Genetic variability and linear relationships between plant architecture and maize grain yield

The objectives of this study were to analyze whether there is genetic variability and assess the linear relationships between plant architecture and maize grain yield. Three experiments were carried out in a complete randomized block design. A group of 51 cultivars was assessed in relation to 22 traits: number of leaves, plant height, ear height, leaf angle, leaf length, leaf width, leaf area, and grain yield. Individual analyses of variance were performed, the assumptions of normality of errors and homogeneity of residual variances were tested, and means were grouped by the Scott-Knott test. The phenotypic correlation matrix was constructed using the 22 traits of the 51 cultivars. Results showed that there is genetic variability among cultivars for number of leaves, plant height, ear height, leaf angle, leaf length, leaf width, leaf area, and grain yield. Leaves close to the ear have smaller leaf angle and larger length, width, and area of the leaves. Leaf angle gradually increases towards the lower and upper ends of the plant. Length, width, and area gradually decreases in leaves towards the lower and upper ends of the plant. Cultivars with higher number of leaves and larger leaf area are associated with higher grain yield.


INTRODUCTION
Because of the great importance of maize (Zea mays L.), plant breeding programs have developed new genotypes seeking to improve plant architecture and enhance grain yield. Therefore, it is necessary to evaluate the genotypes regarding plant architecture traits such as leaf number, plant height, ear height, leaf angle, leaf length, leaf width, leaf area, and grain yield to distinguish the genotypes in the crop environment.
Traits related to plant architecture in maize are important to define population and spatial distribution of plants in the area. Adequate spatial distribution and population can increase the interception of solar radiation and its use efficiency, as well as increase grain yield due to the influence on leaf area index, leaf angle, and leaf distribution in the canopy (ARGENTA et al., 2001). To achieve high grain yields, it is important to understand the morphological, physiological, phenological, and allometric characteristics that contribute to better adaptation of maize to high plant densities (SANGOI et al., 2002).
One of the objectives of maize breeding programs is to select plants with high grain yield. For a direct selection of plants with higher grain yield, it is necessary to harvest the ears to obtain grain weight, destroying the plant. Plant architecture traits, such as leaf number, plant height, ear height, leaf angle, leaf length, leaf width, and leaf area can be measured in a non-destructive way. An indirect selection, without destroying the plant, is possible when there are linear relationships between the mentioned traits and grain yield. The Pearson linear correlation coefficient (r), which varies between -1 (perfect negative linear relationship) and 1 (perfect positive linear relationship), is able to measure the strength of association between two variables and can be used to indicate the traits for indirect plant selection.
It is believed that maize cultivars have varied plant architecture and grain yield, and that it is possible to find linear relationships between these traits. Thus, the objective of this research was to verify the existence of genetic variability and to evaluate the linear relationships between plant architecture and maize grain yield.
Experiment 1 consisted of 26 maize cultivars from the maize cultivar trial network of Rio Grande do Sul, which is coordinated by the State Agricultural Research Foundation (FEPAGRO). Experiments 2 and 3 refer to the national maize cultivar trial network coordinated by the Brazilian Agricultural Research Corporation (EMBRAPA). Experiment 2 included 13 cultivars of early cycle maize from the national trial in the south and experiment 3 included 12 super-early maize cultivars from the national trial (Table 1).
The experiments were carried out in a complete randomized block design, with three replicates in experiment 1 and two replicates in experiments 2 and 3. Plots in all three experiments consisted of two 5-m-rows, 0.80 m apart, and plants in a 0.20 m in-row spacing. Cultivars were sowed by hand on November 19, 2016, using basal fertilization (20 kg ha -1 of N, 80 kg ha -1 of P 2 O 5 , and 80 kg ha -1 of K 2 O).
After crop emergence and establishment, plant thinning was carried out by hand, and plant density was adjusted to 62,500 plants per hectare. Topdressing fertilization was divided into two applications: on the 4 th and 19 th of December 2016, when the plants had four and eight expanded leaves, respectively. Each application consisted of 90 kg ha -1 of N, totalizing 180 kg ha -1 of N topdressed.
At flowering (50% stamens with pollenreleasing anthers), one plant in each plot was labeled, and the leaves were numbered in ascending order from the plant base (the leaf closest to the soil was numbered as 1). In each plant, the number of leaves (NL), the number of leaves below the ear (NLBE) and the number of leaves above the ear (NLAE) were counted. Plant height (PH, in cm) and ear insertion height (EIH, in cm) were measured. Leaf angle (AG, in degrees) was measured on each leaf of each plant. The leaf insertion angle represents the inclination between the central rib of the leaf blade and the stem and was measured using a "Clinometer ® "+ bubble level ® "). Leaf length (LL, in cm) and maximum leaf width (LW, in cm) were measured. The leaf area (LA, in cm 2 ) was estimated for each leaf using the equation: LA = LL×LW×0.75 (ELINGS, 2000).
Following, each plant was divided into portions (lower, middle and upper), according to the Table 1 -Cultivar, company, genetic basis, cycle, and grain texture of the maize cultivars assessed in the three experiments.

Cultivar
Company Genetic basis Cycle Grain texture     At physiological maturity, when 50% of the kernels have formed black layers at the point of attachment of the kernel to the cob, the corn ears were harvested and threshed. The grain was weighed using a digital scale and the moisture content was determined using an electronic moisture meter. Grain mass was corrected to 13% moisture and grain yield was calculated (GY, in g plant -1 ).
In all three experiments, analysis of variance was carried out for each of the 22 traits (NL, NLBE, NLAE, PH, EIH, AGP, AGL, AGM, AGU, LLP, LLL, LLM, LLU, LWP, LWL, LWM, LWU, LAP, LAL, LAM, LAU, and GY), using the following mathematical model: Y ij =m+C i +B j +e ij , where Y ij represents the value of the variable Y of the i th cultivar (i = 1, 2,...,n) in the j th repetition (block) (j = 1, 2, ..., r); μ is the overall mean; C i is the effect of the i th cultivar (i = 1, 2, ..., n) (fixed effect); B j is the effect of the j th repetition (block) (j = 1, 2, ..., r); and e ij is the effect of the experimental error referring to the observation Y ij , supposedly normal, independent and distributed with zero mean and common variance s 2 (STORCK et al., 2016). The following statistics were recorded: F test for cultivar (F), mean, and coefficient of variation (CV). The p-value of the Kolmogorov-Smirnov test was determined for error normality and the p-value of the Bartlett test was determined for residual variance homogeneity. The selective accuracy was estimated using the equation SA = (1-1/F) 0,5 (RESENDE & DUARTE, 2007). The cultivar means were grouped using the Scott-Knott test, at 5% significance.
The Pearson correlation coefficient matrix (r, phenotypic correlation) between the 22 traits was constructed using the means of the repetitions. The Student t test at 5% significance was used to verify the coefficient significance, with n-2 = 49 degrees of freedom, where n = 51 maize cultivars. Statistical analyzes were performed using Microsoft Office Excel application and the Genes program (CRUZ, 2016).

RESULTS AND DISCUSSION
In the 66 experimental cases (22 traits × three experiments), the p-value of the Kolmogorov-Smirnov tests ranged between 0.106 and 0.999 and the Bartlett test between 0.020 and 0.999 (Table 2). For both tests, the greater the p-value the greater the evidence of error normality and residual variance homogeneity. Therefore, at a 2% significance level, it can be affirmed that the assumptions were met in 100% of the cases and the results of the analysis of variance and Scott-Knott test were statistically valid (STORCK et al., 2016).
The F test of the analysis of variance showed significant effect (p≤0.05) of cultivars in 22 traits (100%) in experiment 1 (maize cultivars from Rio Grande do Sul); 4 traits (18.2%) in experiment 2 (early cycle south maize cultivars from the national experiment); and 5 traits (22.7%) in experiment 3 (super-early maize cultivar from the national trial in the Southern Region) ( Table 2). Results indicated that it is possible to select superior genotypes from the genetic variability existing in the germplasm, especially among the 26 cultivars in experiment 1. The experiments 2 and 3 had a lower number of replications and cultivars than experiment 1. This        may have contributed to the lack of differences among cultivars in 18 traits in experiment 2 and in 17 traits in experiment 3. A higher number of replications is important to increase cultivar discrimination, and six replications is recommended for experiments with maize cultivars (CARGNELUTTI FILHO et al., 2018). Coefficient of variation (CV) for the 22 traits ranged between 3.71% and 16.94% in experiment 1; 4.84% and 22.44% in experiment 2; and 4.40% and 24.72% in experiment 3 ( Table  2). CV is a statistical tool widely used to measure the experimental precision. PIMENTEL-GOMES (2009) ranked the CVs in agricultural experiments as follows: low (below 10%); medium (between 10 and 20%); high (between 20 and 30%); and very high (above 30%). Thus, it can be inferred that for 14, 11, and 11 traits in experiments 1, 2, and 3, respectively, the experimental precision was high (CV under 10%); for 8, 10, and 9 traits in experiments 1, 2 and 3, respectively, the experimental precision was medium (CV between 10 and 20%); and for 1 and 2 traits, in experiments 2 and 3, respectively, the experimental precision was low (CV between 20 and 30%).
Selective accuracy (SA), a statistics of experimental precision proposed by RESENDE & DUARTE (2007), varied between 0.76 and 0.94, in experiment 1, between 0.13 and 0.87, in experiment 2, and between 0.21 and 0.93, in experiment 3. Experiments 2 and 3 reached the lowest SA and, because F was below 1, it was not possible to calculate SA for 5 and 6 traits, respectively ( Table  2). Experiment 1 had the highest experimental accuracy compared with experiments 2 and 3, which is in agreement with the findings of CARGNELUTTI FILHO et al. (2018) regarding the need of a higher number of repetitions. Thus, the cases with no significant differences among cultivars identified by the F test are related to lower experimental precision.
For the 22 traits, using the Scott-Knott test, at 5% significance, the groups of cultivars varied between 1 and 4, in experiment 1 and between 1 and 2, in experiments 2 and 3 (Tables 3 and 4). Therefore, the highest number of groups confirmed the greatest variability among cultivars in experiment 1. This can be explained by the highest experimental precision Considering the 51 cultivars (26, 13 and 12 cultivars in experiments 1, 2 and 3, respectively), the number of leaves varied between 12.7 and 17.3, with an average of 15.0 leaves. Similar variations were reported in other studies, between 12 and 16 leaves per plant in 20 maize genotypes (VIEIRA JUNIOR et al., 2005) and between 9 and 14 leaves per plant in 44 maize genotypes (VIEIRA JUNIOR et al., 2006). SANGOI et al. (2002) assessed three genotypes and reported a variation in the average number of leaves between 18.4 and 23.2 leaves. The average number of leaves below the ear (8.2 leaves) was higher in relation to the number of leaves above the ear (6.8 leaves) (Table 3). HANASHIRO et al. (2013) also obtained variation between 6 and 7 leaves above the ear.
Among the 51 cultivars, EIH varied between 103.8 and 150.4 cm and PH between 204.4 and 261.0 cm. The average of the 51 cultivars for the relative position of the ears, as calculated by the ratio between EIH (123.3 cm) and PH (234.9 cm), was 0.52 cm. This may explain the higher number of leaves below the ear (Table 3) SANGOI et al. (2002). Therefore, there is a wide genetic variability of EIH and PH in maize. The development of less tall hybrids and ears closer to the ground reduced the number of lodged and broken plants (SANGOI et al., 2002).
Plant leaf angle (AGP) among the 51 cultivars ranged between 14.8º and 34.1º, with an average of 23.7º. Leaf angle averages in the lower, middle and upper portions were 27.7º, 21.4º, and 21.7º, respectively. This showed a greater inclination of the leaves at the base of the plant in relation to the middle and upper portions ( Table 3). The leaf angle gradually decreased from the basal leaves towards the upper leaves. Similar results were reported by VIEIRA JUNIOR et al. (2005) in a study to estimate the population and spatial arrangement of maize according to the canopy architecture and            Grain yield is increased in plants with more upright leaves, with smaller leaf angles, which allow plant density to be increased, and favor light capture for photosynthesis (TIAN et al., 2011;ZHANG et al., 2014;HUANG et al., 2017). An ideotype of a compact plant, having shorter plants with fewer and more erect leaves, improves the quality of light within the canopy and reduces the dominance of the tassel (apical) over the ears (SANGOI et al., 2002). In this sense, the selection of plants with smaller leaf insertion angle, larger stem diameter, and higher thousand-grain mass may increase grain yield (NARDINO et al., 2016).
A similar pattern was observed in relation to leaf width (LWP), which varied between 7.7 and 10.1 cm, with average of 8.9 cm (Table 4). Higher values were found by VIEIRA JUNIOR et al. (2005): between 21 and 27 cm. Similar values were found by VIEIRA JUNIOR et al., 2006: between 4.5 and 14.5 cm. The average leaf width in this study (8.9 cm) was similar to the results reported by KU et al. (2010) (8.89 cm) and WASSOM (2013) (9.1 cm). Leaf width gradually increased from the lower portion (average= 8.0 cm) and the upper portion (average= 8.5 cm) towards the middle portion (average = 10.4 cm) of the plant.
Plant leaf area (LAP) varied between 6,343 and 10,808 cm 2 , with average of 8,492 cm 2 . The patterns for leaf length and leaf width can explain the gradual increase of the leaf area in the lower portion (average=2,534 cm 2 ) and the upper portion (average= 2,177 cm 2 ) towards the middle portion (average = 3,781 cm 2 ). Similar leaf area, between 1,177.67 and 9,244.24 cm 2 , was estimated by VIEIRA JUNIOR et al. (2006). Conversely, HANASHIRO et al. (2013) assessed maize cultivars and found two groups in relation to the leaf area of the leaf above and opposite to the first ear: the first group varied between 796 and 883 cm 2 and the second group between 668 and 783 cm 2 , which was lower than the results of this study. Cultivars with high leaf areas and leaves with greater insertion angle demand more space between the rows and lower plant density per area, in order to minimize competition for water, light, and nutrients, which results in lower yield.
Results showed that the leaves close to the ear (middle portion) had smaller leaf angle and greater leaf length, leaf width, and leaf area. There was a gradual increase of leaf angle towards the leaves at the lower end of the plant, while a gradual decrease of leaf length, leaf width, and leaf area occurred towards the leaves at the lower and upper end of the plant. Therefore, in relation to the basal leaves, the leaves close to the ear were more erect, longer, wider, and had greater leaf area.
Grain yield (GY) ranged between 119 and 227 g plant -1 , with an average of 179 g plant -1 (Table  4). Similar results were described by HANASHIRO et al. (2013), who found grain yield ranging from 5,926 to 14,419 kg ha -1 in a population of 60,000 plants ha -1 , resulting in 98.77 and 240.32 g plant -1 , respectively. In the 2008/2009harvest year, TOEBE et al. (2014 reported the following values for grain yield per plant: 131.44, 153.25 and 144.85 g plant -1 , for single, triple, and double hybrids, respectively. In the 2009/2010 harvest year, the numbers were recorded as follows: 115.68, 116.62, and 86.37 g plant -1 for single, triple, and double hybrids, respectively, which were values below those found in the present study. The Pearson's correlation coefficient (r) showed a positive linear association between the traits NL and NLBE (r = 0.72) and NL and NLAE (r = 0.63). Plants with greater height are associated with higher ear insertion height (r = 0.75). The traits related to leaf angle (AGP, AGL, AGM, and AGU) had a positive linear correlation (0.45 ≤ r ≤ 0.90). A positive linear relationship was reported between the traits related to leaf length (LLP, LLL, LLM, and LLU; 0.38 ≤ r ≤ 0.93), leaf width (LWP, LWL, LWM, and LWU; 0.40 ≤ r ≤ 0.93), and leaf area (LAP, LAL, LAM, and LAU; 0.36 ≤ r ≤ 0.95) ( Table 5).
Grain yield showed no linear correlation with the groups of traits related to plant height (PH and EIH; 0.03 ≤ r ≤ 0.07), leaf angle (AGP, AGL, AGM, and AGU; -0.07 ≤ r ≤ 0.10), leaf length (LLP, LLL, LLM, and LLU; 0.00 ≤ r ≤ 0.15), and leaf width (LWP, LWL, LWM, and LWU; 0.13 ≤ r ≤ 0.16) ( Table  5). Differently from this study, BELLO et al. (2010) assessed maize hybrids grown in Nigeria and found a positive correlation between plant height (r = 0.56) and ear insertion height (r = 0.45) with grain yield. Conversely, NARDINO et al. (2016) also reported that there was no linear correlation between leaf angle and grain yield (r =-0.004), which agrees with  our results. Therefore, the selection of plants using plant height, ear height, number of seeds per row, and hundred seed weight improves maize grain yield (BEKELE & RAO, 2014). The groups of traits related to the number of leaves (NL, NLBE, and NLAE; 0.21 ≤ r ≤ 0.36) and leaf area (LAP, LAL, LAM, and LAU; 0.21 ≤ r ≤ 0.30) had a positive linear association with GY, but of small magnitude (Table 5). A positive correlation between NLAE and GY (r = 0.21) is important because the physiologically active leaf area above the ear is characterized as the most efficient in grain yield (ALVIM et al., 2010). Therefore, cultivars with higher number of leaves (r = 0.36) or higher leaf area (r = 0.30) are linearly associated with plants with higher grain yield. These results indicated that plants with more leaves and higher leaf area are more productive. NARDINO et al. (2016) also described a positive phenotypic correlation between leaf area and grain yield (r = 0.284). The results of this research are consistent with those of OGUNNIYAN & OLAKOJO (2014), who reported positive phenotypic correlation between number of leaves per plant (r = 0.83) and leaf area (r = 0.37) with grain yield.
The data on the average pattern of plant architecture and the grain yield among the genetic bases, cycles, and regions of adaptation were presented as complementary information, considering it was not the focus of this study. Further studies, using statistical criteria, need to be carried out to detail the comparisons among genetic bases, among cycles, and among regions of adaptation. They also need to include a larger number of cultivars, locations and years (environments), in order to achieve a higher level of representation in the data set.

CONCLUSION
Genetic variability was reported among cultivars for number of leaves, plant height, ear height, leaf angle, leaf length, leaf width, leaf area, and grain yield.
Leaves closer to the ear have smaller leaf angle, greater leaf length, greater leaf width, and greater leaf area. The leaf angle gradually increases towards the leaves at the lower and upper ends of the plant. Leaf length, leaf width, and leaf area gradually decreases towards the leaves of the lower and upper ends of the plant.
Cultivars with a greater number of leaves and a larger leaf area are associated with plants with higher grain yield.