtain genetic gains through these characters, which were disregarded from the following analyses.
The experimental coefficient of variation (CV) ranged from 6.9 to 223.8%.According to Silva et al. (2008), values of CV less than 20% are determinant of good experimental accuracy for this crop; however, high CVs may be related to the genetic nature of the character.The majority of the characters studied are of polygenic nature, and their expressions are greatly affected by the environment (Maia et al., 2006).The highest values of CV, 223.8 and 121.7, correspond to the number of carpelloid and pentandric fruits, respectively.This is consistent with the results obtained by Damasceno Junior et al. (2008), who observed that the occurrence of fruits with anomalies is a factor strongly associated with environmental variations.These authors studied the occurrence rate of floral anomalies that resulted in anomalous fruits, at different periods, and found that the CVs were superior to the number of abnormal flowers.Moreover, it is worth mentioning that, in the present study, the S 2 progenies were evaluated, that is, the genetic material was not genotypically fixed.Thus, variations in the same progeny are usually observed between experimental plots, because in this generation, there is still reduction of dominance deviations as well as variations caused by additive effects (Silva et al., 2013).
the selection precision and refers to the correlation between the predicted and the actual genetic values of progenies (Pimentel et al., 2014).The higher the selective accuracy of the evaluation of a progeny, the higher the genetic value predicted for it.Therefore, the estimates obtained for the characters SDIA18M, DAPFR, and HFF should be indicated.However, for the NCF character, the estimate varied from low to moderate magnitude.This reiterates the particularity of each character (Marin, 2004), providing the evidence that the complexity of the expression of a particular trait is directly proportional to the complexity of the selection process associated with it.
Individual coefficients of heritability of low magnitude within the progenies may be understood as additional information to heritabilities between progenies, when the individual Blup method is used (Pimentel et al., 2014).Selective accuracy was higher than 75% for most of the characters studied, with the exception of PH12M, NCF, and NPENF.Moreover, for the characters in which the accuracy was high, individual coefficients of heritability were greater than 15%, which represents a considerable magnitude.
The assessment of individuals by Blup analysis presented higher implication for information based exclusively on progeny selection.This is supported by the contribution to selection within progenies, evidenced by the increase in accuracy values, when comparing the progeny selection accuracy with the accuracy in the combined selection among progenies, using the individual Blup.The efficiency of information use within progenies was greater than one unit for all traits, and it was obtained as the ratio of the accuracy in the combined selection, among and within progenies, to the accuracy in progeny selection.Under these conditions, individual Blup selection provides additional gains (Pimentel et al., 2014).These gains should range from 0.8% (if the selection is practiced directly through NCF) to 144% (if performed through PH12M).
Individual coefficient of additive genetic variance quantifies the dispersion of the additive values around the general average.Therefore, high values are more appropriate for populations to be susceptible to genetic progress.The highest percentages were observed in the characters referring to production, although there were deviations of 4.94 and 64.75% for the traits PH12M and CARFM, respectively.Production, however, must be analyzed in combination with the coefficient of environmental variance.Moreover, another important parameter obtained by the ratio among the variables, i.e. the coefficient of relative variance, denotes a favorable condition for selection, when values resulting from this computation are equal to or higher than one (1) Genetic value obtained with the general average, and accumulated gain estimated based on the progeny average.HFF, height of the first fruit; PH12M, plant height at 12 months; SDIA18M, stem diameter at 18 months; and DAPFR, days after planting to fruiting.
In order to generate more information about the experimental accuracy, the coefficients of determination of plot effects were estimated.In Resende (2002), ideal estimates are those with magnitudes below 10%; this indicates that the observed phenotypic variation was only slightly affected by environmental variation.This could be confirmed by the minor differences detected between the phenotypic variance within the progenies and the total one.Therefore, for most of the characters, high reliability estimates were generated.
In the analysis of the ten best progenies, four (36, 28, 26, and 20) stood out for most of the evaluated characters (Tables 4 and 5).For example, progeny 28 was one of the most promising for PH12M, NCF, CFM, NCARF, and NPENF.Among these features, progeny 36 did not stand out for NPENF.However, it program for increasing or reducing the expression of the character.However, none of the individuals stood out in this ranking among all analyzed characters, probably due to the lack of correlation among those.However, based on the data obtained, it was observed that among the individuals, 16 (113, 141, 145, 311, 342, 921, 1421, 1422, 1432, 1442, 1443, 2424, 3125, 3134, 3142, and 3144) 6 and 7).The gains that each intensity represents were predicted based on the average genetic value of the populations and the average genetic value of the selected individuals.Among the characters that were evaluated for the purpose of increasing expression, NCF generated the highest average gains -28.8 and 23.0%, respectivelywith both selection intensity of 10 and 20%.However, when the goal is to reduce the expression of characters with unfavorable phenotypes, it is recommended to identify the individuals that provide the greatest negative gains.Among the characters that were  (1) Genetic value obtained with the general average.and accumulated gain estimated based on the progeny average. (2)In the numbering of each individual, its unit number corresponds to the number of the plant within the plot, the tens digit corresponds to the replicate related to the plot, and the remaining digits are derived from the number of the progeny.For example, individual 1421 corresponds to plant one, of the second replicate of progeny 14. (3) The selection pressures of 10 and 20% correspond to the averages of the 72 and 144 genotypes, respectively, which were better ranked to the characters.X G , general average; and X ST , average without the controls.NCF, number of commercial fruit; CFM, mass of commercial fruit; MCFM, mean commercial fruit mass; CARFM, carpelloid fruit mass; and NPENF, number of pentandric fruit.

Conclusions
1.The variability observed for most of the characters allows greater genetic gains if selection is made at the progeny level, and not in individual papaya (Carica papaya) plants.
3. The prediction of the gains is higher for the increase in the expression of the number of commercial fruits and for the decrease in the expression of the number of pentandric fruits.

Table 1 .
Identification of S 2 progenies of papaya (Carica papaya) and commercial hybrids (controls) used in the study.

Table 2 .
Likelihood ratio and F-values for progeny effects, difference between progeny (P) and control (C), variation within progenies and populations composed by different progenies, in 36 S 2 progenies of papaya (Carica papaya) and in two commercial hybrids (controls).

Table 3 .
Variance components and genetic parameters estimated in 36 S 2 progenies of papaya (Carica papaya) and in two commercial hybrids (controls)(1).

Table 5 .
Additive genetic effect (a), additive genetic value (u+a), and accumulated genetic gain (AG, %), estimated for 36 S 2 progenies (Prg) of papaya (Carica papaya)(1).Genetic value obtained with the general average, and accumulated gain estimated based on the progeny average.NCF, number of commercial fruit; CFM, mass of commercial fruit; MCFM, mean commercial fruit mass; CARFM, carpelloid fruit mass; and NPENF, number of pentandric fruit.

Table 7 .
Additive genetic effect (a), individual additive genetic value (u+a), and accumulated genetic gain (AG, %) estimated with the selection of 10 and 20% of the best genotypes (plant) within and among 36 S 2 progenies of papaya (Carica papaya)(1).