Selection indexes and principal components for agronomic and bromatological traits in forage cactus

ABSTRACT The objective of the present work was to compare selection indexes focused on the selection of forage cactus (Opuntia ficus-indica) accessions at initial generations. Sixty-five accessions from different locations in the semiarid region of the state of Bahia, Brazil, were evaluated in a randomized complete block design with three replications. Agronomic and bromatological traits were evaluated. The genetic parameters were predicted by using mixed models (REML/BLUP). The linear correlation degree between variables was estimated through Pearson's correlation analysis. Selection gains were predicted using four selection indexes: Smith-Hazel index, with two combinations of economic weights; rank sum index of Mulamba and Mock; and Elston's multiplicative index. The selection intensity applied was 30%, which allowed the selection of the 20 best accessions. The analysis of deviance showed significant effect for all traits. The estimate of genetic parameters evidenced the existence of genetic variability for the O. ficus-indica accessions. The Smith-Hazel index (combination 1) was important for primary (fresh weight and cladode dry weight) and bromatological traits (acid detergent fiber and neutral detergent fiber), expressing higher selection gains than the other indexes. The rank sum and multiplicative indexes resulted in selection gains for most evaluated traits. The results of accessions 2, 4, 5, 7, 9, 11, 14, 15, 18, 26, 27, 34, 37, 38, 39, 41, 45, 49, 51, 52, 53, and 58 were promising for their inclusion in breeding programs, as they were selected by at least two of the four selection indexes used.


INTRODUCTION
The forage cactus specie Opuntia ficus-indica Mill. is native to Mexico and was introduced into Brazil in the late nineteenth century (LEITE, et al., 2014).Its morphophysiological traits contributed to its local adaptation and made possible its use as a forage resource in a large area of the Northeast region of Brazil (PAIXÃO, et al., 2011).
Forage cactus breeding has involved crossings and selections of more vigorous clones in several countries, such as Mexico, the United States, and South Africa.The State University of Feira de Santana, in the state of Bahia, Brazil, has conducted a breeding program that includes evaluation and selection of genotypes adapted to the region, and has a collection of accessions from different regions of the Northeast of Brazil.
The genetic and environmental contributions to the expression of phenotypes are explained by the analysis of genetic parameters (SALES, et al., 2013), which is indispensable for the conduction of breeding programs, as it provides data about heritability, amplitude of genetic variation, and prediction of Rev. Caatinga, Mossoró, v. 36, n. 1, p. 189 -198, jan. -mar., 2023  selection gains, allowing the measurement of a population's potential and the obtaining of higher efficiency in the selection process (VIANA; RESENDE, 2014).Important information is also obtained through genetic correlations by assessing whether a change in a variable is proportionally correlate to a change in other (NARDINO et al., 2016).These data contribute to obtain selection gains for a trait through indirect selection of another correlated trait, as well as to discard redundant traits (CRUZ; REGAZZI, 2012).However, the selection for quantitative traits is not an easy task for a breeding program, considering that they have complex dynamics, are highly affected by the environment, and can be strongly interrelated, making the selection for a trait to change another.The use of selection indexes is a strategy used by breeders to mitigate this problem, and has been proposed for plant and animal breeding programs to select quantitative traits simultaneously.
Selection indexes were first described by Smith (1936) to maximize the correlation between the index and the genotypic value of individuals.Subsequently, Smith (1936) and Hazel and Lush (1943) adapted them to animal breeding programs and, thus, some authors termed it Smith-Hazel index; however, it requires the establishment of economic weights, which can hinder the selection due to the expression of negative selection gains in the traits (FARIAS et al., 2016).
The multiplicative index, also known as weight-free index, was developed by Elston (1963) and is characterized by not requiring the establishment of economic weights for the several traits and for estimation of phenotypic and genotypic variances and covariances.The rank sum index (MULAMBA; MOCK, 1978) is characterized by ranking genotypes based on their relation to each trait and in an order favorable to the breeder's goals and, similarly to the multiplicative index, it does not require the estimation of phenotypic and genotypic variances and covariances and the establishment of economic weights (FARIAS et al., 2016).Studies using selection indexes have been conducted successfully for different crops, such as eucalyptus (KRAUSE et al., 2021), herbaceous cotton (FARIAS et al., 2016), and sour passion fruit (DALBOSCO et al., 2019).
Considering the lack of studies using selection indexes for forage cactus, the objective of the present work was to compare selection indexes to indicate the best methods for selection of the most promising accessions.

MATERIAL AND METHODS
The experiment was implemented at the Rio Seco Experimental Station, which belongs to the State University of Feira de Santana, in the municipality of Amélia Rodrigues, Bahia, Brazil (12°23'30''S, 38°45'24''W, and altitude of 217 m).The experiment period had a rainfall depth of 1,270 mm, and a mean temperature of 24.6 °C (INMET, 2017).The climate of Amélia Rodrigues was classified as Af, tropical wet, according to the classification of Köppen.
One cladode per pit was used for planting; it was planted in an upright position, with the cut end pointing downwards into the soil, deep enough to prevent lodging, with spacing of 1.0 m between rows and 0.5 m between plants.
The agronomic performance was evaluated by measuring the following traits: plant height (PH; cm); plant width (PW; cm); total number of cladodes (TNC); cladode length (CL; cm); cladode width (CW; cm); cladode diameter (CD; mm); cladode fresh weight (CFW; g); cladode dry weight (CDW; g); dry matter yield (DMY; %), calculated by the expression .Cladode area (CA) was determined using the expression .Cladode total photosynthetic area (CTPA) was calculated by the expression .The measurements were carried out using a tape ruler, a caliper, and a precision balance.
One first-order and one second-order cladode were collected from each plant for bromatological analysis.The cladodes were dehydrated in a forced air circulation oven at 65 °C for approximately 15 days.The samples were then ground in a Willey mill, homogenized, and analyzed.Cladode gross protein (CGP) content was obtained by the Kjeldahl method (AOAC, 2019); acid detergent fiber (ADF) and neutral detergent fiber (NDF) were estimated by the methodology of AOAC (2019); and ethereal extract (EE) was obtained by the Soxhlet method.Total digestible nutrient (TDN; %) contents were estimated by the expression ; and non-fibrous carbohydrates (NFC) were obtained by the expression The data were analyzed using the methodology of mixed linear models (restricted maximum likelihood/best linear unbiased prediction-REML/BLUP).The estimates of genetic parameters were obtained by REML approach and the prediction of genetic values of the accessions, for each characteristic, was obtained by BLUP.The following statistical model was used: , where is the vector of the data, is the vector of the effects of replication (fixed effects) added to the overall mean, is the vector of the effects of accessions (random effects), e is the vector of residues (random), and and are the incidence matrices for fixed and random effects.The analysis of deviance was carried out to test the significance of the effects of accessions using the LRT (likelihood ratio test).The following equation was used: , where is the deviance and is the maximum point of the residual likelihood function (VIANA;RESENDE, 2014).The estimates of the components of variance were obtained by the equations: , where is the individual heritability per plot in the broad The agronomic performance was evaluated by measuring the following traits: plant height (PH; cm 1 Rev. Caatinga, Mossoró, v. 36, n. 1, p. 189 -198, jan. -mar., 2023 191 sense, is the genetic variance of the accessions, is the phenotypic variance; and , where is the heritability in the broad sense for the means of accessions, is the residual variance, and b is the number of replications (blocks) used for the evaluation of the accessions.The REML/BLUP analyses were carried out using the Selegen-REML/BLUP program (RESENDE, 2016).
The correlation between traits was estimated using the predicted genetic values (BLUP) of each accession, added to the overall mean of the experiment, resulting in the mean genotypic values.The analysis was carried out using the corrgram package of the R 3. The selection gains were predicted using four indexes: Smith-Hazel (SMITH, 1936;HAZEL;LUSH, 1943), with two combinations, varying the economic weights; rank sum index (MULAMBA; MOCK, 1978); and multiplicative index (ELSTON, 1963).Several combinations of economic weights were tested for the index that required them, focused on selecting the accessions with the best combinations regarding bromatological and morphological traits, for a selection intensity of 30%, allowing the selection of 20 accessions by all indexes used.The following economic weights were used for the Smith-Hazel index (Table 1).The indexes were calculated using the Selegen program (RESENDE, 2016). 1

RESULTS AND DISCUSSION
According to the analysis of deviance, the effect of accessions was significant for all evaluated traits (Table 2), denoting the existence of genetic variability among accessions and, therefore, the possibility of selection.The experimental precision through the selection accuracy results varied according to the characteristic evaluated.Considering the classification of Resende and Duarte (2007) for experimental evaluations, PH, PW, CD, CFW, ADF, NDF, and NFC had very high accuracy (above 90%); CL, CA, and CTPA had high accuracy (between 70% and 89%); CW, DMY, and TDN had moderate accuracy (between 41% and 69%); and TNC, (   ) 1 CDW, CGP, and EE had low accuracy (below 40%) (Table 3).
The estimates of the coefficient of genetic variation were below 25% for all traits, except for CGP (53.83%) (Table 3).Seven traits had coefficient of genotypic variation to coefficient of residual variance ratio (CVg/CVe) higher than one (PH, PW, CD, CFW, ADF, NDF, and NFC) (Table 3).
The values were higher than 0.80 for PH, PW, CD, CFW, ADF, NDF, and NFC (Table 3).CL, CW, DMY, CA, and CTPA had between 0.28 and 0.61; ; low magnitude estimates (<0.18) were found for TNC, CDW, CGP, and TDN.The genetic variance, confirmed by the significant effects of accessions found for all evaluated traits and expressed by the analysis of deviance, indicated that the collection of accessions in different regions of the state of Bahia contributed to the wide genetic variance found among the 65 forage cactus accessions evaluated.
The estimates of genetic parameters showed that a reliable selection can be done for the traits PH, PW, CW, CD, CFW, ADF, NDF, and NFC (Table 3).These traits had individual heritability in the broad sense (h 2 g) and heritability at genotype level (h 2 mg) above 60%, with a high accuracy (above 0.90).Paixão et al. ( 2011) evaluated eight forage cactus genotypes of the genera Opuntia and Nopalea and found significant genetic variations among the clones for plant height and width and cladode length and width, with heritability estimates above 88%, denoting good genetic control for all traits.Similar results were found in the present work for these traits, except for cladode width, which expressed low heritability.
According to Viana and Resende (2014), heritability is expressed in percentages (0% to 100%.):heritability values from 0% to 20% are low, 20 to 40% are moderate, and above 40% are high.The higher the heritability of a trait, the more accurate its predicted genetic value, resulting in immediate selection gains for the trait.
However, selection accuracy lower than 40% was found for four traits (TNC, CDW, CGP, and EE).This estimate considers the genotypic variance ; thus, the low magnitude of the estimates of this parameter for the four traits may have reduced the experimental precision.
Contrastingly, a high coefficient of residual variance was found in the determination of phenotypic values, implying low heritability, for the traits TNC (0.11), CL (0.34), CW (0.21), CDW (0.03), DMY (0.12), CA (0.30), CTPA (0.32), CGP (0.02), EE (0.03), and TDN (0.07).Quantitative traits are the most interesting for breeding programs, but their analysis is difficult, as hereditary variations of quantitative traits are masked by greater non-hereditary variations, hindering the determination of genotypes values of individuals (SMITH, 1936).Therefore, the analyses indicate that these traits are expressed by a high number of alleles and are highly affected by the environment.The heritability of these traits can be increased by decreasing environmental variation, using more complete statistical designs and more adequate statistical analyses to mitigate environmental effects on the phenotype expression (LIMA NETO; SIQUEIRA, 2017).
1 Heritability impacts of traits on the selection have been studied, showing that predictive models work relatively well, even for low-heritability traits (TOEBE et al., 2017).Grattapaglia and Resende (2011) reported that the accuracy increased by only 10-20% as the heritability increased from 0.2 to 0.6, regardless of the population size, indicating greater individual selection gains even for low-heritability traits.According to Toebe et al. (2017), tests with high selection accuracy present lower residual variance and greater genetic variance.
The analysis of the coefficient of genotypic variation (CVg) showed the amplitude of genetic variability in the studied population.Paixão et al. (2011) found higher CVg for CW (24.52%), and Santos et al. (1994) found CVg of 14.2% for CGP, 1.5% for gross fiber content, and 0.3% for phosphorus content.These results and the information about origin, introduction, and propagation mode of O. ficus-indica denote genetic variability, allowing the selection of accessions with the best allelic combinations for the evaluated traits.
Cladode gross protein (CGP) showed a low genetic variance and a high error variance, resulting in low estimates of heritability and accuracy.CGP is an important bromatological component related to the nutritional quality of O. ficus-indica cactus forage; adequate CGP contents are above 7% (AOAC, 2019).The low accuracy probably hindered the obtaining of selection gains because the CGP variation in the accessions was above 7% (9-18%).
Positive correlations of low magnitudes were found for CTPA × ADF and NDF × EE, showing the importance of selecting alleles that increase light interception capacity of the plant and, consequently, its photosynthetic potential, increasing forage yield and quality in O. ficus-indica plants.Pinheiro et al. (2014) found that the cladode area of the forage cactus clones IPA-Sertânia (N.cochenillifera) and Orelha-de-Elefante-Mexicana (O.stricta) expressed high and positive correlation to total number of cladodes.Similar results to the present study were reported by Guimarães et al. (2018), who also found increases in forage cactus yield due to an increased plant photosynthetic area.
Considering the need to optimize the research work and the positive correlations of high and high magnitudes found, it would be more feasible and practical for the study to measure only cladode dry weight, as the plant material is weighing on a precision balance after drying in an oven; whereas fresh weight may vary depending on the moment of collection until the packaging and transport of the material for weighing, impairing the sampling for these data.Therefore, the obtaining of fresh weight can be excluded from the analysis, proceeding immediately to the drying of cladodes, saving time and labor.
The importance of a large cladode photosynthetic area which results in greater plant yield, the easy measurement of cladode length and width when compared to the great complexity of measuring cladode area, and the positive correlations of high magnitudes between these traits make it possible to suggest a simple collection of data related to cladode dimensions to evaluate plant production.However, the data collection should be wider for taller plants, as they have greater number of cladodes and a higher plant yield.
Rev. Caatinga, Mossoró, v. 36, n. 1, p. 189 -198, jan. -mar., 2023 195 Thus, it is suggested to exclude from the analysis the determination of cladode total photosynthetic area and cladode area.Bromatological traits are correlated to each other and to other traits in a varied way, however, they are directly related to cladode dry weight.In this sense, cladode gross protein (CGP), non-fibrous carbohydrates (NFC), and ethereal extract (EE) area are negatively correlated to each other.Forage cactus plants do not meet adequate contents of these components, thus needing to be associated with other sources of energy, in addition to fiber, minerals, and concentrates.The limitations are great, however, increases in chemical and organic fertilizations may increase the contents of these sources, possibly, allowing for changes in the association of forage cactus with other sources of energy.
The second combination of economic weights of the Smith-Hazel index was evaluated considering the association between traits.The highest values found for traits of greater economic and agronomic impacts for forage cactus and neutral values for those that were directly correlate with these traits were used to reach the highest selection gains.Six traits presented positive selection gains, namely TNC (0.19%), CFW (11.49%),CDW (0.24%), DMY (0.55%), CGP (0.09%), and EE (0.03%) (Table 4).The other traits expressed negative selection gains when using this selection criterion.These results did not significantly favor selection gains for most traits when compared to the first combination.A small increase in traits of great impact was found for dry matter yield (DMY) and cladode gross protein (CGP).
SELECTION INDEXES AND PRINCIPAL COMPONENTS FOR AGRONOMIC AND BROMATOLOGICAL TRAITS IN FORAGE CACTUS M. S. JESUS et al.

Figure 1 .
Figure 1.Coefficients of genetic correlation for 17 agronomic and bromatological traits of 65 accessions of Opuntia ficus-indica.

Table 1 .
Economic weights assigned to bromatological and morphological traits by the Smith-Hazel selection index, in combinations 1 and 2.

Table 2 .
Analysis of deviance for the effects of accessions and the complete model, and maximum likelihood ratio test for agronomic and bromatological traits of 65 accessions of Opuntia ficus-indica.

Table 3 .
Estimates of components of variance and genetic parameters of 65 accessions of Opuntia ficus-indica by the REML/BLUP method.

Table 4 .
Estimates of genetic gains for traits, in unit and percentage, by selection index methods.