Non-destructive Method for Estimating the Leaf Area of Pear cv . ‘ Triunfo ’

The present study had as objective to determine mathematical equations to estimate the leaf area of pear cv. ‘Triunfo’ using linear dimensions of the leaves. For that, 300 healthy leaves of different sizes from each quadrant of plants from the small farm of Boa Vista located in the city of Montanha, at the northern side of the State of Espírito Santo, Brazil were used. The length (L) along the main vein was measured, along with the maximum width (W) of the leaf blade and observed leaf area (OLA), in addition to the product of the length and width (LW) of each leaf. From these measurements models of linear equations of first degree, quadratic and power were adjusted and their respective R using OLA as dependent variable and L, W and LW as independent variable. Based on the proposed equations, the data were validated obtaining the estimated leaf area (ELA). The mean of the ELA and OLA were compared by Student t test 5% probability. The mean error (E), the mean absolute error (MAE) and the root mean squared error (RMSE) was also used as validation criterion. The best equation model was defined based on the non-significant values from the comparison of means of ELA and OLA, E, MAE and RMSE values closer to zero and highest R. The leaf area of pear cv. ‘Triunfo’ can be estimated by the equation ELA = -0.432338 + 0.712862(LW) non-destructively and with a high degree of precision.


Introduction
The pear tree (Pyrus communis L.) belongs to the faimily of the Rosaceae, being the cv. 'Triunfo' a hybrid with characteristics of fast growth, high productivity, vigorous plants, large fruits of green color, oblong shape and punctuation in the shell, firm flesh and with sweet acidulated taste (Nakasu et al., 2007).
The determination of leaf area is a fundamental characteristic in studies involving plant development, light interception, photosynthesis efficiency, evapotranspiration, fertilizer and irrigation related responses, being directly related to the yield and quality of the plant (Blanco & Folegatti, 2005).
The measurement of the leaf area can be done directly or indirectly. Although the direct methods are more efficient, it needs a lot of time, require complex and expensive equipment and are in most cases destructive, preventing successive measurements which often makes their use impracticable (Jonckheere et al., 2004;Pompelli et al., 2012). Indirect methods are based on easy methods to obtain measurements allowing constant measurements of the leaf area, for example during the entire plant development period (Tsialtas & Maslaris, 2005).
One of the most commonly used indirect techniques is based on linear measures of the leaves and the correlation with the leaf area of the plants, generating mathematical models that allow the estimation of the leaf area in a fast and non-destructive way. However this method requires adequate calibration and parameterization to be used. (Peksen, 2007;Costa, Pôças, & Cunha, 2016 (1) where, ELA are the values of the estimated leaf area; OLA are the values of observed leaf area and n is the amount of leaves contained in the validation sample being 50 in the present study.
The choice of the best model to estimate the leaf area of pear cv. 'Triunfo' was based on the highest values obtained from the coefficient of determination (R 2 ) and the non-significant values from comparing the means of ELA, OLA and E, MAE and RMSE with greater proximity to zero. All the statistical analyzes were performed using the R software (R Core Team, 2018) and scripts from the ExpDes.pt data package version 1.2 (Ferreira, Cavalcanti, & Nogueira, 2018).

Results and Discussion
In Table 1, it is possible to observe the minimum, maximum and average values L, W, LW and OLA characteristics from the 250 leaves used to propose the mathematical models of leaf area estimation and of the 50 leaves that were used to validate the data. All the values used in the validation are presented among the values used to propose the mathematical models, these values are adequate since according to Levine, Berenson, Krehbiel, and Stephan (2012) the measurements should not exceed those used to fit the models. When the coefficient of variation (CV) of the leaves used for modeling was analyzed, it was possible to see that the values were presented in a range between 23.63 and 39.97%, furthermore the CV values for the leaves used in the validation had a variation from 23.00 to 43.53% range (Table 1). According to Pimentel-Gomes (2009), all these values are considered high or very high, attesting high variability of the sampled data. However, it is desired a high CV value in works that seek a mathematical model to estimate the leaf area, since equations that take into account different leaves forms and sizes present better adjustments, besides representing all the stages of vegetative development of the plants (Toebe et al., 2011;Espindula et al., 2018;Pezzini et al., 2018).
The adjusted equations and their respective coefficient of determination (R 2 ) are shown in Table 2. All proposed models had a high correlation between the dependent variable (OLA) and the independent variables (L, W and LW) with R 2 greater than 0.8671. However it should be noted that for all LW based models as an independent variable R 2 had a value of 0.989 being superior to the others. Despite that the choice of the best model should not only take into account the highest value of R 2 , since they may be inadequate, provoking a underestimation of the leaf area (Antunes et al., 2008). In this way, the validation of the data becomes indispensable to choose the best model that estimate the leaf area of pear cv. 'Triunfo'. The behavior of the validation equations obtained through the leaves samples and their respective determination coefficient (R 2 ) are represented in Figure 2. It is noted that the highest values of R 2 were obtained using LW as independent variable being the same equations that presented higher values of R 2 in the modeling.
Models that take into account individualized linear dimensions are easier to measure, making work in practice simpler to execute. However, for Espindula el al. (2018) equations that considerer a single linear measure of leaves are less efficient, being used only on certain occasions, in this way, a model to estimate leaf area using combined linear measures such as the interrelation between length and width, presented a higher degree of precision and are more desirable conforming with the results found in the present study.  Vol. 11, No. 7;2019 equation of first degree based on LW for estimating leaf area of a variety of Coffea canephora concluding that this is the best model for such a species.
All equations based on only one linear measure (L and W) presented lower values of R 2 and higher values of E, MAE and RMSE. These results demonstrate that these equations were less precise to estimate of leaf area. Similar results were found by Rouphael et al. (2007) and studying leaf area models of Helianthus annuus L., observed lower values of RMSE and greater value of R 2 of the equation that relates L and W compared to the others, indicating that equations that use these features together have a better fit. Note. * P values greater than 0.05 indicate that the observed leaf area (OLA) and estimated leaf area (ELA) did not differ by Student t test.
Thus, considering the validation criteria defined above, as well as the higher coefficient of determination (R 2 ) of the equation, the linear first-degree model using the product of length along the main vein with the largest width of the leaf limb (LW) as independent variable presents a higher degree of precision. Foliar area estimation models based on more than one measure are more notorious, according to those proposed for several species as Jatropha curcas (Pompelli et al., 2012), Passiflora spp. (Morgado et al., 2013), Vitis vinífera L. (Buttaro et al., 2015), Coffea canephora (Schmildt et al., 2015) and Prunus armeniaca L. (Cirillo et al., 2017), concluding that the best adjustments were found relating L and W in comparison with models that take into account only one dimension.
Therefore, it is recommended to use equation ELA = -0.432338 + 0.712862(LW) to estimate the leaf area of pear tree cv. 'Triunfo'. It should be emphasized as described by Schmildt et al. (2015), for the determination of models that estimate the leaf area is necessary the destruction of the leaves, however after establishing the equation the leaf area can be estimated by obtaining the length along the main vein and the largest width of the leaf blade, with simple equipment such as ruler and or tape measure, non-destructively.

Conclusions
The leaf area of pear cv. 'Triunfo' can be estimated by the length (L) ratio along the main vein and width (W) maximum of the leaf limb, through the following first degree equation ELA = -0.432338 + 0.712862(LW), non-destructively and with a high degree of precision.