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Articles containing the keyword 'generalized algebraic difference approach'

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 10512, category Research article
Mateusz Liziniewicz, Ignacio Barbeito, Andis Zvirgzdins, Lars-Göran Stener, Pentti Niemistö, Nils Fahlvik, Ulf Johansson, Bo Karlsson, Urban Nilsson. (2022). Production of genetically improved silver birch plantations in southern and central Sweden. Silva Fennica vol. 56 no. 1 article id 10512. https://doi.org/10.14214/sf.10512
Keywords: Betula pendula; planting; generalized algebraic difference approach; genetic gain; stand basal area starting function
Highlights: The basal area development of genetically improved birch in Sweden was modeled using a generalized algebraic difference approach; The best model fit, both graphically and statistically was delivered by the Korf base model; The analysis of realized gain trial showed a stability of relative differences in basal area between tested genotypes.
Abstract | Full text in HTML | Full text in PDF | Author Info

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 (email)
  • 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
article id 319, category Research article
Ulises Diéguez-Aranda, José Antonio Grandas-Arias, Juan Gabriel Álvarez-González, Klaus von Gadow. (2006). Site quality curves for birch stands in north-western Spain. Silva Fennica vol. 40 no. 4 article id 319. https://doi.org/10.14214/sf.319
Keywords: site quality; Betula pubescens; generalized algebraic difference approach; base-age invariant dynamic equation; Hossfeld model; Galicia
Abstract | View details | Full text in PDF | Author Info
A model for predicting the height growth of even-aged, birch (Betula pubescens Ehrh.) dominated stands in Galicia (north-western Spain) was developed. Data from stem analysis of 214 trees were used for model construction. Two dynamic site equations derived with the generalized algebraic difference approach (GADA) were tested, which combine compatible site index and height models in one common equation. Both equations are base-age invariant and directly estimate height and site index from any height and age. The fittings were done in one stage using the base-age-invariant dummy variables method. A second-order continuous-time autoregressive error structure was used to correct the inherent autocorrelation of the longitudinal data used in this study. Cieszewski’s model best described the data. This model is therefore recommended for height growth prediction and site classification of birch stands in Galicia.
  • 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 (email)
  • 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

Category: Research note

article id 7818, category Research note
Roberts Matisons, Guntars Šņepsts, Līga Puriņa, Jānis Donis, Āris Jansons. (2018). Dominant height growth of European beech at the northeasternmost stands in Europe. Silva Fennica vol. 52 no. 1 article id 7818. https://doi.org/10.14214/sf.7818
Keywords: site index; Fagus sylvatica; generalized algebraic difference approach; height models
Highlights: The dominant height growth of the introduced European beech was modelled using the generalised algebraic difference approach; The Chapman-Richards and Sloboda models showed the best fit to the data; Height growth of the second generation trees exceeded the first generation trees; In the western part of Latvia, height growth of beech exceeded that in southern Sweden.
Abstract | Full text in HTML | Full text in PDF | Author Info

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 (email)
  • 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

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