scholarly journals Generalized Nonlinear Mixed-Effects Individual Tree Crown Ratio Models for Norway Spruce and European Beech

Forests ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 555 ◽  
Author(s):  
Ram Sharma ◽  
Zdeněk Vacek ◽  
Stanislav Vacek
Keyword(s):  
Norway Spruce ◽  
Model Fitting ◽  
Basal Area ◽  
European Beech ◽  
Logistic Function ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Individual Tree ◽  
Mixed Effects Modeling ◽  
Species Mixture

Tree crowns are commonly measured to understand tree growth and stand dynamics. Crown ratio (CR—crown depth-to-total height ratio) is significantly affected by a number of tree- and stand-level characteristics and other factors as well. Generalized mixed-effects CR models were developed using a large dataset (measurements from 14,669 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica (L.)) acquired from permanent research plots in various parts of the Czech Republic. Among several tree- and stand-level variables evaluated, diameter at breast height, height to crown base, dominant height, basal area of trees larger in diameter than a focal tree, relative spacing index, and variables describing the effects of species mixture and canopy height differentiation significantly contributed to CR variation. We included sample-plot-level variations caused by randomness in the data and other stochastic factors into the CR models using the mixed-effects modeling approach. The logistic function, which predicts the values between 0 and 1, was chosen to develop the generalized CR mixed-effects model. A large proportion of the CR variation (R2adj ≈ 0.63 (Norway spruce); 0.72 (European beech)) was described by generalized mixed-effects model without significant residual trends. Testing the CR model against a part of the model fitting dataset confirmed its high prediction precision. Our CR model can be useful for growth simulation using inventory databases that lack crown measures. Other potential implications of our CR models in forest management are mentioned in the article.

scholarly journals Development of a Mixed-Effects Individual-Tree Basal Area Increment Model for Oaks (Quercus spp.) Considering Forest Structural Diversity

Forests ◽  
2019 ◽  
Vol 10 (6) ◽  
pp. 474 ◽  
Author(s):  
Wenwen Wang ◽  
Xinyun Chen ◽  
Weisheng Zeng ◽  
Jianjun Wang ◽  
Jinghui Meng
Keyword(s):  
Basal Area ◽  
Information Criterion ◽  
Structural Diversity ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Central China ◽  
Basal Area Increment ◽  
Individual Tree ◽  
Final Model ◽  
Quercus Spp

In the context of uneven-aged mixed-species forest management, an individual-tree basal area increment model considering forest structural diversity was developed for oaks (Quercus spp.) using data collected from 11,860 observations in 845 sample plots from the 7th (2004), 8th (2009), and 9th (2014) Chinese National Forest Inventory in Hunan Province, south-central China. Since the data was longitudinal and had a nested structure, we used a linear mixed-effects approach to construct the model. We also used the variance function and an autocorrelation structure to describe within-plot heteroscedasticity and autocorrelation. Finally, the optimal mixed-effects model was determined based on the Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood (Loglik) and the likelihood ratio test (LRT). The results indicate that the reciprocal transformation of initial diameter at breast height (1/DBH), relative density index (RD), number of trees per hectare (NT), elevation (EL) and Gini coefficient (GC) had a significant impact on the individual-tree basal area increment. In comparison to the basic model developed using least absolute shrinkage and selection operator (LASSO) regression, the mixed-effects model performance was greatly improved. In addition, we observed that the heteroscedasticity was successfully removed by the exponent function and autocorrelation was significantly corrected by AR(1). Our final model also indicated that forest structural diversity significantly affected tree growth and hence should not be neglected. We hope that our final model will contribute to the scientific management of oak-dominated forests.

scholarly journals Generalized Nonlinear Mixed-Effects Individual Tree Diameter Increment Models for Beech Forests in Slovakia

Forests ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 451 ◽  
Author(s):  
Ram P. Sharma ◽  
Igor Štefančík ◽  
Zdeněk Vacek ◽  
Stanislav Vacek
Keyword(s):  
Basal Area ◽  
European Beech ◽  
Site Index ◽  
Development Stage ◽  
Mixed Effects ◽  
Site Quality ◽  
Stand Age ◽  
Sample Plot ◽  
Individual Tree ◽  
Diameter Increment

Individual tree growth and yield models precisely describe tree growth irrespective of stand complexity and are capable of simulating various silvicultural alternatives in the stands with diverse structure, species composition, and management history. We developed both age dependent and age independent diameter increment models using long-term research sample plot data collected from both monospecific and mixed stands of European beech (Fagus sylvatica L.) in the Slovak Republic. We used diameter at breast height (DBH) as a main predictor and other characteristics describing site quality (site index), stand development stage (dominant height and stand age), stand density or competition (ratio of individual tree DBH to quadratic mean diameter), species mixture (basal area proportion of a species of interest), and dummy variable describing stand management regimes as covariate predictors to develop the models. We evaluated eight versatile growth functions in the first stage using DBH as a single predictor and selected the most suitable one, i.e., Chapman-Richards function for further analysis through the inclusion of covariate predictors. We introduced the random components describing sample plot-level random effects and stochastic variations on the diameter increment, into the models through the mixed-effects modelling. The autocorrelation caused by hierarchical data-structure, which is assumed to be partially reduced by mixed-effects modelling, was removed through the inclusion of the parameter accounting for the autoregressive error-structures. The models described about two-third parts of a total variation in the diameter increment without significant trends in the residuals. Compared to the age independent mixed-effects model (conditional coefficient of determination, R c 2 = 0.6566; root mean square error, RMSE = 0.1196), the age dependent model described a significantly larger proportion of the variations in diameter increment ( R c 2 = 0.6796, RMSE = 0.1141). Diameter increment was significantly influenced differently by covariate predictors included into the models. Diameter increment decreased with the advancement of stand development stage (increased dominant height and stand age), increasing intraspecific competition (increased basal area proportion of European beech per sample plot), and diameter increment increased with increasing site quality (increased site index) and decreased competition (increased ratio of DBH to quadratic mean diameter). Our mixed-effects models, which can be easily localized with the random effects estimated from prior measurement of diameter increments of four randomly selected trees per sample plot, will provide high prediction accuracies. Our models may be used for simulating growth of European beech irrespective of its stand structural complexity, as these models have included various covariate variables describing both tree-and stand-level characteristics, thinning regimes, except the climate characteristics. Together with other forest models, our models will be used as inputs to the growth simulator to be developed in the future, which is important for decision-making in forestry.

scholarly journals An individual-tree linear mixed-effects model for predicting the basal area increment of major forest species in Southern Europe

2020 ◽  
Vol 29 (3) ◽  
pp. e019
Author(s):  
Lucio Di Cosmo ◽  
Diego Giuliani ◽  
Maria Michela Dickson ◽  
Patrizia Gasparini
Keyword(s):  
Forest Inventory ◽  
Basal Area ◽  
Ordinary Least Squares ◽  
Mixed Effects ◽  
Forest Growth ◽  
Mixed Effects Model ◽  
Basal Area Increment ◽  
Individual Tree ◽  
Diameter At Breast Height ◽  
Breast Height

Aims of the study. Assessment of growth is essential to support sustainability of forest management and forest policies. The objective of the study was to develop a species-specific model to predict the annual increment of tree basal area through variables recorded by forest surveys, to assess forest growth directly or in the context of more complex forest growth and yield simulation models.Area of the study. Italy.Material and methods. Data on 34638 trees of 31 different forest species collected in 5162 plots of the Italian National Forest Inventory were used; the data were recorded between 2004 and 2006. To account for the hierarchical structure of the data due to trees nested within plots, a two-level mixed-effects modelling approach was used.Main results. The final result is an individual-tree linear mixed-effects model with species as dummy variables. Tree size is the main predictor, but the model also integrates geographical and topographic predictors and includes competition. The model fitting is good (McFadden’s Pseudo-R2 0.536), and the variance of the random effect at the plot level is significant (intra-class correlation coefficient 0.512). Compared to the ordinary least squares regression, the mixed-effects model allowed reducing the mean absolute error of estimates in the plots by 64.5% in average.Research highlights. A single tree-level model for predicting the basal area increment of different species was developed using forest inventory data. The data used for the modelling cover 31 species and a great variety of growing conditions, and the model seems suitable to be applied in the wider context of Southern Europe.   Keywords: Tree growth; forest growth modelling; forest inventory; hierarchical data structure; Italy.Abbreviations used: BA - basal area; BAI – five-year periodic basal area increment; BALT - basal area of trees larger than the subject tree; BASPratio - ratio of subject tree species basal area to stand basal area; BASTratio - ratio of subject tree basal area to stand basal area; CRATIO - crown ratio; DBH – diameter at breast height ; DBH0– diameter at breast height corresponding to five years before the survey year; DBHt– diameter at breast height measured in the survey year; DI5 - five-year, inside bark, DBH increment; HDOM - dominant height; LULUCF - Land Use, Land Use Changes and Forestry; ME - mean error; MAE - mean absolute error; MPD - mean percent deviation; MPSE - mean percent standard error; NFI(s) - National Forest Inventory/ies; OLS - ordinary least squares regression; RMSE - root mean squared error; UNFCCC - United Nation Framework Convention on Climate Change.

Comparing individual-tree growth models using principles of stand growth for Norway spruce, Scots pine, and European beech

2015 ◽  
Vol 45 (8) ◽  
pp. 1006-1018 ◽  
Author(s):  
Sonja Vospernik ◽  
Robert A. Monserud ◽  
Hubert Sterba
Keyword(s):  
Norway Spruce ◽  
Scots Pine ◽  
Tree Growth ◽  
Growth Models ◽  
Basal Area ◽  
European Beech ◽  
Growth And Yield ◽  
Individual Tree ◽  
Individual Tree Growth ◽  
Volume Increment

We examined the relationship between thinning intensity and volume increment predicted by four commonly used individual-tree growth models in Central Europe (i.e., BWIN, Moses, Prognaus, and Silva). We replicated conditions of older growth and yield experiments by selecting 34 young, dense plots of Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.), and European beech (Fagus sylvatica L.). At these plots, we simulated growth, with mortality only, to obtain the maximum basal area. Maximum basal area was then decreased by 5% or 10% steps using thinning from below. Maximum density varied considerably between simulators; it was mostly in a reasonable range but partly exceeded the maximum basal area observed by the Austrian National Forest Inventory or the self-thinning line. In almost all cases, simulated volume increment was highest at maximum basal area and then decreased with decreasing basal area. Critical basal area, at which 95% of maximum volume increment can be achieved, ranged from 0.46 to 0.96. For all simulators, critical basal area was lower for the more shade-tolerant species. It increased with age, except for Norway spruce, when simulated with the BWIN model. Age, where mean annual increment culminated, compared well with yield tables.

Modeling individual tree height to diameter ratio for Norway spruce and European beech in Czech Republic

Trees ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1969-1982 ◽  
Author(s):  
Ram P. Sharma ◽  
Zdeněk Vacek ◽  
Stanislav Vacek
Keyword(s):  
Czech Republic ◽  
Norway Spruce ◽  
Tree Height ◽  
European Beech ◽  
Diameter Ratio ◽  
Individual Tree

Linear mixed-effects models and calibration applied to volume models in two rotations of Eucalyptus grandis plantations

2016 ◽  
Vol 46 (1) ◽  
pp. 132-141 ◽  
Author(s):  
Edgar de Souza Vismara ◽  
Lauri Mehtätalo ◽  
João Luis Ferreira Batista
Keyword(s):  
Mixed Model ◽  
Eucalyptus Grandis ◽  
Small Variation ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Stem Form ◽  
Individual Tree ◽  
Linear Mixed Effects ◽  
Fixed Part ◽  
Volume Models

This work presents applications of the linear mixed-effects model calibration to predict individual tree volumes of Eucalyptus grandis W. Hill ex Maiden plantations on first and second rotations located in different farms of the same region in São Paulo, Brazil. We started with the Schumacher and Hall equation in its linearized form to develop our mixed-effects model. Some parameters were considered as random among the different farms, and the calibration was made at the farm level using a small number of sample trees. The approach was developed for univariate models of the first rotation, which were calibrated with first- and second-rotation trees, and for bivariate models of the two rotations, which were calibrated with first-rotation trees. The results showed that the calibrated mixed model provides more reliable predictions than the fixed part of the model alone; however, the benefit is only moderate due to the rather small variation of the stem form between farms and rotations. The results indicate that the approach can reduce the measurement requirements on second-rotation crops.

Stand, species, and tree dynamics of an uneven-aged, mixed conifer forest type

1995 ◽  
Vol 25 (5) ◽  
pp. 803-812 ◽  
Author(s):  
John P. McTague ◽  
William F. Stansfield
Keyword(s):  
Tree Mortality ◽  
Forest Type ◽  
Species Abundance ◽  
Basal Area ◽  
Logistic Function ◽  
Conifer Forest ◽  
Individual Tree ◽  
Recovery Method ◽  
Parameter Recovery ◽  
Tree Survival

Stand-level equations are presented that project future merchantable tree survival, pole-tree basal area, and sawtimber basal area. Total basal area (excluding ingrowth) is the sum of the pole-tree and sawtimber components. Ratio equations are used for eight species (seven softwoods and one hardwood) to compute the change in species abundance and species basal area over time. Individual-tree mortality is predicted with a logistic function, while individual-tree diameter growth is predicted as a function of stand and individual-tree attributes. The individual-tree and species-level equations are adjusted so that tree frequency and basal area are consistent with the stand-level projection equations. Total ingrowth is computed with a stand-level projection equation and is distributed with a parameter recovery method using the uniform distribution. The presence or absence of ingrowth for a given species is determined with a discriminant function, while the proportion of total ingrowth allocated to a species is predicted with a logistic function.

Modelling survival probability of individual trees in Norway spruce stands under different thinning regimes

2005 ◽  
Vol 35 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Kjell Karlsson ◽  
Lennart Norell
Keyword(s):  
Norway Spruce ◽  
Goodness Of Fit ◽  
Basal Area ◽  
Site Index ◽  
Stand Age ◽  
Goodness Of Fit Test ◽  
Individual Tree ◽  
Thinning Intensity ◽  
Diameter At Breast Height ◽  
Breast Height

The probability that an individual tree will remain in even-aged Norway spruce (Picea abies (L.) Karst.) stands subjected to different thinning programmes was modelled, using data from a thinning experiment established in 25 localities in southern Sweden. A logistic regression approach was used to predict the probability and the Hosmer–Lemeshow goodness-of-fit test to evaluate the fit. Diameter at breast height (DBH), quadratic mean DBH, thinning intensity, thinning quotient, basal area, number of stems per hectare, stand age, number of thinnings, and site index were used as explanatory variables. Separate analyses for stands thinned from below, stands thinned from above, and unthinned stands were performed. The modelled probability graphs for trees not being removed, plotted against their diameter at breast height, had clear S-shapes for both unthinned stands and stands thinned from below. The graph for stands thinned from above was bell-shaped.

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