STATISTICAL PARAMETERS TO ESTIMATE THE LEAF AREA OF NATIVE FOREST SEEDLINGS OF GENUS Tabebuia AND Handroanthus

Leaf area (LA) is an important parameter for physiological and phytotechnical studies and its measurement in a fast, accurate, and inexpensive way is essential and desirable. In this context, mathematical modeling is used as a tool to estimate leaf area from its relation with biometrical parameters and biomass. This study aimed to generate, validate, and determine the best mathematical estimation models of leaf area using the linear variables length (with and without petiole) and width of leaves and leaflets, in addition to dry mass of the native species Tabebuia roseoalba, Tabebuia impetiginosa and Handroanthus chrysotrichus collected in Sinop, Mato Grosso State (Brazil), between January and March 2014. The model assessment was performed by the method of weighted values of statistical indicators. The models based on linear measurements as independent variable that provided best performance of LA estimation for T. impetiginosa and T. roseoalba use the average leaflet width (Wla) measurements: LA=10.919×Wla and LA=6.196×Wla, respectively. For H. chrysotrichus, the model was based on the length and width of leaves (L and W): LA=(0.383×L×W)+16.586. The best models of leaf area estimation considering dry mass (DM) were LA=119.510×DM−32.044×DM for H. chrysotrichus, LA=143.610×DM−6.383×DM for T. impetiginosa, and LA=90.623×DM for T. roseoalba.


INTRODUCTION
Leaf area (LA) is an important physiological parameter for studying growth, development, and productivity of plant species considering its relation with processes such as photosynthesis, transpiration, use of light, water and nutrients, radiation interception and energy balance (SMART, 1985;WILLIAMS, 1987;GARDNER et al., 1990;FAVARIN et al., 2002).Its acquisition allows assessing the specific leaf area, net-radiation absorption, evapotranspiration intensity, leaf area ratio, leaf area index, canopy aerodynamic resistance, soil shading, among other interactions with the environment (SILVA et al., 2011;SOUZA et al., 2014).
LA is also an important biometric parameter for assessing plant responses to different environmental conditions.Easy, fast, and nondestructive methods that accurately estimate LA are important for assessing plant growth under field conditions, especially for perennial crops and forest species at initial development stages.According to Aquino et al. (2011), LA quantification can be performed by direct or indirect methods.
Destructive direct methods (as leaf area integrator and weighing) are usually more laborious and demanding time (TOEBE et al., 2012).In these methods the leaves are harvested in order to be evaluated, therefore, plant structure is damaged, becoming impossible carry out successive measurements in the same plant (GIUFFRIDA et al., 2011).
Non-destructive indirect methods present as characteristics a reduced time spent (SERDAR; DEMIRSOY, 2006), greater precision, as well as the possibility of monitoring leaf growth and leaf expansion throughout plant cycle or experiment, reducing data variability (MARSHALL, 1968;PEKSEN, 2007;TOEBE et al., 2012).These methods are indicated for in loco assessments and are useful for studies that require non-destructive methods such as photosynthesis and transpiration (NASCIMENTO et al., 2002).
Considering the information provided by LA and the great biodiversity and potential presented by tropical forest species, the morphological knowledge about them is incipient and extremely necessary.Thus, this study aimed to generate, validate and determine the best estimation models of LA based on linear measurements and dry mass of leaves and leaflets for three tropical native species: Handroanthus chrysotrichus, Tabebuia impetiginosa, and Tabebuia roseoalba.

MATERIAL AND METHODS
The experiment was carried out at the Federal University of Mato Grosso, located in Sinop (11°51′08″ S, 55°30′56″ W, and 376 meters above sea level), in the Cerrado-Amazon transition region, northern Mato Grosso, Brazil.Regional climate is classified as Aw according to Köppen, i.e. a tropical warm and humid climate, with two well-defined stations: a rainy season from October to April and a dry season from May to September.In addition, this region presents low annual thermal amplitude with a monthly average between 23.5 and 25.5 °C and an annual average precipitation of between 1327.29 and 1974.47 mm (SOUZA et al., 2013)).
From January to March 2014, 250 leaves fully expanded, without deformations, non-damaged and with different sizes were collected from the forest species Handroanthus chrysotrichus (Mart.ex A. DC.) Mattos, Tabebuia impetiginosa (Mart.ex DC.) Standl., and Tabebuia roseoalba (Rid.)Sand.An average of five tree matrices with good phytosanitary conditions were used per species.The studied species have compound leaves (leaf blade divided into leaflets) (Figure 1) with three or more leaflets emerging from the apex of the main petiole (VIDAL;VIDAL, 2003).
The maximum length and width of leaves (L and W) and their leaflets (Ll and Wl) were measured by using a ruler and measuring tape (cm).The generated analytical models considered the presence and absence of petiole in the leaves for L. In the first case, L is the distance from the base of petiole to leaf apex; in the second case, L is the distance between the petiole insertion point in the leaf blade and the leaf apex.For leaflets, Ll is the distance between the leaflet apex and its insertion in the rachis whereas W and Wl are the larger perpendicular distance to the longitudinal axis (L or Ll) of leaves and leaflets, respectively.After the linear parameters were measured, the real leaf area (LA, in cm 2 ) was determined by using a photoelectric meter (Li-3000 Model, Li-Cor, Lincoln, NE, USA).Subsequently, dry mass of leaves (DM, in g) was obtained by weighing the plant material in a precision balance (0.001 g) after being dried in a forced air circulation oven at 65 ± 5 °C until constant weight.All collected leaves (250) were used for linear measurements and leaf area without petiole, whereas 50 leaves were used for measurements with petiole, in addition to dry mass measurements (with and without petiole).
With the obtained data, analytical models of leaf area estimation were generated and validated.
For the model generation, leaf characteristics were considered aiming at establishing the highest number of simplified mathematical relations among the measurements performed.Therefore, based on the mathematical combinations proposed by Souza et al. (2014), 40 analytical models (Table 1) were adapted, 36 of them for linear measurements (24 considering the leaflets) and the others for dry mass.
Data homogeneity was verified between the F-test and leaf area values.Normality tests were performed with independent variables (isolated linear measurements of length, width, and dry mass) and real leaf area (dependent variable) for each species.In all cases, the behavior of normal distributions was observed.For the model generation, a linear regression was constructed considering the leaf area as a dependent variable and linear (L, W, Ll, and Wl) and non-linear (DM) parameters as independent variables.The Microsoft Excel Solver tool was used and the adjusted coefficients from regressions were determined by maximizing the coefficient of determination (R 2 ).
In order to assess the performance of generated models in the leaf area estimation, the following statistical indicators were calculated: MBE (mean bias error), RMSE (root mean square error), d (Willmott adjustment index), and c (performance index) (WILLMOTT, 1981;LEITE;ANDRADE, 2002).Considering the statistical indicators and aiming at analyzing the performance of models, the weighted value of statistical indicator (Wv) method was used according to Thiersch (1997).For Wv acquisition, weights from 1 to "n" were assigned for each statistical indicator at each model, where "n" is the number of models tested (36 for linear measurements and 4 for dry mass).Thus, the best model was the one that presented the lowest sum of weights (a low accumulated Wv).

RESULTS
The values of leaf area, linear measurements and dry mass are shown in Table 2. T. impetiginosa presented the highest average values of Lp (L with petiole), W, LA, and DM (with and without petiole) whereas H. chrysotrichus presented the lowest values of linear measurements, LA, and DM (with and without petiole).T. roseoalba presented the highest average of L without petiole and the lowest average of Lp.Regarding the leaflets, the highest average values for Ll were observed in T. impetiginosa and for Wl in T. roseoalba.The lowest averages of leaflet linear measurements were observed in H. chrysotrichus.
The linear regressions calculated between LA area and DM without and with petiole (Figure 2) presented high coefficients of determination (R 2 between 0.99555 and 0.99994), suggesting that the presence of petiole had no considerable influence on these parameters.For this reason, all assessed models in this study are related only to values disregarding the petiole in length, leaf area, and dry mass measurements due to its low influence on these parameters.The regression analyses of the generated models and their respective validations (statistical parameters) are presented in Tables 3, 4, and 5 respectively for H. chrysotrichus, T. impetiginosa, and T. roseoalba.Thus, the two best models for each species were analyzed considering the linear measurements and dry mass (models with lower accumulated weighted value).
The best models based on linear measurements were those of numbers 8 and 12 (∑Wv of 16 and 18, respectively) for H. chrysotrichus, whereas for species from the genus Tabebuia, the best ones were the models number 26 and 23, which presented accumulated Wv

DISCUSSION
Models based on linear measurements with the best performance of LA area estimation for H. chrysotrichus used the combination of leaf measurements (length and width) as independent variables, being the first model based on their multiplication (model 8) and the second model based on their sum (model 12).
Likewise, these models based on L and W products were also the most indicated for forest species such as Mangifera indica (LIMA et al., 2012), Coffea arabica (SCHMILDT et al., 2014), Combretum leprosum (CANDIDO et al., 2013), Hancornia speciosa (FONSECA; CONDÉ, 1994), Zizyphus joazeiro (MARACAJÁ et al., 2008), Citrus limonia (SILVA et al., 2013), Tabebuia aurea, Schinopsis brasiliensis (QUEIROZ et al., 2013) and Pouteria caimito (SILVA et al., 2014).In this sense, Silva et al. (2013), analysing Citrus limonia leaves, obtained a linear model similar to 8 as one the best in the estimation.On the other hand, no models of leaf area estimation based on the sum of L and W as independent variables were found in the literature.
In contrast, the leaf area of T. impetiginosa and T. roseoalba are better estimated by potential models based only on leaflet width as an independent variable (its average value for model 26 and its sum for model 23).Studies that consider leaflet measurements for leaf area estimation are typically unavailable in the literature.For Phaseolus vulgaris, Toebe et al. (2012) concluded that one of their best models on leaf area estimation considering the width of the central leaflet (Cl) as an independent variable was also potential (LA=a 1 ×Cl b ).
For the best models of T. impetiginosa and T. roseoalba, the measurements of all leaf and leaflets are needed, which represent an extra work compared to the measurements performed only in the leaves.Thus, the required accuracy and available time need to be considered prior to carrying out analyses of this nature.
Regarding the models based on dry mass, the best performance for T. roseoalba was observed for the models 37 and 38 whereas, for H. chrysotrichus and T. impetiginosa, the models 39 and 40 stood out.A similar model to the 39 was considered as the best in estimating leaf area in grapevine (MONTERO et al., 2000), as well as similar models to the 38 and 39, allowed a high accuracy in estimating leaf area in Eucalyptus grandis × Eucalyptus urophylla (DIAO et al., 2010).
According to Ma et al. (1992), the leaf area can be estimated by its dry mass.However, although these models present good results, their main disadvantage is the need to destroy the leaves for analysis and, consequently, a minimum structure for its acquisition is required, as a balance and greenhouse.
Regarding dry mass or linear measurements, Montero et al. (2000) emphasize that attention is needed when using only one variable in models of leaf area estimation, because despite the good results provided by them, the specific leaf area is inconstant, and changes may occur in plants due to time, phenological cycles, and environmental conditions.

CONCLUSIONS
Models based on linear measurements as an independent variable, providing the best performance of leaf area (LA) estimation for T. impetiginosa and T. roseoalba, used the average leaflet width (Wla) measurements: LA=10.919×Wla1.854  and LA=6.196×Wla

Figure 2 .
Figure 2. Linear correlations between leaf area and dry mass without and with petiole measured in leaves of H. chrysotrichus (A and B), T. impetiginosa (C and D) and T. roseoalba (E and F).

Table 2 .
Average values (x ത) and standard deviations (σ) for the parameters leaf area (LA), leaf length (L), petiole length (Lp), dry mass (DM), leaflet length (Ll), leaf width (W), and leaflet width (Wl) obtained for leaves used for generating and validating mathematical models of leaf area estimation.

Table 3 .
Regarding the models based on dry mass, T. roseoalba presented a lower accumulated Wv in the models number 37 (∑Wv of 7) and 38 (∑Wv of 8) whereas H. chrysotrichus and T. impetiginosa presented the lowest accumulated Wv for the models 39 (∑Wv of 8 and 9, respectively) and 40 (∑Wv of 8 and 5, respectively).Adjusted coefficients (a n and b), coefficients of determination (R 2 ), and statistical indicators for models based on linear measurements or dry mass of leaf area estimation of Handroanthus chrysotrichus.

Table 4 .
Adjusted coefficients (a n and b), coefficients of determination (R 2 ), and statistical indicators for models based on linear measurements or dry mass of leaf area estimation of Tabebuia impetiginosa.

Table 5 .
Adjusted coefficients (a n and b), coefficients of determination (R 2 ), and statistical indicators for models based on linear measurements or dry mass of leaf area estimation of Tabebuia roseoalba.