Articles containing the keyword 'mixed-effects models'

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 https://orcid.org/0000-0002-6332-7911 E-mail: lars.sprengel@iww.uni-freiburg.de
• 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

The diameter at any point on a stem and tree volume are some of the most important types of information used in forest management planning. One of the methods to predict the diameter at any point on a stem is to develop taper models. Black locust (Robinia pseudoacacia L.) occurs in almost all forests in Poland, with the largest concentration in the western part of the country. Using empirical data obtained from 13 black locust stands (48 felled trees), seven taper models with different numbers of estimated parameters were analysed for section diameters both over and under bark using fixed and mixed-effects modelling approaches. Assuming a lack of additional measurements, the best fitted taper models were used for the prediction of over bark volume using both methods. The predicted volume was compared with the results from different volume equations available for black locust. The variable-form taper model with eight estimated parameters fitted the data the best. The lowest root mean square error for volume prediction was achieved for the elaborated fixed-effects taper model (0.0476), followed by the mixed-effects taper model (0.0489). At the same time, the difference between the volume relative errors achieved based on the taper models does not differ significantly from the results obtained using the volume equations already available for black locust (two of the three analysed).

• Bronisz, Institute of Forest Sciences, Warsaw University of Life Sciences-SGGW, Nowoursynowska 159, PL 02-776 Warsaw, Poland E-mail: karol.bronisz@wl.sggw.pl
• Zasada, Institute of Forest Sciences, Warsaw University of Life Sciences-SGGW, Nowoursynowska 159, PL 02-776 Warsaw, Poland https://orcid.org/0000-0002-4881-296X E-mail: Michal.Zasada@wl.sggw.pl