Estimation of Leaf Area of Jackfruit Through Non-destructive Method

The objective of this study was to determine mathematical equations that estimate the leaf area of jackfruit (Artocarpus heterophyllus) in an easy and non-destructive way based on linear dimensions. In this way, 300 leaves of different sizes and in good sanitary condition of adult plants were collected at the Federal Institute of Espírito Santo, Campus Itapina, located in Colatina, municipality north of the State of Espírito Santo, Brazil. Were measured The length (L) along the midrib and the maximum leaf width (W), observed leaf area (OLA), besides the product of the multiplication of length with width (LW), length with length (LL) and width with width (WW). The models of linear equations of first degree, quadratic and power and their respective R were adjusted using OLA as dependent variable in function of L, W and LW, LL and WW as independent variable. The data were validated and the estimated leaf area (ELA) was obtained. The means of ELA and OLA were compared by Student’s t test (5% probability) and were evaluated by the mean absolute error (MAE) and root mean square error (RMSE) criteria. The choice of the best model was based on non-significant comparative values of ELA and OLA, in addition to the closest values of zero of EAM and RQME. The jackfruit leaf area estimate can be determined quickly, accurately and non-destructively by the linear first-order model with LW as the independent variable by equation ELA = 1.07451 + 0.71181(LW).


Introduction
The jackfruit (Artocarpus heterophyllus) belonging to the family Moraceae, is a species native to India, introduced in Brazil during the colonial period, where the edaphoclimatic conditions were well adapted.Its use varies in the most diverse forms, from the consumption of the fruit in natura or processed, to the medical industry, presenting great economic potential for the internal and external market (Perdomo & Magalhães, 2007;Oliveira, Godoy, & Borges, 2011).
The knowledge of the leaf area is of paramount importance in physiological studies, involving photosynthetic apparatus efficiency, transpiration and response to irrigation and fertilizers, being an essential characteristic in the analysis of plant growth and development (Blanco & Folegatti, 2005;Morgado et al., 2013).
The leaf area can be determined by direct or indirect methods.The direct methods, however precise, require high labor, specific and expensive equipment, besides being destructive, making impossible measurements on the same leaf (Pompelli et al., 2012).The indirect methods are non-destructive and easy to execute, allowing the researcher to make successive measurements on the same leaf, being able to estimate the leaf area accurately over time (Peaksen, 2007;Oliveira, Silva, Costa, Schmildt, & Vitória, 2017).
A of the indirect methods most used to estimate the leaf area of plant species is through mathematical equations. jas.ccsenet.
Subsequently, the models were validated using a sample of 50 sheets specially designed for this purpose.The values of L, W, LW, LL and WW of each leaf were replaced in the equations proposed by the modeling, from where the estimated leaf area (ELA) was obtained, in cm 2 .A simple linear equation represented by and its respective coefficient of determination (R 2 ) was adjusted for each model, in which the ELA values represented the dependent variable as a function of OLA as an independent variable.The means obtained from ELA and OLA were compared by Student's t-test with a 5% probability.The mean absolute error (MAE) and the root mean square error (RMSE) were also determined for all equations by means of the Equations 1 and 2: Where, ELA is the estimated leaf area; OLA, the observed leaf area; n is the total number of leaves used for validation, n = 50 in the present study.
The best model to estimate leaf area of jackfruit was defined based on the non-significant values between ELA and OLA, EAM and RQME values closer to zero, as well as higher coefficient of determination (R 2 ) of the equations.The statistical analysis was performed with the help of software R (R Core Team, 2018), through the data package ExpDes.ptversion 1.2 (Ferreira, Cavalcanti, & Nogueira, 2018).

Results and Discussion
Table 2 shows the descriptive analysis of Artocarpus heterophyllus leaf samples used for modeling and validation.It was verified that for the length (L) there was variation from 3.17 to 25.70 cm, with a mean of 15.57cm and an amplitude of 22.53 cm.The width (W) had variation of 1.88 to 13.90 cm, average of 7.81 cm and amplitude of 12.02 cm.The product of length and width (LW) ranged from 6.09 to 357.23 cm 2 , with a mean of 136.01 cm 2 and an amplitude of 351.23 cm 2 .The product of length and length (LL) ranged from 10.05 to 660.49 cm 2 , with a mean of 273.37 cm 2 , with an amplitude of 650.44 cm 2 .The product of width and width (WW) varied from 3.53 to 193.21 cm 2 , average of 68.39 cm 2 and amplitude of 189.68 cm 2 .The observed leaf area (OLA) ranged from 5.09 to 250.52 cm 2 , with a mean of 97.88 cm 2 and an amplitude of 246.08 cm 2 .These measures are very close to the measures of the sample used for the validation, since they should not exceed the measures used to propose the mathematical models (Levine, Stephan, & Szabat, 2017).
Note that for all measurements the values of the coefficient of variation (CV) for both the sample of the leaves used for the modeling, and for the samples used for the validation was higher than 30% and is classified by Pimentel-Gomes (2009) as very high.However, this high variability is desirable when determining the mathematical equations for the estimation of the leaf area of plant species, since they represent the use of large, medium and small leaves, being representative all the development of the plant and generating more precise models for all phenological stages of the species (Pezzini et al., 2018).Table 3 shows the adjusted equations as well as their respective coefficients of determination (R 2 ) proposed to estimate the leaf area of Artocarpus heterophyllus.With the exception of first degree linear model equations based on L and W, all other models presented R 2 values above 0.95, a value that according to Borghezan et al. (2010) indicates high precision in the estimation of mathematical models.However, the equations that had LW as independent variable showed higher values of R 2 , surpassing 0.99.These results are superior to those found by Peksen (2007) and Oliveira et al. (2017) who verified good adjustments of the leaf area as a function of the product of length and width.
Table 3. Equation with linear adjustment of first degree, quadratic and power and its respective coefficient of determination (R2) using the observed leaf area (OLA) as dependent variable, as a function of length (L), width (W), product of length with width (LW), product of length with length (LL), product of width with width (WW) of leaves of Artocarpus heterophyllus In Figure 2, first degree linear equations for the validation of the data and their respective determination coefficients (R 2 ) are represented.Note that the highest value of R 2 was found in the first degree linear equation based on LW (Figure 2G), showing that 99.88% of the estimated leaf area is explained by the leaf area observed, indicating a high correlation between ELA and OLA for this equation.However, the linear adjustment of first degree did not present the best value of R 2 in the modeling equation, having lower values than the quadratic models and also power based on LW.However, according to Antunes, Pompelli, Carretero, and Damatta (2018), the model should not be proposed only for its high value of R 2 , since this practice can lead to erroneous estimations of the leaf area.Thus, validation of data is fundamental as a criterion of choice for the best model to be adopted (Fascella, Darwich, & Rouphael, 2013).

Figure
Figure 2 using the (A, D, observed

Table 2 .
Minimum, maximum, mean, amplitude and coefficient of variation (CV) values of length (L), width (W), product of length with width (LW), product of length and length (LL), product of width with width (WW) and observed leaf area (OLA) of leaves of Artocarpus heterophyllus