Bee-inspired Radial Basis Function network to estimate tree aboveground wood volume in Brazilian Savanna

Natielle Gomes Cordeiro; Kelly Marianne Guimarães Pereira; Eugênio Monteiro da Silva Júnior; Carlos Alberto Araújo Júnior; Renato Dourado Maia; Moisés Lima Dutra; Christian Dias Cabacinha

doi:10.15287/afr.2026.2684

Authors

Natielle Gomes Cordeiro 1 Department of Forest Sciences, Federal University of Lavras, Lavras, MG, Brazil
Kelly Marianne Guimarães Pereira 1 Department of Forest Sciences, Federal University of Lavras, Lavras, MG, Brazil. | 2Department of Ecology and Conservation, Federal University of Lavras, Lavras, MG, Brazil
Eugênio Monteiro da Silva Júnior 3 Institute of Agricultural Sciences, Federal University of Minas Gerais, Montes Claros, MG, Brazil
Carlos Alberto Araújo Júnior 3 Institute of Agricultural Sciences, Federal University of Minas Gerais, Montes Claros, MG, Brazil
Renato Dourado Maia 3 Institute of Agricultural Sciences, Federal University of Minas Gerais, Montes Claros, MG, Brazil
Moisés Lima Dutra 4 Department of Information Science, Federal University of Santa Catarina, Florianópolis, SC, Brazil
Christian Dias Cabacinha 3 Institute of Agricultural Sciences, Federal University of Minas Gerais, Montes Claros, MG, Brazil

DOI:

https://doi.org/10.15287/afr.2026.2684

Keywords:

cOptBees algorithm, Artificial neural networks, Volumetric models, Brazilian savanna

Abstract

Forest variables such as aboveground wood volume are usually estimated by applying regression analysis. Nevertheless, in the past decades, new alternatives have been used, for example, artificial neural networks. In this sense, our study aimed to evaluate the efficiency of the Radial Basis Function (RBF) neural network in estimating aboveground wood volume for the Brazilian savanna using the cOptBees training algorithm. We fitted 18 allometric models and trained three Multilayer Perceptron (MLP) networks and two RBF networks using two different algorithms: k-means and cOptBees. We selected the MLP and RBF networks, as well as the allometric model with the best accuracy, for comparison. We verified the methods’ accuracy by analysing the statistics of bias, root mean square error (RMSE), and Pearson’s correlation coefficient. The lowest bias value was presented by the RBF network using the cOptBees algorithm (5.90 x 10^-5). The Näslund model showed the highest correlation (9.45 x 10^-1), as well as the lowest RMSE (2.07 x 10^-3). The aboveground wood volume estimates provided by the artificial neural networks showed similar results to those provided by classical regression models. Overall, we may infer that RBF networks trained using the cOptBees algorithm can be used to estimate aboveground wood volume in the Brazilian savanna, being as accurate as MLP or RBF networks trained with the k-means algorithm and allometric models. Finally, all methods showed similar aboveground wood volume estimates. However, neural networks offer advantages in optimizing field surveys because they require less sampling effort.

References

Alvares C.A., Stape J.L., Sentelhas P.C., Gonçalves J.L. de M., Sparovek G., 2013. Köppen’s climate classification map for Brazil. Meteorologische Zeitschrift 22: 711–728. https://doi.org/10.1127/0941-2948/2013/0507

APG., 2016. An update of the Angiosperm Phylogeny Group classification for the orders and families of flowering plants: APG IV. Botanical Journal of the Linnean Society 181: 1-20. https://doi.org/10.1111/boj.12385

Araújo Júnior C.A., Souza P.D. de, Assis A.L. de, Cabacinha C.D., Leite H.G., Soares C.P.B., Silva A.A.L. da, Castro R.V.O., 2019. Artificial neural networks, quantile regression, and linear regression for site index prediction in the presence of outliers. Pesquisa Agropecuária Brasileira 54: e00078. https://doi.org/10.1590/S1678-3921.pab2019.v54.00078

Artero A.O., 2009. Inteligência artificial: teórica e prática. Editora Livraria da Física, São Paulo, 230 p.

Binoti D.H.B., Binoti M.L.M. da S., Leite H.G., 2014. Configuração de redes neurais artificiais para estimação do volume de árvores. Revista Ciência da Madeira 5: 58-67. https://doi.org/10.1590/S0100-67622014000200008

Binoti D.H.B., Binoti M.L.M. da S., Leite H.G., Silva A., Santos A.C. de A., 2012. Modelagem da distribuição diamétrica em povoamentos de Eucalipto submetidos a desbate utilizando autômatos celulares. Revista Árvore 36: 931–939. https://doi.org/10.1590/S0100-67622012000500015

Binoti M.L.M. da S., Binoti D.H.B., Leite H.G., 2013. Aplicação de redes neurais artificiais para estimação da altura de povoamentos equiâneos de Eucalipto. Revista Árvore 37: 639–645. https://doi.org/10.1590/S0100-67622013000400007

Binoti M.L.M. da S., Leite H.G., Binoti D.H.B., Gleriani J.M., 2015. Prognose em nível de povoamento de clones de Eucalipto empregando Redes Neurais Artificiais. Cerne 21: 97–105. https://doi.org/10.1590/01047760201521011153

Braga A. de P., Carvalho A.P. de L.F. de, Ludermir T.B., 2014. Redes neurais artificiais - Teoria e aplicações. LTC – Livros Técnicos e Científicos Editora Ltda, Rio de Janeiro, 226 p.

Bueno L.P., Medanha J.T.R., Rodovalho R.S., Castro V.G.S. de, 2020. Modelagem volumétrica para frutíferas do Cerrado. Revista Mirante 13: 39-54.

Bueno M.L., Pennington R.T., Dexter K.G., Kamino L.H.Y., Pontara V., Neves D.M., Ratter J.A., Oliveira Filho A.T. de, 2016. Effects of Quaternary climatic fluctuations on the distribution of Neotropical savanna tree species. Ecography 39: 001–012. https://doi.org/10.1111/ecog.01860

Cerqueira E.O. de, Andrade J.C. de, Poppi R.J., Mello C., 2001. Redes Neurais e suas aplicações em calibração multivariada. Química Nova 24: 864–873. https://doi.org/10.1590/S0100-40422001000600025

Cheshmberah F., Fathizad, H., Parad, G.A., Shojaeifar, S., 2020. Comparison of RBF and MLP neural network performance and regression analysis to estimate carbon sequestration. International Journal of Environmental Science and Technology 17: 3891–3900. https://doi.org/10.1007/s13762-020-02696-y

Cordeiro N.G., Pereira K.M.G., Terra M. de C.N.S., Mello J.M. de, 2020. Structural and compositional shifts in Cerrado fragments in up to 11 years monitoring. Acta Scientiarum. Biological Sciences 42: e48357. https://doi.org/10.4025/actascibiolsci.v42i1.48357

Cruz D.P.F., Maia R.D., Castro L.N. de, 2015. On the Sensitivity of a Bee-Inspired Algorithm to Its Internal Parameters. International Journal of Computer Information Systems and Industrial Management Applications 7: 84–93.

Cruz D.P.F., Maia R.D, Silva L.A. da, Castro L.N. de, 2016. Neurocomputing BeeRBF: A bee-inspired data clustering approach to design RBF neural network classifiers. Neurocomputing 172: 427–437. https://doi.org/10.1016/j.neucom.2015.03.106

Dantas D., Pinto L.O.R., Lacerda T.H.S., Cordeiro N.G., Calegario N., 2024. Accuracy of tree height estimation with model extracted from artificial neural network and new linear and nonlinear models. Acta Scientiarum. Agronomy 46: e63286. https://doi.org/10.4025/actasciagron.v46i1.63286

Elzhov T.V., Mullen K.M., Spiess A.-N., Bolker B., 2016. R Interface to the Levenberg-Marquardt Nonlinear Least-Squares Algorithm Found in MINPACK, Plus Support for Bounds. [online 16 April 2020] URL: https://cran.rproject.org/web/packages/minpack.lm/ minpack.lm.pdf.

Freese F., 1973. A collection of log rules. Gen. Tech. Rep. FPL-1. U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, 65 p.

Giri K., Jayaraj R.S.C., Pandey R., Nainamalai R., Ashutosh S., 2019. Regression equations for estimating tree volume and biomass of important timber species in Meghalaya, India. Current Science 116: 75–81. https://doi.org/10.18520/cs/v116/i1/75-81

Gorgens E.B., Leite H.G., Santos H. do N., Gleriani J.M., 2009. Estimação do volume de árvores utilizando redes neurais artificiais. Revista Árvore 33: 1141–1147. https://doi.org/10.1590/S0100-67622009000600016

Grace J., José J.S., Meir P., Miranda H.S., Montes R.A., 2006. Productivity and carbon fluxes of tropical savannas. Journal of Biogeography 33: 387-400. https://doi.org/10.1111/j.1365-2699.2005.01448.x

Grosenbaugh L.R., 1948. Improved cubic volume computation. Journal of Forestry, 46: 299-301.

Gujarati D.N., Porter D.C., 2011. Econometria Básica. AMGH Editora Ltda, Porto Alegre, 924 p.

Günlü A., Ercanli I., Senyurt M., Keleş S., 2021. Estimation of some stand parameters from textural features from WorldView-2 satellite image using the artificial neural network and multiple regression methods: a case study from Turkey. Geocarto International 36: 918-935. https://doi.org/10.1080/10106049.2019.1629644

Haykin S.S., 1999. Neural Networks: A Comprehensive Foundation. Prentice Hall, Hoboken, 842 p.

Honda E.A., Mendonça A.H., Durigan G., 2014. Factors affecting the stemflow of trees in the Brazilian Cerrado. Ecohydrology 8:1351-1362. https://doi.org/10.1002/eco.1587

Imaña-Encinas J., Santana O.A., Paula J.E. de, Imaña C.R., 2009. Equações de volume de madeira para o Cerrado de Planaltina de Goiás. Floresta 39: 107–116. https://doi.org/10.5380/rf.v39i1.13731

Inkotte J., Bomfim B., Silva S.C., Valadão M.B.X., Rosa M.G., Viana R.B., Rios P.D., Gatto A., Pereira R.S., 2022. Applied Soil Ecology 169: 104209. https://doi.org/10.1016/j.apsoil.2021.104209

Karlik B., Olgac A.V., 2011. Performance Analysis of Various Activation Functions in Generalized MLP Architectures of Neural Networks. International Journal of Artificial Intelligence and Expert Systems 1: 111–122.

Know S.-K., Jung H.-S., Baek W.-K., Kim D., 2017. Classification of Forest Vertical Structure in South Korea from Aerial Orthophoto and Lidar Data Using an Artificial Neural Network. Applied Sciences 7: 1046. https://doi.org/10.3390/app7101046

Lacerda T.H.S., Cabacinha C.D., Araújo Júnior C.A., Maia R.D., Lacerda K.W. de S., 2017. Artificial Neural Networks for estimating tree volume in the Brazilian Savanna. Cerne 23: 483–491. https://doi.org/10.1590/01047760201723042347

Leon-Delgado H. de, Praga-Alejo R.J., Gonzalez-Gonzalez D.S., Cantú-Sifuentes M., 2018. Multivariate Statistical Inference in a Radial Basis Function Neural Network. Expert Systems with Applications 93: 313–321. https://doi.org/10.1016/j.eswa.2017.10.024

Liu J., Wang X., Wang T., 2019. Classification of tree species and stock volume estimation in ground forest images using Deep Learning. Computers and Electronics in Agriculture 166: 105012. https://doi.org/10.1016/j.compag.2019.105012

Lorenzi H., 1998. Árvores brasileiras: manual de identificação e cultivo de plantas arbóreas nativas do Brasil. Instituto Plantarum de Estudos da Flora Ltda, Nova Odessa, 384 p.

Maia R.D., Castro L.N. de, Caminhas W.M., 2013. Collective Decision-Making by Bee Colonies as Model for Optimization - the OptBees Algorithm. Applied Mathematical Sciences 7: 4327–4351. https://doi.org/10.12988/ams.2013.35271

Mendonça A.R. de, Silva J.C. da, Aozani T.S., Silva E.R. da, Santos J.A., Binoti D.H.B., Silva G.F. da, 2018. Estimação da altura total de árvores de ipê felpudo utilizando modelos de regressão e redes neurais artificiais. Revista Brasileira de Biometria 36: 128–139. https://doi.org/10.28951/rbb.v36i1.154

Miguel E.P., Rezende A.V., Leal F.A., Matricardi E.A.T., Vale A.T. do, Pereira R.S., 2015. Redes neurais artificiais para a modelagem do volume de madeira e biomassa do cerradão com dados de satélite. Pesquisa Agropecuária Brasileira 50: 829–839. https://doi.org/10.1590/S0100-204X2015000900012

Naumov V., Manton M., Elbakidze M., Rendenieks Z., Priednieks J., Uhlianets S., Yamelynets T., Zhivotov A., Angelstam P., 2018. How to reconcile wood production and biodiversity conservation? The Pan-European boreal forest history gradient as an “experiment”. Journal of Environmental Management 218: 1-13. https://doi.org/10.1016/j.jenvman.2018.03.095

Nordström E.-V., Nieuwenhuis M., Başkent E.Z., Biber P., Black K., Borges J.G., Bugalho M.N., Corradini G., Corrigan E., Eriksson L.O., Felton A., Forsell N., Hengeveld G., Hoogstra‑Klein M., Korosuo A., Lindbladh M., Lodin I., Lundholm A., Marto M., Masiero M., Mozgeris G., Pettenella D., Poschenrieder W., Sedmak R., Tucek J., Zoccatelli D., 2019. Forest decision support systems for the analysis of ecosystem services provisioning at the landscape scale under global climate and market change scenarios. European Journal of Forest Research 138:561–581. https://doi.org/10.1007/s10342-019-01189-z

Nunes M.H., Görgens E.B., 2016. Artificial Intelligence Procedures for Tree Taper Estimation within a Complex Vegetation Mosaic in Brazil. Plos One 11: e0154738. https://doi.org/10.1371/journal.pone.0154738

Pereira J.E.S., Barreto-Garcia P.A.B., Paula A. de, Lima R.B. de, Carvalho F.F. de, Nascimento M. dos S., Aragão M. de A., 2020. Form quocient in estimating Caatinga tree volume. Journal of Sustainable Forestry 40: 508-517. https://doi.org/10.1080/10549811.2020.1779090

Pereira K.M.G., Cordeiro N.G., Terra M.C.N.S., Pyles M.V., Cabacinha, C.D., Mello, J.M., van den Berg, E., 2020. Protection status as determinant of carbon stock drivers in Cerrado sensu stricto. Journal of Plant Ecology 13: 361-368. https://doi.org/10.1093/jpe/rtaa024

Pennington R.T., Lehmann C.E.R., Rowland L.M., 2018. Tropical savannas and dry forests. Current Biology 28: R541-R545. https://doi.org/10.1016/j.cub.2018.03.014

R Core Team, 2017. R: A language and environment for statistical computing. R Foundation for Statistical Computing,Vienna, Austria. [online 17 November 2019] URL: https://www.r-project.org/.

Reis L.P., Souza A.L. de, Reis P.C.M. dos R., Mazzei L., Leite H.G., Soares C.P.B., Torres C.M.M.E., Silva L.F. da, Ruschel A.R., Rêgo L.J.S., 2019. Modeling of tree recruitment by artificial neural networks after wood harvesting in a forest in eastern Amazon rain forest. Ciência Florestal 29: 583–594. https://doi.org/10.5902/1980509825808

Reis A.A. dos, Diniz J.M.F. de S., Acerbi Júnior F.W., Mello J.M. de, Batista A.P.B., Ferraz Filho A.C., 2020. Modeling the spatial distribution of wood volume in a Cerrado stricto sensu remnant in Minas Gerais state, Brazil. Scientia Forestalis 48: e2844. https://doi.org/10.18671/scifor.v48n125.15

Rezende A.V., Vale A.T. do, Sanquetta C.R., Figuereido Filho A., Felfili J.M., 2006. Comparação de modelos matemáticos para estimativa do volume, biomassa e estoque de carbono da vegetação lenhosa de um cerrado sensu stricto em Brasília, DF. Scientia Forestalis 65–76.

Ribeiro J.F., Walter B.M.T., 2008. As principais fitofisionomias do bioma Cerrado. Sano S.M., Almeida S.P. de, Ribeiro J.F., (eds.), Cerrado: Ecologia e flora, Embrapa Cerrado, Planaltina, pp. 152-212.

Silva J.P.M., Cabacinha C.D., Assis A.L., Monteiro T.C., Araújo Júnior C.A., Maia R.D., 2018. Redes neurais artificiais para estimar a densidade básica de madeiras do cerrado. Pesquisa Florestal Brasileira 38: 1–10. https://doi.org/10.4336/2018.pfb.38e201801656

Silva J.P.M., Silva M.L.M. da, Silva E.F. da, Silva G.F. da, Mendonça A.R. de, Cabacinha C.D., Araújo E.F., Santos J.S., Vieira G.C., Almeida M.N.F. de, Fernandes M.R. de M., 2019. Computational techniques applied to volume and biomass estimation of trees in Brazilian savanna. Journal of Environmental Management 249: 109368. https://doi.org/10.1016/j.jenvman.2019.109368

Silva Júnior E.M. da, Maia R.D., Cabacinha C.D., 2018. Bee-inspired RBF network for volume estimation of individual trees. Computers and Electronics in Agriculture 152: 401–408. https://doi.org/10.1016/j.compag.2018.07.036

Silva-Júnior C.M., 2012. 100 árvores do Cerrado Sentido Restrito. Rede de Sementes do Cerrado, Brasília, 360 p.

Silveira E.M.O., Reis A.A. dos, Terra M.C.N.S., Withey K.D., Mello J.M. de, Acerbi Júnior F.W., Ferraz Filho A.C., Mello C.R., 2019. Spatial distribution of wood volume in Brazilian savannas. Anais da Academia Brasileira de Ciências 91: e20180666. https://doi.org/10.1590/0001-3765201920180666

Souza P.H.C. de, Sousa H.J. de, Chagas M.P., Binoti, D.H. B., Venturoli F., Resende R.T., 2023. Combining Digital Imaging and Artificial Neural Networks for Individual Volumetric Estimation of Non-Straight Trees. TreeDimensional Journal 11: e2023037, 1-10. https://doi.org/10.55746/treed.2023.12.037

Thomas C., Andrade C.M., Schneider P.R., Finger C.A.G., 2006. Comparação de equações volumétricas ajustadas com dados de cubagem e análise de tronco. Ciência Florestal 16: 319–327. https://doi.org/10.5902/198050981911

Xavier A.C.F., Silva-Neto C. de M., Martins T.O., Ferreira F.G., Monteiro M.M., Oliveira G.M. de, Venturoli F., 2017. Growth and volume of Myracroduon urundeuva Allemão after the year of silvicultural interventions. Australian Journal of Crop Science 11: 271-276. https://doi.org/10.21475/ajcs.17.11.03.pne360

Zhang T., Cao Y., Ye F., Ren J., 2018. Use Multilayer Perceptron in Calibrating Multistage Non-linearity of Split Pipelined-ADC.