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Incorporating topographic factors in nonlinear mixed-effects models for aboveground biomass of natural Simao pine in Yunnan, China

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Abstract

A total of 128 Simao pine trees (Pinus kesiya var. langbianensis) from three regions of Pu’er City, Yunnan Province, People’s Republic of China, were destructively sampled to obtain tree aboveground biomass (AGB). Tree variables such as diameter at breast height and total height, and topographical factors such as altitude, aspect of slope, and degree of slope were recorded. We considered the region and site quality classes as the random-effects, and the topographic variables as the fixed-effects. We fitted a total of eight models as follows: least-squares nonlinear models (BM), least-squares nonlinear models with the topographic factors (BMT), nonlinear mixed-effects models with region as single random-effects (NLME-RE), nonlinear mixed-effects models with site as single random-effects (NLME-SE), nonlinear mixed-effects models with the two-level nested region and site random-effects (TLNLME), NLME-RE with the fixed-effects of topographic factors (NLMET-RE), NLME-SE with the fixed-effects of topographic factors (NLMET-SE), and TLNLME with the fixed-effects of topographic factors (TLNLMET). The eight models were compared by model fitting and prediction statistics. The results showed: model fitting was improved by considering random-effects of region or site, or both. The models with the fixed-effects of topographic factors had better model fitting. According to AIC and BIC, the model fitting was ranked as TLNLME > NLMET-RE > NLME-RE > NLMET-SE > TLNLMET > NLME-SE > BMT > BM. The differences among these models for model prediction were small. The model prediction was ranked as TLNLME > NLME-RE > NLME-SE > NLMET-RE > NLMET-SE > TLNLMET > BMT > BM. However, all eight models had relatively high prediction precision (>90 %). Thus, the best model should be chosen based on the available data when using the model to predict individual tree AGB.

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References

  • Abrams MD, Knapp AK, Hulbert LC (1986) A ten-year record of aboveground biomass in a Kansas tallgrass prairie: effects of fire and topographic position. Am J Bot 73(10):1509–1515

    Article  Google Scholar 

  • Alves LF, Vieira SA, Scaranello MA, Camargo PB, Santos FAM, Joly CA, Martinelli LA (2010) Forest structure and live aboveground biomass variation along an elevational gradient of tropical Atlantic moist forest (Brazil). For Ecol Manage 260(5):679–691

    Article  Google Scholar 

  • Asner GP, Hughes RF, Varga T, Knapp D, Kennedy-Bowdoin T (2009) Environmental and biotic controls over aboveground biomass throughout a tropical rain forest. Ecosystems 12(2):261–278

    Article  Google Scholar 

  • Basuki T, van Laake PE, Skidmore AK, Hussin YA (2009) Allometric equations for estimating the above-ground biomass in tropical lowland Dipterocarp forests. For Ecol Manage 257(8):1684–1694

    Article  Google Scholar 

  • Bennie J, Hill MO, Baxter R, Huntley B (2006) Influence of slope and aspect on long-term vegetation change in British chalk grasslands. J Ecol 94(2):355–368

    Article  Google Scholar 

  • Blackard JA, Finco MV, Helmer EH, Holden GR, Hoppus ML, Jacobs DM, Lister AJ, Moisen GG, Nelson MD, Riemann R, Ruefenacht B (2008) Mapping U.S. forest biomass using nationwide forest inventory data and moderate resolution information. Remote Sens Environ 112:1658–1677

    Article  Google Scholar 

  • Brown S, Lugo AE (1984) Biomass of tropical forests: a new estimate based on forest volumes. Science 223:1290–1293

    Article  PubMed  CAS  Google Scholar 

  • Brown IF, Martinelli LA, Thomas WW, Moreira MZ, Ferreira CA, Victoria RA (1995) Uncertainty in the biomass of Amazonian forests: an example from Rondonia, Brazil. For Ecol Manage 75:175–189

    Article  Google Scholar 

  • Budhathoki CB, Lyneh TB, Guldin JM (2005) Individual tree growth models for natural even-aged Shortleaf pine. Gen. Tech. Rep. SRS-92. U.S. Department of Agriculture, Forest Service, Southern Research Station. Asheville, pp 359–361

  • Calama R, Montero G (2004) Interregional nonlinear height-diameter model with random coefficients for Stone pine in Spain. Can J For Res 34:150–163

    Article  Google Scholar 

  • Calegario N, Maestri R, Leal CL, Daniels RF (2005) Growth estimate of Eucalyptus stands based on nonlinear multilevel mixed-effects model theory. Ciência Florestal 15:285–292

    Google Scholar 

  • Case B, Hall RJ (2008) Assessing prediction errors of generalized tree biomass and volume equations for boreal forest region of west-central Canada. Can J For Res 38:878–889

    Article  Google Scholar 

  • Chapin FS III, Bloom AJ, Field CB, Waring RH (1987) Plant responses to multiple environmental factors. Bioscience 37(1):49–57

    Article  Google Scholar 

  • Chapin FS III, Matson PA, Mooney HA (2002) Principles of Terrestrial Ecosystem Ecology. Springer, New York, p 529

    Google Scholar 

  • Chen DS, Li FR, Sun XM, Jia WW (2011) Models to predict knot size for Larch plantation using linear mixed model. Sci Silvae Sin 47(11):121–128

    Google Scholar 

  • Chojnacky DC (2002) Allometric scaling theory applied to FIA biomass estimation. Proceeding of the third annual forest inventory and analysis symposium, GTR NC-230. North Central Research Station, Forest Service USDA, Minot, pp 96–102

    Google Scholar 

  • Compilation Committee of Yunnan Forest (1986) Yunnan Forest. Yunnan Science and Technology Press, China Forestry Publishing House, Kunming, Beijing

    Google Scholar 

  • de Castilho CV, Magnusson WE, de Araujo RNO, Luizão RCC, Luizão FJ, Lima AP, Higuchi N (2006) Variation in aboveground tree live biomass in a central Amazonian Forest: effects of soil and topography. For Ecol Manage 234(1/3):85–96

    Article  Google Scholar 

  • DeWalt SJ, Chave J (2004) Structure and biomass of four lowland Neotropical forests. Biotropica 36(1):7–19

    Google Scholar 

  • Dorado FC, Diéguez-Aranda U, Anta MB, Rodríguez MS, von Gadow K (2006) A generalized height-diameter model including random components for Radiata pine plantations in Northwestern Spain. For Ecol Manage 229:202–213

    Article  Google Scholar 

  • Fahey TJ, Knapp AK (2007) Principles and standards for measuring primary production. Oxford University Press, New York, p 288

    Book  Google Scholar 

  • Fang Z, Bailey RL (2001) Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. For Sci 47:287–300

    Google Scholar 

  • Fehrmann L, Lehtonen A, Kleinn C, Tomppo E (2008) Comparison of linear and mixed-effect regression models and a K-nearest neighbour approach for estimation of single-tree biomass. Can J For Res 38(1):1–9

    Article  Google Scholar 

  • Fu LY (2012) Nonlinear mixed effects model and its application in forestry. Doctor of Thesis, Chinese Academy of Forestry, Beijing, China

  • Fu LY, Sun H (2013) Individual crown diameter prediction for Cunninghamia lanceolata forests based mixed effects models. Sci Silvae Sin 49(8):65–74

    Google Scholar 

  • Fu LY, Zeng WS, Tang SZ, Sharma RP, Li HK (2012) Using linear mixed model and dummy variable model approaches to construct compatible single-tree biomass equations at different scales –A case study for Masson pine in Southern China. J For Sci 58(3):101–115

    Google Scholar 

  • Fu L, Zeng W, Zhang H, Wang G, Lei Y, Tang S (2014) Generic linear mixed-effects individual-tree biomass models for Pinus massoniana in southern China. Southern Forests 76(1):47–56

    Article  Google Scholar 

  • Garber SM, Maguire DA (2003) Modeling stem taper of three Central Oregon species using nonlinear mixed effects models and autoregressive error structures. For Ecol Manage 179:507–522

    Article  Google Scholar 

  • Gregoire TG, Schabenberger O (1996) A nonlinear mixed-effects model to predict cumulative bole volume of standing trees. J Appl Stat 23:257–271

    Article  Google Scholar 

  • Gregoire TG, Schabenberger O, Barrett JP (1995) Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent- plot measurements. Can J For Res 25:137–156

    Article  Google Scholar 

  • Guilley E, Herve J, Nepveu G (2004) The influence of site quality, silviculture and region on wood density mixed model in Quercus petraea Liebl. For Ecol Manage 189:111–121

    Article  Google Scholar 

  • Hall DB, Clutter M (2004) Multivariate multilevel nonlinear mixed effects models for timber yield predictions. Biometrics 60:16–24

    Article  PubMed  Google Scholar 

  • Henry M, Picard N, Trotta C, Manlay RJ, Valentini R, Bernoux M, Saint-André L (2011) Estimating tree biomass of sub-Saharan African forests: a review of available allometric equations. Silva Fenn 45:477–569

    Article  Google Scholar 

  • Jenkins JC, Chojnacky DC, Heath LS, Bird-se RA (2003) National-scale biomass estimators for United States tree species. For Sci 49:12–35

    Google Scholar 

  • Jiang LC, Li FR (2014) Application of mixed effects models on forestry modelling. Science Press, Beijing, p 143

    Google Scholar 

  • Kang M, Dai C, Ji W, Jiang Y, Yuan Z, Chen HYH (2013) Biomass and its allocation in relation to temperature, precipitation, and soil nutrients in Inner Mongolia grasslands, China. PLoS One 8(7):e69561. doi:10.1371/journal.pone.0069561

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Laird NM, Ware JH (1982) Random effects models for longitudinal data. Biometrics 38:963–974

    Article  PubMed  CAS  Google Scholar 

  • Lappi J, Bailey RL (1988) A height prediction model with random stand and tree parameters: an alternative to traditional site methods. For Sci 34:907–927

    Google Scholar 

  • Laumonier Y, Edin A, Kanninen M, Munandar AW (2010) Landscape-scale variation in the structure and biomass of the hill Dipterocarp forest of Sumatra: implications for carbon stock assessments. For Ecol Manage 259:505–513

    Article  Google Scholar 

  • Laurance WF, Fearnside PM, Laurance SG, Delamonica P, Lovejoy TE, de Merona RJM, Chambers JQ, Gaston C (1999) Relationship between soils and Amazon forest biomass: a landscape-scale study. For Ecol Manage 118:127–138

    Article  Google Scholar 

  • Lei XD, Li YC, Xiang W (2009) Individual basal area growth model using multi-level linear mixed model with repeated measures. Sci Silvae Sin 45(1):74–80

    Google Scholar 

  • Leites LP, Robinson AP (2004) Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. For Sci 50:204–212

    Google Scholar 

  • Li CM (2009) Application of mixed effects models in forest growth model. Sci Silvae Sin 45(4):131–138

    Google Scholar 

  • Li CM (2010) Application of mixed effects models in forest growth models. Doctor of Thesis, Chinese Academy of Forestry, Beijing, China

  • Li J (2010) Dynamics of biomass and carbon stock for young and middle aged plantation of Simao pine (Pinus kesiya var. langbianensis). Doctoral Dissertation, Beijing Forestry University, Beijing, China

  • Li CM (2011) Study on dominant height growth of fir plantation based on a nonlinear mixed modeling approach for longitudinal data. For Res 24(1):68–73

    CAS  Google Scholar 

  • Li CM (2012) The simultaneous equation system of total volume in fir plantation. Sci Silvae Sin 48(6):80–88

    Google Scholar 

  • Li YX, Jiang LC (2013) Modeling wood density with two-level linear mixed effects models for Dahurian larch. Sci Silvae Sin 49(7):91–98

    Google Scholar 

  • Lieth H, Whittaker RH (1975) Primary productivity of the biosphere. Springer, New York, pp 237–263

    Google Scholar 

  • López IF, Lambert MG, Mackay AD, Valentine I (2003) The influence of topography and pasture management on soil characteristics and herbage accumulation in hill pasture in the North Island of New Zealand. Plant Soil 255(2):421–434

    Article  Google Scholar 

  • Mahadev S, John P (2007) Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. For Ecol Manage 249:187–198

    Article  Google Scholar 

  • Malhi Y, Wood D, Bakers TR, Wright J, Phillips O, Cochrane T, Neir P, Chave J, Almeida S, Arroyo L, Higuchi N, Killeen TJ, Laurance SG, Laurance WF, Lewis SL, Monteagudo A, Neill DA, Vargas PN, Pitman NCA, Quesada CA, Salomão R, Silva JNM, Lezama AT, Terborgh J, Matínez RV, Vinceti B (2006) The regional variation of aboveground live biomass in old-growth Amazonian forests. Global change Biol 12(7):1107–1138

    Article  Google Scholar 

  • Matthew BR, Harold EB, Ralph LA (2009) Biomass partitioning in a miniature-scale loblolly pine spacing trial. Can J For Res 39:320–329

    Article  Google Scholar 

  • McEwan RW, Lin YC, Sun IF, Hsieh CF, Su SH, Chang LW, Song GZM, Wang HH, Hwong JL, Lin KC, Yang KC, Chiang JM (2011) Topographic and biotic regulation of aboveground carbon storage in subtropical broad-leaved forests of Taiwan. For Ecol Manage 262:1817–1825

    Article  Google Scholar 

  • Muukkonen P (2007) Generalized allometric volume and biomass equations for some tree species in Europe. Eur J For Res 126(2):157–166

    Article  Google Scholar 

  • Nanos N, Calama R, Montero G, Gil L (2004) Geostatistical prediction of height/diameter models. For Ecol Manage 195:221–235

    Article  Google Scholar 

  • Návar J (2009) Allometric equations for tree species and carbon stocks for forests of northwestern Mexico. For Ecol Manage 257:427–433

    Article  Google Scholar 

  • Paoli GD, Curran LM, Slik JWF (2008) Soil nutrients affect spatial patterns of aboveground biomass and emergent tree density in southwestern Borneo. Oecologia 155(2):287–299

    Article  PubMed  Google Scholar 

  • Pearce HG, Anderson WR, Fogarty LG, Todoroki CL, Anderson SAJ (2010) Linear mixed-effects models for estimation biomass and fuel loads in shrublands. Can J For Res 40(10):2015–2026

    Article  Google Scholar 

  • Phillips OL, Malhi Y, Higuchi N, Laurance WF, Núnez PV, Vásquez RM, Laurance SG, Ferreira LV, Stern M, Brown S, Grace J (1998) Changes in the carbon balance of tropical forests: evidence from long-term plots. Science 282:439–442

    Article  PubMed  CAS  Google Scholar 

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

  • Pinheiro JC, Bates DM (2000) Mixed effects models in S and S-plus. Springer, New York, p 528

    Book  Google Scholar 

  • Polis GA (1999) Why are parts of the world green? Multiple factors control productivity and the distribution of biomass. Oikos 86(1):3–15

    Article  Google Scholar 

  • Popescu SC (2007) Estimating biomass of individual pine trees using airborne lidar. Biomass Bioenergy 31:646–655

    Article  Google Scholar 

  • Popescu SC, Wynne RH, Nelson RF (2003) Measuring individual tree crown diameter with lidar and assessing its influence on estimating forest volume and biomass. Can. J. Remote Sens 29:564–577

    Article  Google Scholar 

  • Ramananantoandro T, Rafidimanantsoa HP, Ramanakoto MF (2015) Forest aboveground biomass estimates in a tropical rainforest in Madagascar: new insights from the use of wood specific gravity data. J For Res 26(1):47–55

    Article  Google Scholar 

  • Rose R, Rosner LS, Ketchum JS (2006) Twelfth-year response of Douglas-fir to area of weed control and herbaceous versus woody weed control treatments. Can J For Res 36(10):2464–2473

    Article  Google Scholar 

  • Shen ZH, Fang JY (2001) Niche comparison of two Fagus species based on the topographic pattern of their populations. Acta Phytoecologica Sinica 25:392–398

    Google Scholar 

  • Shen ZH, Zhang XS, Jin YX (2000) Gradient analysis of the influence of mountain topography on vegetation pattern. Acta Phytoecologica Sinica 24:430–435

    Google Scholar 

  • Simard M, Zhang K, Rivera-Monroy VH, Ross MS, Ruiz PL, Castañeda-Moya E, Twilley RR, Rodriguez E (2006) Mapping height and biomass of mangrove forests in Everglades national park with SRTM elevation data. Photogramm. Eng Rem Sens 72:299–311

    Article  Google Scholar 

  • Southwest Forestry College, Forestry Department of Yunnan Province (1988) Iconographia Arbororum Yunnanicorum. Yunnan Science and Technology Press, Kunming, p 572

    Google Scholar 

  • Stegen JC, Swenson NG, Enquist BJ, White EP, Philips OL, Jørgensen PT, Weiser MD, Mendoza AM, Vargas PN (2011) Variation in aboveground forest biomass across broad climatic gradients. Global Ecol Biogeogr 20(5):744–754

    Article  Google Scholar 

  • Takyu M, Aiba SI, Kitayama K (2003) Changes in biomass, productivity and decomposition along topographical gradients under different geological conditions in tropical lower montane forests on Mount Kinabalu. Borneo. Oecologia 134(3):397–404

    Article  PubMed  Google Scholar 

  • Temesgen H, Monleon VJ, Hann DW (2008) Analysis and comparison of nonlinear tree height prediction strategies for Douglas–fir forests. Can J For Res 38:553–565

    Article  Google Scholar 

  • Ter-Mikaelian MT, Korzukhin MD (1997) Biomass equations for sixty-five North American tree species. For Ecol Manage 97:1–24

    Article  Google Scholar 

  • Valencia R, Condit R, Muller-Landau HC, Hernandez C, Navarrete H (2009) Dissecting biomass dynamics in a large Amazonian forest plot. J Trop Ecol 25:473–482

    Article  Google Scholar 

  • Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57(2):307–333

    Article  Google Scholar 

  • Wang HL (2003) Study on stand growth models for Pinus kesiya var. langbianensis natural secondary woodland. Master Thesis, Kunming: Southwest Forestry College

  • Wang CK (2006) Biomass allometric equations for 10 co-occurring tree species in Chinese temperate forests. For Ecol Manage 222:9–16

    Article  Google Scholar 

  • Weiskittel AR, Maguire DA, Monserud RA (2007) Response of branch growth and mortality to silvicultural treatments in coastal Douglas- fir plantations: implications for predicting tree growth. For Ecol Manage 251:182–194

    Article  Google Scholar 

  • Weiskittel AR, Hann DW, Kershaw JA Jr, Vanclay JK (2011) Forest growth and yield modeling. Wiley, Chichester, p 415

    Book  Google Scholar 

  • Wen QZ, Zhao YF, Chen XM, Yang ZX, Ai JL, Yang XS (2010) Dynamic study on the values for ecological service function of Pinus kesiya forest in China. For Res 23(5):671–677

    Google Scholar 

  • West PW (2009) Tree and forest measurement, 2nd edn. Springer, Berlin, p 192

    Book  Google Scholar 

  • Wu ZL, Dang CL (1992) The biomass of Pinus kesiya var. langbianensis stands in Pu’er district, Yunnan. J Yunnan Univ (Nat Sci Ed) 14(2):161–167

    CAS  Google Scholar 

  • Wu Y, Strahler AH (1994) Remote estimation of Crown size, stand density, and biomass on the Oregon transect. Ecol Appl 4(2):299–312

    Article  Google Scholar 

  • Yan J, Luo YJ, Zheng DF, Wang SC (2014) Source appointment of differences in biomass estimates of Eucalypt Plantation. Sci Silvae Sin 50(2):92–98

    Google Scholar 

  • Yue F, Yang B (2011) Study on carbon sink of Pinus kesiya forests. Jiangsu Agric Sci 39(5):467–469

    Google Scholar 

  • Zeng WS, Tang SZ, Xia ZS, Zhu S, Luo HZ (2011) Using linear mixed model and dummy variable model approaches to construct generalized single- tree biomass equations in Guizhou. Forest Research 24(3):285–291

    Google Scholar 

  • Zhang YJ, Borders BE (2004) Using a system mixed effects modeling method to estimate tree compartment biomass for intensively managed Loblolly pines - an allometric approach. For Ecol Manage 194:145–157

    Article  Google Scholar 

  • Zhao D, Wilson M, Borders BE (2005) Modeling response curves and testing treatment effects in repeated measures experiments: a multi-level nonlinear mixed-effects model approach. Can J For Res 35:122–132

    Article  Google Scholar 

  • Zianis D, Muukkonen P, Mäkipää R, Mencuccini M (2005) Biomass and stem volume equations for tree species in Europe. Silva Fennica Monographs 4, Tammer-Paino Oy: Tampere, Finland

  • Zou WT, Zeng WS, Zhang LJ, Zeng M (2015) Modeling crown biomass for four pine species in China. Forests 6:433–449

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Biodiversity Conservation in Southwest China of State Forest Administration, Southwest Forestry University, Kunming, 650224, Yunnan, China

    Guanglong Ou, Junfeng Wang, Hui Xu, Keyi Chen, Haimei Zheng, Bo Zhang, Xuelian Sun, Tingting Xu & Yifa Xiao

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  1. Guanglong Ou
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  2. Junfeng Wang
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Correspondence to Hui Xu.

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Project funding: This work was supported by National Natural Science Foundation of China (Grant No. 31160157, 31560209) and Application Fundamental Research Plan Project of Yunnan Province, China (Grant No. 2012FD027).

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Corresponding editor: Hu Yanbo

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Ou, G., Wang, J., Xu, H. et al. Incorporating topographic factors in nonlinear mixed-effects models for aboveground biomass of natural Simao pine in Yunnan, China. J. For. Res. 27, 119–131 (2016). https://doi.org/10.1007/s11676-015-0143-8

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