Size of Containers in the Production of Flamboyant Seedlings

The size of the container can affect the quality of the seedlings and, there is no recommendation of containers for the formation of flamboyant seedlings [Delonix regia (Bojerex Hook.) Raf]. Thus, the objective of this study was to evaluate the production of flamboyant seedlings in different container sizes, besides performing trail analysis to identify the growth variables that characterize the quality of these seedlings. The experimental design was a randomized block design with seven container sizes (13 × 13 cm, 15 × 15 cm, 13 × 20 cm, 15 × 25 cm, 17 × 22 cm, 17 × 30 cm or 30 × 40 cm), with four replicates. Each experimental unit was composed of five containers, totaling 20 containers per treatment. The plant height, stem base diameter, number of leaves and the sturdiness quotient were measured at 20, 40, 60, 80 and 100 days after emergence (DAE), and at 100 DAE were also measured the root volume, root dry matter, shoot dry matter, total dry matter, shoot/root dry matter ratio and Dickson quality index (DQI). The flamboyant seedlings have better grow when cultivated in polyethylene bags with size of 30 × 40 cm. The collar diameter, root volume, root dry matter, shoot dry matter and total dry matter are the most adequate variables to indicate the quality of flamboyant seedlings. However, because it is a rapid, simple and non-destructive measurement variable, the root collar diameter is more adequate to identify high-quality flamboyant seedlings.


Introduction
The flamboyant [Delonix regia (Bojerex Hook.)Raf] belongs to the Fabaceae -Caesalpinioideae family and is native from Madagascar; the plant is used in reforestation and afforestation programs (Lorenzi et al., 2003).Due to its exotic nature and high adaptation ability to the tropical climate's environmental conditions, it has been used in the afforestation of squares and streets in every Brazilian region (Lucena et al., 2006;Ataíde et al., 2013).
The size of the proper container to produce seedlings will depend on the plant's growing rate, which may vary according to the species, climate conditions, and the type of substrate that is being used (Viana et al., 2008).For David et al. (2008), we need to identify the ideal container size for each species, considering that larger containers require a greater quantity of substrate, fertilizers, and nursery room.
In commercial nurseries, the standardization of the seedlings has been based especially on the different classes of height, favoring the technical fertilization and irrigation handling, specifically performed to improve the smaller seedlings' growth (Wendling et al., 2005).However, to classify the seedlings' quality, the morphological variables, such as plant height, stem base diameter, leaf area, and dry matter of the roots and aerial part are the most indicated (Binotto et al., 2010).
All these features are used to establish the morphological indexes, from which the most prominent ones are the relation between the plant height and the stem base diameter, the relation of the aerial part and root dry matter, and the Dickson quality index (Chaves & Paiva, 2004).However, to evaluate the seedlings' quality, the features and the morphological indexes cannot be dealt with separately (Fonseca et al., 2002).
Therefore, we need to establish the container size to produce high-quality flamboyant seedlings and identify the variables that have a greater correlation with the seedlings' quality.Consequently, the purpose hereof was to evaluate the production of flamboyant seedlings [Delonix regia (Bojerex Hook.)Raf] in different-sized containers and perform a path analysis to identify the growth variables that characterize the quality of the produced seedling.

Location and Characterization of the Experimental Area
The experiment was performed in a vegetation house at the Agronomic Experimental Station of the State University of Mato Grosso do Sul (UEMS), in Cassilândia, MS (19°06′48″ of South latitude; 51°44′03″ of West longitude, and average altitude of 470 m).
The regional climate, according to the Köppen classification is Aw, characterized as a tropical climate with hot summers and a tendency to high precipitation levels, and dry winters, with a dry season between May and September.The annual average temperature of 30 years is of 24.1 °C, with a minimum of 16.4 °C in July and a maximum of 28.6 °C in January, and an annual average precipitation of 1.520 mm.The temperature and relative humidity were daily monitored in the vegetation house through an Automatic Meteorological Station (CASSILANDIA-A742), and the data gathered during the experimental period (October 14 to January 30, 2017) are presented in Figure 1.

Temperature
Relative humidity

Substrate Used to Produce Seedlings
The soil that was used was the Quartzarenic Neosol, collected in a pasture area at a layer of 0.0-0.20 m deep.
After the collection, the soil was sieved and its chemical characteristics were analyzed according to EMBRAPA's instructions (2009).To know if it was necessary to treat the soil with lime, the base saturation method was used (70%), which corresponds to the proportion of 2.20 Mg ha -1 (1.10 g of limestone per dm³ of soil).The limestone used had the following constitutions: CaO: 38%; MgO: 11%; PRNT: 85%; PN: 62%.After the liming, the manual homogenization of the soil was performed; then it was wet and kept under incubation for 30 days.After that period, the soil was mixed with bird manure at the proportion of 1:1 (v:v), forming the substrate that was used.The substrate's chemical features are presented in Table 1.
Table 1.Some chemical properties of the substrate used in the experiment  Note.O.M.: organic matter; V: base saturation; CEC: cation exchange capacity at pH 7.

Plant Material Employed
The mature fruits of Delonix regia (Bojerex Hook.)Taf ("flamboyant") were harvested in twelve matrices, in a cerrado area located at the east region of the State of Mato Grosso do Sul, at the city of Cassilândia, MS (23°47′40″ S and 54°41′07″ W), during the dry season, in August, 2016.The seeds were previously selected considering their size and weight and then subject to the dormancy break treatment with infusion in hot water (95 °C), followed by infusion in water at room temperature (24 to 28 °C) during 24 hours.After the dormancy breaking, the seeds were immediately sown in the different-sized containers.Three seeds were sown by container, and twelve days after the seedlings' emergence, they were reduced to one plant by container.At 30 days after emergence (DAE), a nitrogen fertilization was performed (Urea -45% N) at the proportion of 50 mg per dm³ of substrate, applied through irrigation water with about 20 mL of water by plant.

Measuring the Plants' Growth and the Seedlings' Quality Indexes
At the 20, 40, 60, 80, and 100 DAE, the following features were evaluated: plant height-determined from the soil surface to the inclusion of the last leaf with the assistance of a millimeter ruler; diameter of the stem base-measured from the stem base level through readings made with a digital caliper (Clarke-150 mm), with a precision level of ±0.01 mm; height (cm)/stem base diameter (mm) relation (PH/SBD); number of leaves-through visual counting.At the 100 th day, the root volume was evaluated also: determined through the water displacement method, using a 100-mL beaker graduated in millimeters (mL) and therefore with a ±1.0-cm³ precision.Then, the plants were separated into aerial part and root system, deposited in paper bags and taken to a forced circulation greenhouse for 72 hours at 65 °C (±1.0 °C) to determine the root and aerial part dry matter, which were weighted in an analytic scale with a precision of 0.0001 g.Based on these evaluations, we determined the total dry matter (TDM) and calculated the morphological indexes: relation between the aerial part/root dry matter (APDM/RDM); the sturdiness quotient (SQ) was determined based on the relation between the plant height, stem base diameter (PH/SBD), and the Dickson quality index (DQI).Based on the plant height (PH), the stem base diameter (SBD), the aerial part dry matter (APDM), and the root dry matter (RDM) were calculated using the Equation 1, proposed by Dickson et al. (1960): Where, TDM is the total dry matter mass (g); PH is the aerial part height (cm); SBD is the stem base diameter (mm); APDM is the aerial part dry matter (g); and RDM is the root dry matter (g).
The experimental data were subjected to the normality and homogenization assumption verification tests.Such assumptions were not met in the case of the root volume, root dry matter, aerial part dry matter, and the Dickson quality index, whose data were transformed with the use of the square root of (x + 0.5) before the variance analysis.After the analysis of the transformed data, we checked if the assumptions were met.However, the data were presented at their original form.The data were subjected to the variance analysis (ANOVA), and when significant, the means were grouped by the Scott-Knott criterion at 5% of probability, using the statistic program Sisvar ® version 5.3 for Windows (Statistic Analysis Software, UFLA, Lavras, MG, BRA).
To measure the direct and indirect effects of the growth features on the seedling's quality (DQI), the path analysis was performed, according to the methodology developed by Wright (1921).To that end, we performed the Pearson correlation analysis to obtain the correlation matrices and their significances by the "t" test, at a 5% probability level.The Pearson correlation coefficients were unfolded, obtaining the coefficients in the path analysis.The statistical analyses were performed using the statistical program Genes ® version 5.1 for Windows (Statistic Analysis Software, UFV, Viçosa, MG, BRA).Before the path analysis, the multicollinearity diagnosis was performed, as detailed in Cruz and Regazzi (1997).The correlation matrix' multicollinearity level, among the independent variables of the regression model, was established based on its number of conditions, which is the ratio between the higher and lower eigenvalue of the phenotypic matrix.Therefore, when the condition number is less than 100, the multicollinearity is weak and do not generate any problem to the analysis; when its value is between 100 and 1,000, the multicollinearity is moderated to strong; and when it is greater than 1,000, the multicollinearity is severe (Montgomery & Peck, 1981).

Results and Discussion
The results obtained indicate a significant effect of the different container sizes for every biometric feature of the evaluated flamboyant seedlings.Such fact is related to this species' growth rate linked to the great amplitude of the studied containers' dimensions.The substrate volume of the bigger container (30 × 40 cm -7752 cm 3 ) has about 17 times the amount of substrate of the smaller container (13 × 13 cm -450 cm 3 ) (Table 2).
Similar results were obtained by other authors with different tree species.Purple ipe seedlings [Tabebuia impetiginosa (Mart.ex D.C.) Standl] produced in black polyethylene bags of 20 × 36.5 cm and 15 × 32 cm had greater height and diameter (Cunha et al., 2005).With Pacara earpod tree, according to Abreu et al. (2015), the black polyethylene bags of 14 × 20 cm resulted in greater values of plant heights, stem base diameters, and sturdiness quotients.In both papers, the authors noticed the direct relation between the increase of the container's size and the addition of these growth biometric features.Such result may be a result of the greater volume of the container, which provides more physical space and nutrients.
At the height of plants up to 100 DAE, we noticed a daily increase of 0.12, 0.12, 0.17, 0.29, 0.27, 0.34, and 0.49 cm day -1 on the containers with the dimensions of 13 × 13 cm, 15 × 15 cm, 13 × 20 cm, 15 × 25 cm, 17 × 22 cm, 17 × 30 cm, and 30 × 40 cm, respectively.In other words, during the development, the flamboyant plants grown in the container of greater volume had the maximum daily increase.This fact may be related to the containers limiting the plants' growth according to the seedlings' permanence in the nursery.That becomes evident in the containers of 13 × 13 cm and 15 × 15 cm because from 80 to 100 DAE there was practically no growth in height and/or increase in the number of leaves by plant.Therefore, for such containers, the flamboyant seedlings should remain on them for 80 DAE tops.
The sturdiness quotient, according to Carneiro (1995), is one of the main features to evaluate the quality of forest seedlings because it provides information regarding the plant height and the stem base diameter, informing if the seedling is weakened or hypertrophied.The seedlings presented sturdiness quotient values under 6.0, a value considered as the superior limit to result in greater survival of seedlings after their transplant under field conditions, especially in windy and dry places (Thompson, 1985).This author also states that a sturdiness quotient above 6.0 is undesirable because it is an indication that the seedlings are weakened and, therefore, have a lower survival capability in the field after their transplant.
Generally, we noticed that the 30 × 40 cm container favored the growth of the roots and aerial part of the plants (Figure 2).Therefore, we can consider that the plants sown in such container had a greater root volume (Figure 2a), root dry matter mass (Figure 2b), aerial part dry matter (Figure 2c), total dry matter (Figure 2d), aerial part dry matter/root dry matter relation (Figure 2e), and Dickson quality index (Figure 2f).However, for the aerial part dry matter/root dry matter relation, there was no significant difference with the dimensions of 15 × 25 cm, 17 × 22 cm, and 17 × 30 cm.These results are similar to the ones obtained by Abreu et al. (2015), who noticed greater values of root dry matter, aerial part dry matter, and Dickson quality index in Pacara earpod trees grown in the larger container.The greatest container resulted in the increase of the number of leaves (Table 3).We know that the leaves have photosynthesizing organs for the biological production of photoassimilates.The plants with the greater number of leaves probably resulted in greater rates of photosynthesis and, consequently, in a greater quantity of photoassimilates available to be distributed to the drains (root system and aerial part).According to Campos et al. (2008), the greater amount of leaves on the seedlings will result in an intense photosynthetic activity and, consequently, the plants' growth in height and diameter will be greater.The flamboyant plant root system, when grown in the 7752 cm 3 volume (30 × 40 cm) container (Figures 2a and  2b), got the greater amount of nutrients due to the container's volume available for exploitation.According to Andrade et al. (2012), the greater containers provided a greater area for exploitation and a better spatial distribution of the root system, enabling a greater water and nutrient absorption.This variable reflects in a strong influence on the plant's growth and development (Taiz & Zeiger, 2009).Therefore, the greater values for the flamboyant plants grown in the 30 × 40 cm container in the variables root volume (Figure 2a), root dry matter (Figure 2b), aerial part dry matter (Figure 2c), and total dry matter (Figure 2d) are a result of the greater water and nutrient absorption, and consequently in a greater rate of photosynthesis and photoassimilate production.
For the APDM/RDM relation, we noticed that there was no difference between the containers of 15 × 25 cm, 17 × 22 cm, 17 × 30 cm, and 30 × 40 cm, whose values were 2.86, 2.87, 2.74, and 2.99, respectively (Figure 2e).This fact may be linked to the balanced growth between the different organs of the plant in these containers, considering that there was no change in the relative distribution of dry matter with the size variation of the container.These values are superior to the ones obtained by Oliveira et al. (2011), who, while evaluating three container sizes (20 × 30 cm; 28 × 40 cm, and 40 × 60 cm) to produce Copernicia hospita seedlings (Copernicia hospita Martius, Palmae family), obtained values between 0.23 and 1.87 for this variable.According to Brissette et al. (1991), the best relation between these parameters should have a value of 2.0.Therefore, these container sizes resulted in seedlings with an APDM/RDM relation value above the recommended, indicating that, during the photoassimilate division between the aerial part and the roots, the aerial part got a greater share.
The Dickson quality index (DQI) represents the relation between the seedling's total dry matter and the sum of the quotient in sturdiness and dry matter of the aerial part and of the roots (Dickson et al., 1960), and since several parameters are necessary to obtain it, it is considered an excellent determinant of the seedlings' quality.
Regarding the DQI's estimates, we notice that the values obtained are superior to the ones proposed by Hunt (1990) as minimum DQI values for good-quality seedlings (DQI = 0.2).However, his work was performed with coniferous species, and the DQI was developed based on pinus spp.species (Dickson et al., 1960).Hereon, the flamboyant seedlings presented DQIs of 1.92 to 3.92 (Figure 2b), indicating, therefore, the high quality of the seedlings produced in every container.Generally, greater DQI values indicate more vigorous seedlings and, consequently, a better quality.With that in mind, the 30 × 40 cm container is the ideal one to grow flamboyant seedlings due to its greater mean.
To Fonseca et al. (2002), the data of the morphological parameters and the relations used to evaluate the seedlings' quality should not be treated separately in the standard classification of the seedlings' quality.Therefore, based on the plant height, on the stem base diameter, on the root volume, on the root dry matter, on the aerial part dry matter, on the total dry matter, on the sturdiness quotient, on the APDM/RDM, and on the DQI, we identified hereon that the container with the dimensions 30 × 40 cm has the favorable characteristics to produce flamboyant seedlings.
We also underscore that the 30 × 40 cm container has the greatest volume in comparison with all the other evaluated ones; it has about 7752 cm³ and it uses about 44 plastic bags per m² in the nursery (Table 2).The containers with greater volumes promote better conditions for the seedlings' development, but they should be used only with species that have a slow development and need to remain in the nursery for a very long time, or when we wish to obtain well developed seedlings to plant them in urban areas, for example (Cunha et al., 2005).
The authors also state that the input, workforce, and transportation requirements impose limits to the size of the containers made to produce seedlings, requiring the establishment of the better cost/benefit relation.Consequently, when these factors impose limits, we can use the 17 × 30 cm container because it presents mean values under the seedlings sown on the 30 × 40 cm container but is satisfactory to grow good-quality seedlings.Additionally, this substrate requires a volume of about 1855 cm³ and occupies around 143 plastic bags per m² in the nursery.In other words, using this container represent an economy of about 76% of substrate and will fit around three times more containers in a similar area.
In multicollinearity, while using the correlation matrix's eigenvalue and eigenvector test on the primary independent variables of this model, we notice that the number of conditions is equal to 281647.69(CN = 281647.69),that is, a severe multicollinearity.Therefore, we used the ridge regression (Hoerl & Kennard, 1970) to calculate the model's coefficients and then avoid the multicollinearity effects.Accordingly, we adopted the value of k = 0.107 to calculate the path coefficients (Table 4).Due to the presence of a severe multicollinearity, they prove themselves unstable as K increased until it was stabilized at the value of k = 0.107.Note.** significant at the 1% level by the t test, respectively.Ns: not significant.
For the path analysis, we followed the model developed by Wright (1921) to better understand the links between several variables (Table 4).According to Nogueira et al. (2012), to interpret the correlations, we must consider three factors: the magnitude, the direction, and the significance.The eigenvalue of the coefficient of determination (R²) in the path analysis model (0.978) and the low effect of the residual variable (0.158) showed that the adopted explanatory model expressed the primary variables' and of the DQI's cause and effect relation.Therefore, we notice through the R² that these variables explained 97.8% of the DQI's variation.
The variables with positive correlation, with the main characteristic and with the direct effect in favorable direction, indicated the presence of the cause and effect relation (Silva et al., 2010).Therefore, we noticed that the stem base diameter, the root volume, the root dry matter, the aerial part dry matter, and the total dry matter culminated in a direct effect on the Dickson quality index.Such results are partially similar to the ones obtained by Dardengo et al. (2013), who noticed in robusta coffee (Coffea canephora) seedlings that only the total dry matter and stem base diameter variables had a great direct effect on the Dickson quality index.
Consequently, selecting flamboyant seedlings with greater root volume, root dry phytomass, aerial dry phytomass, and total dry phytomass will result in the indirect selection of seedlings with greater DQI.It is important to underscore that the stem base diameter is variable and not destructive; therefore, it is possible to select the good-quality seedlings without destroying them.Determining such variables is important to the quality of the flamboyant seedlings formed in different-sized containers.

Figure 2 .
Figure 2. Root volume (a), root dry matter (b), shoot dry matter (c), total dry matter (d), shoot/root dry matter ratio -SDM/RDM (e) and Dickson quality index (f) of the flamboyant (Delonix regia (Bojerex Hook, Raf) seedlings grown in seven containers containing different volumes of substrate.Means followed by the same letter belong to the same group by the Scott-Knott test to 95% probability (means ± SE).Cassilândia, MS, Brazil, 2017.

Table 2 .
Commercial measurements of the plastic bags used in the experiment

Table 3 .
Mean values of developmental characteristics measured for plant height, root collar diameter, plant height/collar diameter ratio and number of leaves at 20, 40, 60, 80 and 100 days after emergence (DAE) of the flamboyant [Delonix regia (Bojerex Hook,) Raf] seedlings grown in seven containers containing different substrate volumes.Cassilândia,MS, Brazil, 2017