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Relaciones lineales entre caracteres de la planta de frijol de cerdo (Canavalia ensiformis).

LINEAR RELATIONS AMONG TRAITS IN JACK BEAN (Canavalia ensiformis)

INTRODUCTION

Research with soil cover crops such as jack bean (Canavalia ensiformis) has demonstrated its importance in biomass production, soil covering rate, and nutrient accumulation (Cavalcante et al., 2012; Carvalho et al., 2013; Duarte et al., 2013). In plant breeding of soil cover crops, it is important to select plants with highest production of fresh and dry matter. In direct selection, the plant destruction is necessary to measure these traits. However, traits such as plant height, stem diameter, number of nodes, number of leaves, and number of pods can be measured nondestructively. These traits may or may not be linearly related with fresh and dry matter. If there are linear relations among these traits with fresh and dry matter it is possible to select indirectly without destroying the plants.

The Pearson's linear correlation coefficient (r) is appropriate for measuring the degree of relation among two traits, and Lenkala et al. (2015) utilized correlation coefficients to identify associations among jack bean traits. On the other hand, path analysis provides information about the interrelations among traits and is appropriate in the study of more than two traits, i.e., a dependent trait (main) in function of several independent traits (explanatories). In path analysis, the correlation coefficients are unfolded into direct and indirect effects, which makes possible to measure the influence of one variable on another independently of the others, i.e., enabling the study of the interrelationships between traits, unlike the Pearson's correlation that involves only two traits. Thus, it is important to apply these statistical procedures to identify cause and effect relations among traits. Traits with cause and effect relation can be used for indirect selection of plants.

Linear relations researches among traits of forage turnip (Raphanus sativus L.) and white lupine (Lupinus albus L.) indicated that the stem diameter and the number of pods per plant, respectively, have a positive linear relation with fresh and dry matter and it can be used for indirect selection of plants (Cargnelutti Filho et al., 2014). In black oat (Avena strigosa) Cargnelutti Filho et al. (2015) concluded that the number of leaves per plant and plant height are positively correlated with fresh and dry matter and can be used for indirect selection.

In 15 jack bean genotypes, Lenkala et al. (2015) found that it is possible to early select plants with largest number, length and mass of pods in order to have higher pods production. However, linear relations studies between the traits plant height, stem diameter, number of nodes, number of leaves, and number of pods with fresh and dry matter in jack bean were not found in the literature. It is supposed that these linear relations exist and that it is possible to use traits for indirect selection of plants with larger fresh and dry matter production. Thus, the objectives of this research were to evaluatethe linear relations amongtraits of jack bean and identifytraitsfor its indirect selection.

MATERIALS AND METHODS

An uniformity trial (experiment without treatments, in which the crop and all procedures performed during the experiment are homogeneous in the experimental area) was conducted with jack bean, cultivar Comum (Mapa, 2004), in experimental area 10m*16m located at 29[degrees]42'S, 53[degrees]49'W, with 95 m altitude. According to Koppen classification, the climate is subtropical humid, with warm summers and without dry season defined (Heldwein et al., 2009). The soil is classified as 'Argissolo Vermelho distrofico arenico' (Santos et al., 2013). A basic fertilization of 40, 150 and 100 kg-[ha.sub.-1] of N, [P.sub.2][O.sub.5]and [K.sub.2]O, respectively, was carried out on November 12, 2010. A row sowing was performed at the same day using 0.5m between rows and 0.125m between seeds in the row, totaling 16 seeds * [m.sup.-2]. Seeds with 99 % of purity and 70 % of germination were utilized.

There were 194 plants randomly selected in the experimental area on June 2nd, 2011 (202 days after sowing). The plants were in the grain maturation stage at this time. The plants were cut at the soil surface. Thereupon, the plant height (PH) and the stem diameter below the first node (SD) of each plant were measured. Also, the number of nodes on the main stem (NN), number of leaves (NL), and number of pods (NP) were counted. In each plant the pods were removed. The fresh matter of pods (FMP) and aerial part without pods (FMAPWP) were obtained by weighing, and the fresh matter of aerial part obtained by FMAP=FMP+FMAPWP. After drying in an oven, the dry matter of pods (DMP), aerial part without pods (DMAPWP), and the aerial part (DMAP=DMP+DMAPWP) were obtained. At harvest time, the number of plants was counted in three rows of 12.5 m randomly taken in the experimental area and obtained the density of 110,933 plants-[ha.sup.-1].

The mean and coefficient of variation of each trait were estimated with the data of 194 plants. The Pearson's linear correlation coefficient matrix was estimated between the traits for the study of linear relations, and the significance of r was verified through the Student's t-test. Following, a multicollinearity diagnosis (Cruz & Carneiro, 2003) was performed in the correlation matrix among PH, SD, NN, NL, and NP traits. The condition number (CN=[lambda]max/[lambda]min), which is obtained by the ratio between the maximum (Amax) and minimum (Amin) eigenvalue of the correlation matrix, was used to interpret the diagnostic of multicollinearity. It was considered low multicollinearity when the condition number was < 100, moderate to severe multicollinearity when 100 [less than or equal to] condition number [less than or equal to] 1,000, and severe multicollinearity when the condition number > 1,000, according to criteria of Montgomery & Peck (1982).

Thus, the path analyzes were conducted with each main traits (FMP, FMAPWP, FMAP, DMP, DMAPWP, and DMAP) in function of all explanatory traits (PH, SD, NN, NL, and NP), totaling six path analysis. The statistical analyzes were performed using Microsoft Office Excel and Genes software (Cruz, 2013).

The quantification of fresh and/or dry matter is usually done in research with soil cover crops such as jack bean (Cavalcante et al., 2012; Carvalho et al., 2013; Duarte et al., 2013). Those traits may show the cover crop potential as they influence the soil conditions and growth of following crops. Although a high association exists between the traits of fresh and dry matter (Cargnelutti Filho et al., 2014; Cargnelutti Filho et al., 2015), in this paper we used both of them as independent main traits under the assumption that they may add replications to the analysis and power the conclusions. The same consideration applies in the case of the summation of individual traits.

RESULTS AND DISCUSSION

The means of the traits (Table 1) showed adequate development of the crop. The coefficient of variation (CV) of 11 traits ranged from 19.04 % for the PH to 109.06 % for DMP, with average of 69.64 %. This variability may be explained by external conditions and possible genetic effects of the seeds from the S2 category (Mapa, 2004). Based on appropriate development of plants and in wide variability of the database allied to the large number of plants (194 plants), it can be inferred that this database provides credibility to the study of linear relations among these traits, through correlation and path analyzes.

The jack bean reached fresh and dry matter of 346.26 g-[plant.sup.-1] (38.41 Mg-[ha.sub.-1]) and 109.35 g-[plant.sup.-1] (12.13 Mg-[ha.sub.-1]), respectively (Table 1). These results are higher than those found by Cavalcanti (2011) and Cavalcante et al. (2012).

The FMP and DMP showed higher degree of linear association (greater r magnitude) with NP [average r = (0.822+0.835)/2 = 0.829], when compared to SD (average r = 0.222), NN (average r = 0.210), PH (average r = 0,150) and NL (average r = -0.123) (Table 1). This indicates that the NP would be most strongly associated with fresh and dry matter of jack bean pods. Therefore, it can be inferred that jack bean plants with larger number of pods also exhibit greater fresh and dry matter of pods. According to Lenkala et al. (2015), the production of pods per plant has a negative correlation with the number of days to 50 % flowering; the authors also observed high pod yield heritability and other production components of the jack bean.

The correlation coefficient of the NP with FMAPWP, FMAP, DMAPWP, and DMAP traits were not significant or significant with low magnitude (r = 0.280) (Table 1). Thereby, generally, it can be inferred the absence of linear relations between the number of pods with these traits.

The linear association of PH with FMAPWP, FMAP, DMAPWP, and DMAP traits presented low magnitude r values, i.e., between 0.485 and 0.539 (Table 1). In the study conducted by Lenkala et al. (2015), it was also found positive association of low magnitude between plant height with number and matter of pods per plant. Insomuch, it can be inferred that jack bean plants with greater height exhibit greater fresh and dry matter of aerial part without pods and greater fresh and dry matter of aerial part. Linear association with similar magnitude, i.e., between 0.475 and 0.547 was observed when comparing NN and FMAPWP, FMAP, DMAPWP, and DMAP traits. This signifies that jack bean plants with greater number of nodes presented greater fresh and dry matter of aerial part without pods and greater fresh and dry matter of aerial part.

Intermediate magnitude of linear association was observed regarding to SD and FMAPWP, FMAP, DMAPWP, and DMAP traits (0.770 [less than or equal to] r [less than or equal to] 0.831). This indicates that plants with greater stem diameter have greater fresh and dry matter of aerial part without pods and greater fresh and dry matter of aerial part. Moreover, linear association with greater magnitude was observed between NL and FMAPWP, FMAP, DMAPWP, and DMAP traits (0.847 [less than or equal to] r [less than or equal to] 0.957), indicating that plants with more leaves also have greater fresh and dry matter of aerial part without pods and greater fresh and dry matter of aerial part.

As mentioned, the FMP and DMP traits showed a greater linear positive association degree with NP and FMAPWP, FMAP, DMAPWP, and DMAP traits with NL (Table 1), which suggests that NP and NL could be used for indirect selection of plants. This linearity pattern is important for the traits identification towards indirect selection. However, it is not possible to infer which of the five explanatory traits studied has direct effect on the six main traits only through the correlation coefficients. Therefore, the path analysis is an appropriate procedure to indicate the true cause and effect relations among traits (Cruz & Carneiro, 2003; Cruz, 2013).

The multicollinearity diagnosis in the Pearson's linear correlation coefficient matrix between the explanatory traits revealed a condition number of 17.16 (Table 2). Therefore, the matrix showed low multicollinearity, according to criteria of Montgomery & Peck (1982). Thereby, it can be infer that path analyzes of the main traits of jack bean, in function of the studied explanatory traits were carried out in appropriate conditions.

The Pearson's linear correlation coefficients between the PH, SD, NN, and NL traits with fresh and dry matter of pods (FMP and DMP) showed low magnitude (r [less than or equal to] [absolute value of (0.249)]) and the direct effects were reduced (direct effect [less than or equal to] [absolute value of (- 0.2578)]), which indicates absence of linear relation of cause and effect between traits. Conversely, high magnitude linear association was observed between the NP and FMP (r = 0.822) and NP and DMP (r= 0.835) with direct effects of 0.8052 and 0.7537, respectively (Table 2). Therefore, as r and direct effect had the same sign and similar magnitude, it can be inferred that the number of pods have positive relation with the fresh and dry matter of pods and it can be used for indirect selection. The high magnitude linear association (r = 0.789) between the FMP and DMP traits (Table 1) explains the similar results of these two path analyzes (Table 2).

The Pearson's linear correlation coefficients between the NP with the FMAPWP, FMAP, DMAPWP, and DMAP traits were with low magnitude (r [less than or equal to] [absolute value of (0.280)]) and the direct effects were reduced (direct effect [less than or equal to] [absolute value of (0.2994)]), which confirms the absence of linear relation of cause and effect.

The traits PH, SD, and NN showed a positive linear correlation (0.475 [less than or equal to] r [less than or equal to] 0.831) with the traits FMAPWP, FMAP, DMAPWP, and DMAP. However, direct effects of PH, SD, and NN (direct effect [less than or equal to] [absolute value of (0.3107)]) on these four traits were reduced and/or inferior magnitude to r. Therefore, the association is explained by higher indirect effects via NL (0.2922 [less than or equal to] indirect effect [less than or equal to] 0.5237) (Table 2).

The NL showed a positive linear correlation (0.847 [less than or equal to] r [less than or equal to] 0.957) with the four traits (FMAPWP, FMAP, DMAPWP, and DMAP) and direct effect (0.6657 [less than or equal to] direct effect [less than or equal to] 0.7912) with the same sign and similar magnitude, confirming cause and effect relation between NL and FMAPWP, FMAP, DMAPWP, and DMAP traits. Thus, it can be inferred that the number of leaves has positive linear relation with fresh and dry matter of aerial part without pods and with fresh and dry matter of aerial part and it can be used for indirect selection.

The high linear association between the traits FMAPWP, FMAP, DMAPWP, and DMAP (0.912 [less than or equal to] r [less than or equal to] 0.993) (Table 1) explains the similar results of these four path analyzes (Table 2).

In practice, it can be inferred that the number of pods and leaves can be used for indirect selection of plants with greater production of fresh and dry matter. It is possible that plants with higher number of pods and leaves has developed better and, consequently, are plants with greater production of fresh and dry matter. The fact of not destroying the plants to count the number of pods and leaves is advantageous because it allows keeping the plants until seed production.

CONCLUSIONS

In jack bean, the number of pods has positive linear relation with fresh and dry matter of pods. The number of leaves has positive linear relation with fresh and dry matter of aerial part without pods and with fresh and dry matter of aerial part. The number of pods and leaves can be used for indirect selection.

ACKNOWLEDGEMENTS

We thank the National Council for Scientific and Technological Development (CNPq) and the Coordination for the Improvement of Higher Education Personnel (Capes) for granting scholarships.

LITERATURE CITED

1. Cargnelutti Filho, A., M. Toebe, C. Burin, B.M. Alves, G. Facco and G. Casarotto. 2014. Linear relations among characters of forage turnips and of white lupine. Ciencia Rural 44: 18-24.

2. Cargnelutti Filho, A., M. Toebe, B. Alves, C. Burin, G. Santos, G. Facco and I. Neu. 2015. Linear relations among characters of black oat. Ciencia Rural 45: 985-992.

3. Carvalho, W., G. Carvalho, D. Abba de Neto and L. Teixeira. 2013. Agronomic performance of cover crops used as ground cover mulching in the fallow period. Pesquisa Agropecuaria Brasileira 48:157-166.

4. Cavalcante, V., V. Santos, A. Santos Neto, M. Santos, C. Santos and L. Costa. 2012. Biomass production and nutrient removal by plant cover. Revista Brasileira de Engenharia Agricola e Ambiental 16:521-528.

5. Cavalcanti, N.B. 2011. Effect of different substrates on emergence the growth seedlings of jack bean (Canavalia ensiformes L.). Engenharia Ambiental 8:51-70.

6. Cruz, C.D. 2013. GENES - a software package for analysis in experimental statistics and quantitative genetics. Acta Scientiarum Agronomy 35:271-276.

7. Cruz, C. and P. Carneiro. 2003. Modelos biometricos aplicados ao melhoramento genetico. UFV, Vicosa. V.2. 585 p.

8. Duarte, R., L. Fernandes, R. Sampaio, L. Santos, P. Grazziotti and H. Silva. 2013. Biomass yields, soil cover, content and accumulation of nutrients of some green manure legumes grown under conditions of north of Minas Gerais, Brazil. African Journal of Agricultural Research 8: 2430-2438.

9. Heldwein, A., G. Buriol and N. Streck. 2009. O clima de Santa Maria. Ciencia e Ambiente 38: 43-58.

10. Lenkala, P., K. RadhaRani, N. Sivaraj, K. Ravinder Reddy and M. Jaya Prada. 2015. Genetic variability and character association studies in Jack bean [Canavalia ensiformis (L.) DC.] for yield and yield contributing traits. Electronic Journal of Plant Breeding 6: 625-629.

11. MAPA (Ministerio da Agricultura, Pecuaria e Abastecimento). 2004. Regulamento da lei-No 10.711, de 5 de agosto de 2003, que dispoe sobre o sistema nacional de sementes e mudas (SNSM). MAPA, Brasilia. 49 p.

12. Montgomery, D. and E. Peck. 1982. Introduction to linear regression analysis. Wiley. New York.

13. Santos, H., P. Jacomine, L. Anjos, V. Oliveira, J. Oliveira, M. Coelho et al. 2013. Sistema brasileiro de classificacao de solos. Embrapa. Brasilia, DF. 353 p.

Alberto Cargnelutti Filho (1), *, Marcos Toebe (2), Bruna Mendonca Alves (3), Claudia Burin (4) y Cleiton Antonio Wartha (5)

Received: October 2, 2017

Accepted: March 26, 2018

(1) Dpto. de Fitotecnia, Centro de Ciencias Rurais (CCR), Universidade Federal de Santa Maria (UFSM), 97105-900, Santa Maria, RS, Brasil. e-mail: alberto.cargnelutti.filho@gmail.com * Corresponding author.

(2) Universidade Federal de Santa Maria, Frederico Westphalen, RS, Brasil. e- mail: m.toebe@gmail.com

(3) Programa de Pos-Graduacao em Agronomia, Universidade Federal de Santa Maria, Santa Maria, RS, Brasil e-mail: brunamalves11@gmail.com

(4) Programa de Pos-Graduacao em Engenharia Florestal, UFSM, Santa Maria, RS, Brasil e-mail: clauburin@gmail.com

(5) Programa de Pos-Graduacao em Fitotecnia, Universidade Federal de Vicosa, UFV, Vicosa, MG, Brasil e-mail: cleiton.ufsm@gmail.com
Table 1. Mean, coefficient of variation (CV) and estimates of the
Pearson's linear correlation coefficients among traits measured
in 194 plants of jack bean (Canavalia ensiformis)._

Trait (1)    Mean    CV (%)       Pearson's linear correlation
                                       coefficients (2)

                               PH      SD      NN       NL       NP

PH          132.51   19.04      1
SD          13.49    25.17    0.559     1
NN          23.18    20.89    0.836   0.560     1
NL          28.51    95.65    0.448   0.662   0.439     1
NP           1.72    91.31    0.114   0.204   0.173   -0.131     1
FMP         55.39    106.32   0.174   0.249   0.236   -0.035   0.822
FMAPWP      290.87   84.14    0.485   0.770   0.475   0.957    -0.067
FMAP        346.26   73.23    0.508   0.801   0.513   0.915    0.127
DMP         23.54    109.06   0.126   0.196   0.184   -0.211   0.835
DMAPWP      85.81    78.07    0.507   0.781   0.494   0.954    -0.032
DMAP        109.35   63.12    0.539   0.831   0.547   0.847    0.280

Trait (1)   Pearson's linear correlation coefficients (2)

             FMP    FMAPWP   FMAP     DMP     DMAPWP   DMAP

PH
SD
NN
NL
NP
FMP           1
FMAPWP      0.032     1
FMAP        0.263   0.973      1
DMP         0.789   -0.141   0.047     1
DMAPWP      0.051   0.993    0.971   -0.111     1
DMAP        0.343   0.912    0.960   0.264    0.929     1

(1) PH-plant height, in cm; SD-stem diameter, in mm; NN-number
of nodes on the main stem; NL-number of leaves; NP-number of pods;
FMP-fresh matter of pods, in g-plant-1; FMAPWP-fresh matter of
aerial part without pods, in g-[plant.sup.-1]; FMAP-fresh matter of
aerial part, in g-[plant.sub.-1]; DMP - dry matter of pods, in
g-[plant.sup.-1]; DMAPWP-dry matter of aerial part without pods,
in g-[plant.sup.-1]; DMAP-dry matter of aerial part, in
g-[plant.sup.-1]. (2) Correlation coefficients > [valor absoluto
de (0,18)] are significant at 1 % of probability for the Student's
t-test with 192 degrees of freedom.

Table 2. Estimates of the direct and indirect effects (path
analysis) of the traits plant height (PH), stem diameter (SD),
number of nodes on the main stem (NN), number of leaves (NL),
and number of pods (NP) on fresh matter of pods (FMP), fresh
matter of aerial part without pods (FMAPWP), fresh matter of
aerial part (FMAP), dry matter of pods (DMP), dry matter of
aerial part without pods (DMAPWP), and dry matter of aerial
part (DMAP), measured at 202 days after sowing in
194 plants of jack bean (Canavalia ensiformis).

Effect                                       Main traits

                                   FMP         FMAPWP       FMAP

Direct of PH on                  -0.0135      -0.0008      -0.0040
Indirect of PH via SD             0.0190       0.1437      0.1431
Indirect of PH via NN             0.0683      -0.0113      0.0050
Indirect of PH via NL             0.0080       0.3548      0.3443
Indirect of PH via NP             0.0919      -0.0015      0.0199
Pearson correlation (r)         0.1738 ns     0.4849 *    0.5084 *
Direct of SD on                   0.0341       0.2572      0.2562
Indirect of SD via PH            -0.0075      -0.0005      -0.0022
Indirect of SD via NN             0.0458      -0.0076      0.0033
Indirect of SD via NL             0.0119       0.5237      0.5082
Indirect of SD via NP             0.1645      -0.0027      0.0356
Pearson's correlation (r)        0.2487 *     0.7702 *    0.8011 *
Direct of NN on                   0.0817      -0.0135      0.0059
Indirect of NN via PH            -0.0113      -0.0007      -0.0033
Indirect of NN via SD             0.0191       0.1440      0.1435
Indirect of NN via NL             0.0079       0.3472      0.3370
Indirect of NN via NP             0.1391      -0.0023      0.0301
Pearson's correlation (r)        0.2365 *     0.4748 *    0.5132 *
Direct of NL on                   0.0179       0.7912      0.7679
Indirect of NL via PH            -0.0061      -0.0004      -0.0018
Indirect of NL via SD             0.0225       0.1703      0.1696
Indirect of NL via NN             0.0359      -0.0059      0.0026
Indirect of NL via NP            -0.1055       0.0017      -0.0228
Pearson's correlation (r)       -0.0352 ns    0.9569 *    0.9154 *
Direct of NP on                   0.8052      -0.0131      0.1744
Indirect of NP via PH            -0.0015      -0.0001      -0.0005
Indirect of NP via SD             0.0070       0.0526      0.0523
Indirect of NP via NN             0.0141      -0.0023      0.0010
Indirect of NP via NL            -0.0024      -0.1037      -0.1006
Pearson's correlation (r)        0.8224 *    -0.0666 ns   0.1267 ns
Coefficient of determination      0.6870       0.9492      0.9313
Residual variable                 0.5594       0.2253      0.2622
Condition number                  17.16        17.16        17.16

Effect                                      Main traits

                                   DMP        DMAPWP       DMAP

Direct of PH on                  0.0007       0.0260      0.0255
Indirect of PH via SD            0.0971       0.1416      0.1736
Indirect of PH via NN            0.0576      -0.0149      0.0070
Indirect of PH via NL            -0.1156      0.3519      0.2985
Indirect of PH via NP            0.0861       0.0022      0.0342
Pearson correlation (r)         0.1258 ns    0.5068 *    0.5387 *
Direct of SD on                  0.1738       0.2535      0.3107
Indirect of SD via PH            0.0004       0.0145      0.0142
Indirect of SD via NN            0.0386      -0.0100      0.0047
Indirect of SD via NL            -0.1707      0.5194      0.4406
Indirect of SD via NP            0.1540       0.0040      0.0612
Pearson's correlation (r)       0.1961 *     0.7814 *    0.8314 *
Direct of NN on                  0.0690      -0.0178      0.0083
Indirect of NN via PH            0.0005       0.0217      0.0213
Indirect of NN via SD            0.0973       0.1419      0.1740
Indirect of NN via NL            -0.1132      0.3444      0.2922
Indirect of NN via NP            0.1301       0.0034      0.0517
Pearson's correlation (r)       0.1838 *     0.4936 *    0.5474 *
Direct of NL on                  -0.2578      0.7847      0.6657
Indirect of NL via PH            0.0003       0.0116      0.0114
Indirect of NL via SD            0.1150       0.1678      0.2056
Indirect of NL via NN            0.0303      -0.0078      0.0037
Indirect of NL via NP            -0.0987     -0.0026     -0.0392
Pearson's correlation (r)       -0.2110 *    0.9538 *    0.8472 *
Direct of NP on                  0.7537       0.0196      0.2994
Indirect of NP via PH            0.0001       0.0030      0.0029
Indirect of NP via SD            0.0355       0.0518      0.0635
Indirect of NP via NN            0.0119      -0.0031      0.0014
Indirect of NP via NL            0.0338      -0.1028     -0.0872
Pearson's correlation (r)       0.8349 *    -0.0315 ns   0.2800 *
Coefficient of determination     0.7305       0.9503      0.9244
Residual variable                0.5191       0.2229      0.2749
Condition number                  17.16       17.16       17.16

* Significant at 1 % of probability for the Student's t-test
with 192 degrees of freedom. ns: non significant.
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Title Annotation:TECHNICAL NOTE
Author:Cargnelutti Filho, Alberto; Toebe, Marcos; Mendonca Alves, Bruna; Burin, Claudia; Antonio Wartha, Cl
Publication:BIOAGRO
Date:Aug 1, 2018
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