Floresta e Ambiente
https://www.floram.org/article/doi/10.1590/2179-8087.043917
Floresta e Ambiente
Original Article Forest Management

Additive and Non-additive Biomass Equations for Black Wattle

Equações de Biomassa Aditivas e não Aditivas para Acácia Negra

Alexandre Behling; Sylvio Péllico Netto; Carlos Roberto Sanquetta; Ana Paula Dalla Corte; Augusto Arlindo Simon; Aurélio Lourenço Rodrigues; Braulio Otomar Caron

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Abstract

ABSTRACT: The objectives of this work were to propose additive equations for biomass components (stem and crown) and total biomass for black wattle (Acacia mearnsii De Wild.) and show the inconsistency of independently adjusted biomass equations. Two procedures were used to fit nonlinear equations of biomass: i) independent and ii) systems of equations. The second procedure, defined by the application of the seemingly unrelated regression model, has better biological and statistical properties to estimate allometric equations of biomass components and total biomass when compared with the independent estimation. An effective property of this procedure is the additivity, i.e., the estimates of component biomass are compatible with those of total biomass. Independent fitted adjusted equations do not consider the dependence between the biomass components, thus, besides the estimates being non-additive, which is an undesirable property, they will result in estimates with larger variance.

Keywords

nonlinear seemingly unrelated regression, error modeling, additivity

Resumo

RESUMO: Os objetivos desse trabalho foram propor equações aditivas de biomassa dos componentes (fuste e copa) com a biomassa total para a espécie acácia negra (Acacia mearnsii De Wild.) e demonstrar a inconsistência de equações de biomassa ajustadas independentemente. Dois procedimentos foram utilizados para ajustar equações não lineares de biomassa: i) independente e ii) sistemas de equações. O segundo procedimento, definido pela aplicação do modelo de regressão aparentemente não relacionada, apresenta melhores propriedades biológicas e estatísticas para estimar equações alométricas de biomassa dos componentes e biomassa total, quando comparado com a estimação independente. Uma propriedade efetiva desse procedimento é a aditividade, isto é, as estimativas de biomassa dos componentes são compatíveis com as de biomassa total. As equações ajustadas independentes não consideram a dependência entre os componentes de biomassa, assim, além das estimativas não serem aditivas, propriedade indesejável, resultarão em estimativas com maior variância.
 

Palavras-chave

regressão não linear aparentemente não relacionada, modelagem do erro, aditividade

References

Affleck DLR, Diéguez-Aranda U. Additive nonlinear biomass equations: a likelihood-based approach. Forest Science 2016; 62(1): 129-140. http://dx.doi.org/10.5849/forsci.15-126.

Barichello LR, Schumacher MV, Vogel MLM. Quantificação da biomassa de Acacia mearnsii De Wild na região sul do Brasil. Ciência Florestal 2005; 15(2): 129-135. http://dx.doi.org/10.5902/198050981830.

Basuki TM, Van Laake PE, Skidmore AK, Hussin YA. Allometric equations for estimating the above-ground biomass in tropical lowland Dipterocarp forest. Forest Ecology and Management 2009; 257(8): 1684-1694. http://dx.doi.org/10.1016/j.foreco.2009.01.027.

Behling A. Modelagem da biomassa de árvores para assegurar aditividade dos seus componentes [tese]. Curitiba: Universidade Federal do Paraná; 2016.

Bi H, Long Y, Turner J, Lei Y, Snowdon P, Li Y et al. Additive prediction of aboveground biomass for Pinus radiata (D. Don) plantations. Forest Ecology and Management 2010; 259(12): 2301-2314. http://dx.doi.org/10.1016/j.foreco.2010.03.003.

Bi H, Murphy S, Volkova L, Weston C, Fairman T, Li Y et al. Additive biomass equations based on complete weighing of sample trees for open eucalypt forest species in south-eastern Australia. Forest Ecology and Management 2015; 349: 106-121. http://dx.doi.org/10.1016/j.foreco.2015.03.007.

Caldeira MVW, Saidelles FLF, Schumacher MV, Godinho TO. Biomassa de povoamento de Acacia mearnsii De Wild., Rio Grande do Sul, Brasil. Scientia Forestalis 2011; 39(90): 133-141.

Caldeira MVW. Quantificação da biomassa e do conteúdo de nutrientes em diferentes procedências de Acácia-negra (Acacia mearnsii De Wild) [dissertação]. Santa Maria: Universidade Federal de Santa Maria; 1998.

Carbonera Pereira J, Schumacher MV, Hoppe JM, Caldeira MVW, Santos EM. Produção de biomassa em um povoamento de Acacia mearnsii De Wild. no Estado do Rio Grande do Sul. Revista Árvore 1997; 21(4): 521-526.

Carvalho JP, Parresol BR. Additivity in tree biomass components of Pyrenean oak ( Quercus pyrenaica Willd.). Forest Ecology and Management 2003; 179(1-3): 269-276. http://dx.doi.org/10.1016/S0378-1127(02)00549-2.

Chave J, Réjou-Méchain M, Búrquez A, Chidumayo E, Colgan MS, Delitti WBC et al. Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology 2014; 20(10): 3177-3190. http://dx.doi.org/10.1111/gcb.12629. PMid:24817483.

Chiyenda SS, Kozak A. Additivity of component biomass regression equations when the underlying model is linear. Canadian Journal of Forest Research 1984; 14(3): 441-446. http://dx.doi.org/10.1139/x84-078.

Cunia T, Briggs RD. Forcing additivity of biomass tables: some empirical results. Canadian Journal of Forest Research 1984; 14(3): 376-384. http://dx.doi.org/10.1139/x84-067.

Dong L, Zhang L, Li F. A compatible system of biomass equations for three conifer species in Northeast, China. Forest Ecology and Management 2014; 329: 306-317. http://dx.doi.org/10.1016/j.foreco.2014.05.050.

Dudley NS, Fownes JH. Preliminary biomass equations for eight species of fast-growing tropical trees. Journal of Tropical Forest Science 1992; 5(1): 68-73.

Fehrmann L, Kleinn C. General considerations about the use of allometric equations for biomass estimation on the example of Norway spruce in central Europe. Forest Ecology and Management 2006; 236(2-3): 412-421. http://dx.doi.org/10.1016/j.foreco.2006.09.026.

Genet A, Wernsdörfer H, Jonard M, Pretzsch H, Rauch M, Ponette Q et al. Ontogeny partly explains the apparent heterogeneity of published biomass equations for Fagus sylvatica in central Europe. Forest Ecology and Management 2011; 261(7): 1188-1202. http://dx.doi.org/10.1016/j.foreco.2010.12.034.

Greene WH. Econometric analysis. Upper Saddle River: Prentice-Hall; 2008.

Harvey AC. Estimating regression models with multiplicative heteroscedasticity. Econometrica 1976; 44(3): 461-465. http://dx.doi.org/10.2307/1913974.

Kozak A. Methods of ensuring additivity of biomass components by regression analysis. Forestry Chronicle 1970; 46(5): 402-404. http://dx.doi.org/10.5558/tfc46402-5.

Maddala GS. Introduction to econometrics. 3rd ed. New York: John Wiley & Sons; 2001.

Mochiutti S. Produtividade e sustentabilidade de plantações de acácia-negra (Acacia mearnsii De Wild.) no Rio Grande do Sul [tese]. Curitiba: Universidade Federal do Paraná; 2007.

Niklas KJ. Size-dependent allometry of tree height, diameter and trunk-taper. Annals of Botany 1995; 75(3): 217-227. http://dx.doi.org/10.1006/anbo.1995.1015.

Parresol BR. Modeling multiplicative error variance: an example predicting tree diameter from stump dimensions in bald cypress. Forest Science 1993; 39(4): 670-679.

Parresol BR. Assessing tree and stand biomass: a review with examples and critical comparisons. Forest Science 1999; 45: 573-593.

Parresol BR. Additivity of nonlinear biomass equations. Canadian Journal of Forest Research 2001; 31(5): 865-878. http://dx.doi.org/10.1139/x00-202

Picard N, Saint-André L, Henry M. Manual for building tree volume and biomass allometric equations: from field measurement to prediction. Rome: Food and Agricultural Organization of the Unites Nations, Centre de Coopération Internationale en Recherche Agronomique pour le Développement; 2012.

Pilli P, Anfodillo T, Carrer M. Towards a functional and simplified allometry for estimating forest biomass. Forest Ecology and Management 2006; 237(1-3): 583-593. http://dx.doi.org/10.1016/j.foreco.2006.10.004.

Poorter H, Niklas KJ, Reich PB, Oleksyn J, Poot P, Mommer L. Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control. The New Phytologist 2012; 193(1): 30-50. http://dx.doi.org/10.1111/j.1469-8137.2011.03952.x. PMid:22085245.

Poudel KP, Temesgen H. Methods for estimating aboveground biomass and its components for Douglas-fir and lodgepole pine trees. Canadian Journal of Forest Research 2016; 46(1): 77-87. http://dx.doi.org/10.1139/cjfr-2015-0256.

Saidelles FLF. Determinação da biomassa e altura de amostragem para a quantificação de nutrientes em Acacia mearnsii De Wild [tese]. Santa Maria: Universidade Federal de Santa Maria; 2005.

Saint-André L, M’Bou AT, Mabiala A, Mouvondy W, Jourdan C, Roupsard O et al. Age-related equations for above – and below: ground biomass of a Eucalyptus hybrid in Congo. Forest Ecology and Management 2005; 205(1-3): 199-214. http://dx.doi.org/10.1016/j.foreco.2004.10.006.

Sanquetta CR, Behling A, Corte AP, Simon A, Pscheidt H, Ruzza MS et al. Estoques de biomassa e carbono em povoamentos de acácia negra em diferentes idades no Rio Grande do Sul. Scientia Forestalis 2014; 42(103): 361-370.

Sanquetta CR, Behling A, Corte APD, Péllico S No, Schikowski AB, Amaral M. Simultaneous estimation as alternative to independent modeling of tree biomass. Annals of Forest Science 2015a; 72(8): 1099-1112. http://dx.doi.org/10.1007/s13595-015-0497-2.

Sanquetta CR, Wojciechowski J, Dalla Corte AP, Behling A, Péllico S No, Rodrigues AL et al. Comparison of data mining and allometric model in estimation of tree biomass. BMC Bioinformatics 2015b; 16(247): 1-9. PMid:26250142.

Sileshi GW. A critical review of forest biomass estimation models, common mistakes and corrective measures. Forest Ecology and Management 2014; 329: 237-254. http://dx.doi.org/10.1016/j.foreco.2014.06.026.

Steel RGD, Torrie JH, Dickey DA. Principles and procedures of statistics: a biometrical approach. 3rd ed. New York: McGraw-Hill; 1996.

Stein PP, Tonietto L. Black wattle silviculture in Brazil. In: Brown AG, Ko HC, editors. Black wattle and its utilization. Barton: Rural Industries Research and Development Corporation; 1997.

Wayson CA, Johnson KD, Cole JA, Olguín MI, Carrillo OI, Birdsey RA. Estimating uncertainty of allometric biomass equations with incomplete fit error information using a pseudo-data approach: methods. Annals of Forest Science 2015; 72(6): 825-834. http://dx.doi.org/10.1007/s13595-014-0436-7.

Williams CJ, LePage BA, Vann DR, Tange T, Ikeda H, Ando M et al. Structure, allometry, and biomass of plantations Metasequoia glyptostroboides in Japan. Forest Ecology and Management 2003; 180(1-3): 287-301. http://dx.doi.org/10.1016/S0378-1127(02)00567-4.

Zapata-Cuartas M, Sierra C, Alleman L. Probability distribution of allometric coefficients and Bayesian estimation of aboveground tree biomass. Forest Ecology and Management 2012; 277: 173-179. http://dx.doi.org/10.1016/j.foreco.2012.04.030.

Zhao D, Kane M, Markewitz D, Teskey R, Clutter M. Additive tree biomass equations for mid-rotation loblolly pine plantations. Forest Science 2015; 61(4): 613-623. http://dx.doi.org/10.5849/forsci.14-193.

Zheng C, Mason EG, Jia L, Wei S, Sun S, Duan J. A single-tree additive biomass model of Quercus variabilis Blume forest in North China. Trees 2015; 29(3): 705-716. http://dx.doi.org/10.1007/s00468-014-1148-1.

Zianis D. Predicting mean aboveground forest biomass and its associated variance. Forest Ecology and Management 2008; 256(6): 1400-1407. http://dx.doi.org/10.1016/j.foreco.2008.07.002.
 

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