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Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch (Larix olgensis) plantations in northeast China

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Abstract

Korean larch (Larix olgensis) is one of the main tree species for afforestation and timber production in northeast China. However, its timber quality and growth ability are largely influenced by crown size, structure and shape. The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots, but crown dynamic models has seldom been constructed. Therefore, this study aimed to develop height to crown base (HCB) and crown length (CL) dynamic models using the branch mortality technique for a Korean larch plantation. The nonlinear mixed-effects model with random effects, variance functions and correlation structures, was used to build HCB and CL dynamic models. The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China. The results showed that HCB progressively increases as tree age, tree height growth (HT growth) and diameter at breast height growth (DBH growth). The CL was increased with tree age in 20 years ago, and subsequently stabilized. HT growth, DBH growth stand basal area (BAS) and crown competition factor (CCF) significantly influenced HCB and CL. The HCB was positively correlated with BAS, HT growth and DBH growth, but negatively correlated with CCF. The CL was positively correlated with BAS and CCF, but negatively correlated with DBH growth. Model fitting and validation confirmed that the mixed-effects model considering the stand and tree level random effects was accurate and reliable for predicting the HCB and CL dynamics. However, the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation, and the fitting precision of the models was reduced. Therefore, from the point of view of application, we should take care to avoid setting up over-complex models. The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.

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References

  • Assmann E (1970) The principles of forest yield study: studies in the organic production, structure, increment and yield of forest stands. Pergamon Press, Oxford

    Google Scholar 

  • Calama R, Montero G (2005) Multilevel linear mixed-model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. Silva Fenn 39(1):37–54

    Article  Google Scholar 

  • Corral-Rivas S, Alvarez-Gonzalez JG, Crecente-Campo F, Corral-Rivas JJ (2014) Local and generalized height-diameter models with random parameters for mixed, uneven-aged forests in Northwestern Durango, Mexico. For Ecosyst 1(6):1–9

    Google Scholar 

  • Dong LB, Liu ZG, Bettinger P (2016) nonlinear mixed-effects branch diameter and length models for natural Dahurian larch (Larix gmelini) forest in northeast China. Trees 30:1191–1206

    Article  Google Scholar 

  • Fahey TD, Cahill JM, Senllgrove TA, Heath LS (1991) Lumber and veneer recovery from intensively managed young growth Douglas-fir US. For Serv Res. 437:1–31

    Google Scholar 

  • Fang ZX, Bailey RL (2001) Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. For Sci 38:2274–2286

    Google Scholar 

  • Fu LY, Sun H, Sharma RP, Lei YC, Zhang HR, Tang SZ (2013) Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China. For Ecol Manag 302:210–220

    Article  Google Scholar 

  • Fu LY, Zhang HR, Lu J, Zang H, Lou MH, Wang GX (2014) Multilevel nonlinear mixed-effect crown ratio models for individual trees of Mongolian Oak (Quercus mongolica) in northeast China. PLoS ONE 8:1–20

    Google Scholar 

  • Fu LY, Zhang HR, Sharma RP, Pang LF, Wang GX (2017) A generalized nonlinear mixed-effects height to crown base model for Mongolian oak (Quercus mongolica) in northeast China. For Ecol Manag 384:34–43

    Article  Google Scholar 

  • Fujimori T (1993) Dynamics of crown structure and stem growth based on knot analysis of a hinoki cypress (Chamaecyparis obtusa). For Ecol Manag 56:57–68

    Article  Google Scholar 

  • Garber SM, Monserud RA, Maguire DA (2008) Crown recession patterns in three conifer species of the Northern Rocky Mountains. For Sci 54:633–646

    Google Scholar 

  • Gonzalez-Benecke CA, Gezan SA, Samuelson LJ, Cropper WP (2014) Estimating Pinus palustris tree diameter and stem volume from tree height, crown area and stand-level parameters. J For Res 25:43–52

    Article  Google Scholar 

  • Hann DW (2014) Revised volume and taper equations for six major conifer species in Southwest Oregon. Oregon State University, Corvallis

    Google Scholar 

  • Hann DW, Hanus ML (2002) Enhanced height-growth-rate equations for undamaged and damaged trees in Southwest Oregon. Oregon State University, Forest Research Laboratory, Research Contribution 41

  • Hann DW, Hanus ML (2004) Evaluation of nonspatial approaches and equation forms used to predict tree crown recession. Can J For Res 34:1993–2003

    Article  Google Scholar 

  • Hann DW, Walters DK, Scrivani JA (1987) Incorporating crown ratio into prediction equations for Douglas-fir stem volume. Can J For Res 17:17–22

    Article  Google Scholar 

  • Hasenauer H, Monserud RA (1996) A crown ratio model for Austrian forests. For Ecol Manag 84(1–3):49–60

    Article  Google Scholar 

  • Houllier F, Leban JM, Colin F (1995) Linking growth modeling to timber quality assessment for Norway spruce. For Ecol Manag 74:91–102

    Article  Google Scholar 

  • Hynynen J (1995) Modelling tree growth for managed stands. Finnish, For Res Inst Res, p 576p

    Google Scholar 

  • Jiang LC, Liu RL (2011) Segmented taper equations with crown ratio and stand density for Dahurian Larch (Larix gmelinii) in Northeastern China. J For Res 22:347–352

    Article  Google Scholar 

  • Jozsa LA, Middleton GR (1994) A discussion of wood quality attributes and their practical implications. Forintek Canada Corp, Vancouver, B.C. Spec. Publ. SP

  • Kraft G (1884) Beiträge zur Lehre von den Durchforstungen, Schlagstellungen und Lichtungshieben. Klindworth, Hannover

    Google Scholar 

  • Krajicek JE, Brinkman KA, Gingrich SF (1961) Crown competition–a measure of density. For Sci 7:35–42

    Google Scholar 

  • Kuprevicius A, Auty D, Achim A, Caspersen JP (2013) Quantifying the influence of live crown ratio on the mechanical properties of clear wood. Forestry 86(3):361–369

    Article  Google Scholar 

  • Ledermann T (2011) A non-linear model to predict crown recession of Norway spruce (Picea abies [L.] Karst.) in Austria. Eur J For Res 130(4):521–531

    Article  Google Scholar 

  • Leites LP, Robinson AP, Crookston NL (2009) Accuracy and equivalence testing of crown ratio models and assessment of their impact on diameter growth and basal area increment predictions of two variants of the Forest Vegetation Simulator. Can J For Res 39:655–665

    Article  Google Scholar 

  • Li FR (2004) Modeling crown profile of Larix olgensis tree. Sci Silvae Sin 40(5):16–24 (in Chinese with English abstract)

    Google Scholar 

  • Lindstrom JM, Bates DM (1990) Nonlinear mixed effects models for repeated measures data. Biometrics 46(3):673–687

    Article  CAS  PubMed  Google Scholar 

  • Liu ZG, Li FR (2009) Crown structure model and three dimensional computer graphics simulation for Mongolian Scots pine plantation. Sci Silvae Sin 6(45):54–61 (in Chinese with English abstract)

    Google Scholar 

  • Lu J, Li FR, Zhang HR, Zhang SG (2011) A crown ratio model for dominant species in secondary forests in Mao’er mountain. Sci Silvae Sin 6(47):70–76 (in Chinese with English abstract)

    Google Scholar 

  • Maguire DA, Hann DW (1987) A stem dissection technique for dating branch mortality and reconstructing past crown recession. For Sci 33:858–871

    Google Scholar 

  • Maguire DA, Hann DW (1990a) A sampling strategy for estimating past crown recession on temporary growth plots. For Sci 36:549–563

    Google Scholar 

  • Maguire DA, Hann DW (1990b) Constructing models for direct prediction of 5-year crown recession in south-western Oregon Douglas-fir. Can J For Res 20:1044–1052

    Article  Google Scholar 

  • Mäkinen H (2002) Effect of stand density on the branch development of silver birch (Betula pendula Roth) in central Finland. Trees 16:346–353

    Google Scholar 

  • Meng SX, Huang S (2009) Improved calibration of nonlinear mixed-effects models demonstrated on a height growth functions. For Sci 55(3):239–248

    Google Scholar 

  • Mitchell KJ (1975) Dynamics and simulated yield of Douglas-fir. For Sci Monogr 17:39–45

    Google Scholar 

  • Monserud RA, Sterba H (1996) A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria. For Ecol Manag 80(1–3):57–80

    Article  Google Scholar 

  • Nguyen TT, Biber P, Pretzsch H (2012) Analysis and management of stand dynamics of Vietnamese dipterocarp forests by applying a dynamic growth model. Ann For Sci 69(5):581–601

    Article  Google Scholar 

  • Pinheiro JC, Bates DM (1995) Approximations to the log-likelihood function in the nonlinear mixed-effects model. J Comput Graph Stat 4:12–35

    Google Scholar 

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

    Book  Google Scholar 

  • Popoola FS, Adesoye PO (2012) Crown ratio models for Tectona ģrandis stands in Osho forest reserve, Oyo state, Nigeria. J For Sci 28(2):63–67

    Google Scholar 

  • Pretzsch H (1992) Modelling the crown competition of Norway spruce and Beech in pure and mixed stands. Allg Forst und Jagdztg 163:203–213

    Google Scholar 

  • Pretzsch H, Biber P, Dursky J (2002) The single tree based stand simulator SILVA. Construction, application and evaluation. For Ecol Manag 162:3–21

    Article  Google Scholar 

  • Rijal B, Weiskittel AR, Kershaw JA (2012) Development of height to crown base models for thirteen tree species of the North American Acadian region. For Chron 88:60–73

    Article  Google Scholar 

  • Ritchie MW, Hann DW (1985) Equations for predicting basal area increment in Douglas-fir and Drand fir. Oregan State University, Forest Research Laboratory, Research Bulletin

  • Ritchie MW, Hann DW (1987) Equations for predicting height to crown base for fourteen tree species in southwest Oregon. Oregon State University, Forestry Research Laboratory, Corvallis

    Google Scholar 

  • Ritchie MW, Zhang JW, Hamilton TA (2013) Aboveground tree biomass for Pinus ponderosa in Northeastern California. Forests 4:179–196

    Article  Google Scholar 

  • Russell MB, Weiskittel AR (2011) Maximum and largest crown width equations for fifteen tree species in Maine. North J Appl For 28:84–91

    Article  Google Scholar 

  • Russell MB, Weiskittel AR, Kershaw JAJ (2014) Comparing strategies for modeling individual tree height and height-to-crown base increment in mixed-species Acadian forests of northeastern North America. Eur J For Res 133:1121–1135

    Article  Google Scholar 

  • Sattlerderek F, LeMay V (2011) A system of nonlinear simultaneous equations for crown length and crown radius for the forest dynamics model SORTIE-ND. Can J For Res 41(8):1567–1576

    Article  Google Scholar 

  • Saud P, Lynch TB, Anup KC, Guldin JM (2016) Using quadratic mean diameter and relative spacing index to enhance height-diameter and crown ratio models fitted to longitudinal data. Forestry 89:215–229

    Article  Google Scholar 

  • Seanm G, Robert M, Maguire DA (2008) Crown recession patterns in three conifer species of the Northern rock mountains. For Sci 54(6):633

    Google Scholar 

  • Sharma RP, Bilek L, Vacek Z, Vacek S (2017) Modelling crown width–diameter relationship for Scots pine in the central Europe. Trees 31(6):1–15

    Article  CAS  Google Scholar 

  • Soares P, Tomé M (2001) A tree crown ratio prediction equation for eucalypt plantations. Ann For Sci 58(2):193–202

    Article  Google Scholar 

  • Spathelf P (2003) Reconstruction of crown length of Norway spruce (Picea abies (L.) Karst.) and Silver fir (Abies alba Mill.)—technique, establishment of sample methods and application in forest growth analysis. Ann For Sci 60:833–842

    Article  Google Scholar 

  • Spiecker H (1990) Growth variation and environmental stresses: long-term observations on permanent research plots in Southwestern Germany. Water Air Soil Poll 54(2):247–256

    Article  Google Scholar 

  • Stage AR (1973) Prognosis model for stand development. USDA Forest Service, Intermountain Forest and Range Experiment Station. Ogden, UT Research Paper INT-137

  • Temesgen H, Lemay V, Mitchell SJ (2005) Tree crown ratio models for multispecies and multi-layered stands of southeastern British Columbia. For Chron 81(1):133–141

    Article  Google Scholar 

  • Toney C, Reeves MC (2009) Equations to convert compacted crown ratio to uncompacted crown ratio for trees in the interior west. West J Appl For 24(2):76–82

    Article  Google Scholar 

  • Valentine HT, Ludlow AR, Furnival GM (1994) Modeling crown rise in even-aged stands of Stika spruce or loblolly pine. For Ecol Manag 69:189–197

    Article  Google Scholar 

  • Valentine HT, Makela A, Green EJ, Amateis RL, Mäkinen H, Ducey MJ (2012) Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce. Trees 26:469–478

    Article  Google Scholar 

  • Wang Y, LeMay VM, Baker TG (2007) Modeling and prediction of dominant height and site index of Eucalyptus globulus plantation using a nonlinear mixed-effects model approach. Can J For Res 37:1390–1403

    Article  Google Scholar 

  • Weiskittel AR, Crookston NL, Radtke PJ (2011) Linking climate, gross primary productivity, and site index across forests of the western United States. Can J For Res 41:1710–1721

    Article  Google Scholar 

  • Wensel LC, Daugherty PJ (1985) CACTOS user’s guide: the California conifer timber output simulator, version 2.0. California Forest Yield Cooperative, University of California, Department of Forest Resource Management, Berkeley, CA Res Nite 10

  • Wykoff WR (1990) A basal area increment model for individual conifers in the Northern Rocky Mountains. For Sci 36(4):1077–1104

    Google Scholar 

  • Wykoff WR, Crookston NL, Stage AR (1982) Users’ guide to the stand prognosis model. US For Serv Gen Tech Rep. INT-GTR-133

  • Young YQ, Huang SM (2011) Estimating a multilevel dominant height- age model from nested data with generalized errors. For Sci 57(2):102–116

    Google Scholar 

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

    Article  Google Scholar 

  • Zumrawi AA, Hann DW (1989) Equations for predicting the height to crown base of six species in the Central Western Willamette Valley of Oregon. Forest Research Laboratory, Oregon State University, Research Paper 52

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Authors and Affiliations

  1. Key Laboratory of Sustainable Forest Ecosystem Management-Ministry of Education, School of Forestry, Northeast Forestry University, Harbin, 150040, Heilongjiang, People’s Republic of China

    Weiwei Jia

  2. Research Institute of Forestry, Chinese Academy of Forestry, Key Laboratory of Tree Breeding and Cultivation, State Forestry Administration, Beijing, 100091, People’s Republic of China

    Dongsheng Chen

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  1. Weiwei Jia
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Project funding: The work was supported by the National Key Research and Development Program of China (2017YFD0600401), and the Fundamental Research Funds for the Central Universities (2572019CP08).

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Corresponding editor: Tao Xu.

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Jia, W., Chen, D. Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch (Larix olgensis) plantations in northeast China. J. For. Res. 30, 2095–2109 (2019). https://doi.org/10.1007/s11676-019-01045-1

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