Acessibilidade / Reportar erro

Use of mathematical models to estimate the total leaf area of banana

Uso de modelos matemáticos para estimar a área foliar total de bananeiras

Abstract

The objective of this work was to adjust and validate a mathematical equation to estimate the total leaf area of banana plants of the cultivars Maça BRS Princesa, Prata BRS Platina, Prata Gorutuba and Prata-Anã together, through the linear dimensions of the third leaf and the total number of leaves. For that, the linear first degree and power models were tested, where was used a dependent variable (y) the total leaf area (TLA) an independent variable (x) the multiplication of the length with the total number of leaves (LN), multiplication of the width with the total number of leaves (WN), and multiplying the length by the width with the total number of leaves (LWN). Analysis of covariance was used to test the possibility of using a single equation to estimate the total leaf area of the analyzed cultivars. For all equations, the mean absolute error, the root mean square error and the Willmott d index were obtained as validation criteria. The power model equation TLA = 3.9292(WN)1.5851 can be used simply and quickly to determine the total leaf area of plants of the four cultivars under study.

Index terms
Musa spp.; non-destructive method; linear dimension; validation

Resumo

O objetivo deste trabalho foi ajustar e validar uma equação matemática para estimar a área foliar total de bananeira das cultivares Maçã BRS Princesa, Prata BRS Platina, Prata Gorutuba e Prata-Anã, de forma conjunta, através das dimensões lineares da terceira folha e do número total de folhas. Para tanto, foram testados os modelos linear de primeiro grau e potência, sendo utilizada como variável dependente (y) a área foliar total (AFT) e como variável independente (x) a multiplicação do comprimento com o número total de folhas (CN), multiplicação da largura com o número total de folhas (LN) e multiplicação do comprimento com a largura, com o número total de folhas (CLN). Utilizou-se a análise de covariância para testar a possibilidade do uso de uma única equação para estimar a área foliar total das cultivares analisadas. Para todas as equações, foram obtidos o erro absoluto médio, a raiz do quadrado média do erro e o índice d de Willmott como critério de validação. A equação de modelo potência AFT = 3,9292(LN)1,5851 pode ser utilizada de maneira simples e rápida para determinar a área foliar total das plantas das quatro cultivares em estudo.

Termos para indexação
Musa spp.; método não destrutivo; dimensões lineares; validação

Introduction

The Brazilian fruit industry has stood out in recent years with increments of new technologies used for the development of the activity. The culture of banana (Musa spp.) is one of the activities that make up the fruit agribusiness and exerts social and economic importance.

Brazil appears as the 4th largest producer of bananas in the world, behind only India, China, and Indonesia (FAO, 2021 FAO. Food and Agriculture Organization of the United Nations. Rome, 2019. Disponível em:https://www.fao.org. Acesso: 25 de jan.2021.
https://www.fao.org....
). In 2020, Brazil produced 6,637,308 tons with a cultivated area of approximately 5.4 million hectares, with the main producer being the state of São Paulo with 1,000,732 tons (IBGE, 2022 IBGE - Instituto Brasileiro de Geografia e Estatística. Produção agrícola municipal: Área destinada à colheita, área colhida, quantidade produzida, rendimento médio e valor da produção das lavouras permanentes. Rio de Janeiro, 2020. Disponível em: https://sidra.ibge.gov.br/tabela/1613#resultado. Acesso em: 01 de jan. 2022.
https://sidra.ibge.gov.br/tabela/1613#re...
).

Leaves are the main organ that produces photoassimilates that supply the physiological needs of plants. In banana plants, they interfere with the development of daughter seedlings and can be a source of inoculum for pests and diseases (RODRIGUES et al., 2009 RODRIGUES, M.G.V.; DIAS, M.S.C.; PACHECO, D.D. Influe^ncia de diferentes ni´veis de desfolha na produc¸a~o e qualidade dos frutos da bananeira ‘Prata-Ana~’. Revista Brasileira de Fruticultura, Jaboticabal, v.31, n.3, p.755-62, 2009 ). Therefore, the determination of leaf area is an important parameter for studying the interaction of the plant with the environment, allowing us to understand factors such as water loss through transpiration, absorption, and conversion of light energy, in addition to the response to irrigation and the use of fertilizers (BLANCO, FOLEGATTI, 2005 BLANCO, F.F.; FOLEGATTI, M.V. Estimation of leaf area for greenhouse cucumber by linear measurements under salinity and grafting. Scientia Agricola, Piracicaba, v.62, n.4, p.305-9, 2005. ). Thus, this characteristic is associated with the accumulation of dry mass, productivity, and crop quality (BUSATO et al., 2010 BUSATO, C.; FONTES, P.C.R.; BRAUN, H.; BUSATO, C.C.M. Estimativa da a´rea foliar da batateira, cultivar Atlantic, utilizando dimenso~es lineares. Revista Cie^ncia Agrono^mica, Fortaleza, v.41, n.4, p.702-8, 2010 ).

The use of mathematical models allows estimating the leaf area of the most diverse species (ZUCOLOTO et al., 2008 ZUCOLOTO, M.; LIMA, J.S.S.; COELHO, R.I. Modelo matemático para estimativa da área foliar total de bananeira ‘Prata-Anã’. Revista Brasileira de Fruticultura, Jaboticabal, v.30, n.4, p.1152-4, 2008. ; OLFATI et al., 2010 OLFATI, J.A.; PEYVAST, G.H.; SHABANI, H.; NOSRATIE-RAD, Z. An estimation of individual leaf area in cabbage and broccoli using non-destructive methods. Journal of Agricultural Science and Technology, Tehran, v.12, p.627-32, 2010. Suppl. ( ; CARVALHO et al., 2017 CARVALHO, J.O.; TOEBE, M.; TARTAGLIA, F.L.; BANDEIRA, C.T.; TAMBARA, A.L. Leaf area estimation from linear measurements in different ages of Crotalaria juncea plants. Anais da Academia Brasileira de Ciências, Rio de Janeiro, v.89, n.3, p.1851-68, 2017. ; SCHMILDT, 2017 SIGNORELL, A. et al. Package ‘DescTools’. 2022. Disponível em: https://cran.r-project.org/web/packages/DescTools/index.html.
https://cran.r-project.org/web/packages/...
; LAVANHOLE et al., 2018 LAVANHOLE, D.F.; OLIVEIRA, P.S.; VITÓRIA, E.L.; AOYAMA, E.M. Estimativa de área foliar por meio de relações alométricas em Aechmea blanchetiana (Baker) L.B.SM sob distintas condições de luminosidade. Iheringia, Série Botânica, Porto Alegre, v.73, n.3, p.363-73, 2018. ; OLIVEIRA et al., 2019 OLIVEIRA, V.S.; COVRE, A.M.; GOUVEA, D.S.; CANAL, L.; SANTOS, K.T.H.S.; SANTOS, J.S.H.; SANTOS, G.P.; PINHEIRO, A.P.B.; SCHMILDT, O.; POSSE, R.P.; CZEPAK, M.P.; ARANTES, S.D.; ALEXANDRE, R.S.; AMARAL, J.A.T.; VITÓRIA, E.L.; SCHMILDT, E.R. Determination of the leaflet area of Schinus terebinthifolius Raddi in function of linear dimensions. Journal of Agricultural Science, Cambridge, v.11, n.14, p.198-204, 2019. ; OLIVEIRA, 2020 OLIVEIRA, V.S. Modelagem estatística de características biométricas para cultivares de macieira pouco exigentes ao frio cultivadas no norte do estado do Espírito Santo. 2020. 52 f. Dissertação (Mestrado em Agricultura Tropical) - Universidade Federal do Espírito Santo, Centro Universitário Norte do Espírito Santo, São Mateus, 2020. ; TOGNERE et al., 2021 TOGNERE, J.; MARQUES, I.R.; OLIVEIRA, I.L.; SCHMILDT, O.; OLIVEIRA, V.S.; TOGNELLA, M.M.P.; SCHMILDT, E.R. Estimação da área foliar de trema micrantha em função das dimensões lineares. Nucleus, Austin, v.18, n.2, p.133-141, 2021. ). In addition, this is a non-destructive method that allows successive evaluations on the same plant, not requiring the use of machinery or specialized labor to carry out the measurements, accurately obtaining the area of the leaves of the cultivars under study (TOEBE et al., 2012 TOEBE, M.; CARGNELUTTI FILHO, A.; LOOSE, L.H.; HELDWEIN, A.B.; ZANON, A.J. Leaf area of snap bean (Phaseolus vulgaris L.) according to leaf dimensions. Semina, Londrina, v.33, p.2491–500, 2012 ).

Specifically, for bananas, Zucoloto et al. (2008) ZUCOLOTO, M.; LIMA, J.S.S.; COELHO, R.I. Modelo matemático para estimativa da área foliar total de bananeira ‘Prata-Anã’. Revista Brasileira de Fruticultura, Jaboticabal, v.30, n.4, p.1152-4, 2008. used linear measurements of the third leaf and the total number of leaves of the plant to adjust an equation that estimates the leaf area of the cultivar Prata-Anã. Viana et al. (2015) VIANA, P.C.; LIMA, J.G.A.; MENEZES, R.V.; COELHO, E.F.; BARROSO, N.I.S.; PEREIRA, M.M. Modelo matema´tico para estimativa da a´rea foliar para cultivar de bananeira platamo “D’Angola”. In: CONIRD – CONGRESSO NACIONAL DE IRRIGAC¸A~O E DRENAGEM, 25., 2015. São Cristóvão. Anais […]. Sa~o Cristo´va~o: Universidade Federal de Sergipe , 2015. , based on linear measurements of the leaf blade, fitted equations to estimate the individual and total leaf area of cultivars D’Angola belonging to the Plantain subgroup. Donato et al. (2020) DONATO, L.T.; DONATO, S.L.R.; BRITO, CLEITON, F.B.B.; FONSECA, V.A.; GOMES, C.N.; RODRIGUES FILHO, V.A. Estimating leaf area of prata-type banana plants with lanceolate type leaves. Revista Brasileira de Fruticultura, Jaboticabal, v.42, n.4, p.e-417, 2020. , adjusted equations to estimate the leaf area of the cultivars Prata-Anã and Platina in the phenological stage of lanceolate leaves. However, few works in the literature seek to adjust mathematical equations for more than one banana cultivar together.

Thus, the objective of this study was to adjust and validate an equation based on mathematical modeling that estimates the total leaf area of banana plants of the cultivars Maça BRS Princesa, Prata BRS Platina, Prata Gorutuba, and Prata-Anã together, through the linear dimensions of the length and width of the third leaf and the total number of leaves of the plants.

Material and methods

The study was carried out in the experimental area of the Center for Agricultural Sciences and Engineering of the Federal University of Espírito Santo (CCAE-UFES), located in the municipality of Alegre, State of Espírito Santo, Brazil, at coordinates 20º 44’ 59.19” latitude. South and 41º 29’ 14.73” West longitude with an altitude of 116 meters. The climate of the region according to the Köppen classification is humid subtropical Cwa, with dry winters and hot summers (ALVARES, 2014 ALVARES, C.A.; STAPE, J.L.; SENTELHAS, P.C.; GONÇALVES, J.L.M.; SPAROVEK, G. Koppen’s climate classification map for Brazil. Meteorologische Zeitschrift, Stuttgart, v.22, n.6, p.711-28, 2014. ).

Plants of four banana cultivars were used: Maça BRS Princesa, Prata BRS Platina, Prata Gorutuba, and Prata-Anã. The plants were 3 years old and planting was carried out in 2018, with 3 m spacing between rows and 2 m between plants. Planting was carried out leaving the mother, daughter, and granddaughter plant in the row. The irrigation system used was located by microsprinkler. At the time of analysis, the plants had a fully formed bunch stage.

All leaves of plants of the four banana cultivars were collected, and the number of plants and leaves varied according to availability, totaling 57 plants and 408 leaves. The total number of plants sampled was defined according to the methodology adopted by Kumar et al. (2002) KUMAR, N.; KRISHNAMOORTHY V.; NALINA, L.; SOORIANATHASUNDHARAM, K. Nuevo factor para estimar el a´rea foliar total en banano. INFOMUSA, Montpellier, v.11, n.2, p.42-3, 2002. (Table 1).

Table 1
Banana cultivars and their respective number of plants and number of leaves used for modeling.

All 408 leaves were measured using the Licor Model LI-3100 electronic meter, and the total leaf area (TLA) of each plant was determined. Also, the total number of leaves (N) per plant was counted. Subsequently, from the third leaf (the leaf that best represents the nutritional status of the plant), of each of the 57 plants, the maximum length (L) along the midrib and the maximum width (W) of the leaf blade were measured, both measurements taken with the help of a measuring tape graduated in centimeters.

It was also determined the product of multiplying the length with the width (LW), the product of multiplying the length with the total number of leaves (LN), the product of multiplying the width with the total number of leaves (WN), and product of the multiplying the length by the width by the total number of leaves (LWN).

To adjust the modeling, the models linear first degree represented by y = b0 + b1x and power represented by y b0 x b1, where TLA was used as the dependent variable (y) in function of LN, WN and LWN as the independent variable (x) were tested. The possibility of using a single equation to estimate the total leaf area of the four banana cultivars was tested, for this, the parameters b0 and b1 of each of the equations based on the same characteristic were submitted to analysis of covariance by the student’s t test at 5 % probability (ZHANG, LIU, 2010 ZHANG, L.; LIU X.S. Non-destructive leaf-area estimation for Bergeria purpurascens across timberline ecotone, southeast Tibet. Annales Botanici Fennici, Helsinki, v.47, n.5, p.346-52, 2010. ; CIRILLO et al., 2017 CIRILLO, C.; PANNICO, A.; BASILE, B.; RIVERA, C.M.; GIACCONE, M.; COLLA, G.; PASCALE, S.; ROUPHAEL, Y. A simple and accurate allometric model to predict single leaf area of twenty-one european apricot cultivars. European Journal of Horticultural Science, Stuttgart, v.82, n.2, p.65-71, 2017. ). To perform the analysis of covariance, the power model was previously linearized with logarithmic base 10 (log) for the variables, dependent (y) and independent (x): log(y)= (b0) + b1log(y). Thus, if the equations are not significant, a single equation would be adjusted for the four cultivars. If there was a significant difference between the cultivars, an equation would be adjusted for each one of the cultivars individually. All equations were fitted by the least squares method. The coefficient of determination (R2) for all equations was also obtained (KVALSETH, 1985 KVALSETH, T.O. Cautionary note about R2. The American Statistician, Washington, v.39, n.4, p.279-85, 1985. ).

The adjusted equations were validated with a sample of leaves obtained from five plants of each cultivar collected specifically for this purpose, in which the values of LN, WN and LWN were substituted in the equations proposed in the modeling, thus obtaining the estimated total leaf area (ETLA) for each equation. As a validation criterion was calculated, the Lin concordance correlation coefficient (CCC) (LIN, 1989 LIN, L.I. A concordance correlation coefficient to evaluatereproducibility. Biometrics, Washington, v.45, n.1, p.255-68, 1989. ), the mean absolute error (MAE), the root mean square error (RMSE) and the Willmott index (d) (WILLMOTT, 1981 WILLMOTT, C.J. On the validation of models. Physical Geography, Windsor, v.2, p.184-94, 1981. ) for all models through the following expressions:

M A E = i = 1 n E T L A - T L A n

R M S E = i = 1 n ( E T L A - T L A ) 2 n

d = 1 - i = 1 n E T L A - T L A 2 i = 1 n E T L A - T L A - + T L A - T L A - 2

where, ETLA are the values of the total leaf area estimated by the equations; TLA are the values of the total leaf area of each plant; TLA are the average values of the total leaf area of each plant; and n is the plant number used for validation.

To select the best model to estimate the leaf area of banana cultivars, the following criteria were adopted: higher CCC, MAE and RMSE values closer to zero, and Willmott’s d index closer to one.

All statistical analyzes and graphic representations were prepared with the help of the R language (R CORE TEAM, 2022 R CORE TEAM. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing, 2022. Disponível em: https://www.R-project.org/.
https://www.R-project.org/...
), with commands performed through the ExpDes.pt package version 1.2 (FERREIRA et al., 2018 FERREIRA, E.B.; CAVALCANTI, P.P.; NOGUEIRA, D.A. Package ‘ExpDes.pt’. 2018. Disponível em: https://cran.r-project.org/web/packages/ExpDes.pt/index.html.
https://cran.r-project.org/web/packages/...
) and DescTools version 0.99.45 (SIGNORELL et al., 2022 SIGNORELL, A. et al. Package ‘DescTools’. 2022. Disponível em: https://cran.r-project.org/web/packages/DescTools/index.html.
https://cran.r-project.org/web/packages/...
).

Results and discussion

The analysis of covariance by the student’s t-test at 5% probability (Table 2) showed that models 6 and 8 presented values of linear coefficient (b0) and angular coefficient (b1) statistically not different for all cultivars.

Table 2
Presentation of the p value in the analysis of covariance of the linear coefficients ( and angular coefficient ( of the equations of model linear first degree and power fitted with the total leaf area (TLA) in function of the product of the length with the total number of leaves (LN), product of the width with the total number of leaves (WN) and product of the length with the width and the total number of leaves (LWN) of the banana cultivars Manzano BRS Princesa, Chunkey BRS Platina, Chunkey Gorutuba, and Chunkey-Anã.

In these models, it is possible to adjust a single equation that estimates the total leaf area of the cultivars, therefore, the data of the four cultivars were grouped. For the other models, the adjustment of a single equation was discarded, since they did not meet this criterion.

The two models were adjusted to jointly estimate the total leaf area of the banana cultivars and the values of the validation criteria are shown in Table 3. It is noted that, although model 6 presents a higher value of the coefficient of determination (R2), model equation 8 had a lower mean absolute error (MAE), root mean square error (RMSE), Willmott index (d) with greater proximity to a and higher Lin concordance correlation coefficient (CCC).

Table 3
Adjusted equations of the model linear first degree and power for estimating the total leaf area jointly of the banana cultivars Manzano BRS Princesa, Chunkey BRS Platina, Chunkey Gorutuba, and Chunkey-Anã, in addition to the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), Willmott index (d) and Lin's concordance correlation coeficiente (CCC).

This finding allows us to say that the model equation 5 (Figure 1) produces less error, being more accurate in estimating the total leaf area of the banana cultivars Maça BRS Princesa, Prata BRS Platina, Prata Gorutuba, and Prata-Anã together.

Figure 1
Power model equation fitted using total leaf area (TLA) in function of the product of the width with the total number of leaves (WN) and coefficient of determination (R2) to estimate the total area of leaves of the banana cultivars Manzano BRS Princesa, Chunkey BRS Platina, Chunkey Gorutuba, and Chunkey-Anã.

Differently from what was found by Zucoloto et al. (2008) ZUCOLOTO, M.; LIMA, J.S.S.; COELHO, R.I. Modelo matemático para estimativa da área foliar total de bananeira ‘Prata-Anã’. Revista Brasileira de Fruticultura, Jaboticabal, v.30, n.4, p.1152-4, 2008. , when they reported that the total leaf area of the Prata-Anã banana can be estimated by the model linear first degree with multiplying the length by the width of the third leaf with the total number of leaves of the plant, the results found in this research show that it is possible to estimate the banana leaf area of the cultivars studied with only a linear measure of the leaf blade. This fact may be related to the difference in leaf length between the cultivars, which ranged from 234.80 cm for Maça BRS Princesa to 201.90 cm for Prata Gorutuba. About width, the variation was smaller, from 79.80 cm for Prata-Anã to 72.20 cm for Maça BRS Princesa evidencing more similarity in width between the four cultivars. Another important fact to mention is that the cultivar BRS Princesa is of the ‘Maça’ type with a higher size, which implies larger leaves than the other cultivars of the ‘Prata’ type (ROSA, 2016 ROSA, A.R.D. Desempenho agronômico de novas cultivares de bananeira (Musa spp.) na região de Piracicaba-SP. 2016. 101 f. Tese (Doutorado) – Escola Superior de Agricultura “Luiz de Queiroz”, Piracicaba, 2016. ).

In practice, the prediction of the leaf area with only one measure of the leaf blade makes the operation easier to be carried out when compared to equations that use more than one leaf dimension, in this way, the work becomes less onerous since there is a 50% reduction in the number of measures necessary to obtain the leaf area (SANTOS et al., 2016 SANTOS, J.C.C.; COSTA, R.N.; SILVA, D.M.R.; SOUZA, A.A.; MOURA, F.B.P.; SILVA JUNIOR, J.M.; SILVA, J.V. Use of allometric models to estimate leaf area in Hymenaea courbaril L.Theoretical and Experimental Plant Physiology, Berlin, v.28, n.4, p.357-69, 2016. ; OLIVEIRA et al., 2019 OLIVEIRA, V.S.; COVRE, A.M.; GOUVEA, D.S.; CANAL, L.; SANTOS, K.T.H.S.; SANTOS, J.S.H.; SANTOS, G.P.; PINHEIRO, A.P.B.; SCHMILDT, O.; POSSE, R.P.; CZEPAK, M.P.; ARANTES, S.D.; ALEXANDRE, R.S.; AMARAL, J.A.T.; VITÓRIA, E.L.; SCHMILDT, E.R. Determination of the leaflet area of Schinus terebinthifolius Raddi in function of linear dimensions. Journal of Agricultural Science, Cambridge, v.11, n.14, p.198-204, 2019. ), without losing the high precision in its estimation (BUTTARO et al., 2015 BUTTARO, D.; ROUPHAEL, Y.; RIVERA, C.M.; COLLA, G.; GONNELLA, M. Simple and accurate allometric model for leaf area estimation in Vitis vinifera L. genotypes. Photosynthetica, Praha, v.53, n.3, p.342-8, 2015. ).

Another advantage associated with the equation adjusted in the present study is that it is possible to contemplate several cultivars, making it more interesting, as it favors data collection and allows its use by researchers and/ or producers in places where there is a large number of cultivars (OLIVEIRA, 2020 OLIVEIRA, V.S. Modelagem estatística de características biométricas para cultivares de macieira pouco exigentes ao frio cultivadas no norte do estado do Espírito Santo. 2020. 52 f. Dissertação (Mestrado em Agricultura Tropical) - Universidade Federal do Espírito Santo, Centro Universitário Norte do Espírito Santo, São Mateus, 2020. ).

It is noteworthy that for the accomplishment of the present study it was necessary to use specific meters to obtain the area of the banana leaves, these equipment demand time for the execution of the measures. In addition, as it is necessary to remove the leaves from the plant, they may not look good for reading, and maybe damaged or lose their turgidity. Another disadvantage of this equipment is the limitation for carrying out experiments, especially those in the field, and the difficulty in collecting and transporting the number of samples to the place where the analyzes will be carried out (LUCENA et al., 2011) LUCENA, R.R.M.; BATISTA, T.M.V.; DOMBROSKI, J.L.D.; LOPES, W.A.R.; RODRIGUES, G.S.O. Medição da área foliar de aceroleira. Revista Caatinga, Mossoró, v.24, n.2, p.40-5, 2011. . However, after adjusting the equation, it is not necessary to use specific equipment, and the total leaf area of the plants can be obtained without the use of more elaborate equipment, requiring only a ruler or a measuring tape. Despite the leaf anatomy of the most diverse banana cultivars being very similar, we only indicate the use of the adjusted equation for the cultivars Maça BRS Princesa, Prata BRS Platina, Prata Gorutuba, and Prata-Anã.

Conclusions

The total leaf area (TLA) of banana plants of the cultivars Maça BRS Princesa, Prata BRS Platina, Prata Gorutuba and Prata-Anã can be estimated through the equation TLA = 3.9292(WN) 1.5851, using the value obtained by multiplying the width of the third leave with the total number of leaves (WN).

  • ALVARES, C.A.; STAPE, J.L.; SENTELHAS, P.C.; GONÇALVES, J.L.M.; SPAROVEK, G. Koppen’s climate classification map for Brazil. Meteorologische Zeitschrift, Stuttgart, v.22, n.6, p.711-28, 2014.
  • ALVES, E.J. Cultivo da bananeira tipo Terra. Cruz das Almas: Embrapa-CNPMF, 2002. 176 p.
  • BLANCO, F.F.; FOLEGATTI, M.V. Estimation of leaf area for greenhouse cucumber by linear measurements under salinity and grafting. Scientia Agricola, Piracicaba, v.62, n.4, p.305-9, 2005.
  • BUSATO, C.; FONTES, P.C.R.; BRAUN, H.; BUSATO, C.C.M. Estimativa da a´rea foliar da batateira, cultivar Atlantic, utilizando dimenso~es lineares. Revista Cie^ncia Agrono^mica, Fortaleza, v.41, n.4, p.702-8, 2010
  • BUTTARO, D.; ROUPHAEL, Y.; RIVERA, C.M.; COLLA, G.; GONNELLA, M. Simple and accurate allometric model for leaf area estimation in Vitis vinifera L. genotypes. Photosynthetica, Praha, v.53, n.3, p.342-8, 2015.
  • CARVALHO, J.O.; TOEBE, M.; TARTAGLIA, F.L.; BANDEIRA, C.T.; TAMBARA, A.L. Leaf area estimation from linear measurements in different ages of Crotalaria juncea plants. Anais da Academia Brasileira de Ciências, Rio de Janeiro, v.89, n.3, p.1851-68, 2017.
  • CIRILLO, C.; PANNICO, A.; BASILE, B.; RIVERA, C.M.; GIACCONE, M.; COLLA, G.; PASCALE, S.; ROUPHAEL, Y. A simple and accurate allometric model to predict single leaf area of twenty-one european apricot cultivars. European Journal of Horticultural Science, Stuttgart, v.82, n.2, p.65-71, 2017.
  • DONATO, L.T.; DONATO, S.L.R.; BRITO, CLEITON, F.B.B.; FONSECA, V.A.; GOMES, C.N.; RODRIGUES FILHO, V.A. Estimating leaf area of prata-type banana plants with lanceolate type leaves. Revista Brasileira de Fruticultura, Jaboticabal, v.42, n.4, p.e-417, 2020.
  • FAO. Food and Agriculture Organization of the United Nations. Rome, 2019. Disponível em:https://www.fao.org. Acesso: 25 de jan.2021.
    » https://www.fao.org.
  • FERREIRA, E.B.; CAVALCANTI, P.P.; NOGUEIRA, D.A. Package ‘ExpDes.pt’. 2018. Disponível em: https://cran.r-project.org/web/packages/ExpDes.pt/index.html
    » https://cran.r-project.org/web/packages/ExpDes.pt/index.html
  • IBGE - Instituto Brasileiro de Geografia e Estatística. Produção agrícola municipal: Área destinada à colheita, área colhida, quantidade produzida, rendimento médio e valor da produção das lavouras permanentes. Rio de Janeiro, 2020. Disponível em: https://sidra.ibge.gov.br/tabela/1613#resultado Acesso em: 01 de jan. 2022.
    » https://sidra.ibge.gov.br/tabela/1613#resultado
  • KUMAR, N.; KRISHNAMOORTHY V.; NALINA, L.; SOORIANATHASUNDHARAM, K. Nuevo factor para estimar el a´rea foliar total en banano. INFOMUSA, Montpellier, v.11, n.2, p.42-3, 2002.
  • KVALSETH, T.O. Cautionary note about R2. The American Statistician, Washington, v.39, n.4, p.279-85, 1985.
  • LAVANHOLE, D.F.; OLIVEIRA, P.S.; VITÓRIA, E.L.; AOYAMA, E.M. Estimativa de área foliar por meio de relações alométricas em Aechmea blanchetiana (Baker) L.B.SM sob distintas condições de luminosidade. Iheringia, Série Botânica, Porto Alegre, v.73, n.3, p.363-73, 2018.
  • LIN, L.I. A concordance correlation coefficient to evaluatereproducibility. Biometrics, Washington, v.45, n.1, p.255-68, 1989.
  • LUCENA, R.R.M.; BATISTA, T.M.V.; DOMBROSKI, J.L.D.; LOPES, W.A.R.; RODRIGUES, G.S.O. Medição da área foliar de aceroleira. Revista Caatinga, Mossoró, v.24, n.2, p.40-5, 2011.
  • OLFATI, J.A.; PEYVAST, G.H.; SHABANI, H.; NOSRATIE-RAD, Z. An estimation of individual leaf area in cabbage and broccoli using non-destructive methods. Journal of Agricultural Science and Technology, Tehran, v.12, p.627-32, 2010. Suppl. (
  • OLIVEIRA, V.S. Modelagem estatística de características biométricas para cultivares de macieira pouco exigentes ao frio cultivadas no norte do estado do Espírito Santo. 2020. 52 f. Dissertação (Mestrado em Agricultura Tropical) - Universidade Federal do Espírito Santo, Centro Universitário Norte do Espírito Santo, São Mateus, 2020.
  • OLIVEIRA, V.S.; COVRE, A.M.; GOUVEA, D.S.; CANAL, L.; SANTOS, K.T.H.S.; SANTOS, J.S.H.; SANTOS, G.P.; PINHEIRO, A.P.B.; SCHMILDT, O.; POSSE, R.P.; CZEPAK, M.P.; ARANTES, S.D.; ALEXANDRE, R.S.; AMARAL, J.A.T.; VITÓRIA, E.L.; SCHMILDT, E.R. Determination of the leaflet area of Schinus terebinthifolius Raddi in function of linear dimensions. Journal of Agricultural Science, Cambridge, v.11, n.14, p.198-204, 2019.
  • R CORE TEAM. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing, 2022. Disponível em: https://www.R-project.org/
    » https://www.R-project.org/
  • RODRIGUES, M.G.V.; DIAS, M.S.C.; PACHECO, D.D. Influe^ncia de diferentes ni´veis de desfolha na produc¸a~o e qualidade dos frutos da bananeira ‘Prata-Ana~’. Revista Brasileira de Fruticultura, Jaboticabal, v.31, n.3, p.755-62, 2009
  • ROSA, A.R.D. Desempenho agronômico de novas cultivares de bananeira (Musa spp.) na região de Piracicaba-SP. 2016. 101 f. Tese (Doutorado) – Escola Superior de Agricultura “Luiz de Queiroz”, Piracicaba, 2016.
  • SANTOS, J.C.C.; COSTA, R.N.; SILVA, D.M.R.; SOUZA, A.A.; MOURA, F.B.P.; SILVA JUNIOR, J.M.; SILVA, J.V. Use of allometric models to estimate leaf area in Hymenaea courbaril L.Theoretical and Experimental Plant Physiology, Berlin, v.28, n.4, p.357-69, 2016.
  • SCHMILDT, E.R.; HUESO, J.J.; PINILLOS, V.; STELLFELDT, A.; CUEVAS, J. Allometric models for determining leaf area of ‘Fino de Jete’ cherimoya grown in greenhouse and in the open field. Fruits, Paris, v.72, n.1, p.24-30, 2017.
  • SIGNORELL, A. et al. Package ‘DescTools’. 2022. Disponível em: https://cran.r-project.org/web/packages/DescTools/index.html
    » https://cran.r-project.org/web/packages/DescTools/index.html
  • TOEBE, M.; CARGNELUTTI FILHO, A.; LOOSE, L.H.; HELDWEIN, A.B.; ZANON, A.J. Leaf area of snap bean (Phaseolus vulgaris L.) according to leaf dimensions. Semina, Londrina, v.33, p.2491–500, 2012
  • TOGNERE, J.; MARQUES, I.R.; OLIVEIRA, I.L.; SCHMILDT, O.; OLIVEIRA, V.S.; TOGNELLA, M.M.P.; SCHMILDT, E.R. Estimação da área foliar de trema micrantha em função das dimensões lineares. Nucleus, Austin, v.18, n.2, p.133-141, 2021.
  • VIANA, P.C.; LIMA, J.G.A.; MENEZES, R.V.; COELHO, E.F.; BARROSO, N.I.S.; PEREIRA, M.M. Modelo matema´tico para estimativa da a´rea foliar para cultivar de bananeira platamo “D’Angola”. In: CONIRD – CONGRESSO NACIONAL DE IRRIGAC¸A~O E DRENAGEM, 25., 2015. São Cristóvão. Anais […]. Sa~o Cristo´va~o: Universidade Federal de Sergipe , 2015.
  • WILLMOTT, C.J. On the validation of models. Physical Geography, Windsor, v.2, p.184-94, 1981.
  • ZHANG, L.; LIU X.S. Non-destructive leaf-area estimation for Bergeria purpurascens across timberline ecotone, southeast Tibet. Annales Botanici Fennici, Helsinki, v.47, n.5, p.346-52, 2010.
  • ZUCOLOTO, M.; LIMA, J.S.S.; COELHO, R.I. Modelo matemático para estimativa da área foliar total de bananeira ‘Prata-Anã’. Revista Brasileira de Fruticultura, Jaboticabal, v.30, n.4, p.1152-4, 2008.

Publication Dates

  • Publication in this collection
    01 Aug 2022
  • Date of issue
    2022

History

  • Received
    08 Feb 2022
  • Accepted
    18 May 2022
Sociedade Brasileira de Fruticultura Via de acesso Prof. Paulo Donato Castellane, s/n , 14884-900 Jaboticabal SP Brazil, Tel.: +55 16 3209-7188/3209-7609 - Jaboticabal - SP - Brazil
E-mail: rbf@fcav.unesp.br