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.

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.

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.

Building a dynamic growth model for trembling aspen in western Canada without age data

2013 ◽  
Vol 43 (3) ◽  
pp. 256-265 ◽  
Author(s):  
Oscar García
Keyword(s):  
Populus Tremuloides ◽  
Site Occupancy ◽  
Basal Area ◽  
Site Index ◽  
Growth And Yield ◽  
Site Quality ◽  
Diameter Distribution ◽  
Stand Age ◽  
Parameter Estimates ◽  
Trembling Aspen

A biologically inspired whole-stand growth and yield model was developed for even-aged thinned or unthinned stands dominated by trembling aspen (Populus tremuloides Michx.). The estimation used permanent sample plot data from British Columbia, Alberta, Saskatchewan, and Manitoba, supplemented by published site index and young stand information. An ingrowth imputation procedure was devised to facilitate the use of plot measurements where small trees are not measured. Two published site index models were closely approximated by a simple age-base invariant equation. Good parameter estimates for mortality and basal area growth were obtained without using age observations, which were unreliable or missing. Four differential equations describe the dynamics of top height, trees per hectare, basal area, and a site occupancy factor. Current values of these variables are used to estimate total and merchantable volumes up to any diameter limit and diameter distribution parameters. When an independent source of site quality estimates is available, the final model does not require stand age knowledge for making growth and yield predictions.

Analyses of a Forest Drainage Experiment in Northern Ontario. I: Growth Analysis

1973 ◽  
Vol 3 (3) ◽  
pp. 387-398 ◽  
Author(s):  
Bijan Payandeh
Keyword(s):  
Water Flow ◽  
Growth Analysis ◽  
Volume Growth ◽  
Basal Area ◽  
Height Growth ◽  
Site Quality ◽  
Stand Age ◽  
Northern Ontario ◽  
Individual Tree ◽  
Forest Drainage

This paper presents a growth analysis of a forest drainage experiment carried out over 40 years in northern Ontario. It is based on remeasurement data obtained in 1969 from 38 growth plots established following drainage in 1929 and from increment cores and sectioned trees.Results indicate that both annual tree diameter and height growth increased significantly after draining; that tree growth before draining was related to site quality only, while after draining it was related also to tree vigor and distance of water flow from the nearest ditch; that both stand diameter and height growth were related to site index, stand age, and initial stocking; and that stand basal area and volume growth were, in addition, related to a product sine function of distance of water flow from the ditch, peat moisture, decomposition, and depth.Both individual tree and stand growth responded well to draining, with younger and more vigorous trees that were growing on better-quality sites showing the greatest response. For a given site, growth response was not greatest for trees and stands nearest the ditch, but for those some distance away.

scholarly journals Effects of heavy thinnings on the increment and selection of trees for tending in Norway spruce monoculture in natural hazard conditions

2017 ◽  
pp. 31-54
Author(s):  
Martin Bobinac ◽  
Sinisa Andrasev ◽  
Andrijana Bauer-Zivkovic ◽  
Nikola Susic
Keyword(s):  
Norway Spruce ◽  
Growth Stage ◽  
Natural Hazard ◽  
Basal Area ◽  
Growth Potential ◽  
Stand Age ◽  
Diameter Increment ◽  
Volume Increment ◽  
Selection Of ◽  
Area And Volume

The paper studies the effects of two heavy selection thinnings on the increment of Norway spruce trees exposed to ice and snow breaks in eastern Serbia. In a thinning that was carried out at 32 years of age, 556 candidates per hectare were selected for tending, and at the age of 40, of the initial candidates, 311 trees per hectare (55.9%) were selected as future trees. In all trees at 41-50 age period, diameter increment was higher by 31%, basal area increment by 64% and volume increment by 67% compared to 32-40 age period. The collective of indifferent trees is significantly falling behind compared to future trees in terms of increment values in both observed periods. However, the value of diameter, basal area and volume increments, of the collective of "comparable" indifferent trees are lower in comparison to the values of increments of future trees by 10-15% in the 32-40 age period, and by 15-21% in the 41-50 age period and there are no significant differences. The results show that heavy selective thinnings, initially directed at a larger number of candidates for tending at stand age that does not differ much from the period of carrying out first "commercial" thinnings, improve the growth potential of future and indifferent trees, where it is rational to do the tree replacement for the final crop in "susceptible" growth stage to snow and ice breaks.

AN EVALUATION OF SEVERAL METHODS OF ESTIMATING SITE INDEX OF IMMATURE STANDS

1952 ◽  
Vol 28 (3) ◽  
pp. 63-74 ◽  
Author(s):  
John W. Ker
Keyword(s):  
Basal Area ◽  
Site Index ◽  
Site Quality ◽  
Average Height ◽  
Office Procedure ◽  
Minimum Sample ◽  
A Site ◽  
The University ◽  
Site Classes

The use of dominant heights for the estimation of site index is compared with the use of the average of dominant and codominant heights. Data collected on the University Research Forest are presented to illustrate the variability in tree heights and diameters within the two upper crown classes in well-stocked stands of immature Douglas fir.HeightIt is shown that the use of dominant heights reduces considerably the number of measurements required for a site index determination of given accuracy. Minimum sample sizes are given for three limits of accuracy for use in different site qualities. A general field and office procedure is outlined for the determination of minimum sample size in stands other than those described.DiameterThe use of diameter in site determination is discussed. Site indices based on the height of the tree of mean diameter, the height of the tree of mean basal area, and mean height are compared.ConclusionsQuick estimates of site quality can best be obtained by the measurement of total height of sample dominant trees, selected at random. For this purpose, tables are presented which list the average height of dominant trees by age and site classes for use in stands of Douglas fir, and western hemlock, respectively.

scholarly journals Influences of Forest Type, Stand Age, and Weather on Deer Weights and Antler Size in the Southern Appalachians

1997 ◽  
Vol 21 (1) ◽  
pp. 11-18 ◽  
Author(s):  
William M. Ford ◽  
A. Sydney Johnson ◽  
Philip E. Hale ◽  
James M. Wentworth
Keyword(s):  
Age Structure ◽  
Forest Type ◽  
Site Index ◽  
Forest Stand ◽  
Site Quality ◽  
Stand Age ◽  
Southern Appalachians ◽  
Study Region ◽  
Pinus Spp ◽  
Percent Area

Abstract We analyzed correlations of forest type, age structure, and site index data with weights and antler characteristics of yearling white-tailed deer (Odocoileus virginianus) bucks from specific localities in the Chattahoochee, Cherokee, Nantahala, and Pisgah national forests in Georgia, Tennessee, and North Carolina. Areas in the northern part of the study region produced larger deer with larger antlers than those in the southern portion of the region. These northern areas differed from those to the south in having more diverse ownership and land use and in origins of deer stock. Weights and antler characteristics were significantly correlated (P < 0.05) with percent area in the cove hardwood type, but otherwise were poorly correlated with forest stand type and site index. Percent area in young (0-8 yr old) cove hardwood and in mid-successional (9-20 and 21-40) cove hardwood, pine (Pinus spp.), and upland oak (Quercus spp.) were significantly correlated (P < 0.05) with deer variables, particularly in years following a poor mast crop. Much of the quantifiable habitat influences on deer in the Southern Appalachians probably is masked by low deer densities and the small site quality differences among areas examined. Because much of the forest consists of mature mast-producing oaks and abundant forage is produced in both mature and younger aged stands, deer numbers seem to be below any threshold of quantifiable effects due to forest stand age structure. South. J. Appl. For. 21(1):11-18.

scholarly journals A Nonlinear Mixed-Effects Height-to-Diameter Ratio Model for Several Tree Species Based on Czech National Forest Inventory Data

Forests ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 70 ◽  
Author(s):  
Ram Sharma ◽  
Zdeněk Vacek ◽  
Stanislav Vacek ◽  
Miloš Kučera
Keyword(s):  
Forest Inventory ◽  
Stand Density ◽  
Development Stage ◽  
National Forest Inventory ◽  
Mixed Effects ◽  
Site Quality ◽  
National Forest ◽  
Stand Development ◽  
Inventory Data ◽  
Canopy Layer

Height-to-diameter at breast height (DBH) ratio (HDR) is an important tree and stand stability measure. Several factors such as stand dynamics, natural and anthropogenic disturbances, and silvicultural tending significantly affect HDR, and, therefore, in-depth investigation of HDR is essential for better understanding of ecological processes in a forest. A nonlinear mixed-effects HDR model applicable to several tree species was developed using the Czech national forest inventory data comprising 13,875 sample plots and 348,980 trees. The predictive performance of this model was evaluated using the independent dataset which was originated from 25,146 trees on 220 research sample plots. Among various tree- and stand-level variables describing tree size, site quality, stand development stage, stand density, inter-tree spacing, and competition evaluated, dominant height (HDOM), dominant diameter (DDOM), relative spacing index (RS), and DBH-to-quadratic mean DBH ratio (dq) were identified as the most important predictors of HDR variations. A random component describing sample plot-specific HDR variations was included through mixed-effects modelling, and dummy variables describing species-specific HDR variations and canopy layer-specific HDR variations were also included into the HDR model through dummy variable modelling. The mixed-effects HDR model explained 79% of HDR variations without any significant trends in the residuals. Simulation results showed that HDR for each canopy layer increased with increasing site quality and stand development stage (increased HDOM) and increasing competition (increased RS, decreased DDOM and dq). Testing the HDR model on the independent data revealed that more than 85% of HDR variations were described for each individual species (Norway spruce, Scots pine, European larch, and European beech) and group of species (fir species, oak species, birch and alder species) without significant trends in the prediction errors. The HDR can be predicted with a higher accuracy using the calibrated mixed-effects HDR model from measurements of its predictors that can be obtained from routine forest inventories. To improve the prediction accuracy, a model needs to be calibrated with the random effects estimated using one to four randomly selected trees of a particular species or group of species depending on the availability of their numbers per sample plot. The HDR model can be applied for stand stability assessment and stand density regulation. The HDR information is also useful for designing a stand density management diagram. Brief implications of the HDR model for designing silviculture strategies and forest management planning are presented in the article.

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