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Forest Ecosystems 2023, 10(4): 100130 https://doi.org/10.1016/j.fecs.2023.100130
Research Article | Open Access | Issue | Published: 27 July 2023

Developing allometric equations to estimate forest biomass for tree species categories based on phylogenetic relationships

Show Author's Information Mingxia Yanga,  Xiaolu Zhoua( ),  Changhui Penga,b( ),  Tong Lia,  Kexin Chena,  Zelin Liua,  Peng Lia,  Cicheng Zhanga,  Jiayi Tanga,  Ziying Zoua
School of Geographic Sciences, Hunan Normal University, Changsha, 410081, China
Institute of Environment Sciences, Department of Biology Sciences, University of Quebec at Montreal, Case Postale 8888, Succursale Centre-Ville, Montreal, Quebec, H3C 3P8, Canada
Keywords:
National Forest Inventory, Wood density, Allometric equation, Forest biomass, Species grouping, Tree architecture
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Yang M, Zhou X, Peng C, et al. Developing allometric equations to estimate forest biomass for tree species categories based on phylogenetic relationships. Forest Ecosystems, 2023, 10(4): 100130. https://doi.org/10.1016/j.fecs.2023.100130
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Abstract Full text About this article

The development of allometric biomass models is important process in biomass estimation because the reliability of forest biomass and carbon estimations largely depends on the accuracy and precision of such models. National Forest Inventories (NFI) are detailed assessments of forest resources at national and regional levels that provide valuable data for forest biomass estimation. However, the lack of biomass allometric equations for each tree species in the NFI currently hampers the estimation of national-scale forest biomass. The main objective of this study was to develop allometric biomass regression equations for each tree species in the NFI of China based on limited biomass observations. These equations optimally grouped NFI and biomass observation species according to their phylogenetic relationships. Significant phylogenetic signals demonstrated phylogenetic conservation of the crown-to-stem biomass ratio. Based on phylogenetic relationships, we grouped and matched NFI and biomass observation species into 22 categories. Allometric biomass regression models were developed for each of these 22 species categories, and the models performed successfully (R2 ​= ​0.97, root mean square error (RMSE) ​= ​12.9 ​t·ha–1, relative RMSE ​= ​11.5%). Furthermore, we found that phylogeny-based models performed more effectively than wood density-based models. The results suggest that grouping species based on their phylogenetic relationships is a reliable approach for the development and selection of accurate allometric equations.


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About this article

Developing allometric equations to estimate forest biomass for tree species categories based on phylogenetic relationships

Show Author's information Mingxia Yanga, Xiaolu Zhoua( ), Changhui Penga,b( ), Tong Lia, Kexin Chena, Zelin Liua, Peng Lia, Cicheng Zhanga, Jiayi Tanga, Ziying Zoua
School of Geographic Sciences, Hunan Normal University, Changsha, 410081, China
Institute of Environment Sciences, Department of Biology Sciences, University of Quebec at Montreal, Case Postale 8888, Succursale Centre-Ville, Montreal, Quebec, H3C 3P8, Canada

Abstract

The development of allometric biomass models is important process in biomass estimation because the reliability of forest biomass and carbon estimations largely depends on the accuracy and precision of such models. National Forest Inventories (NFI) are detailed assessments of forest resources at national and regional levels that provide valuable data for forest biomass estimation. However, the lack of biomass allometric equations for each tree species in the NFI currently hampers the estimation of national-scale forest biomass. The main objective of this study was to develop allometric biomass regression equations for each tree species in the NFI of China based on limited biomass observations. These equations optimally grouped NFI and biomass observation species according to their phylogenetic relationships. Significant phylogenetic signals demonstrated phylogenetic conservation of the crown-to-stem biomass ratio. Based on phylogenetic relationships, we grouped and matched NFI and biomass observation species into 22 categories. Allometric biomass regression models were developed for each of these 22 species categories, and the models performed successfully (R2 ​= ​0.97, root mean square error (RMSE) ​= ​12.9 ​t·ha–1, relative RMSE ​= ​11.5%). Furthermore, we found that phylogeny-based models performed more effectively than wood density-based models. The results suggest that grouping species based on their phylogenetic relationships is a reliable approach for the development and selection of accurate allometric equations.

Keywords: National Forest Inventory, Wood density, Allometric equation, Forest biomass, Species grouping, Tree architecture

References(62)

Akindele, S.O., LeMay, V.M., 2006. Development of tree volume equations for common timber species in the tropical rain forest area of Nigeria. For. Ecol. Manag. 226, 41–48. https://doi.org/10.1016/j.foreco.2006.01.022.
DOI Google Scholar

Anacker, B.L., Strauss, S.Y., 2016. Ecological similarity is related to phylogenetic distance between species in a cross-niche field transplant experiment. Ecology 97, 1807–1818. https://doi.org/10.1890/15-1285.1.
DOI Google Scholar

Burns, J.H., Strauss, S.Y., 2011. More closely related species are more ecologically similar in an experimental test. Proc. Natl. Acad. Sci. U.S.A. 108, 5302–5307. https://doi.org/10.1073/pnas.1013003108.
DOI Google Scholar

Chave, J., Andalo, C., Brown, S., Cairns, M.A., Chambers, J.Q., Eamus, D., Fölster, H., Fromard, F., Higuchi, N., Kira, T., Lescure, J.-P., Nelson, B.W., Ogawa, H., Puig, H., Riéra, B., Yamakura, T., 2005. Tree allometry and improved estimation of carbon stocks and balance in tropical forests. Oecologia 145, 87–99. https://doi.org/10.1007/s00442-005-0100-x.
DOI Google Scholar

Chave, J., Coomes, D., Jansen, S., Lewis, S.L., Swenson, N.G., Zanne, A.E., 2009. Towards a worldwide wood economics spectrum. Ecol. Lett. 12, 351–366. https://doi.org/10.1111/j.1461-0248.2009.01285.x.
DOI Google Scholar

Chave, J., Réjou-Méchain, M., Búrquez, A., Chidumayo, E., Colgan, M.S., Delitti, W.B.C., Duque, A., Eid, T., Fearnside, P.M., Goodman, R.C., Henry, M., Martínez-Yrízar, A., Mugasha, W.A., Müller-Landau, H.C., Mencuccini, M., Nelson, B.W., Ngomanda, A., Nogueira, E.M., Ortiz-Malavassi, E., Pélissier, R., Ploton, P., Ryan, C.M., Saldarriaga, J.G., Vieilledent, G., 2014. Improved allometric models to estimate the aboveground biomass of tropical trees. Glob. Change Biol. 20, 3177–3190. https://doi.org/10.1111/gcb.12629.
DOI Google Scholar

Chinese Academy of Forestry Sciences, Research Institute of Wood Industry, 1982. Wood Physical and Mechanical Properties of Main Tree Species in China, first ed. China Forestry Press, Beijing.

Crisp, M.D., Arroyo, M.T.K., Cook, L.G., Gandolfo, M.A., Jordan, G.J., McGlone, M.S., Weston, P.H., Westoby, M., Wilf, P., Linder, H.P., 2009. Phylogenetic biome conservatism on a global scale. Nature 458, 754–756. https://doi.org/10.1038/nature07764.
DOI Google Scholar

Domke, G.M., Oswalt, S.N., Walters, B.F., Morin, R.S., 2020. Tree planting has the potential to increase carbon sequestration capacity of forests in the United States. Proc. Natl. Acad. Sci. U.S.A. 117, 24649–24651. https://doi.org/10.1073/pnas.2010840117.
DOI Google Scholar

Ducey, M.J., 2012. Evergreenness and wood density predict height-diameter scaling in trees of the northeastern United States. For. Ecol. Manag. 279, 21–26. https://doi.org/10.1016/j.foreco.2012.04.034.
DOI Google Scholar

Dusenge, M.E., Duarte, A.G., Way, D.A., 2019. Plant carbon metabolism and climate change: elevated CO2 and temperature impacts on photosynthesis, photorespiration and respiration. New Phytol. 221, 32–49. https://doi.org/10.1111/nph.15283.
DOI Google Scholar

Fang, J., Chen, A., Peng, C., Zhao, S., Ci, L., 2001. Changes in forest biomass carbon storage in China between 1949 and 1998. Science 291, 2320–2322. https://doi.org/10.1126/science.1058629.
DOI Google Scholar

Fang, J., Chen, A., Zhao, S., Ci, L., 2002. Estimating biomass carbon of China’s forests: supplementary notes on report published in Science (291, 2320-2322) by Fang et al. (2001). Acta Phytoecol. Sin. 26, 243-249 (In Chinese with English abstract).
Google Scholar
Food and Agriculture Organization, 2020. Sustainable Forest Management. Food & Agriculture Organization of the United Nations, Rome.

Forrester, D.I., 2017. Generalized biomass and leaf area allometric equations for European tree species incorporating stand structure, tree age and climate. For. Ecol. Manag. 396, 160–175. https://doi.org/10.1016/j.foreco.2017.04.011.
DOI Google Scholar

Gschwantner, T., Alberdi, I., Bauwens, S., Bender, S., Borota, D., Bosela, M., Bouriaud, O., Breidenbach, J., Donis, J., Fischer, C., Gasparini, P., Heffernan, L., Hervé, J.-C., Kolozs, L., Korhonen, K.T., Koutsias, N., Kovácsevics, P., Kučera, M., Kulbokas, G., Kuliešis, A., Lanz, A., Lejeune, P., Lind, T., Marin, G., Morneau, F., Nord-Larsen, T., Nunes, L., Pantić, D., Redmond, J., Rego, F.C., Riedel, T., Šebeň, V., Sims, A., Skudnik, M., Tomter, S.M., 2022. Growing stock monitoring by European National Forest Inventories: historical origins, current methods and harmonization. For. Ecol. Manag. 505, 119868. https://doi.org/10.1016/j.foreco.2021.119868.
DOI Google Scholar

Guo, Z., Fang, J., Pan, Y., Birdsey, R., 2010. Inventory-based estimates of forest biomass carbon stocks in China: a comparison of three methods. For. Ecol. Manag. 259, 1225–1231. https://doi.org/10.1016/j.foreco.2009.09.047.
DOI Google Scholar

Henry, M., Besnard, A., Asante, W.A., Eshun, J., Adu-Bredu, S., Valentini, R., Bernoux, M., Saint-André, L., 2010. Wood density, phytomass variations within and among trees, and allometric equations in a tropical rainforest of Africa. For. Ecol. Manag. 260, 1375–1388. https://doi.org/10.1016/j.foreco.2010.07.040.
DOI Google Scholar

Henry, M., Cifuentes Jara, M., Réjou-Méchain, M., Piotto, D., Michel Fuentes, J.M., Wayson, C., Cueva Rojas, K., Guier, F.A., Lombis, H.C., López, E.C., Lara, R.C., Rojas, K.C., Del Águila Pasquel, J., Montoya, Á.D, Vega, J.F., Galo, A.J., López, O.R., Marklund, L.G., Milla, F., de Jesús Návar Cahidez, J., Malavassi, E.O., Pérez, J., Zea, C.R., García, L.R., Pons, R.R., Sanquetta, C., Scott, C., Westfall, J., Zapata-Cuartas, M., Saint-André, L., 2015. Recommendations for the use of tree models to estimate national forest biomass and assess their uncertainty. Ann. For. Sci. 72, 769–777. https://doi.org/10.1007/s13595-015-0465-x.
DOI Google Scholar

Holdaway, R.J., McNeill, S.J., Mason, N.W.H., Carswell, F.E., 2014. Propagating uncertainty in plot-based estimates of forest carbon stock and carbon stock change. Ecosystems 17, 627–640. https://doi.org/10.1007/s10021-014-9749-5.
DOI Google Scholar

Huxley, J.S., 1924. Constant differential growth-ratios and their significance. Nature 114, 895–896. https://doi.org/10.1038/114895a0.
DOI Google Scholar

Ishihara, M.I., Utsugi, H., Tanouchi, H., Aiba, M., Kurokawa, H., Onoda, Y., Nagano, M., Umehara, T., Ando, M., Miyata, R., Hiura, T., 2015. Efficacy of generic allometric equations for estimating biomass: a test in Japanese natural forests. Ecol. Appl. 25, 1433–1446. https://doi.org/10.1890/14-0175.1.
DOI Google Scholar

Jandl, R., Lindner, M., Vesterdal, L., Bauwens, B., Baritz, R., Hagedorn, F., Johnson, D.W., Minkkinen, K., Byrne, K.A., 2007. How strongly can forest management influence soil carbon sequestration? Geoderma 137, 253–268. https://doi.org/10.1016/j.geoderma.2006.09.003.
DOI Google Scholar

Jenkins, J.C., Chojnacky, D.C., Heath, L.S., Birdsey, R.A., Notes, A., 2003. National-scale biomass estimators for United States tree species. For. Sci. 49, 12–35. https://doi.org/10.1093/forestscience/49.1.12.
DOI Google Scholar

Jin, Y., Qian, H., 2019. V.PhyloMaker: an R package that can generate very large phylogenies for vascular plants. Ecography 42, 1353–1359. https://doi.org/10.1111/ecog.04434.
DOI Google Scholar

Joosten, R., Schumacher, J., Wirth, C., Schulte, A., 2004. Evaluating tree carbon predictions for beech (Fagus sylvatica L.) in western Germany. For. Ecol. Manag. 189, 87–96. https://doi.org/10.1016/j.foreco.2003.07.037.
DOI Google Scholar

Laiho, R., Laine, J., 1997. Tree stand biomass and carbon content in an age sequence of drained pine mires in southern Finland. For. Ecol. Manag. 93, 161–169. https://doi.org/10.1016/S0378-1127(96)03916-3.
DOI Google Scholar

Lei, X.D., Tang, M.P., Lu, Y.C., Hong, L.X., Tian, D.L., 2009. Forest inventory in China: status and challenges. Int. For. Rev. 11, 52–63. https://doi.org/10.1505/ifor.11.1.52.
DOI Google Scholar

Lines, E.R., Zavala, M.A., Purves, D.W., Coomes, D.A., 2012. Predictable changes in aboveground allometry of trees along gradients of temperature, aridity and competition: predictable variation in tree aboveground allometry. Glob. Ecol. Biogeogr. 21, 1017–1028. https://doi.org/10.1111/j.1466-8238.2011.00746.x.
DOI Google Scholar

Liu, C., Zhou, X., Lei, X., Huang, H., Zhou, C., Peng, C., Wang, X., 2019. Separating regressions for model fitting to reduce the uncertainty in forest volume-biomass relationship. Forests 10, 658. https://doi.org/10.3390/f10080658.
DOI Google Scholar

Losos, J.B., 2008. Phylogenetic niche conservatism, phylogenetic signal and the relationship between phylogenetic relatedness and ecological similarity among species. Ecol. Lett. 11, 995–1003. https://doi.org/10.1111/j.1461-0248.2008.01229.x.
DOI Google Scholar

Loubota Panzou, G.J., Fayolle, A., Jucker, T., Phillips, O.L., Bohlman, S., Banin, L.F., Lewis, S.L., Affum-Baffoe, K., Alves, L.F., Antin, C., Arets, E., Arroyo, L., Baker, T.R., Barbier, N., Beeckman, H., Berger, U., Bocko, Y.E., Bongers, F., Bowers, S., Brade, T., Brondizio, E.S., Chantrain, A., Chave, J., Compaore, H., Coomes, D., Diallo, A., Dias, A.S., Dimobe, K., Djagbletey, G.D., Domingues, T., Doucet, J.-L., Drouet, T., Forni, E., Godlee, J.L., Goodman, R.C., Gourlet-Fleury, S., Hien, F., Iida, Y., Ilondea, B.A., Muledi, J.I., Jacques, P., Kuyah, S., López-Portillo, J., Loumeto, J.J., Marimon-Junior, B.H., Marimon, B.S., Mensah, S., Mitchard, E.T.A., Moncrieff, G.R., Narayanan, A., O’Brien, S.T., Ouedraogo, K., Palace, M.W., Pélissier, R., Ploton, P., Poorter, L., Ryan, C.M., Saiz, G., dos Santos, K., Schlund, M., Sellan, G., Sonke, B., Sterck, F., Thibaut, Q., Van Hoef, Y., Veenendaal, E., Vovides, A.G., Xu, Y., Yao, T.L, Feldpausch, T.R., 2021. Pantropical variability in tree crown allometry. Glob. Ecol. Biogeogr. 30, 459–475. https://doi.org/10.1111/geb.13231.
DOI Google Scholar

Luo, Y., Zhang, X., Wang, X., Lu, F., 2013. Biomass and its Allocation of Chinese Forest Ecosystems. China Forestry Publishing House, Beijing.

Luo, Y., Wang, X., Ouyang, Z., Lu, F., Feng, L., Tao, J., 2020. A review of biomass equations for China’s tree species. Earth Syst. Sci. Data 12, 21–40. https://doi.org/10.5194/essd-12-21-2020.
DOI Google Scholar

Manuri, S., Brack, C., Nugroho, N.P., Hergoualc’h, K., Novita, N., Dotzauer, H., Verchot, L., Putra, C.A.S., Widyasari, E., 2014. Tree biomass equations for tropical peat swamp forest ecosystems in Indonesia. For. Ecol. Manag. 334, 241–253. https://doi.org/10.1016/j.foreco.2014.08.031.
DOI Google Scholar

McCarthy, M.C., Enquist, B.J., 2007. Consistency between an allometric approach and optimal partitioning theory in global patterns of plant biomass allocation. Funct. Ecol. 21, 713–720. https://doi.org/10.111/j.1365-2435.2007.01276.
DOI Google Scholar

Mcgill, B., Enquist, B., Weiher, E., Westoby, M., 2006. Rebuilding community ecology from functional traits. Trends Ecol. Evol. 21, 178–185. https://doi.org/10.1016/j.tree.2006.02.002.
DOI Google Scholar

McRoberts, R.E., Tomppo, E.O., Schadauer, K., Ståhl, G., 2012. Harmonizing National Forest Inventories. For. Sci. 58, 189–190. https://doi.org/10.5849/forsci.12-042.
DOI Google Scholar

Muukkonen, P., 2007. Generalized allometric volume and biomass equations for some tree species in Europe. Eur. J. For. Res. 126, 157–166. https://doi.org/10.1007/s10342-007-0168-4.
DOI Google Scholar
National Forestry, Grassland Administration, 2017. Testing Basic Wood Density of National Dominant Species (Group). NFGA, Beijing.

Pagel, M., 1999. Inferring the historical patterns of biological evolution. Nature 401, 877–884. https://doi.org/10.1038/44766.
DOI Google Scholar

Poorter, H., Jagodzinski, A.M., Ruiz-Peinado, R., Kuyah, S., Luo, Y., Oleksyn, J., Usoltsev, V.A., Buckley, T.N., Reich, P.B., Sack, L., 2015. How does biomass distribution change with size and differ among species? An analysis for 1200 plant species from five continents. New Phytol. 208, 736–749. https://doi.org/10.1111/nph.13571.
DOI Google Scholar

Reich, P.B., Luo, Y., Bradford, J.B., Poorter, H., Perry, C.H., Oleksyn, J., 2014. Temperature drives global patterns in forest biomass distribution in leaves, stems, and roots. Proc. Natl. Acad. Sci. U.S.A. 111, 13721–13726. https://doi.org/10.1073/pnas.1216053111.
DOI Google Scholar

Revell, L.J., 2012. phytools: an R package for phylogenetic comparative biology (and other things). Methods Ecol. Evol. 2, 217–223. https://doi.org/10.111/j.2041-210X.2011.00169.x.
DOI Google Scholar

Richter, D.D., Markewitz, D., Trumbore, S.E., Wells, C.G., 1999. Rapid accumulation and turnover of soil carbon in a re-establishing forest. Nature 400, 56–58. https://doi.org/10.1038/21867.
DOI Google Scholar

Scheller, R.M., Mladenoff, D.J., 2005. A spatially interactive simulation of climate change, harvesting, wind, and tree species migration and projected changes to forest composition and biomass in northern Wisconsin, USA. Glob. Change Biol. 11, 307–321. https://doi.org/10.1111/j.1365-2486.2005.00906.x.
DOI Google Scholar

Sun, H., Wang, X., Fan, D., 2020. Effects of climate, biotic factors, and phylogeny on allometric relationships: testing the metabolic scaling theory in plantations and natural forests across China. For. Ecosyst. 7, 51. https://doi.org/10.1186/s40663-020-00263-y.
DOI Google Scholar

Temesgen, H., Affleck, D., Poudel, K., Gray, A., Sessions, J., 2015. A review of the challenges and opportunities in estimating above ground forest biomass using tree-level models. Scand. J. For. Res. 30, 326–335. https://doi.org/10.1080/02827581.2015.1012114.
DOI Google Scholar

van Breugel, M., Ransijn, J., Craven, D., Bongers, F., Hall, J.S., 2011. Estimating carbon stock in secondary forests: decisions and uncertainties associated with allometric biomass models. For. Ecol. Manag. 262, 1648–1657. https://doi.org/10.1016/j.foreco.2011.07.018.
DOI Google Scholar

Vasseur, F., Violle, C., Enquist, B.J., Granier, C., Vile, D., 2012. A common genetic basis to the origin of the leaf economics spectrum and metabolic scaling allometry. Ecol. Lett. 15, 1149–1157. https://doi.org/10.1111/j.1461-0248.2012.01839.x.
DOI Google Scholar

Wang, X., Feng, Z., Ouyang, Z., 2001. The impact of human disturbance on vegetative carbon storage in forest ecosystems in China. For. Ecol. Manag. 148, 117–123. https://doi.org/10.1016/S0378-1127(00)00482-5.
DOI Google Scholar

Wardle, D.A., Jonsson, M., Bansal, S., Bardgett, R.D., Gundale, M.J., Metcalfe, D.B., 2012. Linking vegetation change, carbon sequestration and biodiversity: insights from island ecosystems in a long-term natural experiment. J. Ecol. 100, 16–30. https://doi.org/10.1111/j.1365-2745.2011.01907.x.
DOI Google Scholar

Weiskittel, A.R., MacFarlane, D.W., Radtke, P.J., Affleck, D.L.R., Temesgen, H., Woodall, C.W., Westfall, J.A., Coulston, J.W., 2015. A call to improve methods for estimating tree biomass for regional and national assessments. J. For., 113, 414–424. https://doi.org/10.5849/jof.14-091.
DOI Google Scholar

Weng, J.K., 2014. The evolutionary paths towards complexity: a metabolic perspective. New Phytol. 201, 1141–1149. https://doi.org/10.1111/nph.12416.
DOI Google Scholar

Xiang, W., Zhou, J., Ouyang, S., Zhang, S., Lei, P., Li, J., Deng, X., Fang, X., Forrester, D.I., 2016. Species-specific and general allometric equations for estimating tree biomass components of subtropical forests in southern China. Eur. J. For. Res. 135, 963–979. https://doi.org/10.1007/s10342-016-0987-2.
DOI Google Scholar

Yin, S., Gong, Z., Gu, L., Deng, Y., Niu, Y., 2022. Driving forces of the efficiency of forest carbon sequestration production: spatial panel data from the national forest inventory in China. J. Clean. Prod. 330, 129776. https://doi.org/10.1016/j.jclepro.2021.129776.
DOI Google Scholar
Zanne, A.E., López-Gonzalez, G., Coomes, D.A., Ilic, J., Jansen, S., Lewis, S.L., Miller, R.B., Swenson, N.G., Wiemann, M.C., Chave, J., 2009. Global wood density database. https://opendata.eol.org/dataset/global-wood-density-database. (Accessed 15 June 2023).

Zeng, W., 2014. Development of monitoring and assessment of forest biomass and carbon storage in China. For. Ecosyst. 1, 20. https://doi.org/10.1186/s40663-014-0020-5.
DOI Google Scholar

Zeng, W., Tomppo, E., Healey, S.P., von Gadow, K., 2015. The national forest inventory in China: history-results-international context. For. Ecosyst. 2, 23. https://doi.org/10.1186/s40663-015-0047-2.
DOI Google Scholar

Zhang, Y., Wang, X., 2021. Study on forest volume-to-biomass modelling and carbon storage dynamics in China. Sci. Sin. Vit. 51, 199–244.
DOI Google Scholar

Zhou, X., Lei, X., Liu, C., Huang, H., Zhou, C., Peng, C., 2019. Re-estimating the changes and ranges of forest biomass carbon in China during the past 40 years. For. Ecosyst. 6, 51. https://doi.org/10.1186/s40663-019-0208-9.
DOI Google Scholar

Zianis, D., Muukkonen, P., Mäkipää, R., Mencuccini, M., 2005. Biomass and stem volume equations for tree species in Europe. Tammer-Paino Oy, Tampere, Finland. https://doi.org/10.14214/sf.sfm4.
DOI Google Scholar
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Received: 04 January 2023
Revised: 15 July 2023
Accepted: 16 July 2023
Published: 27 July 2023
Issue date: August 2023

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© 2023 The Authors.

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We thank Profs. Jing Wang and Jiaxiang Li for their constructive suggestions and valuable comments.

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