, Volume 30, Issue 4, pp 1191–1206 | Cite as

Nonlinear mixed-effects branch diameter and length models for natural Dahurian larch (Larix gmelini) forest in northeast China

  • Lingbo Dong
  • Zhaogang LiuEmail author
  • Pete Bettinger
Original Article


Key message

We developed the generalized branch diameter and length models using the multi-level nonlinear mixed-effects techniques for the natural Dahurian larch ( Larix gmelini ) forest in northeast China.


Dahurian larch (Larix gmelini) is the most commercially cultivated timber species in northeastern China due to its ecological prevalence and its superior wood attribute. However, its timber quality was largely driven by the crown architecture, i.e., the number, size and distribution of branches. The majority of branch-level models in the literature are focused on planted forests, which have substantially different crown architecture than that grown in natural mixed forests. Therefore, the goal of this investigation was to develop branch diameter and length models for Dahurian larch that are grown in natural mixed forests. A multi-level nonlinear mixed-effects model technique, including the fixed-effects, random-effects, variance functions and correlation structures, was employed to develop the branch growth models. The results suggested that the cumulative branch diameter and length were both increased with the increases of branch depth into the crown. Diameter at breast height (DBH) had significant positive influences on the branch size; however, tree height (HT) produced negative influences on the branch size, i.e., larger DBH and smaller HT could lead to larger branch size. Model fitting and validation results confirmed that we should avoid developing over-complex models from the perspective of application. As for the branch diameter and length models in our study, addressing the stand and tree level effects as random component were quite reliable and accurate for predicting the branch growth process of Dahurian larch in northeastern China.


Natural Dahurian larch forest Branch diameter Branch length Nonlinear mixed-effects models 



We would like to thank the faculty members and students of the Department of Forest Management, Northeast Forestry University (NEFU), P.R. China, who collected the data for this study in the Pangu forest farm in 2011. We acknowledge the financial support by the National Science and Technology Pillar Program during the 12th Five-year Plan Period, Project # 2012BAD22B0202 and Project # 2011BAD37B02. We also appreciate the valuable comments and the constructive suggestions from two anonymous referees and the Editor.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Forest Management, College of ForestryNortheast Forestry UniversityHarbinPeople’s Republic of China
  2. 2.Warnell School of Forestry and Natural ResourcesUniversity of GeorgiaAthensUSA

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