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Silva Fennica 1926-1997
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Articles containing the keyword 'mixed model'

Category : Article

article id 5616, category Article
Hannu Hökkä, Virpi Alenius, Timo Penttilä. (1997). Individual-tree basal area growth models for Scots pine, pubescent birch and Norway spruce on drained peatlands in Finland. Silva Fennica vol. 31 no. 2 article id 5616. https://doi.org/10.14214/sf.a8517
Keywords: Pinus sylvestris; site quality; Picea abies; Betula pubescens; forest drainage; mixed models; peatlands; growth models
Abstract | View details | Full text in PDF | Author Info

Models for individual-tree basal area growth were constructed for Scots pine (Pinus sylvestris L.), pubescent birch (Betula pubescens Ehrh.) and Norway spruce (Picea abies (L.) Karst.) growing in drained peatland stands. The data consisted of two separate sets of permanent sample plots forming a large sample of drained peatland stands in Finland. The dependent variable in all models was the 5-year basal area growth of a tree. The independent tree-level variables were tree dbh, tree basal area, and the sum of the basal area of trees larger than the target tree. Independent stand-level variables were stand basal area, the diameter of the tree of median basal area, and temperature sum. Categorical variables describing the site quality, as well as the condition and age of drainage, were used. Differences in tree growth were used as criteria in reclassifying the a priori site types into new yield classes by tree species. All models were constructed as mixed linear models with a random stand effect. The models were tested against the modelling data and against independent data sets.

  • Hökkä, E-mail: hh@mm.unknown (email)
  • Alenius, E-mail: va@mm.unknown
  • Penttilä, E-mail: tp@mm.unknown
article id 5553, category Article
Annika Kangas, Kari T. Korhonen. (1995). Generalizing sample tree information with semiparametric and parametric models. Silva Fennica vol. 29 no. 2 article id 5553. https://doi.org/10.14214/sf.a9204
Keywords: forest inventories; mixed models; volume; nonparametric models; semiparametric models
Abstract | View details | Full text in PDF | Author Info

Semiparametric models, ordinary regression models and mixed models were compared for modelling stem volume in National Forest Inventory data. MSE was lowest for the mixed model. Examination of spatial distribution of residuals showed that spatial correlation of residuals is lower for semiparametric and mixed models than for parametric models with fixed regressors. Mixed models and semiparametric models can both be used for describing the effect of geographic location on stem form.

  • Kangas, E-mail: ak@mm.unknown (email)
  • Korhonen, E-mail: kk@mm.unknown
article id 5546, category Article
Oliver Schabenberger, Timothy G. Gregoire. (1995). A conspectus on Estimating Function theory and its applicability to recurrent modeling issues in forest biometry. Silva Fennica vol. 29 no. 1 article id 5546. https://doi.org/10.14214/sf.a9197
Keywords: modelling; mixed models; statistical methods; longitudinal data; generalized linear models; optimality
Abstract | View details | Full text in PDF | Author Info

Much of forestry data is characterized by a longitudinal or repeated measures structure where multiple observations taken on some units of interest are correlated. Such dependencies are often ignored in favour of an apparently simpler analysis at the cost of invalid inferences. The last decade has brought to light many new statistical techniques that enable one to successfully deal with dependent observations. Although apparently distinct at first, the theory of Estimating Functions provides a natural extension of classical estimation that encompasses many of these new approaches. This contribution introduces Estimating Function Theory as a principle with potential for unification and presents examples covering a variety of modelling issues to demonstrate its applicability.

  • Schabenberger, E-mail: os@mm.unknown (email)
  • Gregoire, E-mail: tg@mm.unknown

Category : Research article

article id 10698, category Research article
Constança Camilo-Alves, Jose Antonio Nunes, Ana Patricia Poeiras, Joao Ribeiro, Cati Dinis, Joao M. Barroso, Margarida Vaz, Nuno Almeida-Ribeiro. (2022). Influence of water and nutrients on cork oak radial growth – looking for an efficient fertirrigation regime. Silva Fennica vol. 56 no. 3 article id 10698. https://doi.org/10.14214/sf.10698
Keywords: irrigation; mixed models; Quercus suber; climate–growth relationship; increments; stem radius
Highlights: Different summer fertirrigation treatments were tested on cork oaks over four years in a 1 ha plot; Radial growth, meteorological parameters and fertirrigation volume were measured every 15–30 days; During summer fertirrigated trees grew significantly more, independently of air vapor pressure deficit; Increments were linearly related with fertirrigation volume up to 140 m3 week–1.
Abstract | Full text in HTML | Full text in PDF | Author Info

The widespread cork oak (Quercus suber L.) mortality and reduced afforestation /regeneration are causing an overall reduction in cork production. To enhance trees’ growth and vitality, afforestation techniques using fertirrigation were tested. The main objective was the promotion of trees’ growth on new dense plantations using minimum water requirements until reaching productive forests. The experimental plot – Irricork – was installed in 2017 in a ≈1 ha stand with 14 years’ age cork oaks summer-fertirrigated since plantation. Four fertirrigation treatments were applied during fertirrigation campaigns. Radial growth, meteorological parameters and fertirrigation volume were measured every 15–30 days over four years. It was observed that weather, tree size, debarking and trees’ intra-competition had a significant effect on radial increments. Fertirrigation significantly enhanced growth during summer drought and decoupled increments from air vapor pressure deficit constraints. There was a linear relationship between trees’ radial increments and fertirrigation volume up to 140 m3 week–1. Above this value, increments were smoother. In conclusion, summer fertirrigation of 140 m3 week–1 efficiently enhanced the radial growth of trees with 50–75 circumference at breast height, under the particular edaphoclimatic conditions of the stand. This study showed to be, therefore, promising in the use of efficient fertirrigation the enhance cork oaks’ radial growth.

  • Camilo-Alves, MED – Mediterranean Institute for Agriculture, Environment and Development & CHANGE – Global Change and Sustainability Institute, Institute for Advanced Studies and Research, University of Evora, Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0001-5156-172X E-mail: calves@uevora.pt (email)
  • Nunes, Department of Plant Science, School of Science and Technology, University of Evora, Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0002-6144-3484 E-mail: jain@uevora.pt
  • Poeiras, MED – Mediterranean Institute for Agriculture, Environment and Development & CHANGE – Global Change and Sustainability Institute, Institute for Advanced Studies and Research, University of Evora, Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0002-6049-807X E-mail: apcp@uevora.pt
  • Ribeiro, Department of Plant Science, School of Science and Technology, University of Evora, Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0001-7242-5866 E-mail: jmrpr@uevora.pt
  • Dinis, ORCID https://orcid.org/0000-0001-6984-1033 E-mail: dinis.cati@gmail.com
  • Barroso, MED – Mediterranean Institute for Agriculture, Environment and Development & CHANGE – Global Change and Sustainability Institute, and Department of Plant Science, School of Science and Technology, University of Evora, Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0002-0160-3845 E-mail: jmmb@uevora.pt
  • Vaz, MED – Mediterranean Institute for Agriculture, Environment and Development & CHANGE – Global Change and Sustainability Institute, and Department of Biology, School of Science and Technology, University of Evora. Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0002-3368-757X E-mail: mvaz@uevora.pt
  • Almeida-Ribeiro, ICT – Institute of Earth Sciences and Department of Plant Science, School of Science and Technology, University of Evora, Pólo da Mitra, Ap. 94, 7006-554 Évora, Portugal ORCID https://orcid.org/0000-0002-0160-3845 E-mail: nmcar@uevora.pt
article id 10196, category Research article
Karri Uotila, Jari Miina, Timo Saksa, Ron Store, Kauko Kärkkäinen, Mika Härkönen. (2020). Low cost prediction of time consumption for pre-commercial thinning in Finland. Silva Fennica vol. 54 no. 1 article id 10196. https://doi.org/10.14214/sf.10196
Keywords: forest vegetation management; early cleaning; release treatment; linear mixed model; topographic wetness index; work productivity
Highlights: Time consumption (TC) in pre-commercial thinning (PCT) can be predicted by variables describing site and stands conditions and previous silvicultural management; Applying variables available in forest resources data the field-assessment of worksite difficulty factors is not needed; The TC model could facilitate the predictions of the labour costs of PCT in forest information systems.
Abstract | Full text in HTML | Full text in PDF | Author Info

The time consumption (TC) of pre-commercial thinning (PCT) varies greatly among sites, stands and forest workers. The TC in PCT is usually estimated by field-assessed work difficulty factors. In this study, a linear mixed model for the TC in PCT was prepared by utilizing forest resources data (FRD). The modelling data included 11 848 and validation data included 3035 worksites with TC information recorded by forest workers within the period of 2008–2018. The worksites represented a range of site and stand conditions across a broad geographical area in Finland. Site and stand characteristics and previous management logically explained the TC in PCT. The more fertile the site, the more working time was needed in PCT. On sites of medium fertility, TC in the initial PCT increased with stand age by 0.5 h ha–1 yr–1. Site wetness increased the TC. PCT in summer was more time consuming than in spring. Small areas were more time consuming to PCT per hectare than larger ones. The between-forest worker variation involved in the TC was as high as 35% of the variation unexplained by the TC model. The coefficient of determination in validation data was 19.3%, RMSE 4.75 h ha–1 and bias –1.6%. The TC model based on FRD was slightly less precise than the one based on field-assessed work difficulty factors (removal quantity and type and terrain difficulty): RMSE 4.9 h ha–1 vs. 4.1 h ha–1 (52% vs. 43%). The TC model could be connected to forest information systems where it would facilitate the predictions of the labour costs of PCT without field-assessing work difficulty factors.

  • Uotila, Natural Resources Institute Finland (Luke), Natural resources, Latokartanonkaari 9, FI-00790 Helsinki, Finland E-mail: karri.uotila@luke.fi (email)
  • Miina, Natural Resources Institute Finland (Luke), Natural resources, Yliopistokatu 6 B, FI-80100 Joensuu, Finland E-mail: jari.miina@luke.fi
  • Saksa, Natural Resources Institute Finland (Luke), Natural resources, Survontie 9, FI-40500 Jyväskylä, Finland E-mail: timo.saksa@luke.fi
  • Store, Natural Resources Institute Finland (Luke), Bioeconomy and environment, Teknologiakatu 7, FI-67100 Kokkola, Finland E-mail: ron.store@luke.fi
  • Kärkkäinen, E-mail: kauko.karkkainen@gmail.com
  • Härkönen, Tornator Oyj, Pielisentie 2–6, FI-81700 Lieksa, Finland E-mail: mika.harkonen@tornator.fi
article id 10055, category Research article
Jaakko Repola, Hannu Hökkä, Hannu Salminen. (2018). Models for diameter and height growth of Scots pine, Norway spruce and pubescent birch in drained peatland sites in Finland. Silva Fennica vol. 52 no. 5 article id 10055. https://doi.org/10.14214/sf.10055
Keywords: Pinus sylvestris; Picea abies; Betula pubescens; drained peatlands; forest drainage; mixed model; tree growth model
Highlights: Tree growth strongly correlated with site drainage status; Between-tree competition had a higher impact on tree diameter growth than on height growth; Growth predicted by the constructed models were calibrated using NFI11 data to ensure generally applicable growth predictions level in whole country.
Abstract | Full text in HTML | Full text in PDF | Author Info

The aim of this study was to develop individual-tree diameter and height growth models for Scots pine, Norway spruce, and pubescent birch growing in drained peatlands in Finland. Trees growing in peatland sites have growth patterns that deviate from that of trees growing in mineral soil sites. Five-year growth was explained by tree diameter, different tree and stand level competition measures, management operations and site characteristics. The drainage status of the site was influencing growth directly or in interaction with other variables. Site quality had a direct impact but was also commonly related to current site drainage status (need for ditch maintenance). Recent thinning increased growth of all species and former PK fertilization increased growth of pine and birch. Temperature sum was a significant predictor in all models and altitude for spruce and birch. The data were a subsample of the 7th National Forest Inventory (NFI) sample plots representing northern and southern Finland and followed by repeated measurements for 15–20 yrs. Growth levels predicted by the models were calibrated using NFI11 data to remove bias originating from the sample of the modelling data. The mixed linear models technique was used in model estimation. The models will be incorporated into the MOTTI stand simulator to replace the current peatlands growth models.

  • Repola, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: jaakko.repola@luke.fi (email)
  • Hökkä, Natural Resources Institute Finland (Luke), Natural resources, Paavo Havaksen tie 3, FI-90014 University OF Oulu, Finland E-mail: hannu.hokka@luke.fi
  • Salminen, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: hannu.salminen@luke.fi
article id 9933, category Research article
Timo Saksa, Jari Miina, Hilkka Haatainen, Kauko Kärkkäinen. (2018). Quality of spot mounding performed by continuously advancing mounders. Silva Fennica vol. 52 no. 2 article id 9933. https://doi.org/10.14214/sf.9933
Keywords: soil preparation; slash; logging residues; forest regeneration; mixed modelling
Highlights: The number and quality of mounds varied considerably according to the operating conditions;The main factors reducing the quality of spot mounding were steep terrain, a thick humus layer, fresh logging residues, stoniness and soil texture;With careful selection of timing and conditions for mounding, the quality obtained by continuously advancing mounders can be improved.
Abstract | Full text in HTML | Full text in PDF | Author Info

Operating conditions affecting the quality of spot mounding by Bracke continuously advancing mounders were investigated on 66 regeneration areas (124 ha) in eastern Finland. The quality of mounds was classified as suitable (good or acceptable after additional compression) or unsuitable for planting. Models were constructed for the number of suitable planting spots obtained per hectare (good and acceptable mounds), the probability of successful mounding (≥1600 planting spots ha–1) and the probability of creating a suitable mound as a function of terrain, site and soil characteristics, as well as slash conditions (removed, fresh or dry logging residues). The average number of mounds created was 1892 ± 290 mounds ha–1, of which 1398 ± 325 mounds ha–1 (74%) were classified as suitable for planting. The quality of spot mounding was reduced by steep terrain, a thick humus layer and fresh logging residues. Stoniness and soil texture also affected the number of planting spots created. Mounding after logging residues had dried increased the number of planting spots by 191 spots ha–1 compared with mounding in the presence of fresh residues. Removing residues did not significantly increase the number of planting spots compared with mounding amongst dry residues. A thick humus layer, very stony soil, steep slopes and valley terrain decreased the number of planting spots by 150–450 spots ha–1. The number and quality of mounds varied considerably according to the operating conditions, but with careful selection of timing and sites the quality obtained by a continuously advancing mounder can be improved.

  • Saksa, Natural Resources Institute Finland (Luke), Juntintie 154, FI-77600 Suonenjoki, Finland E-mail: timo.saksa@luke.fi (email)
  • Miina, Natural Resources Institute Finland (Luke), Yliopistokatu 6, FI-80100 Joensuu, Finland E-mail: jari.miina@luke.fi
  • Haatainen, Faculty of Science and Forestry, School of Forest Sciences, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: hilkka.haatainen@storaenso.com
  • Kärkkäinen, Tornator Oyj, Muuntamontie 2, FI-80100 Joensuu, Finland E-mail: kauko.karkkainen@tornator.fi
article id 1342, category Research article
Blas Mola-Yudego, Gianni Picchi, Dominik Röser, Raffaele Spinelli. (2015). Assessing chipper productivity and operator effects in forest biomass operations. Silva Fennica vol. 49 no. 5 article id 1342. https://doi.org/10.14214/sf.1342
Keywords: mixed models; efficiency; comminution; operator effect; raw material supply; wood chippers
Highlights: A model is constructed to assess the productivity in chipping of wood biomass at roadside; The data includes 172 trials and 67 operators in Italy; The operator effect was included in a mixed model approach; The R2 were 0.76 (fixed part) and 0.88 (incl. operator effects).
Abstract | Full text in HTML | Full text in PDF | Author Info

The present research focuses on the productivity of energy wood chipping operations at several sites in Italy. The aim was to assess the productivity and specifically the effect attributed to the operator in the chipping of wood biomass. The research included 172 trials involving 67 operators across the country that were analysed using a mixed model approach, in order to assess productivity, and to isolate the operator effect from other potential variables. The model was constructed using different predictors aiming to explain the variability due to the machines and the raw-materials. The final model included the average piece weight of raw material chipped as well as the power of the machine. The coefficients of determination (R2) were 0.76 for the fixed part of the model, and 0.88 when the effects due to the operators were included. The operators’ performance compared to their peers was established, and it was compared to a subjective classification based on the operator’s previous experience. The results of this study can help to the planning and logistics of raw material supply for bioenergy, as well as to a more effective training of future forest operators.

  • Mola-Yudego, School of Forest Sciences, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland; NIBIO Norwegian Institute of Bioeconomy Research, P.O. Box 115, 1431 Ås, Norway ORCID http://orcid.org/0000-0003-0286-0170 E-mail: blas.mola@uef.fi (email)
  • Picchi, CNR IVALSA, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy E-mail: picchi@ivalsa.cnr.it
  • Röser, Forest Feedstocks Group, FPInnovations, Vancouver, British Columbia, Canada E-mail: dominik.roser@fpinnovations.ca
  • Spinelli, CNR IVALSA, Via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy E-mail: spinelli@ivalsa.cnr.it
article id 1005, category Research article
Marjut Turtiainen, Jari Miina, Kauko Salo, Juha-Pekka Hotanen. (2013). Empirical prediction models for the coverage and yields of cowberry in Finland. Silva Fennica vol. 47 no. 3 article id 1005. https://doi.org/10.14214/sf.1005
Keywords: generalized linear mixed model; abundance; berry yield; Vaccinium vitis-idaea L.
Highlights: The site fertility significantly affected the abundance of cowberry on mineral soils, spruce mires and pine mires; The stand basal area and dominant tree species were among the most important forest structural predictors in the model for the coverage; In the cowberry yield model developed for mineral soil sites, the stand basal area and coverage of cowberry plants were statistically significant predictors.
Abstract | Full text in HTML | Full text in PDF | Author Info
Empirical models for the coverage and berry yield of cowberry (Vaccinium vitis-idaea L.) were developed using generalized linear mixed models (GLMMs). The percentage coverage of cowberry was predicted as a function of site and stand characteristics using data from the Finnish National Forest Inventory (NFI) in 1995. The average annual yield, including the between-year variation in the yield, was predicted as a function of percentage coverage and stand characteristics using permanent experimental plots (MASI) established in different areas of Finland and measured in 2001-2012. The model for cowberry yields (Model 2) was developed for mineral soil forests. The model for the coverage (Model 1) was constructed so that it considers both mineral soil sites and also many other sites where cowberry occurs in the field layer. According to Model 1, the site fertility significantly affected the abundance of cowberry on mineral soils, spruce mires and pine mires. The stand basal area and dominant tree species were among the most important forest structural predictors in Model 1. The site fertility was not a significant predictor in the cowberry yield model. Instead, the stand basal area and coverage of cowberry plants were found to be statistically significant predictors in Model 2. The estimated models were used to predict the cowberry coverage, average annual yield and its 95 % confidence interval along with stand development. The models of this study can be used for multi-objective forest planning purposes.
  • Turtiainen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: marjut.turtiainen@uef.fi (email)
  • Miina, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: jari.miina@metla.fi
  • Salo, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: kauko.salo@metla.fi
  • Hotanen, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: juha-pekka.hotanen@metla.fi
article id 131, category Research article
Timo Pukkala, Tatu Hokkanen, Teijo Nikkanen. (2010). Prediction models for the annual seed crop of Norway spruce and Scots pine in Finland. Silva Fennica vol. 44 no. 4 article id 131. https://doi.org/10.14214/sf.131
Keywords: flowering; cone crops; seed years; mixed model
Abstract | View details | Full text in PDF | Author Info
Many studies indicate that the flowering abundance of boreal trees strongly correlates with the weather conditions of the previous summer. This study developed prediction models for the seed crops of Norway spruce and Scots pine using weather variables one and two years prior to flowering year as predictors. Weather data, systematically recorded at many weather stations, were obtained from the Finnish Meteorological Institute. Seed crop monitoring data came from 22 spruce stands and 44 pine stands. In every stand, seed crop has been monitored for many years, the longest continuous period being 45 years. Monthly mean temperatures, monthly rainfalls, and periodical temperature sums were used as predictors in the seed crop models. Generally, both tree species flowered abundantly one year after a warm summer and two years after a cool summer. While the models only explained about 45% of the variation in the annual seed crop, they accurately predicted good and bad seed years: when the models predicted good seed crops the likelihood to have at least a medium seed crop was very high and when the models predicted small seed crops, the likelihood to obtain medium or good seed crop was very low. Therefore, the models reliably predict if a particular year will be a good seed year or a poor seed year. These predictions can be used in forestry practice for proper timing of natural regeneration activities, and when activities in seed orchards are planned.
  • Pukkala, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi (email)
  • Hokkanen, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: th@nn.fi
  • Nikkanen, Finnish Forest Research Institute, Finlandiantie 18, FI-58450 Punkaharju, Finland E-mail: tn@nn.fi
article id 181, category Research article
Jari Miina, Juha-Pekka Hotanen, Kauko Salo. (2009). Modelling the abundance and temporal variation in the production of bilberry (Vaccinium myrtillus L.) in Finnish mineral soil forests. Silva Fennica vol. 43 no. 4 article id 181. https://doi.org/10.14214/sf.181
Keywords: vegetation; generalized linear mixed model; heath forest
Abstract | View details | Full text in PDF | Author Info
  • Miina, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: jari.miina@metla.fi (email)
  • Hotanen, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: jph@nn.fi
  • Salo, Finnish Forest Research Institute, Joensuu Research Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: ks@nn.fi
article id 322, category Research article
Jaakko Repola. (2006). Models for vertical wood density of Scots pine, Norway spruce and birch stems, and their application to determine average wood density. Silva Fennica vol. 40 no. 4 article id 322. https://doi.org/10.14214/sf.322
Keywords: Norway spruce; Scots pine; silver birch; wood density; downy birch; mixed models
Abstract | View details | Full text in PDF | Author Info
The purpose of this study was to investigate the vertical dependence of the basic density of Scots pine, Norway spruce, and birch stems, and how such dependence could be applied for determining the average stem wood density. The study material consisted of 38 Scots pine (Pinus sylvestris), 39 Norway spruce (Picea abies [L.] Karst.) and 15 birch (Betula pendula and Betula pubescens) stands located on mineral soil sites in southern Finland. The stem material mainly represented thinning removal from stands at different stages of development. The linear mixed model technique, with both fixed and random effects, was used to estimate the model. According to the fixed part of the model, wood density was dependent on the vertical location along the stem in all three tree species. Wood density in pine decreased from the butt to the top, and the gradient in wood density was steep at the butt but decreased in the upper part of the stem. The vertical dependence was similar in birch, but the density gradient was much smaller. For spruce the vertical dependence of the basic density was moderate. The model can be calibrated for a tree stem when one or more sample disks are measured at freely selected heights. Using treewise calibrated predictions of the vertical density dependence and measured stem diameters, almost unbiased estimates, and lower prediction errors than with traditional methods, were obtained for the average stem wood density. The advantages of the method were greater for pine with a strong vertical dependence in basic density, than for spruce and birch.
  • Repola, Finnish Forest Research Institute, Rovaniemi Research Unit, Eteläranta 55, FI-96300 Rovaniemi, Finland E-mail: jaakko.repola@metla.fi (email)
article id 395, category Research article
Lauri Mehtätalo. (2005). Height-diameter models for Scots pine and birch in Finland. Silva Fennica vol. 39 no. 1 article id 395. https://doi.org/10.14214/sf.395
Keywords: mixed model; longitudinal analysis; random parameter; stand development
Abstract | View details | Full text in PDF | Author Info
Height-Diameter (H-D) models for two shade-intolerant tree species were estimated from longitudinal data. The longitudinal character of the data was taken into account by estimating the models as random effects models using two nested levels: stand and measurement occasion level. The results show that the parameters of the H-D equation develop over time but the development rate varies between stands. Therefore the development of the parameters is not linked to the stand age but to the median diameter of the basal-area weighted diameter distribution (DGM). Models were estimated with different predictor combinations in order to produce appropriate models for different situations. The estimated models can be localized for a new stand using measured heights and diameters, presumably from different points in time, and the H-D curves can be projected into the future.
  • Mehtätalo, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: lauri.mehtatalo@metla.fi (email)
article id 394, category Research article
Rafael Calama, Gregorio Montero. (2005). Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. Silva Fennica vol. 39 no. 1 article id 394. https://doi.org/10.14214/sf.394
Keywords: mixed model; diameter increment; calibration; stone pine
Abstract | View details | Full text in PDF | Author Info
Diameter increment for stone pine (Pinus pinea L.) is described using a multilevel linear mixed model, where stochastic variability is broken down among period, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, dominant height or site index are included in the model as fixed effects in order to explain residual random variability. The effect of competition on diameter increment is expressed by including distance independent competition indices. The entrance of regional effects within the model is tested to determine whether a single model is sufficient to explain stone pine diameter increment in Spain, or if, on the contrary, regional models are needed. Diameter increment model can be calibrated by predicting random components using data from past growth measurements taken in a complementary sample of trees. Calibration is carried out by using the best linear unbiased predictor (BLUP) theory. Both the fixed effects model and the calibrated model mean a substantial improvement when compared with the classical approach, widely used in forest management, of assuming constancy in diameter increment for a short projection period.
  • Calama, CIFOR-INIA, Grupo Selvicultura Mediterranea, Apdo. 8111, 28080 Madrid, Spain E-mail: rcalama@inia.es (email)
  • Montero, CIFOR-INIA, Grupo Selvicultura Mediterranea, Apdo. 8111, 28080 Madrid, Spain E-mail: gm@nn.es
article id 504, category Research article
Sylvain Jutras, Hannu Hökkä, Virpi Alenius, Hannu Salminen. (2003). Modeling mortality of individual trees in drained peatland sites in Finland. Silva Fennica vol. 37 no. 2 article id 504. https://doi.org/10.14214/sf.504
Keywords: Pinus sylvestris; Betula pubescens; simulation; peatlands; mortality; generalized linear mixed models; multilevel models
Abstract | View details | Full text in PDF | Author Info
Multilevel logistic regression models were constructed to predict the 5-year mortality of Scots pine (Pinus sylvestris L.) and pubescent birch (Betula pubescens Ehrh.) growing in drained peatland stands in northern and central Finland. Data concerning tree mortality were obtained from two successive measurements of the National Forest Inventory-based permanent sample plot data base covering pure and mixed stands of Scots pine and pubescent birch. In the modeling data, Scots pine showed an average observed mortality of 2.73% compared to 2.98% for pubescent birch. In the model construction, stepwise logistic regression and multilevel models methods were applied, the latter making it possible to address the hierarchical data, thus obtaining unbiased estimates for model parameters. For both species, mortality was explained by tree size, competitive position, stand density, species admixture, and site quality. The expected need for ditch network maintenance or re-paludification did not influence mortality. The multilevel models showed the lowest bias in the modeling data. The models were further validated against independent test data and by embedding them in a stand simulator. In 100-year simulations with different initial stand conditions, the models resulted in a 72% and 66% higher total mortality rate for the stem numbers of pine and birch, respectively, compared to previously used mortality models. The developed models are expected to improve the accuracy of stand forecasts in drained peatland sites.
  • Jutras, Département des sciences du bois et de la forêt, Université Laval, Ste-Foy, Québec, G1K 7P4, Canada E-mail: sj@nn.ca
  • Hökkä, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN 96301 Rovaniemi, Finland E-mail: hannu.hokka@metla.fi (email)
  • Alenius, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN 96301 Rovaniemi, Finland E-mail: va@nn.fi
  • Salminen, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN 96301 Rovaniemi, Finland E-mail: hs@nn.fi
article id 513, category Research article
Marjut Ihalainen, Kauko Salo, Timo Pukkala. (2003). Empirical prediction models for Vaccinium myrtillus and V. vitis-idaea berry yields in North Karelia, Finland. Silva Fennica vol. 37 no. 1 article id 513. https://doi.org/10.14214/sf.513
Keywords: mixed models; berry yield index; Vaccinium myrtillus; Vaccinium vitis-idaea
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Forest berries and the outdoor experiences related to berry collection are important goods and services provided by Finnish forests. Consequently, there is a need for models which facilitate the prediction of the impacts of alternative forest management options on berry yields. Very few such models are available. In particular, empirical models are lacking. Models used in forest management should express the effect of variables altered in forest management such as stand density and mean tree size. This study developed empirical models for bilberry and cowberry yields in North Karelia. The data consisted of 362 measurements of 40 m2 sample plots. The plots were located in clusters. The same plot was measured over 1 to 4 years. Besides berry yield some site and growing stock characteristics of each plot were measured. A random parameter model was used to express the berry yield as a function of site fertility, growing stock characteristics, and random parameters. The random part of the models accounted for the effect of plot, measurement year, and cluster. The fixed predictors of the model for bilberry were stand age and forest site type. Stand basal area, mean tree diameter and forest site type were used to predict cowberry yields. The most significant random parameter was the plot factor. The fixed model part explained only a few per cent of the variation in berry yields. The signs of regression coefficients were logical and the model predictions correlated rather well with the predictions of earlier models.
  • Ihalainen, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: marjut.ihalainen@joensuu.fi (email)
  • Salo, The Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FIN-80101 Joensuu, Finland E-mail: ks@nn.fi
  • Pukkala, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: tp@nn.fi

Category : Research note

article id 10679, category Research note
Jari Miina, Mikko Kurttila. (2022). A model for the sap yield of birches tapped by citizen scientists. Silva Fennica vol. 56 no. 2 article id 10679. https://doi.org/10.14214/sf.10679
Keywords: Betula spp.; non-timber forest product; linear mixed model; crowdsourcing
Highlights: Tree diameter and mean stand height positively affected the sap yield of birches; The sap yield varied between trees, stands, and years; The sap yield model can be utilised in profitability analyses for sap tapping.
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The sap yield of birches (Betula pendula Roth and B. pubescens Ehrh.) was modelled as a function of tree diameter (girth) at breast height, as well as site and stand characteristics measured and reported by citizen scientists representing mainly non-industrial private forest owners in the South Savo, North Karelia, and Northern Ostrobothnia regions in Finland. Birches (tree species not recorded) growing on both mineral and peatland sites were tapped during the springs of 2019 and 2020. Citizen scientists were mainly voluntary forest owners who received the instructions and equipment (spouts, drop lines and buckets) for collecting sap from three birches of different diameters in the same birch stand. Citizen scientists were instructed to measure and report the sap yield and girth of the trees, as well as stand characteristics from the forest resource data, if available. Based on the linear mixed model fitted to the data, the sap yield increased with the increasing tree diameter and mean stand height, and varied between years, stands, and trees; between-region variation was not significant. In a birch stand, the simulated total sap yield ha–1 was depended on the average tree size and the stem number ha–1 and was at its highest just before the first commercial thinning and again before the second thinning. The sap model can be used to predict the necessary sap yield in profitability analyses for sap tapping.

article id 1573, category Research note
Marjut Turtiainen, Jari Miina, Kauko Salo, Juha-Pekka Hotanen. (2016). Modelling the coverage and annual variation in bilberry yield in Finland. Silva Fennica vol. 50 no. 4 article id 1573. https://doi.org/10.14214/sf.1573
Keywords: abundance; berry yield; generalised linear mixed model; Vaccinium myrtillus L.
Highlights: The highest bilberry coverage was found in mesic heath forests and fell forests; On peatlands the coverage was, on average, lower than on mineral soil sites; The approach introduced in this study to calculating annual berry yield indices is a promising way for estimating total annual bilberry yields over a given period of time.
Abstract | Full text in HTML | Full text in PDF | Author Info

The coverage of bilberry (Vaccinium myrtillus L.) was modelled as a function of site and stand characteristics using the permanent sample plots of the National Forest Inventory (NFI) (Model 1). The sample sites consisted of mineral soil forests as well as fells and peatland sites. Annual variation in the bilberry yield (Model 2) was analysed based on measurements over 2001–2014 in the permanent sample plots (so-called MASI plots) in various areas of Finland. We derived annual bilberry yield indices from the year effects of Model 2 and investigated whether these indices could be used to estimate annual variation in bilberry crops in Finland. The highest bilberry coverage was found in mesic heath forests and fell forests. On peatlands the coverage was, on average, lower than on mineral soil sites; the peatland sites with most bilberry coverage were meso-oligotrophic and oligotrophic spruce mires and oligotrophic pine mires. Our bilberry yield indices showed similar variation to those derived from the mean annual berry yields reported and calculated earlier using the MASI plots; the correlation between the indices was 0.795. This approach to calculating annual berry yield indices is a promising way for estimating total annual bilberry yields over a given period of time. Models 1 and 2 can be used in conjunction with the Miina et al.’s (2009) bilberry yield model when bilberry coverage, average annual yield and annual variation in the yield are to be predicted in forest planning.

  • Turtiainen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: marjut.turtiainen@uef.fi (email)
  • Miina, Natural Resources Institute Finland (Luke), Management and Production of Renewable Resources, Box 68, FI-80101 Joensuu, Finland E-mail: jari.miina@luke.fi
  • Salo, Natural Resources Institute Finland (Luke), Bio-based Business and Industry, Box 68, FI-80101 Joensuu, Finland E-mail: kauko.salo@luke.fi
  • Hotanen, Natural Resources Institute Finland (Luke), Management and Production of Renewable Resources, Box 68, FI-80101 Joensuu, Finland E-mail: juha-pekka.hotanen@luke.fi

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