Improving yield and fruit quality traits in sweet passion fruit: evidence for genotype by environment interaction and cross-compatibility in selected genotypes

Breeding for yield and fruit quality traits in passion fruits is complex due to the polygenic nature of these traits and the existence of genetic correlations among them. Therefore, studies focused on crop management practices and breeding using modern quantitative genetic approaches are still needed, especially for Passiflora alata, an understudied crop, popular known as the sweet passion fruit. It is assumed to be a self-incompatible species and is highly appreciated for its typical aroma and flavor characteristics. With the aim of estimating the genetic and phenotypic parameters related to fruit traits, our group has already investigated a sweet passion fruit progeny consisting of 100 individuals from which 30 genotypes were selected. In this study, we reevaluated these superior genotypes in three environmental conditions. The results of the multi-environment trial analysis indicate that the genotypes do not behave consistently across these environments, and this was taken into account when selecting genotypes. Pairwise genetic correlations among the fruit traits were evaluated, and different genotype rankings obtained depending on the trait and environment, providing further evidence of genotype by environment interaction. Finally, we used a multiplicative selection index to select 20% of genotypes for weight of pulp and against thickness and weight of the fruit skin. The response to selection was positive for all traits except soluble solids, and the superior (six) genotypes were ranked. The consensus is that open-pollinated populations can be used as commercial varieties in crop species that are sensitive to inbreeding depression or within breeding programs that are not well developed. For these reasons, we performed a complete diallel cross for evaluating the capability of the selected genotypes to be fertilized and set fruits. Most of the crosses were compatible, resulting in over 50% fruit set. It is worth noting that all genotypes produce fruits if used as females, which is essential to guarantee yields in commercial orchards.


Introduction
crops, and for estimating genetic parameters (heritability, genetic correlations, etc.). In this case, the preferred approach is REML/BLUP (Restricted Maximum Likelihood/Best Linear Unbiased Predictor) allowing genetic parameters to be estimated simultaneously and facilitating the prediction of genotypic values maximizing the correlation between true and predicted genotypic values (Searle et al., 2009).
With the aim of estimating the genetic and phenotypic parameters related to fruit traits and identifying the quantitative trait loci (QTLs) underlying these traits, our group has already researched a sweet passion fruit population consisting of 100 full-sibs from which 30 superior genotypes were selected (Pereira et al., 2017). In this study, we reevaluate these genotypes in three environments, with a view to estimating the heritability coefficient and genetic correlations using VCOV matrices, investigating the GEI and predicting genetic values for fruit traits. We tried to obtain a more representative picture of these genotypes for identifying promising material that could be used to advance the research, or even make them available to local producers. Finally, due to the existence of incompatibility mechanisms in P. alata and the fact that the selected genotypes were full-sibs and therefore incompatible crosses might occur, a complete diallel cross was performed for evaluating whether they could be fertilized and set fruits.

Plant Material
The population under selection (N= 30) was part of a full-sib progeny derived from a single cross between two outbred and divergent accessions of sweet passion fruit. The male parent, denoted SV3, was an indoor selection cultivated in the Southeast of Brazil (22°17′ S, 51°23′ W). The female parent, denoted 2(12), belongs to the progeny of a wild accession collected in a region between the Amazon and Cerrado ecosystems (15°13′ S, 59°20′ W); for details, see (Ferreira et al., 2010).
The SV3 accession is vigorous, develops faster and has vegetative organs larger than those of accession 2(12). It produces medium-sized to small egg-shaped fruits, and abundant aromatic pulp of a deep orange color. Accession 2(12) produces rounder, larger fruits with a thicker skin and less pulp that is a paler color. Thus, in this study, we examined 32 genotypes, consisting of the 30 full-sibs and the two parents. Note that these genotypes were previously selected from the above-mentioned progeny of 100 individuals that were evaluated in two environments over a period of two growing seasons (see Pereira et al., 2017).

Field Sites and Measurements
Field experiments were conducted in three environments (A, B and C): A was conducted from January 2014 to August 2015 (1st season) and B from October 2015 to August 2016 (2nd season), both at the same locality (22º47' S, 48º07' W, 500 m above sea level); C was conducted during the 2nd season but at a different locality (22º42' S, 47º38' W, 546 m above sea level). Both sites are located in the Southeast of Brazil. All crop management practices were performed throughout the entire agricultural cycle. A randomized complete block design with six (environment A) or three (environments B and C) replicates was used, with three plants per plot arranged in rows. Plant and row spacing was 5 m (A) and 3 m (B and C).
Plants were tied to 2-meter high wire trellises.
At the fruit set stage, up to 10 fruits per plant were harvested every week when the skin turned from green to yellow. The 30 fruits from each plot were then used to evaluate nine fruit traits: weight (WF, in g), diameter at the widest point (DF, in mm); length of the fruit (LF, in mm); thickness of skin at the widest point (TS, in mm); weight of skin (WS, in g); weight (WP, in g) and yield of fruit pulp (YP, estimated based on WP and WF); soluble solids (SS, in °Brix), and yield (tonnes per ha). DF, LF and TS were measured using a stainless 0−200 mm digital caliper, and WF and WS using a digital scale (Tecnal, 1300 g). WP was calculated by subtracting WS from WF, and SS measured using a portable sucrose refractometer with 0−32 °Brix scale (Instrutherm RTA-50). In addition, the number of fruits produced per plant was noted at three different times prior to harvesting, and counting only those fruits present at about 3 weeks after blooming. Fruit production per plant (in kg) was calculated by multiplying the average number of fruits per plant by the mean fruit weight for the respective genotype. Finally, individual plant production was extrapolated on a per hectare basis as a function of the number of plants per hectare for estimating yield in tonnes per hectare.

Statistical Analysis
Single-and multi-environment trials analysis were fitted via linear mixed models to estimate the generalized measurement of heritability, find the adjusted means to obtain genetic correlations among traits, and rank genotypes for selection. Single-environment analysis was fitted for each trait using the following linear model: where is the phenotype of the th genotype ( = 1, … , ; = 32) in the th block, is the intercept, is the random effect of the th genotype, is the fixed effect of the th block and is the random error; ∼ (0, 2 ).
Multi-environment trial analysis was performed based on the fixed effect of environment and random effects of genotype and GEI, using: where is the phenotype of the th genotype ( = 1, … , ; = 32) in the th block and the th environment, is the intercept, is the fixed effect of the th environment, ( ) is the fixed effect of the th block within the th environment, is the random effect of the th genotype in the th environment, and is the random error; ~ (0, ⊗ + ).
For genotypes, it was assumed that vector = ( 11 , … , )′ had a multivariate normal distribution with zero mean vector and genetic VCOV matrix = ⊗ , i.e., ∼ (0, ), where ⊗ represents the Kronecker direct product of both genetic and identity matrices with respective dimensions × , and × is the number of environments and genotypes. Linear mixed-model analysis was performed using the ASReml-R package (Butler et al., 2009) in which different VCOV structures were investigated for G, a matrix of random effects, and R, a matrix of residuals. A total of eight VCOV structures for random genetic effects (ID: identity; DIAG: diagonal; CShom: homogeneous compound symmetry; Ar1: first order autoregressive; Ar1H: heterogeneous first order autoregressive; CSHet: heterogeneous compound symmetry; UNST: unstructured; FA1: first order factor analysis) and two structures for the R matrix residual effects (identity and diagonal matrix) were tested and selected according to Akaike Information Criteria (AIC; Akaike, 1974) and Bayesian Information Criteria (BIC; Schwarz, 1978). Due to the unbalanced situation, Residual Maximum Likelihood (REML; Patterson and Thompson, 1971) was applied for each trait. Based on the most appropriate models, the following estimates were then found: ̂2(residual variance), ̂2(phenotypic variance), ̂2(genetic variance), ̂2 (environmental variance), ̂2 (GEI variance).
The genotypic correlations were estimated between environments by the expression , ′ =̂, ′ √(̂2 ̂′ 2 ) . In addition, genotypic correlations among traits were calculated for adjusted means, such as the Pearson coefficient, using program R (R Development Core Team, 2017) and psych (Revelle, 2014) to produce diagrams of dispersion between pairs of traits and plot the correlation networks.
Heritability was estimated using the approach in Cullis et al. (2006) which proposes an alternative expression when working with unbalanced data and mixed models: where: 2 is the heritability value for each trait; variance is the average of the difference of two BLUPs (Best Linear Unbiased Prediction), and ̂2 is the genetic variance.
The coefficient of genetic variation ( ) was calculated as = ̂ . 100, where ̂ is the square root of the estimated genetic variance and the average for the population.
For selecting the superior 20% of full-sibs with the desired traits, four scenarios were created: the first three were based on single traits: selecting against TS; selecting against WS; and selecting for WP. In a fourth scenario, selection was based on a multiplicative selection index (MSI). The MSI was applied with the aim of increasing WP and decreasing TS and WS. It was calculated following the procedure proposed by Elston (1963): for each individual , = ∏ (̂− ) =1 was found, where ̂ is the average adjusted value of the i th genotype for the t th trait, and is the lower limit value accepted for the t th trait.
Thus, we determined: where: is the response to selection given by the BLUP values for the selected individuals ( ); 0 is the average for the original population and (%) is the percentage response to selection.
Finally, in order to investigate GEI, the GGE biplot (Genotype main effects + Genotype by environment interaction) (Yan et al., 2000) was generated using the GGEBiplotGUI software implemented in R.

Cross Compatibility Between Selected Genotypes
As potential incompatible crosses might occur due to the existence of incompatibility mechanisms in P. alata, the selected genotypes were crossed and fruit set evaluated at the same site (C), using a complete 6 × 6 diallel cross during the 2017/18 and 2018/19 growing seasons.
The plants were artificially pollinated (Figure 1a-j) using a procedure similar to that described by Bruckner and Otoni (1999). One day before anthesis, the flowers were protected with paper bags to avoid contamination. At the beginning of anthesis, the flowers were carefully emasculated using fine forceps and the anthers collected (Figure 1c-d). Pollination was performed by rubbing the anthers from one parent against the stigma of the other (Figure 1d). The flowers were then labeled and covered again with paper bags for 24 hours. Seven days after pollination, those flowers that had initiated fruit development were considered fertilized. Finally, the fruits were protected with a nylon bag to prevent falling during ripening. At least 10 pollinations were carried out for each cross, including reciprocal crosses and selfpollinations. The crosses were considered compatible (+) when > 50% of the pollinated flowers set fruits (Figure 1e-g) and incompatible (-) in the absence of fruit set (Figure 1h-j).

Single-and Multi-environment Trial Analysis
Before carrying out the MET analysis, the phenotypic data from the single environment trials was analyzed. The likelihood ratio test, performed for each of the three environments, detected significant differences among genotypes for all the traits studied, revealing the levels of genetic variability within the population herein evaluated (Supplementary material 1).
To perform MET analysis, several VCOV structures for the G and R matrices were investigated and compared via AIC and BIC, attempting to find the most appropriate model for each trait (Table 1). For WF, LF and WS, the best model was found by fitting an UNST VCOV matrix (heteroscedasticity and different genetic covariances) to the genotype effects, and an ID VCOV matrix (homogeneous variance for all the environments with no covariance) to the residual effect. For TS and YP, the VCOV matrices that resulted in the lowest AIC and BIC values were CSHet (heteroscedasticity and same covariance among genotypes) for G, and DIAG (heterogeneous variances between environments and no covariance) for R. For WP, the best VCOV for G was Ar1H (approximates UNST, but with a reduced the number of estimated parameters), and DIAG for R. Finally, for SS, the selected VCOV matrices were CSHom (homoscedasticity for genetic effects and same covariance among genotypes) for G, and DIAG for R. Once the most appropriate models were obtained, statistical analysis was performed in order to estimate the genetic parameters. Since fruit ripening was not synchronous for the genotypes, the covariate 'days to harvest (DH)' was also added to the models. However, no significant differences were found (data not shown).
The MET analysis suggested that the environment significantly affected all traits, except WS. This implies that traits vary with the environment or that both locality and crop season influence the performance of fruit traits (Table 2). Furthermore, the random effect of GEI significantly affected all traits. These findings also indicate that genotypes do not show consistent behavior across environments, and this should be taken into account when selecting genotypes.
Mean phenotypic values and the range of values, heritability, coefficient of variation and genetic, phenotypic and residual variances for each of the nine traits are summarized in Table  2. The generalized measurement of heritability, proposed by Cullis et al. (2006), varied considerably from one trait to another and one environment to another, ranging from 0.41 (Yield, environment B) to 0.94 (TS, environment C). Comparing the heritability estimates for different environments, the values for C (season 2015-16) were the highest (except for YP), followed by those of A and B (2014-15 and 2015-16, respectively, both in the same locality). Even though there are exceptions (e.g. Yield), these results show that much of the observed phenotypic variation can be attributed to genetic differences.
Although studying a semi-perennial species using large experimental areas (~2 ha per trial), relatively low values of CV were obtained for all traits, ranging from 5.32% (SS, environment C) to 22.56% (WP, environment C), an indication of good experimental precision. The only exception was Yield, where high CV values were observed regardless of the environment. Furthermore, the estimated CVs for each trait in A, B and C were very similar, denoting that all experimental conditions were equally reliable.

Correlation Between Environments and Traits
Pairwise genetic correlations among the nine fruit traits and scatter charts are shown in Figure  2. Based on the values obtained, the correlations were grouped into three classes: weak (|r| ≤ 0.45), moderate (0.46 ≤ |r| < 0.76) and strong ( We also investigated the genetic correlation between environments for all traits (Supplementary material 2). Between A and B, r A, B ranged from 0.17 to 0.95 (DF and YP, respectively), whereas between A and C, r A, C ranged from 0.39 to 0.96 (WP and SS, respectively). Finally, between B and C, r B, C values were higher but with lower amplitude, ranging from 0.19 (YP) to 0.91 (WF and DF). This pattern of correlation values has implications for genotype ranking, depending on the trait and environment, lending further weight to the existence of GEI.
Also, with the aim of studying genetic correlations and assessing the behaviour of groups of traits, a correlation network was built for each environment. In this analysis, circles represent the traits, line colour indicates positive (green) and negative (red) correlations, and line thickness denotes magnitude ( Figure 3). Overall, correlation network plots corroborate the average genetic correlations ( Figure 2). Comparing environments, in A the genetic correlations among traits were overall positive and higher (Figure 3a) than those found in B (thinner lines showing weak and moderate correlations - Figure 3b). In C, there was a pattern more similar to that found in A, though not as strong ( Figure 3c). Moreover, YP and SS showed weak to moderate negative correlation with most of the other traits for the three environments, specially A. Finally, all traits other than YP and SS showed mainly positive correlations with each other (Figure 3).

Genotype by Environment Interaction Analysis
GGE biplot analysis was performed in order to provide a comprehensible view of the GEI and allow better interpretation of MET results. This approach is useful for evaluating genotypic performance across environments, comparing different test environments and elucidating how traits are interrelated (Yan et al., 2000). The GGE biplot is constructed by plotting the first two principal components (PC1 and PC2) derived from singular value decomposition of the environment-centered data. Briefly, when environments are allocated to different sectors, it means that genotype performance diverges, indicating a crossover GEI pattern. Otherwise, if all the environments are allocated to the same sector, GEI is weaker. In terms of genotype performance, the best genotypes are those located at the polygon vertices.
The first two principal components account for 76.56% of the variation (PC1 = 59.78% and PC2 = 16.74%), showing the efficiency of this kind of analysis in explaining most of the variance resulting from all trait data sets ( Figure 4). Genotype distribution over the entire graph and positions in different sectors indicate the existence of high levels of variability within the population.
The most strongly correlated traits are those related to fruit size and shape (WF, LF, DF, WS and TS) that are located within a single sector of the polygon (Figure 4). In this sector, genotype 21 is positioned at the polygon vertex indicating high performance for these traits.
Other interesting genotypes are 49, 107 and 140, which appear in the sector formed by WP and Yield; genotype 122 showed greater YP. On the other side of the biplot, SS was negatively correlated with all traits, except YP ( Figure 4). The SS sector, it groups genotypes with high SS values, such as 69, 52 and 44. However, despite the sweetness of the fruit, these genotypes are inferior in terms of WF, DF, LF, WS, TS, WP and Yield. Regarding the parent plants, while the male (SV3) is placed near the intersection, and thus of average performance only, the female 2(12) is positioned at a single polygon vertex (Figure 4). Nevertheless, even though it does not share the sector with any trait, the positioning of 2(12) in relation to WP and Yield reflects its wild, unimproved attributes.
In terms of fruit yield in all environments (A, B and C), the best performing genotypes were 21, 49, 136, 52 and 69. For yield specifically, a different genotype performed better in each environment: 21 in A, 151 in B and 49 in C, showing how influential GEI can be.
Additionally, environment C was more discriminating of genotypes, while environment B did not allow any clear conclusions to be drawn.
The Average Environment Coordination (AEC) view of the GGE biplot is shown in Figure 5b.
In the graph, genotype average values in the different environments create an "average environment" point represented by the small blue circle. Genotypes exhibiting high stability are located near this circle, including genotype 152. The AEC abscissa is the straight line that passes through the biplot origin and the "average environment", and the AEC ordinate is the line perpendicular to the abscissa. The projections of the genotype on the abscissa represent the main genetic effects and therefore rank the genotypes in relation to their mean performance. Thus, according to this ranking, the genotypes were classified according to yield, as follows: 49 > 21 > 85 > 140 > 150 > ... > 151 > overall mean > 145 > 122 > ... > 52 > 69. The AEC ordinate approximates the genotypes contribution to GEI, a measurement of stability. Since genotype 152 is located almost on the AEC abscissa with near-zero projection onto the AEC ordinate, it is the most stable genotype. In contrast, 21 and 136 were two of the least stable genotypes. Finally, in terms of the ideal genotype, 49 was ranked at the top and exhibited stable performance.
The new GGE biplot shown in Figure 6 was based only on the traits used to create the MSI (WP, WS and TS). The reduced size of the polygon compared to those in Figure 4 and 5 reflects lower variability since only three traits are used. WP, WS and TS were grouped into two sectors, one formed by WP in the three environments and other by WS and TS. The polygon vertices are formed by genotypes 49, 21, 85, 2(12), 93 and 122. Once again, genotype 49 was the frontrunner with the higher WP values, while 21 was best performer in terms of WS and TS.

Selection Strategy
In fruit crops, the main objective of breeding programs is to increase genetic gains to ensure fruit quality and high yield. In this study, we selected six genotypes from a population of 30 preselected full-sibs (Pereira et al., 2017), representing a selection intensity (SI) of 20%. Table 3 shows response to selection (RS) values that, for mixed models, correspond to BLUP values, and Percentage RS (RS%) based on four different selection scenarios. The first two scenarios relate to the result obtained if genotypes were selected with the aim of decreasing TS and WS; the third selection is aimed at increasing WP and the forth is based on a multiplicative selection index (MSI) for simultaneously selecting for WP and against TS and WS.
In the first scenario (selecting against TS), the six selected genotypes were 93, 69, 44, 52, 140 and 154, and the reduction in TS was 13.2%. Since there is a high correlation between TS and other traits, there was a decrease in WF, WS and Yield (18.6%, 23.6% and 13.3%, respectively), as well as a significant increase in YP (11.4%). The second scenario (selecting against WS) produced similar results. The selected genotypes were 69, 93, 52, 44, 87 and 122, and the decrease in WS was 26.1%; other traits were also reduced, including WF and WS, and especially Yield (21.8%, 26.1% and 30.4%, respectively); YP was increased (9%). The third scenario selected for WP, and 49, 107, 122, 140, 21 and 125 were the selected genotypes. The response to selection was positive for all traits, except SS. In addition to WP (24.9%), the highest gains were obtained for WF, WS and Yield (22.4%, 21% and 41.5%, respectively). Finally, in the fourth scenario, using the MSI resulted in the same set of genotypes as in the third scenario. However, the ranking was different (49, 21, 107, 125, 140 and 122). As a consequence of selecting the same genotypes, all responses to selection were the same as in the third scenario.

Compatibility Between Selected Genotypes
Based on the MSI, six genotypes were selected: 21, 49, 107, 122, 125 and 140 (Supplementary materials 3 and 4). Since these genotypes are full-sibs, it is essential to test whether they can be crossed with each other and set fruits. Furthermore, although P. alata is assumed to be self-incompatible (Braga et al., 2005) as corroborated by molecular markerbased studies (Ferreira et al., 2010), the crossing studies necessary to prove this hypothesis have not been conducted. For this reason, we carried out a complete 6 × 6 diallel crossing, with reciprocals and self-pollinations, involving all the selected genotypes.
Our results show that most of the crosses were compatible (over 50% fruit set). This value is the percentage of pollinated flowers ultimately forming fruits. As expected, the occurrence of self-incompatibility within the species was evidenced by the absence of fruit set in all selfpollinations. Some of the crosses also did not produce fruits (e.g. 21 × 107, 125 × 140 and 140 × 122), possibly because of genotype relationships. In addition, there were cases in which fruits were produced but at rates lower than 50% (49 × 122, 107 × 21, 122 × 125, 122 × 140, 125 × 107, 125 × 122, and 140 × 125), indicating partial compatibility (Table 4). It is worth noting that all genotypes produce fruits if used as females, which is essential to guarantee yields in commercial orchards.

Discussion
Despite the great potential and the prospects for higher consumption and utilization of P. alata as a fruit crop, production remains low and unstable, mainly due to the lack of improved varieties. In passion fruit, like other fruit crops, the main purpose of breeding is to meet the demand for quality (Cavalcante et al., 2017;Pereira et al., 2017;Viana et al., 2017). According to Jung et al. (2007), sweet passion fruits should weigh 200 to 300 g, be oval in shape, free from apical softening, with a firm skin, rich pulp yield (over 30%), high sugar content and significant yield. However, all these goals are not easily achieved in a few selection cycles, requiring a medium-term program that takes into account correlations between these traits.
To face this challenge, our research group conducted breeding programs using modern quantitative genetics to generate information and select genotypes that can lead to the development of varieties with improved fruit quality and yield. To do this, a segregating population (F1) was developed by crossing two outbred, divergent accessions of P. alata. In parallel, this full-sib family (N= 180) was genotyped using molecular markers  and used to construct a unique linkage map for the species . One hundred 100 individuals were then sampled and field-evaluated, and QTL mapping analysis performed to identify loci associated with fruit quality traits. The MSI was also used to select the 30 most promising genotypes (Pereira et al., 2017).
In the present study, we reevaluated these full-sibs in three environments and estimated genetic and phenotypic parameters for nine fruit traits to confirm that there was still some genetic variability within the selected population for continuing the breeding process. The six most promising genotypes were then selected and their fruit set capability evaluated.
To summarize, linear mixed models were applied to analyze the MET so that several VCOVs could be investigated for the G and R matrices and for each trait. Based on the AIC and BIC values, the best models for WF, LF and WS were UNST (unstructured) for G and ID for R. For TS and YP, CSHet was the best for G, and DIAG for R. For WP, Ar1H was used for G and DIAG for R. Finally, for SS, CSHom was used for G, and DIAG for R (Table 1).
As is usually the case for datasets with complex GEI, our results show that none of the simplest VCOV, ID and DIAG matrices were selected for G. Furthermore, breeding data are frequently unbalanced since diversified sets of genotypes are evaluated in different trials. Statistical methods should therefore be used to model different variances and covariances between environments. Thus, approaches that model complex VCOV matrices, such as UNST, are better because they can capture both the heterogeneity of genetic variance and complex covariance structures, resulting in a more accurate prediction of single-or multienvironment trials. However, it is important to note that the number of estimated parameters in unstructured models can inflate rapidly as the number of trials increases, which can make UNST models less parsimonious, requiring alternative VCOV models when analyzing moderate to large MET datasets (Kelly et al., 2007;Smith et al., 2001).
The low CV values observed herein for all traits show the high precision of the environmental conditions, and these values are particularly interesting due to the semi-perennial behavior of passion fruit orchards and the large experimental areas used (over 2 ha per trial). The exceptions were the high Yield CVs, which may be trait-intrinsic but could also be attributable to the methodology used to estimate Yield, which based on both the number of fruits per plant and the average weight of the fruits.
High heritabilities (H 2 ≥ 0.50) were estimated for each environment, reaching values up to 0.94 (SS) ( Table 2). Although heritabilities were highest overall in environment C, low values were found in B, especially for Yield (0.41). In the original population (N= 100), high heritabilities for the same fruit traits (except Yield) were estimated, varying from 0.59 (WP) to 0.82 (SS). These significant broad sense heritability values are particularly important since the species can be propagated by cuttings and thus all types of genetic variance can be exploited to predict responses to selection (RS).
Genetic correlations between traits showed mostly intermediate to high values, especially for correlations associated with fruit size and shape. The highest values (some exceeding 0.76) were found among WF, DF, WS, TS and Yield (Figure 2). These findings are also supported by the correlation networks, especially in environments A and C (Figure 3).
According to Martins et al. (2003), DF and LF are strongly correlated with each other and with TS, but no correlation with YP were found, indicating that larger fruits in P. alata populations do not necessarily have higher pulp content. For P. edulis, there are several reports of negative correlations between TS and WF, WP, DF, LF, number of fruits and Yield (Moraes et al., 2005;Oliveira et al., 2011;Silva et al., 2017;Viana et al., 2017) enabling breeders to successfully select against TS.
Comparing the genetic correlations found herein (N= 30) with those reported for the original population (N= 100), there were some differences in correlation magnitudes. Analyzing in detail the traits that comprise the MSI (TS, WS and WP), we found significant variation in the correlation between WP and WS; the initial value was 0.55 but dropped to 0.48 after selection. In addition, the correlation between WP and TS dropped from 0.28 to 0.27. This occurred because the selection was for WP and against both WS and TS. What is particularly interesting is that these dissociations were obtained with only one cycle. For breeders, even a slight detachment of correlated traits is of great interest, since it allows selection for one trait with little impact on others.
For all the traits we evaluated (except WS), the MET analysis indicated that the effect of the environment was significant. There was also a significant random effect of GEI, indicating that genotypes do not perform consistently across environments. The GEI was then analyzed and interpreted by GGE biplot. Our findings revealed the existence, albeit small, of variability in the population, corroborating Pereira et al. (2017), especially for WF and WS. Furthermore, the strong correlation among traits was also confirmed by this method. In addition, some of the genotypes subsequently selected by the MSI, were significant according to their position at polygon vertices (21, 49, 122 and 140) (see Figure 4).
Yield performance across environments was also revealed by the GGE biplot model, showing the importance of this trait in the GEI. The analysis indicated that genotypes 21, 49, 52, 69 and 136 were the most promising (Figure 5a). The AEC view of the GGE biplot allowed us to study the stability of genotypes across environments ( Figure 5b) and showed that, for Yield, the most stable genotype was 152, while 21 and 136 were two of the less stable genotypes. Yan et al. (2007) proposed that the ideal genotype must have both high average performance and high stability within a mega-environment. In our analysis, in contrast to 21 and 136, which were unstable despite the high yield, genotype 49 showed high yield and a very stable pattern. It is therefore a promising candidate for selection. Still on the subject of Yield, in all three environments low estimates were obtained, averaging 1.9 (A), 1.2 (B) and 4.0 (C) tonnes per ha (Table 2). Although these values are relatively low, it is worth noting that they represent average phenotypic values for the entire population, since in terms of Yield, the most promising genotypes (21, 49 and 136) produced maximal values of 11.5 (A), 5.0 (B) and 12.8 (C) tonnes per ha.
In an attempt to select superior individuals, we applied a selection intensity of 20% and simulated four scenarios seeking to decrease skin-related traits and increase WP. Because of the high correlations between traits, selection based on the MSI in environment (C) produced the most satisfactory results, optimizing WP gain and TS and WS losses. For example, if selection was applied only against TS, the thickness of fruit skin would decrease 13.2% (Table 3), but other important traits such as Yield would also be significantly reduced (13.3%). Comparing the results with those obtained in the source population (Pereira et al., 2017), higher percentages of selection gain for all traits were achieved by using the MSI. Furthermore, selection based on the MSI was the only method that resulted in higher WP and lower TS and WS. Thus, according to the MSI, the selected genotypes were: 49, 21, 107, 125, 140 and 122 (Supplementary materials 3 and 4).
GGE biplot analysis was also performed using only MSI traits. Again genotype 49 was the best genotype, with high WP. Moreover, 21 and 122, selected by MSI, were also positioned in the polygon vertices, as were 107 and 140. Although some genotypes, such as 49 and 122, were highly stable for yield (Figure 5b), when compared on a performance basis, WS, TS and WP in the three environments were ranked differently, reflecting the complex GEI interaction (Supplementary material 5).
Pulp yield determines how much of the weight of the fruit can be attributed to the weight of the pulp. As mentioned above, P. alata is almost wild and its low YP is the result of its heavy skin and low pulp content. For the original population (N= 100), the estimated and expected YP values were 22.43% and 23.37% (Pereira et al., 2017). However, in our study, YP values were even higher using the MSI, reaching 29.6% (A), 33.3% (B) and 26.6% (C). These YP gains are high, and similar results close to the 30% proposed as ideal for the species have been obtained in other breeding populations (Jung et al., 2007a(Jung et al., , 2007bMartins et al., 2003).
Since the selected genotypes (49,21,107,125,140 and 122;Supplementary material 3 and 4) belong to a full-sib family, diallel crosses were carried out in all possible reciprocal plant combinations to check their ability to produce fruits. Cross-compatibility of the selected genotypes is essential to continue with breeding programs, and even provide genotypes to farmers with commercial orchards. These commercial genotypes should be mutually compatible and produce a uniform, superior commercial population in terms of fruit quality.
In conclusion, we have provided evidence of self-incompatibility in P. alata, confirming previous findings obtained using molecular markers (Ferreira et al., 2010). For all reciprocal combinations, 10% (3/30) were found to be incompatible and 23% (7/30) partially compatible. Importantly, most of the combinations were found to be compatible (20/30) and all the six genotypes produced fruits if used as females.
According to Bruckner et al. (1995), the incompatibility mechanisms in Passiflora represent a direct challenge to breeders if they are to produce hybrids, release synthetic varieties and establish clones. The genotypes used to set up commercial orchards must be very carefully chosen in order to guarantee highly efficient pollination. In this study, the predominance of compatible crosses indicates that genotypes 21, 49, 107, 122, 125 and 140 could be used, for instance, to produce a recurrent selection population for increasing the frequency of favorable alleles involved in genetically controlling fruit quality traits and yield, and even recommend it to farmers.         Cullis et al. (2006).  Percentage in which fruit set was observed but below 50%. 18