Scale and spatial structure effects on tree size distributions: implications for growth and yield modelling

2006 ◽  
Vol 36 (11) ◽  
pp. 2983-2993 ◽  
Author(s):  
Oscar García
Keyword(s):  
Spatial Structure ◽  
Growth Models ◽  
Growth And Yield ◽  
Size Distributions ◽  
Spatial Correlations ◽  
Forest Patch ◽  
Individual Tree ◽  
Plot Size ◽  
Central Canada ◽  
Distribution Parameters

Diameter and other size distributions are extensively used in growth modelling. These are usually obtained from sample plot data and assumed to apply both at the stand level, of interest for production planning, and at the forest patch level, the level relevant for tree growth interactions. However, spatial correlation can cause distribution parameters and their estimates to vary with the extent of ground considered. Using mapped tree data from four forest stands in central Canada, it is shown that differences in DBH variance with plot size can be substantial. In addition, size correlations between neighbouring trees were positive, rather than negative as implied by current distance-dependent growth models. Biases in mean DBH are also found. It is proved that plot totals and frequencies are unbiased estimates of stand parameters, but variances and some other statistics are not. The expected variance is expressed in terms of plot size and shape and of second-order stand spatial structure properties. Some possible approaches for reducing bias in stand-level variance estimates are discussed, and the desirability of modelling microsite or genetic spatial correlations in individual-tree simulators is pointed out.

scholarly journals Plasticity as a Link Between Spatially Explicit, Distance-Independent, and Whole-Stand Forest Growth Models

2021 ◽  
Author(s):  
Oscar García
Keyword(s):  
Spatial Structure ◽  
Growth Models ◽  
Forest Growth ◽  
Mean Field Approximation ◽  
Future Research ◽  
Size Distributions ◽  
Ecological Processes ◽  
Individual Tree ◽  
Perfect Plasticity ◽  
Advantages And Disadvantages

Abstract Models at various levels of resolution are commonly used for both forest management and ecological research. They all have comparative advantages and disadvantages, making desirable a better understanding of the relationships between various approaches. Accounting for crown and root morphological plasticity in the limit where equilibrium among neighbors is reached (perfect plasticity) transforms spatial models into nonspatial, distance-independent versions. The links between spatial and nonspatial models obtained through a perfect plasticity assumption are more realistic than ignoring spatial structure by a mean field approximation. This article also reviews the connection between distance-independent models and size distributions and how distributions evolve over time and relate to whole-stand descriptions. In addition, some ways in which stand-level knowledge feeds back into detailed individual-tree formulations are demonstrated. This presentation is intended to be accessible to nonspecialists. Study Implications Introducing plasticity improves the representation of physio-ecological processes in spatial modelling. Plasticity explains in part the practical success of distance-independent models. The nature of size distributions and their relationship to individual-tree and whole-stand models are discussed. A size distribution is a one-variable distribution; joint distributions for two or more trees depend on the distances between them unless spatial structure is negligible. Limitations of current individual-tree models and questions for future research are discussed.

Impact of plot size on individual-tree competition measures for growth and yield simulators

2003 ◽  
Vol 33 (3) ◽  
pp. 455-465 ◽  
Author(s):  
Jari Hynynen ◽  
Risto Ojansuu
Keyword(s):  
Picea Abies ◽  
Norway Spruce ◽  
Growth Models ◽  
Model Performance ◽  
Stand Density ◽  
Growth And Yield ◽  
Average Radius ◽  
Sample Plot ◽  
Individual Tree ◽  
Plot Size

The study addresses the effect of sample plot size on the bias related to measured stand density. We analyzed the effect of plot size on model coefficients and model performance in the simulation. Alternative growth models were developed for Norway spruce (Picea abies (L.) Karst.) on the basis of data obtained from permanent inventory sample plots of varying size. The competition measures were estimated from small plots with an average radius of 6 m, large plots with an average radius of 10 m, a cluster of three small plots within a stand, and a cluster of three large plots within a stand. The response of the models to competition varied depending on the plot size. Increasing the plot size increased the sensitivity of the models to the variation of overall stand density and the competitive status of a tree. The development of repeatedly measured, unthinned and thinned Norway spruce sample plots was simulated with the models, and the predictions were compared with the observed development. In the unthinned stand, the model with competition measures based on small plots resulted in a higher and more biased prediction of growth and mortality than the models based on larger plots. In the thinned stand, the differences between the models were negligible.

Calibrating predicted diameter distribution with additional information in growth and yield predictions

2003 ◽  
Vol 33 (3) ◽  
pp. 430-434 ◽  
Author(s):  
Annika Kangas ◽  
Matti Maltamo
Keyword(s):  
Growth Models ◽  
Basal Area ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Individual Tree ◽  
Forest Management Planning ◽  
Growing Stock ◽  
Additional Information ◽  
Tree Models ◽  
Diameter Distributions

Diameter distribution of the growing stock is essential in many forest management planning problems. The diameter distribution is the basis for predicting, for example, timber assortments of a stand. Usually the predicted diameter distribution is scaled so that the stem number (or basal area) corresponds to the measured value (or predicted future value), but it may be difficult to obtain a distribution that gives correct estimates for all known variables. Diameter distributions that are compatible with all available information can be obtained using an approach adopted from sampling theory, the calibration estimation. In calibration estimation, the original predicted frequencies are modified so that they respect a set of constraints, the calibration equations. In this paper, an example of utilizing diameter distributions in growth and yield predictions is presented. The example is based on individual tree growth models of Scots pine (Pinus sylvestris L.). Calibration estimation was utilized in predicting the diameter distribution at the beginning of the simulation period. Then, trees were picked from the distribution and their development was predicted with individual tree models. In predicting the current stand characteristics, calibrated diameter distributions proved to be efficient. However, in predicting future yields, calibration estimation did not significantly improve the accuracy of the results.

scholarly journals The SOHARC Model System for Growth and Yield of Southern Hardwoods

2008 ◽  
Vol 32 (4) ◽  
pp. 173-183 ◽  
Author(s):  
John Paul McTague ◽  
David O'Loughlin ◽  
Joseph P. Roise ◽  
Daniel J. Robison ◽  
Robert C. Kellison
Keyword(s):  
Tree Growth ◽  
Growth Models ◽  
Basal Area ◽  
Tree Height ◽  
Growth And Yield ◽  
Permanent Plots ◽  
Red Maple ◽  
Yellow Poplar ◽  
Individual Tree ◽  
Individual Tree Growth

Abstract A system of stand level and individual tree growth-and-yield models are presented for southern hardwoods. These models were developed from numerous permanent growth-and-yield plots established across 13 states in the US South on 9 site types, in even-aged (age classes from 20 to 60 years), fully stocked, naturally regenerated mixed hardwood and mixed hardwood-pine stands. Nested plots (⅕ and ac) were remeasured at 5-year intervals. The system of permanent plots was established and maintained by private and public members in the North Carolina State University Hardwood Research Cooperative. Stand level models are presented for dominant height, survival, basal area prediction and projection, and the ingrowth component. Individual tree diameter growth and tree height models were constructed for the most common species: sweetgum, tupelo, yellow-poplar, blackgum, and red maple. All other species were grouped according to growth dynamics into four species groups using cluster analysis. A ranking variable was incorporated into the individual tree growth models to account for competition.

scholarly journals Possibilities and limitations of individual-tree growth models – A review on model evaluations

2017 ◽  
Vol 68 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Sonja Vospernik
Keyword(s):  
Tree Growth ◽  
Growth Models ◽  
Wood Quality ◽  
Rotation Period ◽  
Growth And Yield ◽  
Tree Age ◽  
Emergent Properties ◽  
Management Scenarios ◽  
Individual Tree ◽  
Individual Tree Growth

Summary Individual-tree growth models are the new standard for modeling growth and yield. Their main purpose is to simulate future forest management scenarios but they can also be used to predict wood quality, rockfall protection or habitat quality. Individual tree growth models may consist of different models but core models are diameter increment, height increment, crown ratio (often used as a predictor for increment) and mortality. The model differentiation is based on how these four models include tree age (size), competition and site. Four common growth simulators in Central Europe are BWIN, Moses, Prognaus and Silva. These four models are commonly deployed to simulate 30 years of growth, but a prospective application is the simulation of a whole rotation period (80–150 years). It is therefore crucial to understand the possibilities and limitations of these models by evaluating them. This review paper summarizes the statistical and emergent properties’ evaluation results for these models. Statistical evaluations focus on individual models of a simulator, whereas the evaluation of emergent properties evaluates the entire simulator, by testing if the models conform to known principles of stand growth. Further, the meaning of these evaluation results for the development and improvement of individual-tree growth models is discussed.

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.

Eucalyptus growth and yield system: Linking individual-tree and stand-level growth models in clonal Eucalypt plantations in Brazil

2019 ◽  
Vol 432 ◽  
pp. 1-16 ◽  
Author(s):  
Henrique Ferraco Scolforo ◽  
John Paul McTague ◽  
Harold Burkhart ◽  
Joseph Roise ◽  
Otavio Campoe ◽  
...  
Keyword(s):  
Growth Models ◽  
Growth And Yield ◽  
Individual Tree ◽  
Eucalypt Plantations

scholarly journals Precommercial Thinning Increases Spruce Yields in Boreal Mixedwoods in Alberta, Canada

Forests ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 412
Author(s):  
Ivan Bjelanovic ◽  
Phil Comeau ◽  
Sharon Meredith ◽  
Brian Roth
Keyword(s):  
Growth Models ◽  
Growth And Yield ◽  
Diameter Growth ◽  
Growth Responses ◽  
Projection System ◽  
Precommercial Thinning ◽  
Thinning Intensity ◽  
Boreal Mixedwoods ◽  
Using Data ◽  
Mixedwood Stands

A few studies in young mixedwood stands demonstrate that precommercial thinning of aspen at early ages can improve the growth of spruce and increase stand resilience to drought. However, information on tree and stand responses to thinning in older mixedwood stands is lacking. To address this need, a study was initiated in 2008 in Alberta, Canada in 14 boreal mixedwood stands (seven each at ages 17 and 22). This study investigated growth responses following thinning of aspen to five densities (0, 1000, 2500, 5000 stems ha−1 and unthinned (control)). Measurements were collected in the year of establishment, and three and eight years later. Mortality of aspen in the unthinned plots was greater than in the thinned plots which were not significantly different amongst each other. Eight years following treatment, aspen diameter was positively influenced by thinning, while there was no effect on aspen height. The density of aspen had no significant effect on the survival of planted spruce. Spruce height and diameter growth increased with both aspen thinning intensity and time since treatment. Differentiation among treatments in spruce diameter growth was evident three years from treatment, while differentiation in height was not significant until eight years following treatment. Yield projections using two growth models (Mixedwood Growth Model (MGM) and Growth and Yield Projection System (GYPSY)) were initialized using data from the year eight re-measurements. Results indicate that heavy precommercial aspen thinning (to ~1000 aspen crop trees ha−1) can result in an increase in conifer merchantable volume without reducing aspen volume at the time of harvest. However, light to moderate thinning (to ~2500 aspen stems ha−1 or higher), is unlikely to result in gains in either deciduous or conifer merchantable harvest volume over those of unthinned stands.

Deriving Tree Diameter Growth and Probability of Survival Equations from Successive Diameter Distributions

2008 ◽  
Vol 54 (1) ◽  
pp. 31-35
Author(s):  
Thomas G. Matney ◽  
Emily B. Schultz
Keyword(s):  
General Procedure ◽  
Growth And Yield ◽  
Diameter Distribution ◽  
Diameter Growth ◽  
Individual Tree ◽  
Statistical Probability ◽  
Growth And Survival ◽  
Tree Diameter ◽  
Growth And Yield Models ◽  
Diameter Distributions

Abstract Many growth and yield models have used statistical probability distributions to estimate the diameter distribution of a stand at any age. Equations for approximating individual tree diameter growth and survival probabilities from dbh can be derived from these models. A general procedure for determining the functions is discussed and illustrated using a loblolly pine spacing study. The results from the spacing study show that it is possible to define tree diameter growth and survival probability functions from diameter distributions with an accuracy sufficient to obtain a link between the individual tree and diameter growth and yield models.

scholarly journals A Novel Approach to Modelling Stand-Level Growth of an Even-Aged Forest Using a Volume Productivity Index with Application to New Zealand-Grown Coast Redwood

Forests ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1155 ◽  
Author(s):  
Mark O. Kimberley ◽  
Michael S. Watt
Keyword(s):  
New Zealand ◽  
Growth Model ◽  
Growth Models ◽  
Stand Density ◽  
Site Index ◽  
Growth And Yield ◽  
Productivity Index ◽  
Site Quality ◽  
Spatial And Temporal Variation ◽  
Coast Redwood

Empirical growth models are widely used to predict the growth and yield of plantation tree species, and the precise estimation of site quality is an important component of these models. The most commonly used proxy for site quality in growth models is Site Index (SI), which describes the mean height of dominant trees at a specified base age. Although SI is widely used, considerable research shows significant site-dependent variation in height for a given volume, with this latter variable more closely reflecting actual site productivity. Using a national dataset, this study develops and describes a stand-level growth and yield model for even-aged New Zealand-grown coast redwood (Sequoia sempervirens). We used a novel modelling approach that quantifies site quality using SI and a volume-based index termed the 300 Index, defined as the volume mean annual increment at age 30 years for a reference regime of 300 stems ha−1. The growth model includes a number of interrelated components. Mean top height is modelled from age and SI using a polymorphic Korf function. A modified anamorphic Korf function is used to describe tree quadratic mean diameter (Dq) as a function of age, stand density, SI and a diameter site index. As the Dq model includes stand density in its formulation, it can predict tree growth for different stand densities and thinning regimes. The mortality model is based on a simple attritional equation improved through incorporation of the Reineke stand density index to account for competition-induced mortality. Using these components, the model precisely estimates stand-level volume. The developed model will be of considerable value to growers for yield projection and regime evaluation. By more robustly describing the site effect, the growth model provides researchers with an improved framework for quantifying and understanding the causes of spatial and temporal variation in plantation productivity.

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