Skip to main content

Advertisement

SpringerLink
Log in

Crown width prediction for Larix olgensis plantations in Northeast China based on nonlinear mixed-effects model and quantile regression

  • Original Article
  • Published:
Trees Aims and scope Submit manuscript

Abstract

Key message

New allometric crown width models were developed for Larix olgensis based on a large dataset from plantations in northeastern China using the nonlinear mixed-effects model and quantile regression, and multiple variables were included in the developed models and calibration was performed to enhance their applicability.

Abstract

Crown width (CW) is an essential indicator of the general health, vigor, and stability of living trees. It is used as a predictor in various tree models, such as growth, biomass, mortality, stem taper, and volume models. In this study, models of tree crown width were developed and evaluated using data from 343 permanent sample plots (PSPs) of Larix olgensis plantations in Heilongjiang Province, Northeast China. A logistic function with several predictor variables, including diameter at breast height (DBH), total tree height (H), height to live crown base (HCB), and height–diameter ratio (HD), was selected as the basic crown width model to provide acceptable model generality. Four modeling approaches were evaluated: (1) a mixed-effects model, (2) a three-quantile regression method, (3) a five-quantile regression method, and (4) a nine-quantile regression method. The mixed-effects and quantile regression models were calibrated using simple random sampling (SRS) and different sampling numbers (1 to 12 trees per plot). The evaluation results of the jackknifing technique indicated that both the mixed-effects and quantile regression approaches outperformed the generalized model. The prediction performance of the models improved as the sampling number increased, but the gains in performance gradually decreased. In general, the use of six sample trees per plot was considered a good compromise between the investigation cost and predictive accuracy for calibrating the mixed-effects model and quantile regression methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Availability of data and materials

The data used in this article cannot be shared publicly because these data are being used in ongoing studies. The data will be shared upon reasonable request by the corresponding authors.

References

  • Arnab R (2017) Unequal probability sampling. Survey sampling theory and applications. Elsevier, Amsterdam, pp 117–166

    Book  Google Scholar 

  • Bassett GW, Chen HL (2001) Portfolio style: return-based attribution using quantile regression. Empir Econ 26:293–305

    Article  Google Scholar 

  • Biging GS, Dobbertin M (1992) A comparison of distance-dependent competition measures for height and basal area growth of individual conifer trees. For Sci 38:695–720

    Google Scholar 

  • Bohora SB, Cao QV (2014) Prediction of tree diameter growth using quantile regression and mixed-effects models. For Ecol Manage 319:62–66

    Article  Google Scholar 

  • Bragg DC (2001) A local basal area adjustment for crown width prediction. North J Appl For 18:22–28

    Article  Google Scholar 

  • Bronisz K, Mehtätalo L (2020) Mixed-effects generalized height-diameter model for young silver birch stands on post-agricultural lands. For Ecol Manage 460:117901

    Article  Google Scholar 

  • Buchacher R, Ledermann T (2020) Interregional crown width models for individual trees growing in pure and mixed stands in Austria. Forests 11:114

    Article  Google Scholar 

  • Buchman RG, Pederson SP, Walters NR (1983) A tree survival model with application to species of the Great Lakes region. Can J for Res 13:601–608

    Article  Google Scholar 

  • Cade BS, Noon BR (2003) A gentle introduction to quantile regression for ecologists. Front Ecol Environ 1:412–420

    Article  Google Scholar 

  • 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 

  • Cao QV, Wang J (2015) Evaluation of methods for calibrating a tree taper equation. For Sci 61:213–219

    Article  Google Scholar 

  • Cawley GC, Talbot NLC (2003) Efficient leave-one-out cross-validation of kernel Fisher discriminant classifiers. Pattern Recognit 36(11):2585–2592

    Article  Google Scholar 

  • Chen Q, Duan G, Liu Q, Ye Q, Sharma RP, Chen Y, Liu H, Fu L (2021) Estimating crown width in degraded forest: a two-level nonlinear mixed-effects crown width model for Dacrydium pierrei and Podocarpus imbricatus in tropical China. For Ecol Manage 497:119486

    Article  Google Scholar 

  • Crecente-Campo F, Tomé M, Soares P, Dieguez-Aranda U (2010) A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. For Ecol Manage 259:943–952

    Article  Google Scholar 

  • Cristiano C, Giorgio V, Maurizio M, Piermaria C (2017) Projecting nonnative douglas fir plantations in southern europe with the forest vegetation simulator. For Sci 63:101–110

    Article  Google Scholar 

  • Crookston NL, Dixon GE (2005) The forest vegetation simulator: a review of its structure, content, and applications. Comput Electron Agric 49:60–80

    Article  Google Scholar 

  • Davies O, Pommerening A (2008) The contribution of structural indices to the modelling of Sitka spruce (Picea sitchensis) and birch (Betula spp.) crowns. For Ecol Manage 256:68–77

    Article  Google Scholar 

  • Dawkins H (1963) Crown diameters: their relation to bole diameter in tropical forest trees. Com for Rev 42:114

    Google Scholar 

  • De-Miguel S, Mehtatalo L, Shater Z, Kraid B, Pukkala T (2012) Evaluating marginal and conditional predictions of taper models in the absence of calibration data. Can J for Res 42:1383–1394

    Article  Google Scholar 

  • Dong L, Zhang L, Li F (2014) A compatible system of biomass equations for three conifer species in Northeast, China. For Ecol Manage 329:306–317

    Article  Google Scholar 

  • Dong L, Zhang L, Li F (2018) Additive Biomass Equations Based on Different Dendrometric Variables for Two Dominant Species (Larix gmelini Rupr. and Betula platyphylla Suk.) in Natural Forests in the Eastern Daxing’an Mountains, Northeast China. Forests 9:261

    Article  Google Scholar 

  • Dong L, Pukkala T, Li F, Jin X (2021) Developing distance-dependent growth models from irregularly measured sample plot data—a case for Larix olgensis in Northeast China. For Ecol Manage 486:118965

    Article  Google Scholar 

  • Dorado FC, Diéguez-Aranda Anta MB, Rodríguez MS, Gadow KV (2006) A generalized height-diameter model including randomcomponents for radiate pine plantations in northwestern Spain. For Ecol Manage 229:202–213

    Article  Google Scholar 

  • Fang Z, Bailey RL, Shiver BD (2001) A multivariate simultaneous prediction system for stand growth and yield with fixed and random effects. For Sci 47:550–562

    Google Scholar 

  • Flora Reipublicae Popularis Sinicae (1978). Science Press, Beijing. 7, pp 190

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

    Article  Google Scholar 

  • Fu L, Zhang H, Lu J, Zang H, Lou M, Wang G (2015) Multilevel nonlinear mixed-effects crown ratio models for individual trees of Mongolian Oak (Quercus mongolica) in Northeast China. PLoS ONE 10:e0133294

    Article  PubMed  PubMed Central  Google Scholar 

  • Fu L, Sharma RP, Wang G, Tang S (2017a) Modelling a system of nonlinear additive crown width models applying seemingly unrelated regression for Prince Rupprecht larch in northern China. For Ecol Manage 386:71–80

    Article  Google Scholar 

  • Fu L, Zhang H, Sharma RP, Pang L, Wang G (2017b) A generalized nonlinear mixed-effects height to crown base model for Mongolian oak in northeast China. For Ecol Manage 384:34–43

    Article  Google Scholar 

  • Fu L, Sharma RP, Hao K, Tang S (2017c) A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China. For Ecol Manage 389:364–373

    Article  Google Scholar 

  • Fu L, Duan G, Ye Q, Meng X, Liu Q (2020) Prediction of individual tree diameter using a nonlinear mixed-effects modeling approach and airborne lidar data. Remote Sens 12:1066

    Article  Google Scholar 

  • Gill SJ, Biging GS (2002) Autoregressive moving average models of crown profiles for two California hardwood species—ScienceDirect. Ecol Model 152:213–226

    Article  Google Scholar 

  • Glover GR, Hool JN (1979) A basal area ratio predictor of loblolly pine plantation mortality. For Sci 25:275–282

    Google Scholar 

  • Grégoire TG, Schabenberger O, Barrett JP (2011) Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Can J for Res 25:137–156

    Article  Google Scholar 

  • Hamilton GJ (1969) The dependence of volume increment of individual trees on dominance, crown dimensions, and competition. Forestry 2:133–144

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Hein S, Mäkinen H, Yue C, Kohnle U (2007) Modelling branch characteristics of Norway spruce from wide spacings in Germany. For Ecol Manage 242:155–164

    Article  Google Scholar 

  • Hetherington JC (1967) Crown diameter: stem diameter relationships in managed stands of sitka spruce. Commonwealth Forestry Rev 46:278–281

    Google Scholar 

  • Hoffmann CW, Usoltsev VA (2002) Tree-crown biomass estimation in forest species of the Ural and of Kazakhstan. For Ecol Manage 158:59–69

    Article  Google Scholar 

  • Horntvedt R (1993) Crown density of spruce trees related to needle biomass. For Ecol Manage 59:225–235

    Article  Google Scholar 

  • Huuskonen S, Miina J (2007) Stand-level growth models for young Scots pine stands in Finland. For Ecol Manage 241:49–61

    Article  Google Scholar 

  • Jiang L, Li Y (2008) Nonlinear mixed modeling approach—an application to tree growth data. IEEE 1:646–649

    Google Scholar 

  • Kangas A, Maltamo M (2006) Forest inventory: methodology and applications, managing forest ecosystems, vol 10. Springer, Dordrecht, p XX–362. https://doi.org/10.1007/1-4020-4381-3

    Book  Google Scholar 

  • Koenker R (2005) Quantile regression. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Koenker R, Bassett GW (1978) Regression quantiles. Econometrica 46:211–244

    Article  Google Scholar 

  • Koenker R, Portnoy S, Ng PT, Melly B, Zeileis A, Grosjean P, Moler P, Saad Y, Chernozhukov V, Fernandez-Vsl V, Ripley BD (2021) quantreg: Quantile regression. R Package Version 5.85

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

    Google Scholar 

  • Kramer H (1966) Crown development in conifer stands in Scotland as influenced by initial spacing and subsequent thinning treatment. Forestry 39:40–58

    Article  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 86:361–369

    Article  Google Scholar 

  • Larocque GR, Marshall PL (1994) Crown development in red pine stands. I. Absolute and relative growth measures. Can J for Res 24:762–774

    Article  Google Scholar 

  • Lei Y, Fu L, Affleck DL, Nelson AS, Shen C, Wang M, Zheng J, Ye Q, Yang G (2018) Additivity of nonlinear tree crown width models: aggregated and disaggregated model structures using nonlinear simultaneous equations. For Ecol Manage 427:372–382

    Article  Google Scholar 

  • Liu X, Hao YS, Widagdo FRA, Xie LF, Dong LH, Li FR (2021) Predicting height to crown base of Larix olgensis in Northeast China Using UAV-LiDAR data and nonlinear mixed effects models. Remote Sens 13:1834

    Article  Google Scholar 

  • Marshall DD, Johnson GP, Hann DW (2003) Crown profile equations for stand-grown western hemlock trees in northwestern Oregon. Can J for Res 33:2059–2066

    Article  Google Scholar 

  • Mehtätalo L, Gregoire TG, Burkhart HE (2008) Comparing strategies for modeling tree diameter percentiles from remeasured plots. Environmetrics 19:529–548

    Article  Google Scholar 

  • Meng SX, Huang S, Yang Y, Trincado G, Vanderschaaf CL (2009) Evaluation of population-averaged and subject-specific approaches for modeling the dominant or codominant height of lodgepole pine trees. Can J for Res 39:1148–1158

    Article  Google Scholar 

  • Miao Z, Widagdo FR, Dong L, Li F (2021) Prediction of branch growth using quantile regression and mixed-effects models: An example with planted Larix olgensis Henry trees in Northeast China. For Ecol Manage 496:119407

    Article  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 Manage 80:57–80

    Article  Google Scholar 

  • Nykänen ML, Peltola H, Quine C, Kellomäki S, Broadgate M (1997) Factors affecting snow damage of trees with particular reference to European conditions. Silva Fenn 31:193–213

    Article  Google Scholar 

  • Özçelik R, Cao QV, Trincado G, Gocer N (2018) Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey. For Ecol Manage 419–420:240–248

    Article  Google Scholar 

  • Paulo JA, Faias SP, Ventura-Giroux C, Tomé M (2015) Estimation of stand crown cover using a generalized crown diameter model: application for the analysis of Portuguese cork oak stands stocking evolution. iForest. 422:437–444

    Google Scholar 

  • Peng W, Timo P, Jin X, Li F (2018) Optimal management of larch (Larix olgensis A. Henry) plantations in Northeast China when timber production and carbon stock are considered. Ann for Sci 75:63

    Article  Google Scholar 

  • Pinheiro J, Bates D (2000) Mixed-effects models in S and S-Plus. Springer, New York

    Book  Google Scholar 

  • Pinheiro J, Bates D, Debroy S, Sakar D, EISPACK, Heisterkamp S, Willigen BV, R-core (2020) nlme: Linear and Nonlinear Mixed Effects Models. R package version 3.1–149

  • Power H, LeMay V, Berninger F, Sattler D, Kneeshaw D (2012) Differences in crown characteristics between black (Picea mariana) and white spruce (Picea glauca). Can J for Res 42:1733–1743

    Article  Google Scholar 

  • R Development Core Team (2020) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Raptis D, Kazana V, Kazaklis A, Stamatiou C (2018) A crown width-diameter model for natural even-aged black pine forest management. Forests 9:610–628

    Article  Google Scholar 

  • Sánchez-González M, Cañellas I, Montero G (2007) Generalized height-diameter and crown diameter prediction models for cork oak forests in Spain. Inv Agrar Sist Recursos Fores 16:76–88

    Article  Google Scholar 

  • Sharma RP, Vacek Z, Vacek S (2016) Individual tree crown width models for Norway spruce and European beech in Czech Republic. For Ecol Manage 366:208–220

    Article  Google Scholar 

  • Sharma RP, Bílek L, Vacek Z, Vacek S (2017) Modelling crown width-diameter relationship for Scots pine in the central Europe. Trees-Struct Funct 31:1875–1889

    Article  CAS  Google Scholar 

  • Sillett SC, Bailey MG (2003) Effects of tree crown structure on biomass of the epiphytic fern Polypodium scouleri (Polypodiaceae) in redwood forests. Am J Bot 90:255–261

    Article  PubMed  Google Scholar 

  • Sönmez T (2009) Diameter at breast height-crown diameter prediction models for Picea orientalis. Afr J Agric Res 4:214–219

    Google Scholar 

  • State Forestry and Grassland Administration (2019) The ninth forest resource survey report (2014–2018). China forestry press, Beijing

    Google Scholar 

  • Sun YX, Gao HL, Li FR (2017) Using linear mixed-effects models with quantile regression to simulate the crown profile of planted Pinus sylvestris var. Mongolica Trees. Forests 8:446

    Article  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 

  • Thorpe HC, Astrup R, Trowbridge A, Coates KD (2010) Competition and tree crowns: a neighborhood analysis of three boreal tree species. For Ecol Manage 259:1586–1596

    Article  Google Scholar 

  • Uzoh F, Oliver WW (2008) Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model. For Ecol Manage 256:438–445

    Article  Google Scholar 

  • Vonesh EF, Chinchilli VM (1997) Linear and nonlinear models for the analysis of repeated measurements. J Qual Technol 29:493–494

    Article  Google Scholar 

  • West PW, Ratkowsky DA, Davis AW (1984) Problems of hypothesis testing of regressions with multiple measurements from individual sampling units. For Ecol Manage 7:207–224

    Article  Google Scholar 

  • Westfall JA, Nowak DJ, Henning JG, Lister TW, Edgar CB, Majewsky MA, Sonti NF (2020) Crown width models for woody plant species growing in urban areas of the U.S. Urban Ecosyst 23:905–917

    Article  Google Scholar 

  • Wonn HT, O’Hara KL (2001) Height: diameter ratios and stability relationships for four northern rocky mountain tree species. West J Appl for 16:87–94

    Article  Google Scholar 

  • Xie L, Widagdo FR, Dong L, Li F (2020) Modeling Height-Diameter Relationships for Mixed-Species Plantations of Fraxinus mandshurica Rupr. and Larix olgensis Henry in Northeastern China. Forests 11:610

    Article  Google Scholar 

  • Xie L, Widagdo FR, Miao Z, Dong L, Li F (2021) Evaluation of the mixed effects model and quantile regression approaches for predicting tree height in larch (Larix olgensis) plantations in northeastern China. Can J for Res 52(3):309–319

    Article  Google Scholar 

  • Xu H, Sun Y, Wang X, Wang J, Fu Y (2015) Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian Province, southeast China. PLoS ONE 10:e0122257

    Article  Google Scholar 

  • Zang H, Lei X, Zeng W (2016) Height–diameter equations for larch plantations in northern and northeastern China: a comparison of the mixed-effects, quantile regression and generalized additive models. Forestry 89:434–445

    Article  Google Scholar 

  • Zarnoch SJ, Bechtold WA, Stolte KW (2004) Using crown condition variables as indicators of forest health. Can J for Res 34:m1057-1070

    Article  Google Scholar 

  • Zhang L, Bi H, Gove JH, Heath LS (2005) A comparison of alternative methods for estimating the self-thinning boundary line. Can J for Res 35:1507–1514

    Article  Google Scholar 

  • Zhang B, Sajjad S, Chen K, Zhou L, Zhang L, Yong K, Sun Y (2020) Predicting tree height-diameter relationship from relative competition levels using quantile regression models for Chinese Fir (Cunninghamia lanceolata) in Fujian Province, China. Forests 11:183

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We are deeply indebted to the academic staff and past and present graduate students of the Department of Forest Management, School of Forestry, Northeast Forestry University, who collected the data in the field.

Funding

This research was financially supported by the Joint Funds for Regional Innovation and Development of the National Natural Science Foundation of China (Grant no. U21A20244), the Fundamental Research Funds for the Central Universities (2572020DR03), the Provincial Funding for National Key R&D Program of China in Heilongjiang Province (GX18B041) and the Heilongjiang Touyan Innovation Team Program (Technology Development Team for High-efficient Silviculture of Forest Resources).

Author information

Author notes

  1. Aiyun Ma and Zheng Miao contributed equally.

Authors and Affiliations

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

    Aiyun Ma, Zheng Miao, Longfei Xie, Lihu Dong & Fengri Li

Authors
  1. Aiyun Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Miao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Longfei Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lihu Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Fengri Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Lihu Dong or Fengri Li.

Ethics declarations

Conflict of interest

The authoe declares that they no conflcict of interest.

Additional information

Communicated by Rüdiger Grote.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, A., Miao, Z., Xie, L. et al. Crown width prediction for Larix olgensis plantations in Northeast China based on nonlinear mixed-effects model and quantile regression. Trees 36, 1761–1776 (2022). https://doi.org/10.1007/s00468-022-02326-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00468-022-02326-9

Keywords

Search

Navigation