iForest - Biogeosciences and Forestry


Deriving tree growth models from stand models based on the self-thinning rule of Chinese fir plantations

Xiongqing Zhang (1-2), Quang V Cao (3), Yancheng Qu (1), Jianguo Zhang (1)   

iForest - Biogeosciences and Forestry, Volume 15, Issue 1, Pages 1-7 (2022)
doi: https://doi.org/10.3832/ifor3792-014
Published: Jan 13, 2022 - Copyright © 2022 SISEF

Research Articles

Self-thinning due to density-dependent mortality usually occurs during the forest development. To improve predictions of such processes during forest successions under climate change, reliable stand-level models are needed. In this study, we developed an integrated system of tree- and stand-level models by deriving tree diameter and survival models from stand growth and survival models based on climate-sensitive self-thinning rule of Chinese fir plantations in subtropical China. The resulting integrated system, having a unified mathematical structure, should provide consistent estimates at both tree and stand levels. Predictions were reasonable at both stand and tree levels. Because stand-level values aggregated from the tree model outputs are different from those predicted directly from the stand models, the disaggregation approach was applied to provide numerical consistency between models of different resolutions. Compared to the unadjusted approach, predictions from the disaggregation approach were slightly worse for tree survival but slightly better for tree diameter. Because the stand models were developed under the climate-sensitive self-thinning trajectory, the integrated system could offer reasonable predictions that could aid in managing Chinese fir plantations under climate change.


Chinese Fir, Self-thinning Rule, Disaggregation, Stand Model, Tree Model

Authors’ address

Xiongqing Zhang 0000-0001-5592-6730
Yancheng Qu
Jianguo Zhang
Key Laboratory of Tree Breeding and Cultivation of the National Forestry and Grassland Administration, Research Institute of Forestry, Chinese Academy of Forestry, Beijing 100091 (P. R. China)
Xiongqing Zhang 0000-0001-5592-6730
Collaborative Innovation Center of Sustainable Forestry in Southern China, Nanjing Forestry University, Nanjing, 210037 (P. R. China)
Quang V Cao 0000-0002-0155-4940
School of Renewable Natural Resources, Louisiana State University (USA)

Corresponding author

Jianguo Zhang


Zhang X, Cao QV, Qu Y, Zhang J (2022). Deriving tree growth models from stand models based on the self-thinning rule of Chinese fir plantations. iForest 15: 1-7. - doi: 10.3832/ifor3792-014

Academic Editor

Alessio Collalti

Paper history

Received: Feb 24, 2021
Accepted: Nov 17, 2021

First online: Jan 13, 2022
Publication Date: Feb 28, 2022
Publication Time: 1.90 months

Breakdown by View Type

(Waiting for server response...)

Article Usage

Total Article Views: 4145
(from publication date up to now)

Breakdown by View Type
HTML Page Views: 1305
Abstract Page Views: 1622
PDF Downloads: 1001
Citation/Reference Downloads: 1
XML Downloads: 216

Web Metrics
Days since publication: 856
Overall contacts: 4145
Avg. contacts per week: 33.90

Article Citations

Article citations are based on data periodically collected from the Clarivate Web of Science web site
(last update: Feb 2023)

(No citations were found up to date. Please come back later)


Publication Metrics

by Dimensions ©

Articles citing this article

List of the papers citing this article based on CrossRef Cited-by.

Allen MGII, Coble DW, Cao QV, Yeiser J, Hung I (2011)
A modified stand table projection growth model for unmanaged loblolly and slash pine plantations in east Texas. Southern Journal of Applied Forestry 35: 115-122.
CrossRef | Gscholar
Bailey RL, Clutter JL (1974)
Base-age invariant polymorphic site curves. Forest Science 20: 155-159.
Online | Gscholar
Berger U, Hildenbrandt H, Grimm V (2002)
Towards a standard for the individual-based modeling of plant populations: self-thinning and the field-of-neighborhood approach. Natural Resource Modelling 15: 39-54.
CrossRef | Gscholar
Berger U, Hildenbrandt H, Grimm V (2004)
Age-related decline in forest production: modelling the effects of growth limitation, neighbourhood competition and self-thinning. Journal of Ecology 92 (5): 846-853.
CrossRef | Gscholar
Bi H (2001)
The self-thinning surface. Forest Science 47: 361-370.
Online | Gscholar
Bi H (2004)
Stochastic frontier analysis of a classic self-thinning experiment. Austral Ecology 29: 408-417.
CrossRef | Gscholar
Burkhart HE (2013)
Comparison of maximum size-density relationships based on alternate stand attributes for predicting tree numbers and stand growth. Forest Ecology and Management 289: 404-408.
CrossRef | Gscholar
Burkhart HE, Tomé M (2012)
Modeling forest trees and stands. Springer Science and Business Media, Dordrecht, The Netherlands, pp. 458.
Online | Gscholar
Cao QV (2017)
An integrated system for modeling tree and stand survival. Canadian Journal of Forest Research 47: 1405-1409.
CrossRef | Gscholar
Cao QV (2019)
A method to derive a tree survival model from any existing stand survival model. Canadian Journal of Forest Research 49: 1598-1603.
CrossRef | Gscholar
Carretero AC, Alvarez ET (2013)
Modelling diameter distributions of Quercus suber L. stands in “Los Alcornocales” Natural Park (Cádiz-Málaga, Spain) by using the two-parameter Weibull functions. Forest Systems 22: 15-24.
CrossRef | Gscholar
Charru M, Seynave I, Morneau F, Rivoire M, Bontemps JD (2012)
Significant differences and curvilinearity in the self-thinning relationships of 11 temperate tree species assessed from forest inventory data. Annals of Forest Science 69 (2): 195-205.
CrossRef | Gscholar
Daniels RF, Burkhart HE (1988)
An integrated system of forest stand models. Forest Ecology and Management 23 (2): 159-177.
CrossRef | Gscholar
DeSiervo MH, Jules ES, Bost DS, De Stigter EL, Butz RJ (2018)
Patterns and drivers of recent tree mortality in diverse conifer forests of the Klamath Mountains, California. Forest Science 64 (4): 371-382.
CrossRef | Gscholar
Eid T, Tuhus E (2001)
Models for individual tree mortality in Norway. Forest Ecology and Management 154: 69-84.
CrossRef | Gscholar
García O (2001)
On bridging the gap between tree-level and stand-level models. In: Proceedings of IUFRO 4.11 Conference “Forest Biometry, Modelling and Information Science” (Renols K ed). University of Greenwich, London, UK, pp. 311-323.
Ge F, Zeng W, Ma W, Meng J (2017)
Does the slope of the self-thinning line remain a constant value across different site qualities? An implication for plantation density management. Forests 8 (10): 355.
CrossRef | Gscholar
Hann DW, Wang CH (1990)
Mortality equations for individual trees in the mixed-conifer zone of southwest Oregon. Bulletin no. 76, Forest Research Laboratory, Oregon State University, Corvallis, OR, USA, pp. 17.
Online | Gscholar
Hevia A, Cao QV, Alvarez-González JG, Ruiz-González AD, Von Gadow K (2015)
Compatibility of whole-stand and individual-tree models using composite estimators and disaggregation. Forest Ecology and Management 348: 46-56.
CrossRef | Gscholar
Huuskonen S, Miina J (2007)
Stand-level growth models for young scots pine stands in Finland. Forest Ecology and Management 241: 49-61.
CrossRef | Gscholar
Lam TY, Guan BT (2020)
Modeling stand basal area growth of Cryptomeria japonica D. Don under different planting densities in Taiwan. Journal of Forest Research 25: 174-182.
CrossRef | Gscholar
Lei JF (2005)
Forest resources in China. China Forestry Publish House. Beijing, China, pp. 172. [in Chinese]
Mabvurira D, Miina J (2002)
Individual-tree growth and mortality models for Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe. Forest Ecology and Management 161: 231-245.
CrossRef | Gscholar
Monserud RA, Sterba H (1999)
Modeling individual tree mortality for Austrian forest 465 species. Forest Ecology and Management 113: 109-123.
CrossRef | Gscholar
Monserud RA, Ledermann T, Sterba H (2004)
Are self-thinning constraints needed in a tree-specific mortality model? Forest Science 50 (6): 848-858.
Online | Gscholar
Nepal SK, Somers GL (1992)
A generalized approach to stand table projection. Forest Science 38: 120-133.
Online | Gscholar
Ogawa K (2018)
Mathematical consideration of the age-related decline in leaf biomass in forest stands under the self-thinning law. Ecological Modelling 372: 64-69.
CrossRef | Gscholar
Ogawa K, Adu-Bredu S, Yokota T, Hagihara A (2010)
Leaf biomass changes with stand development of Hinoki cypress (Chamaecyparis obtusa [Sieb. et Zucc.] Endl.). Plant Ecology 211: 79-88.
CrossRef | Gscholar
Puettmann KJ, Hann DW, Hibbs DE (1993)
Evaluation of the size-density relationships for pure red alder and Douglas-fir stands. Forest Science 39: 7-27.
Online | Gscholar
Qin J, Cao QV (2006)
Using disaggregation to link individual-tree and whole-stand growth models. Canadian Journal of Forest Research 36: 953-960.
CrossRef | Gscholar
Reineke LH (1933)
Perfecting a stand-density index for even-age forests. Journal of Agricultural Research 46: 627-638.
Ritchie MW, Hann DW (1997)
Implications of disaggregation in forest growth and yield modeling. Forest Science 43 (2): 223-233.
Online | Gscholar
SAS Institute (2011)
SAS/STAT 9.3 user’s guide. SAS Institute, Cary, NC, USA, pp. 3316.
Scolforo HF, Mctague JP, Burkhart H, Roise J, Alvares CA, Stape JL (2019)
Modeling whole-stand survival in clonal eucalypt stands in Brazil as a function of water availability. Forest Ecology and Management 432: 1002-1012.
CrossRef | Gscholar
Stankova TV, Diéguez-Aranda U (2020)
Dynamic structural stand density management diagrams for even-aged natural stands and plantations. Forest Ecology and Management 458 (2): 117733.
CrossRef | Gscholar
Subedi N, Sharma M (2011)
Individual-tree diameter growth models for black jack pine plantations in northern Ontario. Forest Ecology and Management 261: 2140-2148.
CrossRef | Gscholar
Tang S, Meng CH, Meng FR, Wang YH (1994)
A growth and self-thinning model for pure even-age stands: Theory and applications. Forest Ecology and Management 70: 67-73.
CrossRef | Gscholar
VanderSchaaf CL, Burkhart HE (2012)
Development of planting density-specific density management diagrams for loblolly pine. Southern Journal of Applied Forestry 36: 126-129.
CrossRef | Gscholar
Woodall CW, Miles PD, Vissage JS (2005)
Determining maximum stand density index in mixed species stands for strategic-scale stocking assessments. Forest Ecology and Management 216: 367-377.
CrossRef | Gscholar
Wyckoff PH, Clark JS (2002)
The relationship between growth and mortality for seven co-occurring tree species in the southern Appalachian Mountains. Journal of Ecology 90: 604-615.
CrossRef | Gscholar
Yang Y, Titus SJ, Huang S (2003)
Modeling individual tree mortality for white spruce in Alberta. Ecological Modelling 163 (3): 209-222.
CrossRef | Gscholar
Yoda K (1963)
Self-thinning in overcrowded pure stands under cultivated and natural conditions (intraspecific competition among higher plants XI). Journal of Biology, Osaka City University 14: 107-129.
Zhang X, Lei Y, Cao QV (2010)
Compatibility of stand basal area predictions based on forecast combination. Forest Science 56 (6): 552-557.
Online | Gscholar
Zhang X, Lei Y, Cao QV, Chen X, Liu X (2011)
Improving tree survival prediction with forecast combination and disaggregation. Canadian Journal of Forest Research 41: 1928-1935.
CrossRef | Gscholar
Zhang X, Cao QV, Duan A, Zhang J (2016)
Self-thinning trajectories of Chinese fir plantations in Southern China. Forest Science 62 (6): 594-599.
CrossRef | Gscholar
Zhang X, Lu L, Cao QV, Duan A, Zhang J (2018)
Climate-sensitive self-thinning trajectories of Chinese fir plantations in south China. Canadian Journal of Forest Research 48 (11): 1388-1397.
CrossRef | Gscholar
Zhang X, Cao QV, Wang H, Duan A, Zhang J (2020)
Projecting stand survival and basal area based on a self-thinning model for Chinese fir plantations. Forest Science 66: 361-370.
CrossRef | Gscholar

This website uses cookies to ensure you get the best experience on our website. More info