Impaginato 301 Adv. Hort. Sci., 2020 34(3): 301­311 DOI: 10.13128/ahsc­8103 Genetic parameters, correlations and path analysis in cowpea genotypes for yield and agronomic traits grown in Cerrado/Amazon Rainforest ecotone D. Herênio Gonçalves Júnior (*), L. De Melo Rodrigues, J. Alves de Santana Filho, W. Nascimento Lima, A. Ferreira Alves Laboratory of Plant Genetic Breeding (LMGV), Center for Agricultural Sciences and Technologies (CCTA), Brazil. Key words: genetic characterization, lines, plant breeding, productivity, Vigna unguiculata (L.) Walp. Abstract: The development of superior genotypes is the main objective of all plant breeding programs. To determine the genetic variability, heritability and correlations, 20 cowpea genotypes were grown in a randomized block design with four replications in Cerrado/Amazon Rainforest ecotone region. The data recorded were plant height, pod length, pod mass, pod grain mass, grain index, pod grain number and yield. Analysis of variance revealed significant differ­ ences between genotypes for all traits studied. The genotypic determination coefficient was high for all traits evaluated. Similarly, the accuracy parameter presented high estimates (>0.90). The magnitudes of the genotypic correlation coefficients were higher than the environmental and phenotypic correlations for most correlations, showing a greater influence of the genetic factor than the environmental factors. The direct and indirect effects provided greater reliabili­ ty in the cause and effect interpretations between the studied traits, indicating that yield can be explained through the effects of the analyzed traits. The traits pod mass (0.9628) and pod grain mass (0.7835) showed the greatest favorable direct effect, showing a strong association between the analyzed characters and can be used in direct or indirect selection for yield in cowpea. 1. Introduction Cowpea [Vigna unguiculata (L.) Walp.] is one of the oldest crops known to man and, because its moderate drought resistance, grows mainly in tropical climate areas (Egbadzor et al., 2014). Recent studies suggest it originated from Central Africa over 4,000 years ago (Ogunkanmi et al., 2014). According to Rocha et al. (2009), cowpea is a valuable legume, predominantly cultivated in Brazil, Africa and the United States. In the Brazilian North and Northeast regions, it is one of the main popula­ tion’s diet components, especially in rural areas (Santos et al., 2014). This crop still has low yields, despite the fact that its high adaptive potential to the conditions of tropical climate environments is verified (*) Corresponding author: juniorherenio@gmail.com Citation: HERÊNIO GONÇALVES JÚNIOR D., DE MELO RODRIGUES L., ALVES DE SANTANA FILHO J., NASCIMENTO LIMA W., FERREIRA ALVES A., 2020 ­ Genetic parameters, correlations and path analysis in cowpea genotypes for yield and agro‐ nomic traits grown in Cerrado/Amazon Rainforest ecotone. ­ Adv. Hort. Sci., 34(3): 301­311 Copyright: © 2020 Herênio Gonçalves Júnior D., De Melo Rodrigues L., Alves de Santana Filho J., Nascimento Lima W., Ferreira Alves A.This is an open access, peer reviewed article published by Firenze University Press (http://www.fupress.net/index.php/ahs/) and distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Competing Interests: The authors declare no competing interests. Received for publication 17 February 2020 Accepted for publication 30 June 2020 AHS Advances in Horticultural Science http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/ Adv. Hort. Sci., 2020 34(3): 301­311 302 (Leite et al., 2009). Teixeira et al. (2010) point out as causes the management techniques adopted and, mainly, the inefficiency of the technologies used and the use of traditional cultivars without breeding for yield. In Brazil there are cultivars with good commer­ cial acceptance, but breeding programs aimed at evaluation and recommendation in specific environ­ ments are concentrated only in large producing cen­ ters (Oliveira et al., 2002; Barili et al., 2015). One of the cowpea breeding programs basic goals is to obtain more productive genotypes. The avail­ ability of variance components estimates and genetic parameters such as coefficient of genetic variation, heritability and correlation coefficients for yield and their components are essential for the plant breeding programs development. These genetic parameters are characteristic of each population and may change in consequence of selection, changes in manage­ ment, methods and estimation models, among other causes. However, an important aspect about yield is that it is characterized as a complex variable, i.e., resulting from the expression and different components asso­ ciation (Santos et al., 2018). Correlation quantifies the association between any two variables. However, it does not allow inferences about cause and effect (Furtado et al., 2002). The path analysis, proposed by Wright (1921), allows to partition the correlation coefficient into direct and indirect effects (path coef­ ficient). For Cruz et al. (2014), this analysis can be defined as a standardized regression coefficient, being an expansion of the multiple regression analy­ sis when complex interrelationships are involved. In this sense, knowing the association between these traits allows the breeder to explore the possi­ bility of indirect selection in cases of traits with com­ plex inheritance and low heritability, such as yield. Correlation coefficient estimates make it possible to evaluate the magnitude and direction of the relation­ ship between two traits and, consequently, the possi­ bility of obtaining gains for one of them using indirect selection for the other trait. In some cases, indirect selection based on correlated response may be more effective and faster than direct selection of the desired trait (Cruz et al., 2014). Thus, this research was conducted with the objec­ tive of estimating the genetic parameters for the yield and its components in 20 cowpea genotypes population cultivated in the Cerrado/Amazon Rainforest ecotone region in Brazil. As well as, inves­ tigate the associations between traits to direct selec­ tion strategies in breeding programs with this crop. Study results may assist in strategies for breeding and manipulation of traits by cowpea breeders in Brazil or other similar environments. 2. Materials and Methods The experiment was carried out in Imperatriz city, Maranhão State, Brazil, in the experimental field of the Centro de Difusão Tecnológica (CDT) on premises of Empresa Brasileira de Infraestrutura Aeroportuária (INFRAERO) of geographic coordinates Latitude South 5°31’32’’ and Longitude West 47°26’35’’, and altitude of 123.30 meters. According to the Köppen climate classification, the region’s climate is Aw, tropical savanna, with tropical wet and dry climate (Peel et al., 2007). The survey of climate monitoring data for the region over the past 20 years was carried out. Data on annual total precipitation, maximum, minimum and average annual temperatures were collected. The data were obtained from an automatic climate monitoring station made available in the governmen­ tal meteorological database Banco de Dados Meteorológicos para Ensino e Pesquisa (BDMEP) administered by the Brazilian meteorology institute Instituto Nacional de Meteorologia (INMET). The time series graphs were produced using the ggplot2 pack­ age in the R software. The treatments consisted in twenty erect habit cowpea genotypes from the Active Germplasm Bank (AGB) from the Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA Meio Norte) cowpea genet­ ic breeding program, located in Teresina, Brazil, 15 lines and 5 cultivars, respectively: LF­3; LF­21; LF­30; LF­48; LF­49; LF­62; LF­104; LF­143; LF­144; LF­148; LF­153; LF­154; LF­155; LF­159; LF­168; BRS­Guariba; BRS­Tumucumaque; BRS­Nova Era; BRS­Itaim; and BRS­Cauamé. The soil physical and chemical characteristics were determined before the experiment beginning, from the superficial soil samples collected at random points in the experimental field up to 0.20 m depth. Soil texture was analyzed by the modified soil sedi­ mentation Bouyoucos method after addition of a dis­ persing agent. Potential acidity was estimated from SMP pH after pH determination in calcium chloride 0,01 mol L­1 (Shoemaker et al., 1961). Soil macronu­ trients and micronutrients analysis was performed to develop fertilizer recommendations. The experimental design was a randomized com­ plete block with 20 treatments and four replications. Herênio Gonçalves Júnior et al. ‐ Genotypic variability of cowpea in Amazon Rainforest 303 The experimental plot consisted of two lines of 4.0 m and spacing of 0.50 m between lines and 0.20 m between plants, constituting a total experimental area of 220.00 m². Soil tillage was carried out in a conventional manner with one plow and two har­ rows. The digging and sowing operations were manu­ al. From the chemical soil analysis, was performed the fertilization according to the requirements of the crop (Table 1). Irrigation was carried out by means of a sprinkler system sized to the crop and the region requirements, applying a daily water of 3.8 mm h­1. Invasive plants were controlled by hand weeding, performed weekly. Phytosanitary treatments were carried out through regular monitoring of pests and diseases, using the commercial insecticide Conect® when necessary. The harvest was performed when the pods of the plot were dry, totaling two harvests. The drying of the pods was completed in a forced air circulation oven, where the pods remained for two days at a temperature of 38°C. In the useful area of each plot were recorded the following data: plant height (PH): average height in cm randomly measured in five plants of the plot; pod length (PL): average length in cm of five randomly harvested pods in the plot useful area; pod mass (PM): in grams, considering the five previously har­ vested pods; pod grain mass (PGM): in grams, consid­ ering the grains of the five pods submitted to the aforementioned evaluations; grain index (GI): refers to the dry grain mass in the dried pods. It is obtained by the expression: GI = PGM/PM X 100 seeds per pod (SPP): performed by counting the seeds in the five pods harvested for the previous samples; and yield: estimate considering the yield in all the useful plot area (m2), extrapolating the value obtained for kg ha­1 correcting the value for grain mass to 13% moisture. The collected data were initially submitted to the Shapiro­Wilk test to verify the data set normality and the Bartlett test to verify if the error has homogene­ ity of variance (homoscedasticity), not presenting the need for data transformation. Subsequently, one­ way analysis of variance was performed to test the variability between genotypes, adopting the statisti­ cal model described in the equation below: Yij = µ + Gi + Bj + Ɛij where: Yij = observed trait value of the i­th genotype in the j­ th block; µ = general experimental mean; Gi = effect of the i­th genotype considered fixed; Bj = effect of the j­th block considered random; Ɛij = random error associated to the i genotype and j block observations. To understand the genotypic variability between the different traits measured, the components of phenotypic variance and genetic parameters were also estimated using the expressions suggested by Cruz et al. (2014): a) Phenotypic variance: σ 2P = MSg/b b) Environmental variance: σ 2E = MSE/b c) Genotypic variance: σ2G= (MSg ­MSE)/b d) Genotypic determination coefficient: R2 (σ2G/σ2P) x 100 e) Intraclass correlation coefficient: ICC = σ2G/(MSE+σ2G) x 100 f) Phenotypic coefficient of variation (%): PVC = √σ2P x 100 x ̅ g) Genotypic coefficient of variation (%): GCV = √σ2G x 100 x ̅ h) Environmental coefficient of variation (%): ECV = √MSE x 100 x ̅ i) b quotient: GCV ratio = σ 2G ECV MSE where: MSg is the mean square of genotypes; MSE is the mean square of error; b = number of blocks (replications) and x ̅ is the is the average of each trait. j) Accuracy: r ̂= (1 ­ 1/F) 0.5 where Snedecor’s F is the value of the variance ratio Table 1 ­ Soil chemical characterization used in the field experiment OM= organic matter; P= phosphorus; K= potassium; Ca= calcium; Mg= magnesium; Al= Aluminium; H+Al= potential acidity; SB= sum of bases; CEC= Cation exchange capacity; V= base saturation. pH (CaCl2) OM (g Kg­1) P (mg dm­³) K (cmol dm­³) Ca (cmol dm­³) Mg (cmol dm­³) Al (cmol dm­³) H+Al (cmol dm­³) SB (cmol dm­³) CEC (cmol dm­³) V (%) 4.8 18.4 13.5 0.26 1.66 0.69 0.00 1.70 2.61 4.31 60.5 Adv. Hort. Sci., 2020 34(3): 301­311 304 for treatment effects (genotypes) associated with analysis of variance (ANOVA). In the estimates of the correlations were used the expressions cited by Falconer (1987) and Ramalho et al. (1993): a) Phenotypic correlation: ϒP(XY) = COVP(XY) σ2PX ·σ2PY b) Genotypic correlation: ϒG(XY) = COVG(XY) σ2GX ·σ2GY c) Environmental correlation: ϒE(XY) = COVE(XY) σ2EX ·σ2EY where: ϒXY is the correlation between the characters X and Y; COVXY is the covariance between the charac­ ters X and Y; and, and σ2y ad σ2x are the variances of the characters X e Y, respectively. The unfolded of these correlations into direct and indirect effects of the six agronomic traits on yield was performed using the path analysis described by Cruz et al. (2014). The level of the multicollinearity of the X’X singular matrix was established by the prod­ uct of the respective diagonal element of X’X by the component of the residual variance according to the methodology proposed by Montgomery et al. (2012). After verifying the multicollinearity of the phenotypic correlation matrix, this was implanted in direct and indirect effects, considering the following equation: Y = p1X1 + p2X2 + .... + pnXn + pƐu where Y is the main dependent variable yield. X1, X2......, Xn are the independent variables. p1, p2, .. pn are the path coefficients. The coefficient of determi­ nation was calculated by the expression R2 = p21y + p22y + ... 2p2y.p2nϒ2n The estimates of the components of the pheno­ typic variance, genetic parameters, correlations between traits and path analysis were obtained using the computational application GENES (Cruz, 2013). 3. Results and Discussion Timeless climate data and information Over the past 20 years, the average annual air temperature has varied between 27.37 and 28.84°C (Fig. 1). The highest annual temperature observed was 35.22, in 2015. On the other hand, the lower annual temperature observed was 20.78°C, in 2018. The deviations observed for the maximum, minimum and average annual temperatures were ±0.57°C, ±0.70°C and ±0.41°C, respectively. Total annual pre­ cipitation ranged from 1961.30 mm in 2016, to 498.50 mm in 2000 (Fig. 1). Because this great differ­ ence between the results collected for total annual precipitation, there was a large deviation for this parameter, value equal to ±0358.38. The average of annual total precipitation over the last 20 years was 1395.85 mm. Estimates of genetic parameters The analysis of variance showed a significant effect (p<0.01) between the genotypes according to the F test for all evaluated characteristics (Table 2), showing genetic variability presence in the popula­ tion. Considering the existence of genetic variability in a population is a determining factor for any breed­ ing program (Ramalho et al., 2012), at first, the germplasm under study is promising for selection or hybridization work with potential for new cultivars development. Similarly, Araméndiz­Tatis et al. (2018) also detected significant differences for the same traits evaluated in an assay where they estimated the genetic parameters of traits associated with yield in 42 white seed cowpea genotypes. The relative standard deviation (RSD), which is used to estimate the experiments precision, present­ ed values considered low for the traits PH, PL, PM, MGV and GI, which indicates excellent experimental precision. While for the characteristics SPP and Yield presented RSD equal to 12.24% and 21.86%, there­ fore, they are considered regular values, indicating good experimental precision (Cruz et al., 2014; Ferreira, 2018) (Table 2). Similar results for the same Fig. 1 ­ Annual maximum temperature, annual minimum tempe­ rature, average annual temperature and total annual precipitation of the last twenty years (1998­2018) in a region characterized by the Cerrado/Amazon Rainforest ecotone (INMET, 2019). Herênio Gonçalves Júnior et al. ‐ Genotypic variability of cowpea in Amazon Rainforest 305 traits were obtained by Carvalho et al. (2012) and Correa et al. (2015). The variation index (VI), another parameter relat­ ed to the experimental precision, proposed by Gomes (1991), which is more adequate than the RSD, as it also considers the number of repetitions used in the experiment, besides the residual variation, pre­ sented low values for all traits, except for productivi­ ty that presented value of IV considered of medium magnitude. The success of the selection depends on the exis­ tence and magnitude of the observed genetic vari­ ability for yield and its components in the material under breeding (Adewale et al., 2010; Raturi et al., Table 2 ­ Analysis of variance summary for the traits plant height (PH), pod length (PL), pod mass (PM), pod grain mass (PGM), grain index (GI), seeds per pod (SPP) and Yield in 20 cowpea genotypes evaluated in Cerrado/Amazon Rainforest ecotone region, Brazil, 2019 DF= degrees of freedom; (**) significant at 1% probability of error by the F test; RSD= relative standard deviation; VI= variation index. Variation source DF PH (cm) PL (cm) PM (g) PGM (g) GI (%) SPP Yield (Kg ha­1) Mean square Blocks 3 46.46 1.61 5.54 5.05 112.71 75.61 120831.01 Genotypes 19 319.08 ** 4.28 ** 34.85 ** 13.43 ** 112.71 ** 238.99 ** 136000.33 ** Error 57 6.46 0.70 0.99 0.55 16.19 21.72 20004.46 Mean ­ 65.36 20.22 18.57 14.40 78.12 75.74 647.03 RSD (%) ­ 3.89 4.14 5.35 5.17 5.15 6.15 21.86 I.V. (%) ­ 1.95 2.07 2.68 2.59 2.58 3.08 10.93 2015; Shereen and El­Nahrawy, 2018). Table 3 shows there was low phenotypic variation (s) for the traits PL, PM, PGM, while for PH, GI and SPP a certain phe­ notypic variation was observed. For yield, there is a high phenotypic variation (s). The values estimated for genotypic variance (s) ranged from 0.89 for pod length (PL) to 78.15 for plant height (PH) (Table 3). Analyzing the genotypic variance (s) in relation to the phenotypic variance (s), it was observed there was a major contribution of genotypic variance (s) to the present phenotypic vari­ ability. These results were confirmed by the esti­ mates of the genotypic determination coefficient (R2) (Table 3). Table 3 ­ Estimates of genetic parameters for traits plant height (PH), pod length (PL), pod mass (PM), pod grain mass (PGM), grain index (GI), seeds per pod (SPP) and Yield in 20 cowpea genotypes evaluated in Cerrado/Amazon Rainforest ecotone region, Brazil, 2019 σ2F = phenotypic variance; σ2E = environmental variance; σ2G = genotypic variance; R2= genotypic determination coefficient; ICC= intra class correlation coefficient; PCV= phenotypic coefficient of variation; GCV= genotypic coefficient of variation; ECV= environmental coeffi­ cient of variation; b quocient = GCV/ECV ratio; r ̂= accuracy. Genetic parameters Traits PH (cm) PL (cm) PM (g) PGM (g) GI (%) SPP Yield (Kg ha­1) σ2F 79.77 1.07 8.71 3.36 28.18 59.75 34000.08 σ2E 1.61 0.17 0.71 0.14 4.05 5.43 5001.11 σ2G 78.15 0.89 8.46 3.22 24.13 54.32 28998.96 R2 (%) 97.98 83.15 97.17 95.87 85.64 90.91 85.29 ICC (%) 92.37 56.15 89.55 85.30 59.85 71.44 59.18 PCV (%) 13.66 5.12 15.89 12.73 6.80 10.21 28.50 GCV (%) 13.52 4.68 16.67 12.46 6.29 9.73 26.32 ECV (%) 3.89 4.14 5.35 5.17 5.15 6.15 21.86 b = GCV/ECV 3.48 1.13 2.93 2.41 1.22 1.58 1.20 r ̂ 0.99 0.91 0.99 0.98 0.93 0.95 0.92 Mean 65.36 20.22 18.57 14.40 78.12 75.74 647.03 306 Adv. Hort. Sci., 2020 34(3): 301­311 Cruz et al. (2014) mention that when the adopted statistical model considers genotypes as a fixed effect, as in the present study, heritability becomes the genotypic determination coefficient. The values of the genotypic determination coefficient (R2) ranged from 83.15% for PL to 97.9% for PH. All evalu­ ated traits presented high (R2) estimates (>75%). This parameter provides indications of the expected per­ formance of a given population for traits selection, which allows us to infer that the population in study is promising for the trait selection under study. However, it is noteworthy that for complex inheri­ tance characteristics such as yield, which are the expression result of many alleles and they are greatly influenced by the environmental conditions to which population undergoes, the high values of R2 may be overestimated by genotype x environment interac­ tion, since the present study was conducted in only one year and in a single environment. Torres et al. (2015), in a study to determine the number of measurements required, evaluated 40 genotypes of prostrate and semi­prostrate cowpea types in the state of Mato Grosso do Sul, in ten assays, the R2 ranged from 51.50% to 92.64%. While Shimelis and Shiringani (2010), in a study to deter­ mine the variance components and heritability in ten cowpea lines, obtained the genotypic determination coefficient of 55.00% for yield, lower than the value found in the present work. Given the high value of R2, it can be inferred that it is caused by the inherent genetic variability of the tested genotypes, because each of them contributes a distinct genetic identity (Teixeira et al., 2007). Fehr (1987) mentions that higher genotypic determination coefficients may be associated with lower environ­ ment variation and lower genotype­environment interaction. And according to Gomes (2009), there is low to medium accuracy in environmental control, since the relative standard deviations (RSD) were below 21% for all characters. The intraclass correlation coefficient (ICC), which corresponds to the repeatability coefficient, indicates an estimate of the total measurement variability frac­ tion owing to variations between individuals. The ICC ranged from 56.15% to 92.37% for pod length and plant height, respectively (Table 3). When character­ istics have a lower intraclass correlation coefficient require a greater number of measurements (replica­ tions) to predict the real value of a given trait and vice versa. Therefore, it can be inferred for the supe­ rior genotypes selection, the number of measure­ ments in the present study is satisfactory. The coefficients of variation provide information about the variation nature and magnitude. They clari­ fy if the variations are owing to genetic or environ­ mental causes. Typically, the GCV values are bigger than ECV. If the differences between GCV and ECV are excessive, so the environmental effects will be more noticeable on the trait. Thus, in the observed results, the relative proportion (%) of the deviations from the mean because of genetic effects (GCV) were higher when compared to the environmental ones (ECV), for all traits (Table 3). The genotypic coefficient of variation (GCV) ranged from 4.68% for pod length and from 26,32 to 26.32% for yield (Table 3). The highest estimates (GCV) were recorded for pod grain mass (12.46%), plant height (13.52%), pod mass (16.67%) and yield (26.32%), indicating that these traits offer greater selection perspectives to obtain genotypes much more aligned to the proposed, as they are erect habit and determined growth genotypes. These results are consistent with those found by Lopes et al. (2017) for yield and pod mass; Regis et al. (2014) for pod grain mass and grain index, and Bhagasara et al. (2017) for yield in this species. The characteristics plant height, pod length and seeds per pod showed lower GCV and, therefore, present greater difficulties in the selection process and expected genetic advance. Fact in agreement with Correa et al. (2015) and Silva and Neves (2011). However, Gerrano et al. (2015), found higher GCV values for plant height (67.41%), pod length (19.97%) and seeds per pod (24.82%). The b quotient is an auxiliary tool for the breeder. According to the interpretation of Cruz et al. (2014) for this parameter, when the value is greater than or equal to 1.00, it indicates that there is genetic vari­ ability within the population in study, which can therefore, be explored, and in the case, the trait is favorable to selection. The quotient b ranged from 1.13 for PL to 3.48 for PH (Table 3). Thus, it can con­ cluded that the b quotient values found for all evalu­ ated characteristics are favorable to selection in order to obtain more productive genotypes. Genotype evaluation assays should be approached from a genetic and statistical point of view, not just from a statistical perspective. In the context of genotypic evaluation, accuracy is the most important statistical parameter. It has the property of informing about the correct ordering of genotypes for selection purposes and also about the effective­ ness of inference about the genotypic value of each genotype (Resende, 2002). Herênio Gonçalves Júnior et al. ‐ Genotypic variability of cowpea in Amazon Rainforest 307 Accuracy depends not only on the residual varia­ tion magnitude and the number of replication, but also on the proportion between the genetic and resid­ ual variations associated with the trait under evalua­ tion. Accuracy refers to the correlation between the true genotypic value of genetic treatment and that estimated or predicted from the information from the experiments. As a correlation, it ranges from 0 to 1, and the appropriate accuracy values are those close to the unit or 100% (Henderson, 1984). Therefore, for all evaluated characteristics in the present experiment, the observed values for accura­ cy are considered very high, as they are above 0.90. High accuracy variables indicate small absolute devia­ tions between true genotypic values and those esti­ mated from experimental information. Resende and Duarte (2007) emphasize the importance of achiev­ ing optimal selective accuracy greater than 0.90 for safe statistical inference. Correlation between traits and path analysis Correlation estimates indicate good signal agree­ ment between phenotypic and genotypic correla­ tions (Table 4). In general, genotypic correlations pre­ sent values higher than their corresponding pheno­ typic and environmental correlations. Similar results were obtained by Andrade et al. (2010), Correa et al. (2015), Almeida et al. (2014), Gerrano et al. (2015), Teixeira et al. (2007) and Manggoel et al. (2012) in studies conducted with cowpea, evaluating yield components. There was a significant (p≤0.01) and high magni­ tude positive phenotypic correlation (ϒP) between the traits pod grain mass (PGM) and pod mass (PM), which was already expected, insofar that pod grain mass increase happens, it should also increase the pod mass, or vice versa. However, the traits grain index and seeds per pod presented negative pheno­ typic correlation at 1% probability (Table 4). For the other pairs of characteristics there were no signifi­ cant phenotypic correlations. Genotypic correlations (ϒG) showed the same sign and, in most cases, values higher than their corre­ sponding phenotypic correlations, indicating that the phenotypic expression is decreased because of envi­ ronmental influences. Although the yield compo­ nents were positively correlated with yield, the ϒP and ϒG estimates showed low magnitude and they Table 4 ­ Estimates of the correlation coefficients phenotypic (ϒP), genotypic (ϒG) and environmental (ϒE) between the traits plant height (PH), pod length (PL), pod mass (PM), pod grain mass (PGM), grain index (GI), seeds per pod (SPP) and Yield in 20 cowpea genotypes evaluated in Cerrado/Amazon Rainforest ecotone region, Brazil, 2019 NS= not significant; (*), (**) significant at 5% and 1%, respectively, by the t test. Characteristics ϒ PH PL PM PGM GI SPP Yield PH P 1 ­0.47* ­0.14 NS ­0.06 NS 0.15 NS ­0.35 NS 0.18 NS G 1 ­0.52* ­0.14 NS ­0.05 NS 0.18 NS ­0.37 NS 0.20 NS E 1 ­0.04 NS ­0.07 NS ­0.09 NS ­0.16 NS ­0.02 NS ­0.07NS PL P 1 0.06 NS 0.14 NS 0.11 NS ­0.02 NS 0.05 NS G 1 0.07 NS 0.14 NS 0.12 NS ­0.00 NS 0.04 NS E 1 0.04 NS 0.14 NS 0.06 NS 0.21 NS 0.07 NS PM P 1 0.90 ** ­0.64 ** 0.32 NS ­0.14 NS G 1 0.91 ** ­0.66 ** 0.34 NS ­0.16 NS E 1 0.44 ** ­0.47 ** 0.10 NS 0.10 NS PGM P 1 ­0.23 NS 0.18 NS ­0.03 NS G 1 ­0.31 NS 0.19 NS ­0.04 NS E 1 0.55 ** 0.04 NS 0.04 NS GM P 1 ­0.39 NS 0.26 NS G 1 ­0.43 NS 0.33 NS E 1 ­0.12 NS ­0.12 NS SPP P 1 0.12 NS G 1 0.12 NS E 1 0.11 NS Yield P 1 G 1 E 1 Adv. Hort. Sci., 2020 34(3): 301­311 308 were, mostly, non­significant. Cruz et al. (2012) attribute the genetic correla­ tions occurrence, mainly to the pleiotropy or to the genetic links between traits pairs, in the latter case, transient causes. In any case, genetic correlations favor the simultaneous selection of two or more traits by selecting only one of these. On the other hand, according to these authors, the selection of one trait may lead to an undesirable selection of another. The negative estimates of correlation between pairs of traits indicate that improving one trait will decrease the other, and in these cases, the selection based on this one is not recommended. The charac­ teristic plant height was phenotypically and geneti­ cally negatively correlated with pod length, indicating that the smaller the plant, the longer the pod length, which directly influences the yield. According to Falconer and Mackay (1996), genotypic and environ­ ment correlations of exchanged signals, as can be observed in some characteristics pairs (Table 4), reveal that the causes of genetic and environmental variation influenced the traits through different phys­ iological mechanisms. Given the complexity among the yield compo­ nents that contribute to yield, the selection of cow­ pea genotypes is difficult. Thus, it is evident the need to unfold the correlations in direct and indirect effects, evaluating the importance degree of each of the explanatory variables in relation to the main or basic variable (Daros et al., 2004). Cruz et al. (2014) report that the parameter esti­ mates under multicollinearity may assume absurd values or with no consistency to the studied biologi­ cal phenomena. Thus, for greater reliability of the path analysis results, the phenotypic correlation matrix between characteristics was tested for multi­ collinearity by the condition number proposed by Montgomery et al. (2012). The correlation matrix had a condition number equal to 993.97, that is, collinearity between the characters considered moderate to strong, present­ ing no problem for the path coefficients estimates. The coefficient of determination (R2) and the residual effect indicate how much the explanatory variables determine the yield. The coefficient of determination was 0.2025 and the residual effect was 0.8930 (Table 5). The direct effects magnitudes of the traits ana­ lyzed on yield were higher than the estimates magni­ tudes of their respective simple correlations with Table 5 ­ Estimates of direct and indirect effects involving the main variable, Yield in kg ha­1, and the explanatory vari­ ables: plant height, pod length, pod mass, pod grain mass, grain index, seeds per pod concerning to 20 cow­ pea genotypes evaluated in Cerrado/Amazon Rainforest ecotone region, Brazil, 2019 Characteristics Association effects Path coefficients Plant height Direct on Yield 0.3671 Indirect via PL ­0.0805 Indirect via PM ­0.1327 Indirect via PGM 0.0434 Indirect via GI 0.1162 Indirect via SPP ­0.1302 Total 0.1833 Pod length Direct on Yield 0.1711 Indirect via PH ­0.1727 Indirect via PM 0.0612 Indirect via PGM ­0.1058 Indirect via GI 0.0845 Indirect via SPP 0.0082 Total 0.0466 Pod mass Direct on Yield 0.9628 Indirect via PH ­0.0506 Indirect via PL 0.0109 Indirect via PGM ­0.7015 Indirect via GI ­0.4831 Indirect via SPP 0.1191 Total ­0.1425 Pod grain mass Direct on Yield 0.7835 Indirect via PH ­0.0203 Indirect via PL 0.0231 Indirect via PM 0.8621 Indirect via GI ­0.1774 Indirect via SPP 0.0664 Total ­0.0295 Grain index Direct on Yield 0.7593 Indirect via PH 0.0561 Indirect via PL 0.0190 Indirect via PM ­0.6126 Indirect via PGM 0.1831 Indirect via SPP ­0.1444 Total 0.2605 Seeds per pod Direct on Yield 0.3702 Indireto via PH ­0.1291 Indirect via CV 0.0038 Indirect via PM 0.3097 Indirect via PGM ­0.1407 Indirect via GI ­0.2963 Total 0.1177 Coefficient of determination 0.2025 Residual variable effect 0.8930 Herênio Gonçalves Júnior et al. ‐ Genotypic variability of cowpea in Amazon Rainforest 309 yield (Table 5). Based on this information, it is possi­ ble to infer there are other traits influencing both the magnitude and the correlation direction between the yield components. Considering the direct effects on yield, included in Table 5, the trait pod mass (0.9628) has the greatest effect, indicating a major contribution to the yield increase, surpassing the pod grain mass, which also had a high direct effect (0.7835). In contrast, pod length (0.1711) was the trait with the lowest effect. Important to mention there was no negative direct effect of any trait on yield. Still in Table 5, it can be seen that although the character PM had a high direct effect on yield, in general, the indirect effects via PM on yield were low. Indicating that indirect truncation selection in the auxiliary character may not provide satisfactory gains in the main variable (yield). In these cases, the best strategy is the multi­trait selection (Cruz et al., 2012). Indirect effects on yield were relatively low, except for the trait PGM via PM, which pointed to an estimate of 0.8621. This result is indicative of the indirect selection viability via pod mass to obtain gains on the most important character. The trait PH had negative indirect effect via all the characteristics, except GI, which indicates that the plant height reduction induces the increase in the other charac­ teristics, which is very important in this crop produc­ tion system, considering that plants very high hinder crop handling and harvesting. Considering the total effect, the traits have had the greatest effect on yield were as follows grain index (0.2605), plant height (0.1833), seeds per pod (0.1177) and pod length (0.0466) (Table 5). This result of the total effect in relation to the direct effects on yield was owing to the negative indirect effects via the other characteristics, which confirms the need to apply a multi­trait selection. Considering that the existence of genetic variabili­ ty in population is a determining factor for any breeding program (Ramalho et al., 2012), the germplasm under study is, initially, promising for selection or hybridization work with potential for the new cultivars development. 4. Conclusions The study concluded there is a considerable degree of genotypic variation between important agronomic traits in cowpea. Genotypic variation con­ tributed most of the phenotypic variation. Result cor­ roborated by the high estimates of genotypic deter­ mination coefficient. Thus, the genetic parameters estimates obtained for yield and agronomic traits, in the present study, will provide a basis for selection in order to obtain gains in the breeding for cowpea yield. The path analysis indicated the pod mass and pod grain mass had the greatest favorable effect on yield in cowpea, and could also be used for indirect selec­ tion aiming at the development of new genotypes with high yield potential. 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