### Mathematical models in determining leaf area in eggplant and scarlet eggplant seedlings

#### Abstract

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 H_{0}: β_{0} = 0 versus H_{a}: β_{0} ≠ 0 and H_{0}: β_{1} = 1 versus H_{a}: β_{1} ≠ 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.

#### Keywords

#### Full Text:

PDF#### References

SANTOS, Ronaldo, O., SOARES, Rubiene, N., PIMENTEL, Mickelly, P. Q., ABREU, Jadso, C., LIMA, Robson, B., SILVA, Breno, M. S. Modeling the leaf area of Ormosia paraenses Ducke by statistical models and artificial neural networks. Chilean Journal Of Agricultural Research. v.78, n.4, p.511-520, 2018.

POMPELLI, Marcelo, F., ANTUNES, Werner, C., FERREIRA, Débora, T. R. G., CAVALCANTE, Polyana, G. S., WANDERLEY FILHO, H. C. L., ENDRES, Laurício. Allometric models for non-destructive leaf area estimation of Jatropha curcas. Biomass and Bioenergy, v.36, n.1, p.77-85, 2012.

TOEBE, Marcos, SOUZA, Rafael, R., MELLO, Anderson, C., MELO, Patrícia, J., SEGATTO, Alexandre, CASTANHA, Ana, C. Leaf area estimation of squash ‘Brasileirinha’ by leaf dimensions. Ciência Rural. v.49, n.4, p.1-11, 2019.

LEITE, Maurício, L. M. V., LUCENA, Leandro, R. R., CRUZ, Manoela, G., SÁ JÚNIOR, Eduardo, H., SIMÕES, Vicente, J. L. P. Leaf area estimate of Pennisetum glaucum by linear dimensions. Acta Scientiarum Animal Sciences. v.41, p.1-7, 2019

ACHTEN, Wouter, M. J., MAES, Wouter, H., REUBENS, Bert, MATHIJS, Erik, SINGH, Virendra, P., VERCHOT, Louis, MUYS, Bart. Biomass production and allocation in Jatropha curcas L. seedlings under different levels of drought stress. Biomass and Bioenergy, v.34: p.667-676, 2010.

ROUPHAEL, Youssef, COLLA, Giuseppe, FANASCA, S, KARAM, Fadi. Leaf area estimation of sunflower leaves from simple linear measurements. Photosynthetica, v.45, n.2, p.306–308, 2007.

TOEBE, Marcos, BRUM, Betânia, LOPES, Sidinei, J., CARGNELUTTI FILHO, Alberto, SILVEIRA, Tatiani, R. Estimate leaf area of Crambe abyssinica for leaf discs and digital photos. Ciência Rural. v.40, n.2, p.445-448, 2010.

SCHMILDT, Edilson, R., OLIARI, Layane, S., SCHMILDT, Omar, ALEXANDRE, Rodrigo, S., PIRES, Fábio, R. Determinação da área foliar de Passiflora mucronata a partir de dimensões lineares do limbo foliar. Revista Agro@mbiente On-line, v.10, n.4, p.351-354, 2016.

OLIVEIRA, Pablo, S., SILVA, Wilton, COSTA, Adriana, A. M., SCHMILDT, Edilson, R., VITÓRIA, Edney, L. Leaf area estimation in litchi by means of allometric relationships. Revista Brasileira de Fruticultura. v.39, p.1-6, 2017.

OLIVEIRA, Vinicius, S., SANTOS, Karina, T. H., MORAIS, Andréia, L., SANTOS, Gleyce, P., SANTOS, Jéssica, S. H., SCHMILDT, Omar, CZEPAK, Marcio, P., GONTIJO, Ivoney, ALEXANDRE, Rodrigo, S., SCHMILDT, Edilson, R. Non-destructive Method for Estimating the Leaf Area of Pear cv. ‘Triunfo’. Journal of Agricultural Science. v.11, n.7, p.14- 21, 2019.

ALVARES, Clayton, A., STAPE, José, L., SENTELHAS, Paulo, C., GONÇALVES, José, L. M., SPAROVEK, Gerd. Köppen's climate classification map for Brazil. Meteorologische Zeitschrift. v.22, n.6, p.711-728, 2014.

SCHINDELIN, Johannes, RUEDEN, Curtis, T., HINER, Mark, C., ELICEIRI, Kevin, W. The ImageJ Ecosystem: An Open Platform for Biomedical Image Analysis. Molecular Reproduction and Development. v.82, p.518–529, 2015.

ZHANG, Lin, LIU, Xin, S. Non-destructive leaf-area estimation for Bergeria purpurascens across timberline ecotone, southeast Tibet. Annales Botanici Fennici. v.47, n.5, p.346-352, 2010.

R CORE TEAM. R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing, 2022.

LEVINE, David, M., STEPHAN, David, F., SZABAT, Kathryn, A. Estatistic for managers using Microsoft Excel: global edition. 8th ed. London: Person. 2017, 728p.

PIMENTEL-GOMES, Frederico. Curso de estatística experimental. 15th ed. Piracicaba, SP: Fealq. 2009.

PEZZINI, Rafael, V., CARGNELUTTI FILHO, Alberto, ALVES, Bruna, M., FOLLMANN, Diego, N., KLEINPAUL, Jéssica, A., WARTHA, Cleiton, A., SILVEIRA, Daniela, L. Models for leaf area estimation in dwarf pigeon pea by leaf dimensions. Bragantia. v.77, n.2, p.221-229, 2018.

MALDANER, Ivan, C., HELDWEIN, Amo, B., LOOSE, Luis, H., LUCAS, Dionéia, D. P., GUSE, Fabricio, I., BORTOLUZZI, Mateus, P. Modelos de determinação não-destrutiva da área foliar em girassol. Ciência Rural. v.39, n.5, p.1356-1361, 2009.

ESPINDULA, Marcelo, C., PASSOS, Alexandre, M.A., ARAÚJO, Larissa, F.B., MARCOLAN, Alarto, L., PARTELLI, Fábio, L., RAMALHO, André, R. Indirect estimation of leaf area in genotypes of 'Conilon' coffee (Coffea canephora Pierre ex A. Froehner). Australian Journal of Crop Science. v.12, n.6, p.990-994, 2018.

DOI: https://doi.org/10.55747/bjedis.v2i2.52835

### Refbacks

- There are currently no refbacks.

Copyright (c) 2022 Brazilian Journal of Experimental Design, Data Analysis and Inferential Statistics

This work is licensed under a Creative Commons Attribution 4.0 International License.

INDEXED BY: INTERNATIONAL INNOVATIVE JOURNAL IMPACT FACTOR