Mathematical Modeling to Estimation Leaf Area of Pimenta dioica from Linear Dimensions

Vinicius de Souza Oliveira *

Postgraduate Program in Tropical Agriculture, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Lucas Caetano Gonçalves

Postgraduate Program in Tropical Agriculture, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Amanda Costa

Postgraduate Program in Tropical Agriculture, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Karina Tiemi Hassuda dos Santos

Departament of Agrarian and Biological Sciences, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Jéssica Sayuri Hassuda Santos

Departament of Agrarian and Biological Sciences, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Gleyce Pereira Santos

Departament of Agrarian and Biological Sciences, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Hérica Chisté

Postgraduate Program in Tropical Agriculture, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Omar Schmildt

Postgraduate Program in Tropical Agriculture, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Marcio Paulo Czepak

Departament of Agrarian and Biological Sciences, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Edney Leandro da Vitória

Departament of Agrarian and Biological Sciences, Federal University of Espírito Santo, São Mateus, ES, Brazil.

Edilson Romais Schmildt

Departament of Agrarian and Biological Sciences, Federal University of Espírito Santo, São Mateus, ES, Brazil.

*Author to whom correspondence should be addressed.


Abstract

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.

Keywords: Pimenta dioica, non-destructive method, leaf dimension


How to Cite

Souza Oliveira, Vinicius de, Lucas Caetano Gonçalves, Amanda Costa, Karina Tiemi Hassuda dos Santos, Jéssica Sayuri Hassuda Santos, Gleyce Pereira Santos, Hérica Chisté, Omar Schmildt, Marcio Paulo Czepak, Edney Leandro da Vitória, and Edilson Romais Schmildt. 2019. “Mathematical Modeling to Estimation Leaf Area of Pimenta Dioica from Linear Dimensions”. International Journal of Plant & Soil Science 28 (2):1-8. https://doi.org/10.9734/ijpss/2019/v28i230104.