Nonparametric indices for the selection of hybrid citrus as rootstocks grafted with 'Valência' sweet orange

The objective of this work was to evaluate five nonparametric selection indices for the selection of hybrid citrus rootstocks grafted with 'Valência' sweet orange, using horticultural traits relevant for the juice processing industry. Forty-six rootstocks were evaluated in a randomized complete block design, with three replicates and five trees in the plot, in the period from 2009–2015, in a rainfed cultivation. The means of the variables plant height, accumulated fruit yield, fruit yield efficiency, total soluble solids concentration, juice yield, and drought-tolerance were used to calculate the following indices: multiplicative index (IEi), sum of classification (IMMi), genotype-ideotype distance (DiI), and ranking indices (IRKi, based on simple means; and IRKii, based on linear normalization). The indices were efficient to classify the hybrids in relation to general performance. Spearman’s correlation showed a high similarity between most nonparametric indices, notably between IRKi and IRKii. The ranking indices, mainly IRKii, provide a more coherent classification of the hybrids, which allows of the selection of more productive and drought-tolerant rootstocks to produce high-quality fruit for processing.


Introduction
Despite its socioeconomic importance, Brazilian citrus production is vulnerable to several abiotic and biotic stresses because of the low variability of the available genetic material, mainly of rootstock cultivars (Bastos et al., 2014). The citrus rootstock influences more than 20 characteristics of the scion variety, from drought-tolerance to pest resistance, tree size, and fruit traits (Castle, 2010). This fact poses a challenge for the appropriate selection of superior genotypes in breeding programs that, in turn, have been introducing hundreds of new hybrid rootstocks to promote varietal diversification (Soares Filho, 2012).
Traditionally, citrus rootstock breeding has been based on the massal selection of hybrid progenies obtained from crossing a female parental, preferably monoembryonic, which usually has lowerheterozygosis levels, and a male parental of Poncirus trifoliata (L.) Raf. (Schinor et al., 2013). However, due to the high genetic segregation of citrus (Navarro et al., 2002), obtaining hybrids that combine good performance in multiple traits is seldom an easy task. In this sense, nonparametric indices are auxiliary tools that involve the simultaneous combination of several attributes of interest, to allow a more efficient selection of promising genotypes (Vilarinho et al., 2003).
The nonparametric indices do not require the estimation of genetic parameters and can be used for random samples, selected genotypes, or hybrids, that is, fixed samples (Vilarinho et al., 2003). Some indices that are frequently used to assist the breeding of annual and perennial crops (Ferreira et al., 2005;Lessa et al., 2010;Dovale et al., 2011;Almeida et al., 2014;Lessa et al., 2017) are the following: the multiplicative index (Elston, 1963), the classification sum index (Mulamba & Mock, 1978), and the genotype-ideotype distance (Schwarzbach, 1972).
Few papers have reported the application of nonparametric indices to select citrus genotypes. Selection is commonly based on the empiric experience of the breeder, as well as on classic univariate analyses of extensive datasets and, in some cases, on multivariate analyses. However, the interest in indices to assist citrus breeding is increasing, as for instance, by the following authors: Caputo et al. (2012), who used a performance index to select early-ripening sweet orange cultivars; Yacomelo et al. (2018), who selected 'Margaritera' orange genotypes through an index based on fruit quality traits; and Costa et al. (2016), who classified hybrid citrus rootstocks according to a ranking index. Selection indices should consider variables that are highly relevant for the market acceptance, such as juice content and quality, fruit yield, a high-canopy production efficiency, dwarfism, and drought-tolerance Castle, 2010;Khalid et al., 2012). Therefore, different selection indices should be investigated for key traits, in order to assess and select citrus genotypes more precisely.
The objective of this work was to evaluate five nonparametric selection indices for the selection of hybrid citrus rootstocks grafted with 'Valência' sweet orange, using relevant horticultural traits for the juice processing industry.

Materials and Methods
The datasets come from an experiment that was planted in 2007, in the municipality of Colômbia, in the state of São Paulo, Brazil (20°19'22"S, 48°41'10"W, at 492 m altitude). The scion cultivar was 'Valência' IAC sweet orange [Citrus sinensis (L.) Osbeck], which was grafted onto 46 citrus rootstocks, most of them were hybrids introduced or obtained by the Citrus Breeding Program of Embrapa Mandioca e Fruticultura, in the municipality of Cruz das Almas, in the state of Bahia, Brazil (Tables 1 to 5). 'Cravo Santa Cruz' Rangpur lime (Citrus limonia Osbeck) was the commercial standard rootstock. The experimental design was carried out in randomized complete blocks, with 46 treatments, three replicates, and five trees per plot.
The local climate type is Aw, according to the Köppen-Geiger's classification (hot rainy summer, and dry winter typical of savannah), with 1,322 mm mean annual rainfall, and 26.3°C mean annual air temperature (Cepagri, 2018). Tree spacing was 6.0x2.5 m, in a rainfed orchard on a Latossolo Vermelho escuro (Oxisol), medium texture, with moderate A layer. Crop management followed the standard recommendations for orange trees in São Paulo (Mattos Jr. et al., 2014).
In the period 2009-2017, trees were assessed annually for the following variables, which are the most important ones to the juice processing industry: accumulated fruit production (AP), determined by weighing fruit from all trees on a digital scale (kg per tree, in 2009-2015); mean canopy production efficiency (EF), calculated by the mean ratio between  (Stuchi et al., 2000;Schinor et al., 2013). Data were subjected to the analysis of variance, to obtain the coefficient of variation and significance (p < 0.01 and p < 0.05) of the variables used in the selection indices. The multiplicative index [I Ei ] (Elston, 1963) was calculated as in which: I Ei is the multiplicative index; x ij is the mean of the trait j, measured in genotype I; and k j is the lowest value to select n(mín.x ij -máx.x ij K j = (-----------------), n -1 in which: n is the number of genotypes; and min.
x ij and max. x ij are, respectively, the lowest and the highest mean of trait j. The classification sum index [I MMi ] (Mulamba & Mock, 1978) was calculated by m I MMi = ∑ n ij j=1 in which: I MMi is the classification sum indices; and n ij is the number of classifications of genotype i in relation to trait j.
The weights of each variable were determined according to their relevance from researcher experience. I RK was calculated in two manners: I RKi , using the weight sum equal to 1 (simple means of data); and I RKii -whose data were subjected to linear normalization for the interval [0, 1]) -was determined by F(x i ) = (x i -x min )/(x max -x min ), where x i is the numerical value of the variable for each rootstock, and x min and x max are the minimum and maximum values of each variable.
The genotype-ideotype distance index [D iI ] was determined (Schwarzbach, 1972) by the Euclidean distance according to the following equation: in which: D iI is the Euclidean distance between genotype i and ideotype I; and d ij is the standard deviation between the mean of trait j, measured in genotype i (x ij ), and the value given to the ideotype for this trait (x Ij ), that is, d ij = (x ij -x Ij ) / σ j . The standardization prevents traits measured in greater units from having greater influence than other traits on the value of the indices, and, consequently, on the genotype classification (Lessa et al., 2017).
The values given to the ideotype were based on information provided by juice processors, according to our experience, as follows: SS > 11 ºBrix, JC > 50%, AP > 250 kg per tree, EF > 4 kg m -3 , DT ≥ 2, and TH < 3 m. The weight given to each variable in the formula followed the empirical relative importance of the variable for the selection, as AP = EF > SS = JC > DT > TH.
After the calculation of the indices, the genotypes were classified according to the recommendations of Garcia & Souza Júnior (1999). Spearman correlation coefficients among the evaluated indices were calculated to observe the degree of agreement; and the significance of the estimates was tested at 1% and 5% probabilities (Costa Neto, 2002).

Results and Discussion
All assessed variables showed significant differences, which allowed of the ranking of the hybrid citrus rootstocks, therefore confirming the variability within the evaluated genotypes. The coefficient of variation (CV) of the variables used to calculate the indices were AP (16.13%), EF (20.37%), SS (3.37%), JC (4.13%), DT (10.37%), and TH (6.33%) ( Table 1). Not only this wide genetic variability reflects the diverse parental background of the evaluated genotypes, but it is also commonly reported within populations of hybrid citrus rootstocks (Raga et al., 2012;Schinor et al., 2013).
The application of the I Ei to the dataset of the evaluated variables indicated that 52.17% of the hybrid citrus rootstocks were superior to the standard 'Santa Cruz' Rangpur lime (25 th position), which was the Rangpur lime with highest position. The genotypes in the five first positions in the ranking were TSKC × (LCR x TR) -059 (1 st ), TSKC × CTQT 1434 -010 (2 nd ), TSKC × (LCR x TR) -017 (3 rd ), TSK × TR 'Benecke' -CO (4 th ) and 'San Diego' citrandarin (5 th ). Therefore, the I Ei led to the selection of rootstocks that combined lower-tree height (3.14 m), intermediate accumulated production (253.8 kg per tree), high-production efficiency (3.68 kg m -3 ), good drought-tolerance (1.98), high-SS (11.88 o Brix), and juice yield close to that of the standard genotype (48.23%) ( Table 1).For the I MMi , the best ranked rootstocks were TSKC × (LCR x TR) -059 (1 st ), TSKC × CTQT 1434 -010 (2 nd ), TSKC × (LCR x TR) -017 (3 rd ), TSK × TR 'Benecke' -CO (4 th ) and LCR × TR -001 (5 th ), in comparison to 'Cravo Santa Cruz' Rangpur lime (11 st ) ( Table 2). Therefore, the I MMi led to the selection of rootstocks combining lowertree height (3.07 m), intermediate accumulated yield (243.15 kg per tree), high-yield efficiency (3.81 kg m -3 ), good drought-tolerance (2.02), high-SS (11.79 o Brix), and juice yield close to that of the standard genotype (47.82%). This ranking prioritized the concentration of soluble solids and the production efficiency in a similar way to that obtained with I Ei ; however, some selected hybrids showed low yield due to their smaller tree size. By contrast, large-size inducing rootstocks led to low-production efficiency (Cantuarias-Avilés et al., 2011). Lessa et al. (2010) studied diploid banana hybrids, and they pointed out that the multiplicative index (I Ei ) and the classification sum index (I MMi ) also provided an adequate selection with high correlation, which allowed of a better adequacy of the results that helped with decision making.
Pesq. agropec. bras., Brasília, v.55, e01592, 2020 DOI: 10.1590/S1678-3921.pab2020.v55.01592       × 'English Palmira' -CO, and TSKC × (LCR x TR) -059 ranked very often among the best genotypes for all indices. CNPMF -004 Rangpur lime also surpassed the standard 'Cravo Santa Cruz' Rangpur lime. These results confirm the initial good performance of these hybrids, which are promising rootstocks for 'Valência' orange in rainfed cultivation, in São Paulo, Brazil, as reported by Ramos et al. (2015). The Spearman correlation indicated a high similarity among the nonparametric indices, except for D iI ( Table 6). The correlations were highly significant for I MMi x I RKi , I MMi x I RKii , I MMi x I Ei , I RKi x I RKii , I RKi x I Ei , I RKi x D iI , I RKii x I Ei , and I RKii x D iI . The multiplicative index, as well as the classification sum and the genotypeideotype distance indices have been shown also to correlate well for other crops and to provide selection gains in hybrid populations (Lessa et al., 2010(Lessa et al., , 2017Almeida et al., 2014). However, in the present work, the genotype-ideotype index was the most divergent because it prioritized relatively productive yet less efficient hybrid rootstocks. Nevertheless, D iI indicated several hybrids ranking above the ideotype for most variables; hence, it still helped out with the selection of promising genotypes.
The selection of new citrus rootstocks is a lifelong challenge for horticulturists, since dozens of traits should be observed, considering all influences that come from climate, soil type, tree management, scion/ rootstock combinations, occurrence of pests, and economic aspects (Castle, 2010). The highest yield of fruits that meet the industrial standards is still the most important criterion, although reduced tree size is increasing in importance (Bowman et al., 2016). Classic univariate analyses such as LSD and other mean comparison and grouping tests are usually used to support decisions; however, for citrus, the analyses are still difficult due to their large genetic variability within several attributes.
The association of selection indices with other statistical tools was recommended, for more robust selection of genotypes (Ferreira et al., 2005). This is particularly important, since the indices discriminate, or should discriminate, the best genotypes, despite the challenges to attain a perfect correspondence because a single genotype will rarely satisfy all traits of interest (Lessa et al., 2010). Nonetheless, citrus breeders should choose the variables and indices that best fit the breeding objectives or economic interests, aiming at a more accurate selection gain, and further criteria can be applied, such as responses to diseases in the long term.
The five nonparametric indices were efficient to sort hybrid citrus rootstocks, even though each one prioritized different variables for selection. Moreover, the high correlations among indices showed that most of them can be similarly used to assist the selection of rootstocks with good overall performance. The ranking indices provided a more coherent classification of hybrids, particularly the I RKii , which made it possible the ranking of the most productive genotypes with fair drought-tolerance and high-quality fruit for processing.

Conclusions
1. The use of nonparametric indices is suitable to assist the breeding programs for the selection of hybrid citrus rootstocks.
2. The ranking index based on the linear normalization of means allows of a more reliable classification of hybrid citrus rootstocks, since it highlights those presenting the greatest accumulated fruit production, in addition to good drought-tolerance, and efficient production of high-quality fruit to obtain juice. Table 6. Spearman's correlation among five nonparametric indices, using the variables accumulated fruit production, canopy production efficiency, concentration of soluble solids, juice yield, drought-tolerance (visual scoring of leaf wilting), and tree height of 'Valência' sweet orange grafted on 46 hybrid citrus rootstocks, in the north of São Paulo state, Brazil.  (Mulamba & Mock, 1978); I RKi , ranking index using simple means (Costa et al., 2016); I RKii , ranking index using linearly normalized means; I Ei , multiplicative index (Elston, 1963); D iI , genotype-ideotype distance index (Schwarzbach, 1972). *, **Significant at 5% and 1% probability, respectively. ns Nonsignificant.