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Articles containing the keyword 'nonlinear mixed-effects model'

Category: Research article

article id 10544, category Research article
Lars Sprengel, Heinrich Spiecker, Shuirong Wu. (2022). Two subject specific modelling approaches to construct base-age invariant polymorphic site index curves with varying asymptotes. Silva Fennica vol. 56 no. 1 article id 10544. https://doi.org/10.14214/sf.10544
Keywords: generalized algebraic difference approach; stem analysis; dummy variable approach; gnls; nonlinear mixed-effects models; nlme; Zhongtiaoshan forest region
Highlights: Base-age invariant families of height growth curves with polymorphism and varying asymptotes are presented for the seven economically most important tree species in Zhongtiaoshan forest region, China; The nonlinear fixed-effects approach outperforms the nonlinear mixed-effects approach according to the AIC, but according to RMSE and bias these results are not fully supported.
Abstract | Full text in HTML | Full text in PDF | Author Info

For constructing growth and yield models the concept of site index as measure of productivity is crucial. Here, we use nonlinear mixed-effects models (NLME) with random individual effects and nonlinear models with dummy variables as fixed individual effects (NLFE) to fit mechanistic growth functions to stem analysis data of the economically most important tree species in Zhongtiaoshan forest region, China. The Richards and Lundqvist function are formulated into five dynamic equations (R1, R2, L1, L2 and L3) applying the generalized algebraic difference approach (GADA), which inherit polymorphism, varying asymptotes and base-age invariance. According to Akaike information criterion the R1 model as NLFE fits height growth data of Pinus tabuliformis Carrière, Pinus armandii Franch., Quercus liaotungensis Koidz., Quercus aliena Blume and Betula platyphylla Sukaczev best, while for Quercus variabilis Blume R2 as NLFE fits height growth data best. For Larix principis-rupprechtii Mayr L1 as NLME has been selected as best model, as R1 and R2 both as NLFE and NLME are not extrapolating the comparably short length of height growth data well enough. However, according to the root mean square error and bias differences between model fits of both the selected equation and the chosen model fitting approach are not so clear. Presented families of height growth curves serve as planning tools to identify site index and therefore assess productivity of forest stands in the studied region. A direct comparison of the productivity of forest stands of the same tree species is possible due to base-age invariance of the selected models.

  • Sprengel, Chair of Forest Growth and Dendroecology, Albert-Ludwigs-University Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany ORCID https://orcid.org/0000-0002-6332-7911 E-mail: lars.sprengel@iww.uni-freiburg.de (email)
  • Spiecker, Chair of Forest Growth and Dendroecology, Albert-Ludwigs-University Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany E-mail: instww@uni-freiburg.de
  • Wu, Research Institute of Forest Policy and Information, Chinese Academy of Forestry, No. 1 Dongxiaofu, Haidian District, Beijing 100091, China E-mail: shuirongwu@126.com
article id 10612, category Research article
Daesung Lee, Jouni Siipilehto, Jari Hynynen. (2021). Models for diameter distribution and tree height in hybrid aspen plantations in southern Finland. Silva Fennica vol. 55 no. 5 article id 10612. https://doi.org/10.14214/sf.10612
Keywords: Näslund’s height curve; Weibull distribution; parameter recovery; Populus tremula × P. tremuloides; clonal plantation; nonlinear mixed-effects model
Highlights: Parameter recovery method for the Weibull function fitted diameter distributions well by means of sum and mean forest stand characteristics for hybrid aspen plantations; Arithmetic and weighted mean diameters performed better for the recovery method than the corresponding median diameters; Two alternative Näslund’s height curve models with stand characteristics and tree dbh predictors provided unbiased tree height predictions.
Abstract | Full text in HTML | Full text in PDF | Author Info

Hybrid aspen (Populus tremula L. × P. tremuloides Michx.) is known with outstanding growth rate and some favourable wood characteristics, but models for stand management have not yet been prepared in northern Europe. This study introduces methods and models to predict tree dimensions, diameter at breast height (dbh) and tree height for a hybrid aspen plantation using data from repeatedly measured permanent sample plots established in clonal plantations in southern Finland. Dbh distributions using parameter recovery method for the Weibull function was used with Näslund’s height curve to model tree heights. According to the goodness-of-fit statistics of Kolmogorov-Smirnov and the Error Index, the arithmetic mean diameter (D) and basal area-weighted mean diameter (DG) provided more stable parameter recovery for the Weibull distribution than the median diameter (DM) and basal area-weighted median diameter (DGM), while DG showed the best overall fit. Thus, Näslund’s height curve was modelled using DG with Lorey’s height (HG), age, basal area (BA), and tree dbh (Model 1). Also, Model 2 was tested using all predictors of Model 1 with the number of trees per ha (TPH). All predictors were shown to be significant in both Models, showing slightly different behaviour. Model 1 was sensitive to the mean characteristics, DG and HG, while Model 2 was sensitive to stand density, including both BA and TPH as predictors. Model 1 was considered more reasonable to apply based on our results. Consequently, the parameter recovery method using DG and Näslund’s models were applicable for predicting tree diameter and height.

  • Lee, Natural Resources Institute Finland (Luke), Natural resources, Latokartanonkaari 9, FI-00790 Helsinki, Finland ORCID https://orcid.org/0000-0003-1586-9385 E-mail: daesung.lee@luke.fi (email)
  • Siipilehto, Natural Resources Institute Finland (Luke), Natural resources, Latokartanonkaari 9, FI-00790 Helsinki, Finland E-mail: jouni.siipilehto@luke.fi
  • Hynynen, Natural Resources Institute Finland (Luke), Natural resources, Vipusenkuja 5, FI-57200 Savonlinna, Finland ORCID https://orcid.org/0000-0002-9132-8612 E-mail: jari.hynynen@luke.fi

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