Non-destructive method for estimating leaf area of Ocimum gratissimum L. using leaf dimensions

ABSTRACT Basil (Ocimum gratissimum - Lamiaceae), is a sub-shrub plant species with great economic importance for several regions, and studies on its growth, physiology, and reproduction become needed. The aimed research was to obtain a regression equation to estimate leaf area of O. gratissimum. 250 basil leaves were collected and the linear dimensions (length and width) and real leaf area of each leaf were measured. From these data, the products between length and width, length and length were calculated. Equations were obtained using regression models: linear, linear without intercept, quadratic, cubic, power, and exponential. The best equation was selected based on determination coefficient, Pearson’s correlation coefficient, Willmott’s agreement index and CS index, Akaike information criterion, mean absolute error and root mean square error. All equations proposed using the product between length and width (LW) can be used to predict the leaf area of O. gratissimum. However, the equation LA=0.54*LW1.03 (power model) is the most recommended to estimate the leaf area of this species.

Due to the importance of the species, studies related to its growth, production, physiology and reproduction are of great relevance.Leaf rea measurement is one of the most important analyzes since leaves hold numerous functions, such as light interception and absorption, net CO 2 assimilation, evapotranspiration, stomatal opening and closing, and biomass accumulation (Taiz et al., 2017).
Leaf area can be measured by methods classified as direct and indirect, destructive and non-destructive (Marshall, 1968;Peksen, 2007;Sousa et al., 2015).Destructive methods are simple and precise, but they are laborious João Everthon da Silva Ribeiro et al. besides leading to the destruction of all the plant biomass, making long-term research unfeasible (Mota et al., 2014).
Non-destructive methods based on leaf area estimation through regression equations, provide precise and fast analyzes in addition to allowing successive evaluations of plants at different growth stages (Ribeiro et al., 2020a;Santos et al., 2021).

MATERIAL AND METHODS
The experiment was carried out under a greenhouse at the Federal University of Paraíba, municipality Areia, Paraíba state, Northeastern Brazil.The climate of the region is classified as As that is tropical with rains during the summer (Alvares et al., 2013).Altitude ranges from 400 to 600 m, annual rainfall is around 1,400 mm, and temperature of 22 °C (Ribeiro et al., 2018a).The average temperature inside the greenhouse was 28.5 °C and air relative humidity was 54% during the experiment, which was monitored using a digital thermo-hygrometer.
At 150 days after sowing, 250 leaf blades were randomly collected from the middle, lower and upper thirds of each plant, selecting healthy leaves, without damages caused by biotic and abiotic factors.The leaves were transported to the Laboratory of Plant Ecology Laboratory at the Federal University of Paraíba, Areia, Paraíba state, Brazil.Length (L) and width (W) of each leaf blade were measured using a millimetric ruler (Figure 1).The product of length by width (LW), length by length (LL), and width by width (WW) were calculated.Also, real leaf area (LA) was determined through digital images.For this, each leaf was scanned in a flatbed scanner (380 model, Epson) and the images were processed individually using the ImageJ ® software (Ribeiro et al., 2018b).
A descriptive analysis was performed with data, calculating maximum and minimum values, mean, amplitude, median, standard deviation, standard error, coefficient of variation, asymmetry, and kurtosis coefficient.To determine the most suitable equation to estimate basil leaf area (LA) as a function of linear dimensions of leaves, equations were adjusted using the linear, linear without intercept, quadratic, cubic, power, and exponential regression models.
where: ŷ i : estimated leaf area; y i : observed leaf area; ȳ i : mean of observed values; ŷ´i= ŷ i -ȳ; y´i= y i -ȳ; L(x\ θ): maximum likelihood function, defined as the product of density function; p: number of model parameters; and n: number of observations.
Non-destructive method for estimating leaf area of Ocimum gratissimum L. using leaf dimensions

RESULTS
Descriptive analysis of L, W, LW, LL, WW, and LA of 250 leaf blades of basil is shown in  2).There was linear relationship between LW and LA, LL and LA, and WW and LA, and non-linear between L and LA, and W and LA (Figure 2).
Regarding percentage distribution of LA size classes of 250 basil leaves, it was found that 47.18% of the leaf area was between 0.50 and 10.00 cm², and 22.07% was between 30.01 and 92.00 cm², showing that most of the leaves in this species are small (Figure 3).
Table 2 shows the regression models and equations obtained from the relationship between the leaf linear dimensions and real leaf area.Power model, adjusted using with the product of length by width showed the highest R² (0.9974), r (0.9980), d (0.9990), and CS index (0.9969), and the lowest AIC (773.8),MAE (0.853), and RMSE (1.264) (Table 2).
Therefore, the equation LA = 0.54*LW 1.03 is the most suitable for prediction basil leaf area through dimensions of leaves, since there was low data dispersion to the model fit (R² = 0.9974) (Figure 4A).The leaf area estimated by the indicated equation had a high positive correlation with the actual leaf area, with a high determination coefficient (R² = 0.9958) (Figure 4B).Non-destructive method for estimating leaf area of Ocimum gratissimum L. using leaf dimensions

DISCUSSION
Leaf linear dimensions (length and width) showed less variability than the LW, LL, WW, and LA.High data variability is important for generating regression models aimed at estimating leaf area using linear dimensions of leaves, allowing multiple analyzes in different plants developmental stages.Therefore, the number of samples ( 250leaves) used in this study was sufficient to build allometric equations to estimate the basil leaf area.High variation in LW, LL, WW, and LA were also recorded in other studies (Macário et al., 2020;Donato et al., 2020;Ribeiro et al., 2020b;Toebe et al., 2021).
Scatter plots fitted between the analyzed variables showed linear and non-linear relationships, which was observed by other studies (Carvalho et al., 2017;Cargnelutti Filho et al., 2021).The determination coefficients (R²) of the equations were above 0.88, showing that at least 88% of the variations in basil leaf area were explained by the models obtained through linear dimensions.As compared to the equations fitted using L or W, those equations adjusted using the LW showed the best criteria for estimating leaf area (Bezerra et al., 2020;Cargnelutti Filho et al., 2021;Lucena et al., 2021;Toebe et al., 2021), except for the exponential, which showed best indexes when using leaf length (L).

CONCLUSIONS
The equations proposed using the LW can be used to estimate the leaf area of O. gratissimum.
The equation LA = 0.54*LW1.03(power model) is the most suitable to meaningfully estimate leaf area of O. gratissimum.

Figure 1 :
Figure 1: Linear dimensions [length (L) and width (W)] used to estimate the leaf area of Ocimum gratissimum.

Figure 2 :
Figure 2: Histogram and scatter plots between leaves dimensions [length, width (W), product of length by width (LW), product of length by length (LL), product of width by width (WW)], and real leaf area (LA) of 250 Ocimum gratissimum leaves.

Figure 3 :
Figure 3: Percentage of real leaf area size classes of 250 Ocimum gratissimum leaves.

Figure 4 :
Figure 4: (A) Real leaf area and product of length by width by the proposed equation for estimating Ocimum gratissimum leaf area.(B) Relationship between real leaf area and leaf area estimated by the proposed equation (LA = 0.54*LW 1.03 ).

Table 1
and 4.169) andLA (1.437 and 4.673)that presented high values for these coefficients (Table1).Scatterplots between L, W, LW, LL, WW, and LA indicated different patterns suggesting adjustments to linear and non-linear models (Figure

Table 1 :
Descriptive statistics on Ocimum gratissimum leaf data a Asymmetry differs from zero by the t-test at 5% probability; b Kurtosis differs from three by the t-test at 5% probability;