Modeling the leaf area of Ormosia paraensis Ducke by statistical models and artificial neural networks

Abstract

The leaf is a very important plant structure because it allows gas exchange and transformation of light energy into chemical energy. The objective of this research study was to test artificial neural networks (ANNs) to estimate the leaf area (LA) of Ormosia paraensis Ducke and compare their performance with adjusted statistical models. One hundred forty leaves were selected from seedlings of the species at the leaf age of 100 days after sowing (DAT). The LA was calculated by indirect estimation with ImageJ software, and the linear length (L) and width (W) dimensions were measured with a ruler graduated in centimeters. Afterward, 90 leaves were randomly separated to generate mathematical equations of LA (Y) as a function of linear dimensions (L and W), and 50 leaves to validate the equations. Similarly, 100 networks of the multilayer perceptron (MLP) type were trained with the backpropagation algorithm and the best networks were selected for later validation. The choice of the best equations and ANNs was based on precision and dispersion statistics. The quadratic equation obtained from model (4) demonstrated consistent statistics with the coefficient of determination (R²aj = 87.39) and a low result for the standard error of estimate (SEE = 12.07%). For the ANNs, a correlation coefficient (Ryŷ), varying between 0.9316 and 0.9521, was obtained in the training phase, while it ranged from 0.8522 to 0.8825 in the validation phase, generating lower residues. It is concluded that the ANN performance was higher compared with the conventional regression technique.

Modeling of the Leaf Area of <i>Maytenus obtusifolia</i> Mart. from Scanned Images

“…In this way, the quadratic model regression based on the product of length analyzing the results of the residual distribution, note that the points were homogeneously distributed (Figure 4(a)) and that the frequency followed the trend of normality (Figure 4(b)). According to [2] is indicative of satisfactory statis-tical analyzes for this model, following a trend of biological parameters. Thus, the use of non-destructive methods such as modeling equations is extremely important in studies that want to make plant growth assessments without destroying them [28].…”

“…For this reason, the use of models of mathematical equations is an important tool in studies that require the determination of leaf area, since this feature is directly linked to the photosynthetic performance of the plants, influencing its development. Thus, it is essential to investigate this methodology for the different plant species [2].…”

“…The leaf is the organ that performs vital functions, being responsible for carrying out the photosynthesis and the gas exchanges of the plant. which implies a higher cost for the analysis [2]. On the other hand, the indirect methods allow a precise and fast estimate of the leaf area, without the need of leaf destruction, and can be used throughout the crop cycle, being possible the successive measurements in the same plant [3].…”

“…seek the adjustment of mathematical equations that estimates the leaf area of various crops through the linear dimensions of its leaves as reported by several authors Cucumis sativus L. [4], Vicia faba L. [5], Helianthus annuus L. [6], Crambe abyssinica [7], Jatropha curcas [8], Coffea canephora [9], Vitis vinífera L. [10], Rosa hybrida L. [11], Crotalaria juncea [12], Litchi chinensis Sonn. [13], Ormosia paraensis Ducke [2], guava [14], Artocarpus heterophyllus [15] and Plectranthus barbatus Andrews [16]. However, no work was found in the literature involving the species Maytenus obtusifolia Mart.…”

“…extrapolated, these equations can be used in the estimation of leaf area of seedlings of the same species, as well as plants of similar ages and climatic conditions, otherwise, the estimated values of the leaf area from a given variable can be biased and imprecise[2].Note, inFigure 2that the dispersion diagram of the measurements of the leaf surface measurements of the length, width and the combination of both, presented a trend of linear and non-linear behavior when related to the actual leaf area observed from the leaves. In this way, linear models of first degree, quadratic and power were tested to fit the best equation for estimation of the leaf area of Maytenus obtusifolia Mart.…”