Leaf Area Estimation of Garden Boldo From Linear Dimensions

The objective of this work was to determine a mathematical equation using linear measures that allows estimating a leaf area of the specie Plectranthus barbatus Andrews, a plant with medicinal properties popularly known as garden boldo. For this was performed a direct measurement of the leaf blade considering the length (L) along the midrib and the maximum width (W) perpendicular to the midrib of 500 leaves of different specimens and the observed foliar area (OLA), which were obtained by digitized images. A regression study with linear, quadratic, potential and exponential models was performed using a random sample of 400 from the evaluated leaves using OLA as a function of L, W or LW and then obtaining the estimated leaf area (ELA) of each model. From the remaining 100 leaves a validation of the tested models was performed using ELA as a function of OLA in a simple linear regression. From the residues between ELA and OLA the root-square-mean error and Willmot index (d) was obtained and the normality was verified. The parameters used for validation were: statistically linear and angular coefficient equal to zero and one respectively; coefficient of determination closest to the unit; RQME closer to zero; d index closest to the unit; normal distribution of residues. The equation that best represents the estimated leaf area of the garden boldo is ELA = 0.1389 + 0.6779 (LW).


Introduction
The specie Plectranthus barbatus Andrews, commonly known as Boldo-de-jardim, boldo, boldo-do-reino, alum, among others (Lorenzi & Matos, 2008), belong to Lamiaceae family (synonymy Labiateae), which have about 300 species widely distributed throughout tropical Africa, Asia and Australia, and some are well adapted in Brazil.

P. barbatus
Andrews is an herbaceous or sub-shrub, aromatic, perennial, erect plant when young and decumbent after 1-2 years, slightly branched, up to 1.5 meters in height.With leaves opposite, simple, oval of jagged edges, hairy, measuring 5 to 8 cm long and very bitter taste, flexible even when dry, being thicker and juicy when fresh.Blue flowers arranged in apical racemous inflorescences.It originated in India, probably brought to Brazil in the colonial period (Lorenzi & Matos, 2008).
Among the utilities of the garden boldo are the ornamental and medicinal properties (Lukhoba, Simmonds, & Paton, 2006).
The medicinal properties found in this species are possibly related to the presence of diterpenoids, essential oils and phenolic compounds (Abdel-Mogib, Albar, & Batterjee, 2002).In popular medicine, P. barbatus Andrews is indicated in cases of abdominal colic (Dubey, Srimal, & Nityanand, 1981), gastrointestinal diseases such as constipation, gastritis, intestinal spasms; hepatic and dental diseases, in addition, to respiratory diseases such as asthma, bronchitis and pneumonia (Lukhoba et al., 2006).
Aoyama and Furlan (2017) report the existence of several species known as Boldo including of different genera.Concerning the use in popular medicine, Milaneze-Gutierre, Famelli, Capel, and Romagnolo (2007) report that the incorrect botanical recognition of a specie can cause serious consequences such as phytotherapeutic innocuity and poisoning.
The leaves are responsible for important functions in the plant such as interception and absorption of light, photosynthesis, gas exchange and transpiration (Taiz & Zeiger, 2009).Zhang and Liu (2010) report the influence of leaf area in the light interception, and therefore plant growth and productivity, becoming one of the key traits in ecophysiological and agronomic studies.An easy economical and accurate estimate of the leaf surface area is a recurrent interest of scientists (Pandey & Singh, 2011), and mathematical equations have been used to determine the leaf area with high accuracy (Carvalho, Bianco, Galati, & Panosso, 2011).Estimating the leaf area in a plant where the leaves are the most interesting product is very important.
There are several methods to measure with accuracy the leaf area, being classified in direct and indirect methods (Olfati, Peyvast, Shabani, & Nosratie-rad, 2010).The indirect methods usually involve the use of regression equations, allow for successive evaluations in the same plant and rapidity in these evaluations, preserving the leaves for later studies, as well as not causing damage to plants (Zanetti, Pereira, Sartori, & Silva, 2017).The regression equations are obtained from modeling studies involving the leaf area observed as a function of length and width measurements of the leaf blade.

Material and Methods
The garden boldo samples (Plectranthus barbatus Andrews) were loaned by the Residents Association of Nova Esperança in São Mateus (South Latitude 18°40′32″, West Longitude 39°51′39″ and with an average elevation of 37.7 m).The collect of material and measurements were performed on the same day in November 2014.The Köppen weather classification of the region is AW, presenting rain in summer and dry in winter (Alvares, Stape, Sentelhas, Gonçalves, & Sparovek, 2014).
In the sampling 500 leaves of a population of adult garden plants were collected.In each plant were harvested leaves at all stages of development in the four cardinal points that did not present damage or attack of diseases or plagues as recommended by Oliveira, Silva, Costa, Schmildt, and Vitória (2017).The leaves were harvested, properly packed in plastic bags and quickly transferred to the Laboratory of Plant Breeding of the Postgraduate Program in Tropical Agriculture of the Centro Universitário Norte do Espírito Santo (CEUNES/UFES), where the allometric measurements were performed.
The length (L) and width (W) dimensions of the leaves were measured with a ruler in centimeters.The length was defined as the distance between the insertion point of the petiole in the leaf blade and the opposite end of the leaf and the width as the largest dimensions perpendicular to the axis of the length, as can be seen in Figure 1.The leaf petiole was removed with scissors.With the data of length and width, the product was also determined between L and W (LW, in cm 2 ).After these measurements the direct measure of the observed foliar areas was determined, (OLA, in cm 2 ) using scanned images using the open source ImageJ ® Software (Schindelin, Rueden, Hiner, & Eliceiri, 2015).The 500 leaves were scanned using an HP ® C4280 multifunctional scanner and the images saved in tif format and 75 dpi resolution.
af area was pe e sample of 1 egression (y = ression was ad versus H 0 :β 0 root-mean-squ (Equation 6). = (3) (4) The , the y the t, for d the uares.rough ion 5) (5) (6) rom i n the ELA i osco, ria of n one, RMSE closer to zero, Willmont index (d) closer to one and residues showing normal distribution.The statistics analysis were performed using R software (R Core Team, 2018) and the graphics using Microsoft Office Excel (Levine, Stephan, & Szabat, 2017).

Results and Discussion
The minimum, maximum, mean, standard deviation and coefficient of variation (CV) values of the allometric measures of length (L), width (W), product of the length by the width (LW) and observed leaf area (OLA) of the set of leaves used for both adjust and validation of the equations are shown in Table 1.
The minimum and maximum values of L, W, LW and AFO used in validation showed interval indices with those detected in the leaves used in the equation estimation.This is an interesting confirmation, because according to Levine et al. (2017), using regression model for estimation, the values of the independent variable, which wants to estimate, must not extrapolate the values used in the construction of the regression equation.The mean found for L, in both modeling and validation, was similar to the found by Milaneze-Gutierre et al. (2007).
Table 1.Minimum, maximum, average, standard deviation and coefficient of variation in length along the midrib (L, cm), maximum width (W, cm), length of the product by the maximum width (LW, cm 2 ) and observed leaf area (OLA, cm 2 ) of Plectranthus barbatus Andrews leaves In relation to variability measured by CV, in the leaves sample used in the adjust of the regression equations, all the allometric measures (L, W, LW and OLA) showed values of CV very high (Table 1), according to Pimentel-Gomes' (2009) criteria.According to Pezzini et al. (2018) the high value of CV is important for models generation, because it can be explained by the collection of leaves in several growth stages, characterizing the growth of the plants.In the 100 leaves used for validation, the variability found in the measures of L, W, LW and OLA was also considered high, according to Pimentel-Gomes' (2009) criteria, showing suitable for this type of analyze, as also stood out Schmildt, Hueso, Pinillos, Stellfeldt, and Cuevas (2017).
The 12 equations obtained for estimated leaf area (ELA), as well as the respective coefficient of determination (R 2 ), are shown in Table 2.In general, a good adjust is verified between the OLA and the allometric models, with R 2 higher than 0.82.Among the adjusted equations (Table 2) observe that the highest R 2 was obtained using LW as an independent variable for linear (Equation 3), quadratic (Equation 6) and power (Equation 9) models, showing R 2 higher than 0.99.A good adjust was not verified for exponential model, differently from the observed by Silva et al. (2017) in modeling of another boldo species, the Plectranthus ornatus.
However, a model must not be selected only for the high value of R 2 , during the modeling, but by the interpretation of all the statistical measures of validation from an independent sample of that used for modeling (Bosco et al., 2012;Fascella, Darwich, & Rouphael, 2013;Schmildt et al., 2016;Walia & Kumar, 2017).The validation made from the sample of garden boldo leaves verified that from the 12 adjusted equations, only those that used LW as an independent variable in the linear, quadratic and power models are suitable, according to the criteria of statistically linear coefficient equal to zero and statistically angular coefficient equal to one (Figure 2).These three equations showed the highest values of R 2 and are the same ones that showed the highest values of R 2 in modeling (Table 2), as also observed by other researches (Schmildt, Hueso, & Cuevas, 2014b;Tartaglia et al., 2016).The three equations also showed suitable for use, when it analyzes the other criteria of validation, showing values of RMSE closer to zero and Willmott's index d (1981) closer to one, when it compares with the other obtained equations, and showed a normal distribution of residues.According to Figure 2, the less adjusted model to the objectives of this work was the exponential, differently from the observed by Silva et al. (2007) for another boldo species (Plectranthus ornatus), which claim to have found the best adjust in exponential model using the width.
In practice, the use of linear model equations based only on one dimension of the leaves is preferable due to simplicity of application, mainly on the field (Tsialtas & Maslaris, 2005), as performed by Schmildt et al. (2016), who indicated the use of length of leaves in Bauhinia monandra, and by Tartaglia et al. (2016), who indicated the use of width of leaves in canola.However, in relation to garden boldo leaves, none of the models was suitable using only one allometric measure, as can be seen in Figure 2.
These results point out the need of suitable use of the criteria of validation, and must also be interpreted together, as observed by Schmildt, Amaral, Schmildt, and Santos (2014a) in the determination of leaf area in different cultivars of Arabic coffee.
Thus, considering the ease of interpretation, the equation ELA = 0.1389 + 0.6779(LW) (Table 2) is recommended for use, whose criteria of validation are seen in Figure 2. In this figure can be also observed the good adjust of the simple linear equation through straight 1:1.

Conclusions
The leaf area of garden boldo can be estimated with accuracy through non-destructive methods using measures of the dimensions of length (L) and width (W) of leaves in different mathematical models.
The equation ELA = 0.1389 + 0.6779 LW provided the highest accuracy for the estimation and simplified the calculations.

Table 2 .
Regression models for the estimation of Plectranthus barbatus Andrews leaf area (ELA, cm²) with the respective coefficients of determination (R²)