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Wu Xinhua, Miao Zheng, Hao Yuanshuo, Dong Lihu. Mixed effect model of stem density of Populus nigra × P. simonii based on beta regression[J]. Journal of Beijing Forestry University, 2023, 45(5): 67-78. DOI: 10.12171/j.1000-1522.20220450
Citation: Wu Xinhua, Miao Zheng, Hao Yuanshuo, Dong Lihu. Mixed effect model of stem density of Populus nigra × P. simonii based on beta regression[J]. Journal of Beijing Forestry University, 2023, 45(5): 67-78. DOI: 10.12171/j.1000-1522.20220450

Mixed effect model of stem density of Populus nigra × P. simonii based on beta regression

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  • Received Date: November 06, 2022
  • Revised Date: March 14, 2023
  • Accepted Date: March 14, 2023
  • Available Online: March 16, 2023
  • Published Date: May 24, 2023
  •   Objective  This paper aims to explore the influencing factors and variation rules of wood density in the longitudinal stem of Populus nigra × P. simonii, so beta regression models with mixed effect of sapwood, heartwood, bark and stem density of the poplar were constructed, which was used as a reference for stem biomass prediction and wood timber properties.
      Method  Mixed effect beta regression models for sapwood, heartwood, bark and stem density of P. nigra × P. simonii were established, which based on the analytical data of 90 trees of P. nigrax × P. simonii plantation in Shangzhi City, Heilongjiang Province of northeastern China. Using correlation analysis and optimal subset methods to screen the variables of the beta regression base model, and the goodness of fit of the convergence model was evaluated by −2log-likehood value, akaike information criterion, bayesian information criterion, adjusted certainty coefficient (Ra 2) and likelihood ratio test. The leave-one-out-cross-validation was used to test the model, the indexes were mean absolute error (MAE) and mean absolute error percentage. Two sampling methods were combined (scheme Ⅰ: no relative height; scheme Ⅱ: limit relative height below 0.1) to correct the model.
      Result  The densities of sapwood, heartwood, bark and stem were not only affected by relative height, but also closely related to the average growth of DBH, age and DBH, respectively. Ra 2 of the mixed-effect beta regression model based on tree factors was 0.53, 0.52, 0.52, 0.63, respectively, and the MAE < 0.05 g/cm3. Sapwood density and heartwood density decreased first and then increased from the base to the top of the stem, with an inflection point at a relative height of 0.2. Bark density first increased and then decreased from the base of the stem to the top of the tree, and there was an inflection point at the relative height of 0.6. The stem density increased gradually along the stem. When fixed relative height, the densities of sapwood and heartwood were both negatively correlated with the average growth of DBH. The densities of bark and stem were negatively correlated with age and DBH, respectively. Without limiting the relative height, the wood density value corresponding to the height of 4 discs randomly sampled along the stem was calibrated to obtain stable prediction accuracy. When the sampling height was limited to 0.1 (2.0 m) or less, there was little difference in the prediction accuracy between the optimal sampling combination and the density values (1.0, 1.3, 2.0, 1.0 m, respectively) of sapwood, heartwood, bark and stem at a disc height. Relative height, average growth of DBH, age and DBH were significant influencing factors of wood density of P. nigra × P. simonii.
      Conclusion   The beta regression model can directly simulate the stem density of P. nigra × P. simonii in the (0, 1) interval, and the random effect can improve the prediction accuracy of the model. The longitudinal variations of sapwood, heartwood, bark and stem density are different. The constructed mixed-effect beta regression model can lay a foundation for biomass estimation and wood property study of P. nigra × P. simonii.
  • [1]
    Nelson R A, Francis E J, Berry J A, et al. The role of climate niche, geofloristic history, habitat preference, and allometry on wood density within a California plant community[J]. Forests, 2020, 11(1): 105. doi: 10.3390/f11010105
    [2]
    Krajnc L, Hafner P, Gricar J. The effect of bedrock and species mixture on wood density and radial wood increment in pubescent oak and black pine[J]. Forest Ecology and Management, 2021, 481: 118753. doi: 10.1016/j.foreco.2020.118753
    [3]
    Vanninen P, Makela A. Needle and stem wood production in Scots pine (Pinus sylvestris) trees of different age, size and competitive status[J]. Tree Physiology, 2000, 20(8): 527−533. doi: 10.1093/treephys/20.8.527
    [4]
    Francis E J, Muller-Landau H C, Wright S J, et al. Quantifying the role of wood density in explaining interspecific variation in growth of tropical trees[J]. Global Ecology and Biogeography, 2017, 26(10): 1078−1087. doi: 10.1111/geb.12604
    [5]
    Sarmiento C, Patino S, Paine C E T, et al. Within-individual variation of trunk and branch xylem density in tropical trees[J]. American Journal of Botany, 2011, 98(1): 140−149. doi: 10.3732/ajb.1000034
    [6]
    Vieilledent G, Fischer F J, Chave J, et al. New formula and conversion factor to compute basic wood density of tree species using a global wood technology database[J]. American Journal of Botany, 2018, 105(10): 1653−1661. doi: 10.1002/ajb2.1175
    [7]
    Wright S J, Kitajima K, Kraft N J B, et al. Functional traits and the growth-mortality trade-off in tropical trees[J]. Ecology, 2010, 91(12): 3664−3674. doi: 10.1890/09-2335.1
    [8]
    Santiago L S, Goldstein G, Meinzer F C, et al. Leaf photosynthetic traits scale with hydraulic conductivity and wood density in Panamanian forest canopy trees[J]. Oecologia, 2004, 140(4): 543−550. doi: 10.1007/s00442-004-1624-1
    [9]
    Meinzer F C, Campanello P I, Domec J C, et al. Constraints on physiological function associated with branch architecture and wood density in tropical forest trees[J]. Tree Physiology, 2008, 28(11): 1609−1617. doi: 10.1093/treephys/28.11.1609
    [10]
    Zimprich D. Modeling change in skewed variables using mixed beta regression models[J]. Research in Human Development, 2010, 7(1): 9−26. doi: 10.1080/15427600903578136
    [11]
    Fayolle A, Doucet J L, Gillet J F, et al. Tree allometry in Central Africa: testing the validity of pantropical multi-species allometric equations for estimating biomass and carbon stocks[J]. Forest Ecology and Management, 2013, 305: 29−37. doi: 10.1016/j.foreco.2013.05.036
    [12]
    Jacobsen A L, Agenbag L, Esler K J, et al. Xylem density, biomechanics and anatomical traits correlate with water stress in 17 evergreen shrub species of the Mediterranean-type climate region of South Africa[J]. Journal of Ecology, 2007, 95(1): 171−183. doi: 10.1111/j.1365-2745.2006.01186.x
    [13]
    罗云建. 华北落叶松人工林生物量碳计量参数研究[D]. 北京: 中国林业科学研究院, 2007.

    Luo Y J. Study on biomass carbon accounting factors of Larix principis-rupprechtii plantation[D]. Beijing: Chinese Academy of Forestry, 2007.
    [14]
    Guilley E, Hervé J C, Huber F, et al. Modelling variability of within-ring density components in Quercus petraea Liebl. with mixed-effect models and simulating the influence of contrasting silvicultures on wood density[J]. Annals of Forest Science, 1999, 56: 449−458.
    [15]
    Poorter L, Wright S J, Paz H, et al. Are functional traits good predictors of demographic rates? Evidence from five neotropical forests[J]. Ecology, 2008, 89(7): 1908−1920. doi: 10.1890/07-0207.1
    [16]
    Virgulino P C C, Gardunho D C L, Silva D N C, et al. Wood density in mangrove forests on the Brazilian Amazon coast[J]. Trees-Structure and Function, 2020, 34(1): 51−60. doi: 10.1007/s00468-019-01896-5
    [17]
    Kimberley M O, Mckinley R B, Cown D J, et al. Modelling the variation in wood density of New Zealand-grown douglas-fir[J]. New Zealand Journal of Forestry Science, 2017, 47(1): 15. doi: 10.1186/s40490-017-0096-0
    [18]
    方升佐, 杨文忠. 杨树无性系木材基本密度和纤维素含量株内变异[J]. 植物资源与环境学报, 2004, 13(1): 19−23. doi: 10.3969/j.issn.1674-7895.2004.01.005

    Fang S Z, Yang W Z. Within tree variation in wood basic density and cellulose content of poplar clones[J]. Journal of Plant Resources and Environment, 2004, 13(1): 19−23. doi: 10.3969/j.issn.1674-7895.2004.01.005
    [19]
    彭雨欣, 李凤日, 刘福, 等. 人工长白落叶松树干边材、心材和树皮密度预测模型[J]. 应用生态学报, 2020, 31(4): 1113−1120. doi: 10.13287/j.1001-9332.202004.007

    Peng Y X, Li F R, Liu F, et al. Prediction models of sapwood density, heartwood density, and bark density in Larix olgensis plantation[J]. Chinese Journal of Applied Ecology, 2020, 31(4): 1113−1120. doi: 10.13287/j.1001-9332.202004.007
    [20]
    姜立春, 刘铭宇, 刘银帮. 落叶松和樟子松木材基本密度的变异及早期选择[J]. 北京林业大学学报, 2013, 35(1): 1−6. doi: 10.13332/j.1000-1522.2013.01.014

    Jiang L C, Liu M Y, Liu Y B. Variation of wood basic density and early selection of dahurian larch and Mongolian pine[J]. Journal of Beijing Forestry University, 2013, 35(1): 1−6. doi: 10.13332/j.1000-1522.2013.01.014
    [21]
    Iida Y, Poorter L, Sterck F J, et al. Wood density explains architectural differentiation across 145 co-occurring tropical tree species[J]. Functional Ecology, 2012, 26(1): 274−282. doi: 10.1111/j.1365-2435.2011.01921.x
    [22]
    Zhang S Y, Owoundi R E, Nepveu G, et al. Modelling wood density in European oak (Quercus petraea and Quercus robur) and simulating the silvicultural influence[J]. Canadian Journal of Forest Research, 1993, 23: 2587−2593. doi: 10.1139/x93-320
    [23]
    Vaughan D, Auty D, Kolb T E, et al. Climate has a larger effect than stand basal area on wood density in Pinus ponderosa var. scopulorum in the southwestern USA[J]. Annals of Forest Science, 2019, 76(3): 85. doi: 10.1007/s13595-019-0869-0
    [24]
    Wassenberg M, Chiu H S, Guo W F, et al. Analysis of wood density profiles of tree stems: incorporating vertical variations to optimize wood sampling strategies for density and biomass estimations[J]. Trees-Structure and Function, 2015, 29(2): 551−561. doi: 10.1007/s00468-014-1134-7
    [25]
    Krajnc L, Farrelly N, Harte A M. The influence of crown and stem characteristics on timber quality in softwoods[J]. Forest Ecology and Management, 2019, 435: 8−17. doi: 10.1016/j.foreco.2018.12.043
    [26]
    Deng X, Zhang L, Lei P F, et al. Variations of wood basic density with tree age and social classes in the axial direction within Pinus massoniana stems in Southern China[J]. Annals of Forest Science, 2013, 71(4): 505−516.
    [27]
    徐有明, 林汉, 江泽慧, 等. 橡胶树生长轮宽度、木材密度变异及其预测模型的研究[J]. 林业科学, 2002, 38(1): 95−102. doi: 10.3321/j.issn:1001-7488.2002.01.015

    Xu Y M, Lin H, Jiang Z H, et al. Variation of growth ring width and wood basic density of rubber tree and their modelling equations[J]. Scientia Silvae Sinicae, 2002, 38(1): 95−102. doi: 10.3321/j.issn:1001-7488.2002.01.015
    [28]
    Ferrari S L P, Cribari-Neto F. Beta regression for modelling rates and proportions[J]. Journal of Applied Statistics, 2004, 31(7): 799−815. doi: 10.1080/0266476042000214501
    [29]
    Eskelson B N I, Madsen L, Hagar J C, et al. Estimating riparian understory vegetation cover with beta regression and copula models[J]. Forest Science, 2011, 57(3): 212−221.
    [30]
    Kimura J, Fujimoto T. Modeling the effects of growth rate on the intra-tree variation in basic density in hinoki cypress (Chamaecyparis obtusa)[J]. Journal Wood Science, 2014, 60(5): 305−312. doi: 10.1007/s10086-014-1416-0
    [31]
    Repola J. Models for vertical wood density of Scots pine, Norway spruce and birch stems, and their application to determine average wood density[J]. Silva Fennica, 2006, 40(4): 673−685.
    [32]
    Mutz R, Guilley E, Sauter U H, et al. Modelling juvenile-mature wood transition in Scots pine (Pinus sylvestris L.) using nonlinear mixed-effects models[J]. Annals of Forest Science, 2004, 61(8): 831−841. doi: 10.1051/forest:2004084
    [33]
    Molteberg D, Hoibo A. Modelling of wood density and fibre dimensions in mature Norway spruce[J]. Canadian Journal of Forest Research, 2007, 37(8): 1373−1389. doi: 10.1139/X06-296
    [34]
    Mohsenkhani Z F, Mohhamadzadeh M, Baghfalaki T. Augmented mixed beta regression models with skew-normal independent distributions: Bayesian analysis of labor force data[J]. Communications in Statistics-Simulation and Computation, 2019, 48(7): 2147−2164. doi: 10.1080/03610918.2018.1435802
    [35]
    Rogers J A, Polhamus D, Gillespie W R, et al. Combining patient-level and summary-level data for Alzheimer’s disease modeling and simulation: a beta regression meta-analysis[J]. Journal of Pharmacokinetics and Pharmacodynamics, 2012, 39(5): 479−498. doi: 10.1007/s10928-012-9263-3
    [36]
    Verkuilen J, Smithson M. Mixed and mixture regression models for continuous bounded responses using the beta distribution[J]. Journal of Educational and Behavioral Statistics, 2012, 37(1): 82−113. doi: 10.3102/1076998610396895
    [37]
    Ni C, Nigh G D. An analysis and comparison of predictors of random parameters demonstrated on planted loblolly pine diameter growth prediction[J]. Forestry: an International Journal of Forest Research, 2012, 85(2): 271−280. doi: 10.1093/forestry/cps001
    [38]
    谢龙飞, 董利虎, 李凤日. 人工长白落叶松立木叶面积预估模型[J]. 应用生态学报, 2018, 29(9): 2843−2851. doi: 10.13287/j.1001-9332.201809.011

    Xie L F, Dong L H, Li F R. Predicting models of leaf area for trees in Larix olgensis plantation[J]. Journal of Applied Ecology, 2018, 29(9): 2843−2851. doi: 10.13287/j.1001-9332.201809.011
    [39]
    Calama R, Montero G. Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach[J]. Silva Fennica, 2005, 39(1): 37−54.
    [40]
    马丽娜, 付孝德, 张明, 等. 人工林杨树木材密度变异规律的研究[J]. 安徽农业大学学报, 2003, 30(4): 410−413. doi: 10.3969/j.issn.1672-352X.2003.04.014

    Ma L N, Fu X D, Zhang M, et al. Variation patterns of wood density in plantation poplar[J]. Journal of Anhui Agricultural University, 2003, 30(4): 410−413. doi: 10.3969/j.issn.1672-352X.2003.04.014
    [41]
    张倩, 周亚菲, 刘珊杉, 等. 速生杨清林材基本密度与含水率特性分析[J]. 林业科技, 2017, 42(3): 25−27.

    Zhang Q, Zhou Y F, Liu S S, et al. Study on basic density and moisture content of fast-growing clear poplar[J]. Forestry Science & Technology, 2017, 42(3): 25−27.
    [42]
    Fukatsu E, Nakada R. The timing of latewood formation determines the genetic variation of wood density in Larix kaempferi[J]. Trees, 2018, 32(5): 1233−1245. doi: 10.1007/s00468-018-1705-0
    [43]
    Kunstler G, Lavergne S, Courbaud B, et al. Competitive interactions between forest trees are driven by species’ trait hierarchy, not phylogenetic or functional similarity: implications for forest community assembly[J]. Ecology Letters, 2012, 15(8): 831−840. doi: 10.1111/j.1461-0248.2012.01803.x
    [44]
    Dias D, Marenco R. Tree growth, wood and bark water content of 28 Amazonian tree species in response to variations in rainfall and wood density[J]. iForest-Biogeosciences and Forestry, 2016, 9(3): 445−451. doi: 10.3832/ifor1676-008
    [45]
    曾辉, 刘晓玲, 符韵林, 等. 顶果木树皮率、心材率及木材密度研究[J]. 西北林学院学报, 2014, 29(1): 161−164,173. doi: 10.3969/j.issn.1001-7461.2014.01.00

    Zeng H, Liu X L, Fu Y L, et al. Bark percentage, heartwood percentage and density of Acrocarpus fraxinifolius[J]. Journal of Northwest Forestry University, 2014, 29(1): 161−164,173. doi: 10.3969/j.issn.1001-7461.2014.01.00
    [46]
    Fajardo A. Insights into intraspecific wood density variation and its relationship to growth, height and elevation in a treeline species[J]. Plant Biology, 2018, 20(3): 456−464. doi: 10.1111/plb.12701
    [47]
    祖勃荪. 国外对杨树湿心材的研究[J]. 林业科学, 2000, 36(5): 85−91. doi: 10.3321/j.issn:1001-7488.2000.05.015

    Zu B S. Foreign studies on wet heart wood of poplars[J]. Scientia Silvae Sinicae, 2000, 36(5): 85−91. doi: 10.3321/j.issn:1001-7488.2000.05.015
    [48]
    Hietz P, Valencia R, Wright S J. Strong radial variation in wood density follows a uniform pattern in two neotropical rain forests[J]. Functional Ecology, 2013, 27(3): 684−692. doi: 10.1111/1365-2435.12085
    [49]
    Fajardo A. Wood density is a poor predictor of competitive ability among individuals of the same species[J]. Forest Ecology and Management, 2016, 372: 217−225. doi: 10.1016/j.foreco.2016.04.022
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