Articles containing the keyword 'algebraic difference approach'

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

Investing in planting genetically improved silver birch (Betula pendula Roth) in Swedish plantations requires understanding how birch stands will develop over their entire rotation. Previous studies have indicated relatively low production of birch compared to Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.). This could result from using unrepresentative basic data, collected from unimproved, naturally-regenerated birch (Betula spp.) growing on inventory plots often located in coniferous stands. The objective of this study was to develop a basal area development function of improved silver birch and evaluate production over a full rotation period. We used data from 52 experiments including planted silver birch of different genetic breeding levels in southern and central Sweden. The experimental plots were established on fertile forest sites and on former agricultural lands, and were managed with different numbers of thinnings and basal area removal regimes. The model best describing total stand basal area development was a dynamic equation derived from the Korf base model. The analysis of the realized gain trial for birch showed a good stability of the early calculated relative differences in basal area between tested genotypes over time. Thus, the relative difference in basal area might be with cautious used as representation of the realized genetic gain. On average forest sites in southern Sweden, improved and planted silver birch could produce between 6–10.5 m³ ha^–1 year^–1, while on fertile agriculture land the average productivity might be higher, especially with material coming from the improvement program. The performed analysis provided a first step toward predicting the effects of genetic improvement on total volume production and profitability of silver birch. However, more experiments are needed to set up the relative differences between different improved material.

• Liziniewicz, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: mateusz.liziniewicz@skogforsk.se
• Barbeito, Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Alnarp, Sweden; Université de Lorraine, AgroParisTech, INRAE, UMR Silva, Nancy, France E-mail: ignacio.barbeito@slu.se
• Zvirgzdins, Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Box 49, 23053 Alnarp, Sweden E-mail: andis.zvirgzdins@slu.se
• Stener, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: lg.stener@telia.com
• Niemistö, Natural Resources In-stitute Finland (Luke), Natural resources, Seinäjoki, Finland E-mail: pentti.niemisto@luke.fi
• Fahlvik, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: nils.fahlvik@skogforsk.se
• Johansson, Tönnersjöheden Experimental Forest, SLU, Simlångsdalen, Sweden E-mail: ulf.johansson@slu.se
• Karlsson, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: curly.birch@gmail.com
• Nilsson, Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Box 49, 23053 Alnarp, Sweden E-mail: urban.nilsson@slu.se

Growth and yield tables are constrained by a standard production regime and the stand-level dynamic models are an attractive alternative for the even-aged monospecific stands. The objective of this study is to derive a parsimonious and biologically sound whole-stand dynamic growth model and to validate its consistency and relevance for prediction of stand growth and yield. The state-space modelling approach was employed, introducing several novelties in comparison with its current usage. The model consists of a three-dimensional state vector, defined by dominant stand height, number of trees per hectare and mean stem volume, and three transition functions. A site index model was incorporated for height growth projection and transition functions for stand density and mean stem volume with respect to dominant height increase were derived from simple allometries and biological rationale. The model was examined with data from 79 permanent sample plots in Scots pine plantations. Nonlinear Seemingly Unrelated Regression was used to account for cross-equation correlations, and the Base-Height-Invariant dummy variable method was employed to estimate dynamic-form equations. Model consistency was validated in terms of accuracy of predictions and applicability to both thinned and unthinned stands. The new dynamic growth model is a parsimonious biometric whole-stand model that simulates the expected stand development for a broad spectrum of potential management alternatives and can be incorporated in a computer program for further use. It may be especially useful for application when a scarcity of longitudinal data prevents the use of more complicated modelling approaches.

• Stankova, Forest Research Institute of Bulgarian Academy of Sciences, Department of Forest Genetics, Physiology and Plantations, 132 “St. Kliment Ohridski” Blvd., 1756 Sofia, Bulgaria http://orcid.org/0000-0002-9932-7286 E-mail: tatianastankova@yahoo.com

• Diéguez-Aranda, Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela. Escuela Politécnica Superior, Campus universitario, 27002 Lugo, Spain E-mail: udieguez@lugo.usc.es
• Grandas-Arias, Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela. Escuela Politécnica Superior, Campus universitario, 27002 Lugo, Spain E-mail: jaga@nn.es
• Álvarez-González, Departamento de Ingeniería Agroforestal, Universidad de Santiago de Compostela. Escuela Politécnica Superior, Campus universitario, 27002 Lugo, Spain E-mail: jgag@nn.es
• Gadow, Institut fur Waldinventur und Waldwachstum, George-Auguts-Universität Göttingen. Büsgenweg 5, D-37077 Göttingen, Germany E-mail: kg@nn.de

The height growth of trees influences the productivity of stands and the competitiveness of species, shaping the range of their distribution. Dominant height growth was assessed for European beech (Fagus sylvatica L.), growing outside of its natural distribution range in the western part of Latvia. In 10 neighbouring experimental stands, 20 dominant trees were felled for stem analysis. Height growth was modelled using the generalised algebraic difference approach, applying several non-linear equations and mixed procedures. The Chapman-Richards and Sloboda models showed the best fit to the data. Height growth of the second generation (younger) trees exceeded that of the first generation, and followed curve for a higher site index, suggesting sufficient adaptation and improving conditions. Height growth of the studied beech exceeded predictions for beech in southern Sweden, which is considered to be the northern limit of the species range, yet the growth pattern differed. In Latvia, slower height growth was estimated for site indices < 32 m (in 100 years) during the first 60 years, yet larger maximal height was predicted, suggesting a longer establishment period. Nevertheless, the improving height growth indicated increasing potential for the application of the species in commercial forestry, and an expansion of the species within the region even during the 21th century.

• Matisons, Latvian State Forest Research Institute “Silava”, Rīgas str. 111, Salaspils, Latvia, LV2169 E-mail: robism@inbox.lv
• Šņepsts, Latvian State Forest Research Institute “Silava”, Rīgas str. 111, Salaspils, Latvia, LV2169 E-mail: guntars.snepsts@silava.lv
• Puriņa, Latvian State Forest Research Institute “Silava”, Rīgas str. 111, Salaspils, Latvia, LV2169 E-mail: liga.purina@silava.lv
• Donis, Latvian State Forest Research Institute “Silava”, Rīgas str. 111, Salaspils, Latvia, LV2169 E-mail: janis.donis@silava.lv
• Jansons, Latvian State Forest Research Institute “Silava”, Rīgas str. 111, Salaspils, Latvia, LV2169 E-mail: aris.jansons@silava.lv