Non-destructive method for predicting the area and weight of red pitaya cladodes using linear dimensions

Understanding the leaf area is essential in plant physiology and ecological studies, as it directly influences photosynthesis, transpiration and plant productivity. This study aimed to develop non-destructive allometric models to estimate the leaf area of three species from the Caatinga biome: Cynophalla flexuosa, Libidibia ferrea and Tabebuia aurea. A total of 1293 leaves were collected from these species, scanned, and analysed using ImageJ software to obtain their length, width, and actual leaf area. In addition, the product of length and width was calculated. Linear, power and exponential regression models were used. The best equations were chosen based on the coefficient of determination, Pearson’s linear correlation coefficient, Willmott’s agreement index, mean squared error, root mean squared error, mean absolute error and mean absolute percentage error. The best equations for all species were constructed using linear and power models, which were indicated for accurate prediction of leaf area. These findings confirm the efficiency of allometric equations as a non-destructive method for predicting leaf area, providing an accessible and economical alternative for ecological studies in semi-arid environments.

The objective of this work was to obtain regression equations and to indicate the most appropriate from different mathematical models for the estimation of the leaf area of ​​ Allspice (Pimenta dioica) by non - destructive method. 500 leaves of plants located in the municipality of São Mateus, North of Espírito Santo State, Brazil, were collected, 400 of which were used to adjust the equations and 100 for validation. The length (L) along the main midrib, the maximum width (W), the product of the length with the width (LW) and the observed leaf area (OLA) were measured from all leaves. We fitted models of linear equations of first degree, quadratic and power, where OLA was the dependent variable in function of L, W and LW. From the 100 sheets intended for validation, and using the adjusted equations for each mathematical model, the estimated leaf area (ELA) was obtained. Subsequently, a simple linear regression was fitted for each model of the proposed equation in which ELA was the dependent variable and OLA the independent variable. The mean absolute error (MAE), the root mean square error (RMSE) and Willmott's index d also determined. The best fit had as selection criterion the non-significance of the comparative means of ELA and OLA, MAE and RMSE values ​​closer to zero and value of the coefficient of determination coefficient (R2) close to one. Thus, the power model (ELA = 0.7605(LW)0.9926, R2 = 0.9764, MAE = 1.0066, RMSE = 1.7759 and d = 0.9950) based on the product of length and width (LW) is the most appropriate for estimating the leaf area of ​​Pimenta dioica.

ABSTRACT: Using non-destructive and low-cost methods to determine leaf area has gained important applications. The research objectives were (i) to propose a non-destructive method to estimate the leaf area of castor bean crops and (ii) to build equations that accurately and quickly estimate the leaf area of specie. One thousand healthy and expanded leaves of five castor bean cultivars (New Zealand Purple, Sipeal, Carmencita, Amarelo de Irecê, and IAC-80) were collected, and 200 leaves were collected from each. The maximum length, maximum width, and leaf area were calculated for each leaf. The product between length and width (LW) were calculated. We performed tests with different linear and non-linear regression models between leaf area and linear leaf dimensions of each cultivar. The models used were linear, linear without intercept, and power. The criteria for choosing the best models to estimate the leaf area of castor beans were a higher coefficient of determination, more elevated Pearson’s linear correlation coefficient, lower Akaike information criterion, higher Willmott agreement index, and smallest root mean square error. The equations that presented the best criteria for estimating the leaf area of castor bean cultivars were those that used the product between length and width, compared to equations that used only one leaf dimension. The model ŷ = 0.439 × LW can be used to accurately and quickly estimate the castor bean leaf area through linear measurements of the leaves, using the product between length and width (LW), regardless of the cultivar chosen.

Estimating leaf area using non-destructive methods from regression equations has become a more efficient, quick, and accurate way. Thus, this study aimed to propose an equation that significantly estimates the leaf area of Psychotria colorata (Rubiaceae) through linear leaf dimensions. For this purpose, 200 leaves of different shapes were collected, and length (L), width (W), product of length by width (L.W), and real leaf area (LA) of each leaf blade were determined. Then, equations were adjusted for predicting leaf area using simple linear, linear (0.0), quadratic, cubic, power, and exponential regression models. The proposed equation was selected according to the coefficient of determination (R²), Willmott's agreement index (d), Akaike's information criterion (AIC), mean absolute error (MAE), mean squared error (RMSE) and BIAS index. It was noted that the equations adjusted using L.W met the best criteria for estimating leaf area, but the equation LA = 0.59 * L.W from linear regression without intercept was the most suitable. This equation predicts that 59% of leaf area is explained by L.W. Concluding, the leaf area of P. colorata can be estimated using an allometric equation that uses linear leaf blade dimensions.

The objective of this work was to obtain mathematical equations and indicate the most appropriate estimation of the leaf area of Dalbergia frutescens, by a non-destructive method through the linear dimensions of the leaves. A total of 370 leaves of D. frutescens were collected, 270 of which were used to adjust the equations and 100 for validation. The length (L) along the main vein, the maximum width (W), the product of multiplying the length and width (LW), and the observed leaf area (OLA) was measured for all leaves. First degree, quadratic, and power linear equation models were fitted, where OLA was the dependent variable as a function of L, W and LW. From the 100 leaves destined for validation, and using the adjusted equations for each mathematical model, the estimated leaf area (ELA) was obtained. The means obtained from ELA and OLA were compared using Student's t test at 5% probability. The mean absolute error, the root mean square error, and the d Willmott index were also determined. The first-degree linear model represented based on the product of multiplying the length by the width is the most suitable to determine the leaf area of D. frutescens with high precision.

The leaf area is a parameter of fundamental importance in studies on plant growth and physiology. The objective of this study was to build allometric equations for the accurate and fast estimation of sapodilla leaf areas. In total, 250 leaves of different shapes and sizes were collected from sapodilla matrices trees growing at the Universidade Federal Rural do Semi-Árido, Mossoró-RN, Brazil. For each leaf, the length, width, product of length and width (LW), product of length and length, product of width and width, and leaf area were measured. Linear and nonlinear models were used to construct the allometric equations. The best equations were chosen on the basis of the following criteria: the highest coefficient of determination, Pearson’s linear correlation coefficient, and Willmott’s index of agreement; and the lowest Akaike information criterion and root mean square error. It was verified that the models that used the LW value presented the best criteria for estimating the leaf area. Specifically, the equations ŷ = 0.664 × LW1.018 and ŷ = 0.713 × LW, which use LW values, are the most suitable for estimating the leaf area of sapodilla quickly and accurately.

Sky vine (Thunbergia grandiflora Roxb) is a vine with important structural components for forest environments. Studies on growth and development are necessary, because of the environmental and economic importance. The leaf area determination is essential for ecophysiological studies to understand the relationship of the plant with the environment. The objective of this work was to estimate an allometric equation to estimate the leaf area of T. grandiflora from linear dimensions. 200 leaves of different shapes and sizes were collected from adult plants and the length (L), width (W), the product between length and width (LW), and real leaf area (LA) were measured. The linear regression, linear without intercept, quadratic, cubic, power, and exponential models were used to estimate the equations. The criteria for determining the best model were higher determination coefficient (R2), Willmott's agreement index (d), lower Akaike information criterion (AIC), the root of the mean error square (RMSE), and BIAS index closer to zero. The leaf area of T. grandiflora can be estimated satisfactorily by the equation ŷ = 0.58*LW.

The objective of this research was to select the equation that best estimates the leaf area of the coffee tree Coffea dewevrei, from the linear dimensions of the leaves. For this purpose, 140 leaves of adult plants were collected from the Capixaba Institute for Research, Technical Assistance and Rural Extension, in the city of Linhares, North of the State of Espírito Santo, Brazil. The length (L), the width (W), the product of the multiplication between the length and width (LW) and the leaf area observed (OLA) were determined from all leaves. For the modeling, a 100 leaves sample was used, where OLA was used as a dependent variable in function of L, W and LW as independent variable, being obtained the following models: linear first degree, quadratic and power. For the validation, a sample of 40 leaves was used, where the values of L, W LW were substituted in the equations generated in the modeling, thus obtaining the estimated leaf area (ELA). A simple linear equation model was fitted for each modeling equation relating ELA in function of OLA. The hypotheses H0: β0 = 0 versus Ha: β0 ≠ 0 and H0: β1 = 1 versus Ha: β1 ≠ 1, were tested using Student's t test at 5% probability. The mean absolute error (MAE), root mean square error (RMSE) and Willmott's index d for all equations were also determined. The best model that estimates the area of Coffea dewevrei was chosen through the following criteria: β0 not different from zero, β1 not different from one, MAE and RMSE values closer to zero and index d closer to the unit. The area of the leaves can be determined by its greater width (W), through the quadratic model equation ELA=-10.255+1.020(W)+1.293(W)2.

We compared two nondestructive methods for leaf area estimation using leaves of 16 common plant species classified into six types depending on leaf shape. Relatively good linear relationships between actual leaf area (LA) and leaf length (L), width (W), or the product of length and width (LW) were found for ordinary leaves with lanceolate, oblanceolate, linear and sagitttate shapes with entire margins, serrate margins, mixed margins with a entire form and shallow lobes, and ordinary incised margins. LA was better correlated with LW than L or W, with <TEX>$R^2$</TEX> > 0.91. However, for deeply incised lobes, LA estimation using LW showed low correlation coefficient values, indicating low accuracy. On the other hand, a method using photographic paper showed a good correlation between estimates of area based on the mass of a cut-out leaf image on a photographic sheet (PW) and actual leaf area for all types of leaf shape. Thus, the PW method for LA estimation can be applied to all shapes of leaf with high accuracy. The PW method takes a little more time and has a higher cost than leaf estimation methods using LW based on leaf dimensions. These results indicate that researchers should choose their nondestructive LA estimation method according to their research goals.

The objective of this study was to obtain the best mathematical equation that estimates the leaf area seedlings of eggplant (Solanum melongena) and scarlet eggplant (Solanum gilo Raddi) through the linear dimensions of the leaves. Leaves of seedlings produced in a protected environment in the horticulture sector of the Instituto Federal do Espírito Santo – Campus Itapina, Colatina, in the Northwest region of the State of Espírito Santo, Brazil, were used. At 45 days after sowing, the length (L) along the midrib and the maximum width (W) of the leaf blade were determined, the product of the multiplication between the length and width (LW) and the observed leaf area (OLA). With the measurements in hand, the first degree linear model equations were obtained, potencyand its respective coefficient of determination. it was foundby analysis of covariance the possible adequacy of only one model to meet the two species. The models were validated, through a sample of leaves intended for this purpose, where their values of L, W and LW were substituted in the modeling equations, obtaining the estimated leaf area (ELA). A simple linear equation was fitted ELA and OLA. The hypotheses H0: β0 = 0 versus Ha: β0 ≠ 0 and H0: β1 = 1 versus Ha: β1 ≠ 1 were tested by Student's t test at 5% probability. The mean absolute error (MAE) and the root mean square error (RMSE) were also determined for all equations. The power () and exponential () model equations better predicted the area of eggplant and scarlet eggplant leaves, being the most recommended for these species.

A total of 200 stems of Caragana korshinskii and 210 stems of Salix psammophila were collected in the late August of 2015 in the Liudaogou catchment of Shenmu County, Shaanxi Pro-vince, China. Basal diameter (D), length (H), water content (W0), fresh mass (WF) and dry mass (W) were measured for each stem of the two species. Exponential and allometric equations were used to establish relationship models relating stem biomass to its morphological parameters. Altogether four models were established for each species, and their accuracy of estimation was also validated. The results showed that, the allometric model that used D2H as input variable was optimal in estimating stem biomass for C. korshinskii and S. psammophila, after transformed into its linear form. Meanwhile, the heteroscedasticity of the biomass data was greatly eliminated. This model had a maximum value of coefficient of determination (R2), and meanwhile minimum values of mean error (ME), mean absolute error (MAE), total relative error (TRE), mean systematic error (MSE), and mean absolute percentage error (MPSE), thus basically meeting the requirement of the accuracy in ecological study.

Determination of photosynthetic area of a plant, leaf or cladode is a fundamental tool in study of transpiration intensity, specific leaf area and leaf area index. The objective of this study was to evaluate Nopalea cochenillifera (L.) Salm-Dyck). cladode area, in a non- destructive way, using digital images and test its relation with the variables: product of length and maximum width and real cladode area through regression models. The design used randomized blocks with three replicates and using the N. cochenillifera forage cactus clone, Giant Sweet. To determine the real cladode area of cactus forage, 432 cladodes in different stages of growth were randomly collected (162 primary cladodes, 127 secondary and 143 tertiary cladodes), all free from damage, disease or pest attacks. All cladodes were photographed with a digital camera (Sony Mark, model DSC-P72) generating a sample of 432 1200 x 2500 pixel digital images of N. cochenillifera cladodes. Linear, gamma and power regression models were adjusted to test the relation between the digital cladode area and the explanatory variables real cladode area and product of length by width. Models were evaluated with the following criteria: Coefficient of model determination, Akaike information criterion, sum of squares of residuals and Willmott index. The power model gave the best performance, with explanatory power higher than 99.5%, while the Willmott index exceeded 0.99. Sum of squares of residuals and Akaike information criterion had lower values. The digital cladode area of N. cochenillifera can be explained by the linear dimensions of cladodes in, and independent of, branching order. The digital cladode area (DCA) of N. cochenillifera can be explained as a function of the power model -DCA = LW0.98Sconsidering the product of length by width (LW) with explanatory variable, and by D-CA = RCA1.002considering real cladode area (RCA) with explanatory variable.

The present study had as objective to determine mathematical equations to estimate the leaf area of pear cv. &amp;lsquo;Triunfo&amp;rsquo; 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 Esp&amp;iacute;rito 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 R2, 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 R2. The leaf area of pear cv. &amp;lsquo;Triunfo&amp;rsquo; can be estimated by the equation ELA = -0.432338 + 0.712862(LW) non-destructively and with a high degree of precision.

The aim of this study was to develop mathematical models to estimate the leaf area of common bean (Phaseolus vulgaris) in irrigated and non-irrigated water regimes from linear dimensions. An experiment was carried out in a completely randomized design with a 3×2 factorial arrangement (three cultivars: Triunfo, Garapiá and FC 104; two water regimes: irrigated and non-irrigated) with 25 replicates each. A total of 523 trifoliates were collected throughout the crop cycle. The length (L, cm) and width (W, cm) of the central leaflet of the trifoliate were measured and their product (LW) (cm²) calculated. Then, the leaf area of these trifoliates was determined by digital photography methods using ImageJ® software, and using leaf discs. The number of samples required to estimate the leaf area of a trifoliate was determined to define which method is the most accurate to be used as the real leaf area in generating equations to estimate the leaf area in common bean. The relationship between area by digital photographs and the dimensions of the central leaflet of the trifoliate (L, W and LW) was fitted by linear, quadratic and power models. Subsequently, the predictive capacity of the equations was assessed by the root mean square error (cm2 trifoliate-1), mean absolute error (cm2 trifoliate-1), index of agreement and Pearson’s correlation coefficient. Sample size varied between cultivars, water regimes and evaluation methods. It is more appropriate to use the leaf area provided by ImageJ® as real for comparison purposes in generating models to estimate leaf area from linear measurements, in common bean. The general equation LA = 1.092L1.945 can be used in the tested regimes without accuracy losses.

The determination of leaf area is of fundamental importance in studies involving ecological and ecophysiological aspects of forest species. The objective of this research was to adjust an equation to determine the leaf area of Ceiba glaziovii as a function of linear measurements of leaves. Six hundred healthy leaf limbs were collected in different matrices, with different shapes and sizes, in the Mata do Pau-Ferro State Park, Areia, Paraíba state, Northeast Brazil. The maximum length (L), maximum width (W), product between length and width (L.W), and leaf area of the leaf limbs were calculated. The regression models used to construct equations were: linear, linear without intercept, quadratic, cubic, power and exponential. The criteria for choosing the best equation were based on the coefficient of determination (R²), Akaike information criterion (AIC), root mean square error (RMSE), Willmott concordance index (d) and BIAS index. All the proposed equations satisfactorily estimate the leaf area of C. glaziovii, due to their high determination coefficients (R² ≥ 0.851). The linear model without intercept, using the product between length and width (L.W), presented the best criteria to estimate the leaf area of the species, using the equation 0.4549*LW.