Alometric Model for Estimation of Leaf Area of Garcinia brasiliensis Mart. Through Non-destructive Method

Abstract

The objective of the present study was to test and establish mathematical models to estimate the leaf area of Garcinia brasiliensis Mart. through linear dimensions of the length, width and product of both measurements. In this way, 500 leaves of trees with age between 4 and 6 years were collected from all the cardinal points of the plant in the municipality of São Mateus, North of the State of Espírito Santo, Brazil. 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 obtained for all leaves. From these measurements were adjusted linear equations of first degree, quadratic and power, in which OLA was used as dependent variable as function of L, W and LW as independent variable. For the validation, the values of L, W and LW of 100 random leaves were substituted in the equations generated in the modeling, thus obtaining the estimated leaf area (ELA). The values of the means of ELA and OLA were tested by Student’s t test 5% of probability. The mean absolute error (MAE), root mean square error (RMSE) and Willmott’s index d for all proposed models were also determined. The choice of the best model was based on the non significant values in the comparison of the means of ELA and OLA, values of MAE and RMSE closer to zero and value of the index d and coefficient of determination (R2) close to unity. The equation that best estimates leaf area of Garcinia brasiliensis Mart. in a way non-destructive is the power model represented by por ELA = 0.7470(LW)0.9842 and R2 = 0.9949.

Adjustment of Mathematical Equations to Determine the Area Leaf of <i>Cordia myxa</i> L.

“…This high variation was also found by several authors when studying mathematical models to estimate the leaf area of other species [7] [10] [11]. These data point out that in the sample collected there are leaves of different stages of development and consequently of different sizes, which is a fundamental characteristic in the study of modeling, since the adjusted equations can later be used throughout the crop cycle [5] [8].…”

“…Adjusted equation of power model and its coefficient of determination (R 2 ), using the real leaf area (RLA) as dependent variable, as a function of the product of length and width (LW) of leaves of Cordia myxa L.The equations adjusted with only one measurement of the leaf surface (L or W) are easier to use in practice[8]. However, this type of equation is less accurate and may require different adjustments throughout the vegetative cycle of the plants, thus requiring different equations for the different stages of development[19].…”

Use of Mathematical Equations to Estimate Leaf Area of Psidium Cattleyanum

“…Table 2 shows the descriptive statistics of the sampled data for modeling, and validation. The high coefficient of variation (CV) found can be explained by the high amplitude of the sample data with the presence of leaves used in the modeling with an area ranging from 11.94 to 70.23 cm 2 , this characteristic becomes fundamental in mathematical modeling studies, since in this interval there are small, medium, and large leaves, covering most of the possible number of phenological stages (13,4). An important fact to be mentioned is that the values used in the validation should not be smaller or larger than those used for the modeling, this should also be respected in future estimations, as extrapolated values can generate inaccurate information on the leaf area ( 14).…”

“…Table 4. Observed leaf area (OLA), and estimated leaf area (ELA) from equations of linear first degree, quadratic , and power for the independent variables length (L), width (W) , and product of length , and width (LW), in addition to the p-value, mean absolute error (MAE), the root mean square error (RMSE) , and It is worth mentioning that the combined use of more than one measure in the estimation of leaf area can be more laborious in practice because it is necessary to measure one more variable (17), however, as observed in the literature, several plant species have their leaf area best estimated from the union of two variables such as, for example, length, and width (18,19,20,4,21) demonstrating that these equations have greater acceptability in the prediction of leaf area.…”

“…A way to determine the leaf area in a simplified way is through the use of mathematical equations, which, from known, and easy to dimension measures of the leaf surface, accurately estimate the leaf area. Several authors have proposed mathematical equations to estimate the leaf area of several species (4,5,6,7). However, it was not identified in the literature fitted equations to estimate the area of the leaves of Psidium cattleyanum.…”