Evaluating the performance of semi-distance-independent competition indices in predicting the basal area growth of individual trees

2010 ◽  
Vol 40 (4) ◽  
pp. 796-805 ◽  
Author(s):  
Thomas Ledermann
Keyword(s):  
Spatial Information ◽  
Growth Models ◽  
Basal Area ◽  
Local Variation ◽  
Small Sample ◽  
Sample Plot ◽  
Competition Index ◽  
Individual Tree ◽  
Tree Increment ◽  
Competition Indices

Recent individual-tree growth models use either distance-dependent or distance-independent competition measures to predict tree increment. However, both measures have deficiencies: the latter because the effects of local variation in spacing are not represented, and the former because they cannot be calculated from normal inventory data for lack of spatial information. To overcome these shortcomings, the new class of semi-distance-independent competition indices was proposed. A semi-distance-independent competition index is a distance-independent competition measure that uses only the trees of a single small sample plot that includes the subject tree. Moreover, a semi-distance-independent competition index can be calculated in an analogous way to a distance-dependent competition index by using sample plot size, tree attributes, and intertree distances. However, many semi-distance-independent competition measures are based on simple tree attributes. Therefore, the objective of this study was to analyze if the semi-distance-independent competition indices explain the variation in measurements of tree increment more or less effectively than a set of classical distance-dependent competition indices. The results show that some of the semi-distance-independent competition indices explain at least as much variation in measurements of tree increment as any of the distance-dependent competition indices.

Effects of competitor spacing in a new class of individual-tree indices of competition: semi-distance-independent indices computed for Bitterlich versus fixed-area plots

2008 ◽  
Vol 38 (4) ◽  
pp. 890-898 ◽  
Author(s):  
Albert R. Stage ◽  
Thomas Ledermann
Keyword(s):  
Basal Area ◽  
Area Ratio ◽  
Individual Tree ◽  
Competitive Effects ◽  
New Class ◽  
Distance Effects ◽  
Fixed Area ◽  
Tree Increment ◽  
Competition Indices ◽  
Selection Of

We illustrate effects of competitor spacing for a new class of individual-tree indices of competition that we call semi-distance-independent. This new class is similar to the class of distance-independent indices except that the index is computed independently at each subsampling plot surrounding a subject tree for which growth is to be modelled. We derive the effects of distance for this class as the expected value over independent samples containing a particular subject tree. In a previous paper, we illustrated distance effects implicit in eight indices of the distance-dependent class. Here, we present distance effects of four semi-distance-independent indices: density, sum of diameters, basal area, and tree-area ratio; each determined for small fixed-area plots of 0.04 ha and for Bitterlich samples of 6 m2·ha–1. We show that several members of this new class have distance effects very similar to the distance-dependent class and should, therefore, be equally effective in accounting for competitive effects in individual-tree increment models. The comparisons should inform selection of competition indices and sampling designs for growth modelling.

Predicting basal area increment in a spatially explicit, individual tree model: a test of competition measures with black spruce

2003 ◽  
Vol 33 (3) ◽  
pp. 435-443 ◽  
Author(s):  
Daniel Mailly ◽  
Sylvain Turbis ◽  
David Pothier
Keyword(s):  
Black Spruce ◽  
Basal Area ◽  
Basal Area Increment ◽  
Spatially Explicit ◽  
Competition Index ◽  
Individual Tree ◽  
Spatial Indices ◽  
Crown Shape ◽  
Spruce Stands ◽  
Competition Indices

A current trend in the development of forest stand models is to use spatially explicit, individual-tree information to simulate forest dynamics with increased accuracy. By adding spatial information, such as tree coordinates, crown shape, and size, it is hypothesized that the computation of the model's driving function is improved over traditional competition indices, especially when simulating multistoried stands. In this paper, we want to test whether computationally demanding competition indices outperform traditional indices in predicting mean basal area increment. The study was undertaken in old, uneven-aged black spruce (Picea mariana (Mill.) BSP) stands in northeastern Quebec, Canada. The predictability of individual tree growth rates was related to crown dimensions and other stand and tree variables measured in the field. Data were collected from 90 trees coming from stands of varying site quality (range 9.6–16.5 m height at 50 years, age taken at 1 m) and age (range 66–257 years). Hegyis's distance-dependent competition index was found to be the most strongly correlated competition measure (r = 0.57) with mean basal area growth of the last 20 years. This value, 12% higher than the value obtained from the best distance-independent competition index (r = 0.45), clearly shows that precision gains can be achieved when estimating basal area increment with spatial indices in black spruce stands. Using indices computed from virtual hemispherical images did not prove superior to simpler distance-dependent indices based on their individual correlations with basal area increment. When included in a basal area increment model for the last 20 years of growth, however, the gains in precision were comparable to Hegyi's competition index. This indicates that indices derived from a hemispherical approach have some value in spatially explicit forest simulations models but that further tests using younger stands are needed to confirm this result in black spruce stands.

A New Index Representing Individual Tree Competitive Status

1973 ◽  
Vol 3 (4) ◽  
pp. 495-500 ◽  
Author(s):  
James A. Moore ◽  
Carl A. Budelsky ◽  
Richard C. Schlesinger
Keyword(s):  
Spatial Distribution ◽  
Strong Correlation ◽  
Basal Area ◽  
Tree Size ◽  
Competition Index ◽  
Individual Tree ◽  
Silvicultural Practices ◽  
Basal Area Growth ◽  
Hardwood Species ◽  
Area Growth

A new competition index, modified Area Potentially Available (APA), was tested in a complex unevenaged stand composed of 19 different hardwood species. APA considers tree size, spatial distribution, and distance relationships in quantifying intertree competition and exhibits a strong correlation with individual tree basal area growth. The most important characteristic of APA is its potential for evaluating silvicultural practices.

Intertree competition in uneven-aged ponderosa pine stands

2003 ◽  
Vol 33 (9) ◽  
pp. 1719-1726 ◽  
Author(s):  
C W Woodall ◽  
C E Fiedler ◽  
K S Milner
Keyword(s):  
Pinus Ponderosa ◽  
Ponderosa Pine ◽  
Basal Area ◽  
Growth Efficiency ◽  
Tree Size ◽  
Basal Area Increment ◽  
Diameter Class ◽  
Individual Tree ◽  
Sapwood Area ◽  
Competition Indices

Intertree competition indices and effects were examined in 14 uneven-aged ponderosa pine (Pinus ponderosa var. scopulorum Engelm.) stands in eastern Montana. Location, height, diameter at breast height (DBH), basal area increment, crown ratio, and sapwood area were determined for each tree (DBH >3.8 cm) on one stem-mapped plot (0.2-0.4 ha) in each sample stand. Based on tree locations, various competition indices were derived for each sample tree and correlated with its growth efficiency by diameter class. In addition, trends in individual tree attributes by diameter class and level of surrounding competition were determined. For trees with a DBH <10 cm, growth efficiency was most strongly correlated with the sum of surrounding tree heights within 10.6 m. The index most highly correlated for larger trees was the sum of surrounding basal area within 6.1 m. Regardless of tree size, individual tree growth efficiency, basal area increment, and crown ratio all decreased under increasing levels of competition, with the effect more pronounced in smaller trees. These results suggest that individual trees in uneven-aged stands experience competition from differing sources at varying scales based on their size, with response to competition diminishing as tree size increases.

Assessing model performance in forecasting long-term individual tree diameter versus basal area increment for the primary Acadian tree species

2011 ◽  
Vol 41 (12) ◽  
pp. 2267-2275 ◽  
Author(s):  
Matthew B. Russell ◽  
Aaron R. Weiskittel ◽  
John A. Kershaw
Keyword(s):  
Random Effects ◽  
Mean Squared Error ◽  
Growth Models ◽  
Secondary Growth ◽  
Model Performance ◽  
Basal Area ◽  
Nonlinear Mixed Effects Models ◽  
Absolute Deviation ◽  
Individual Tree

Tree basal area (ba) or diameter at breast height (dbh) are universally used to represent tree secondary growth in individual tree based growth models. However, the long-term implications of using either ba or dbh for predictions are rarely fully assessed. In this analysis, Δba and Δdbh increment equations were fit to identical datasets gathered from six conifer and four hardwood species grown in central Maine. The performance of Δba and Δdbh predictions from nonlinear mixed-effects models were then compared with observed growth measurements of up to 29 years via a Monte Carlo simulation. Two evaluation statistics indicated substantial improvement in forecasting dbh using Δdbh rather than Δba. Root mean squared error (RMSE) and percentage mean absolute deviation (MAD%) were reduced by 14% and 15% on average, respectively, across all projection length intervals (5–29 years) when Δdbh was used over Δba. Differences were especially noted as projection lengths increased. RMSE and MAD% were reduced by 24% when Δdbh was employed over Δba at longer projection lengths (up to 29 years). Simulations found that simulating random effects rather than using local estimates for random effects performed as well or better at longer interval lengths. These results highlight the implications that selecting a growth model dependent variable can have and the importance of incorporating model uncertainty into the growth projections of individual tree based models.

Modelling growing space requirement for Alnus nepalensis D. Don in Nepal

1970 ◽  
Vol 16 (2) ◽  
pp. 30-36 ◽  
Author(s):  
Ram Prasad Sharma
Keyword(s):  
Prediction Models ◽  
Growth Models ◽  
Basal Area ◽  
Individual Tree ◽  
Area Density ◽  
Space Requirement ◽  
Space Model ◽  
Alnus Nepalensis ◽  
Crown Diameter ◽  
Individual Trees

Relationship between crown diameter and stem diameter of individual trees can be translated into mathematical model, and used to generate information of growing space requirement for individual trees and crown competition index for growth models. Nine different crown diameter prediction models were developed using inventory data of Alnus nepalensis trees from a part of Parbat and Syanja districts in Nepal. Among those developed, a non-linear three parameter-based model (W = β0 {1 – exp( - β1D)}β2) explained the greatest proportion of variations of crown diameter (R2adj = 0.78), and showed desirable behaviour of flexibility and robustness. An individual tree growing space model was then derived from crown model to generate important information of shocking limits and stand basal area density for monoculture plantation or natural stands of Alnus nepalensis. Because of its flexibility, crown model is seemed potentially useful for extrapolation purpose also. However, the model cannot be applied for buttressed, wolfed and malformed trees. Key words: Alnus nepalensis; crown model; growing space model; stocking limit; basal area density Banko Janakari Vol.16(2) 2006 pp.30-36

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 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 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.

Evaluation of distance-independent competition indices in predicting tree survival and diameter growth

2019 ◽  
Vol 49 (5) ◽  
pp. 440-446 ◽  
Author(s):  
Shuaichao Sun ◽  
Quang V. Cao ◽  
Tianjian Cao
Keyword(s):  
Loblolly Pine ◽  
Relative Position ◽  
Basal Area ◽  
Diameter Ratio ◽  
Cumulative Distribution ◽  
Permanent Plots ◽  
Diameter Growth ◽  
Individual Tree ◽  
Tree Survival ◽  
Competition Indices

Competition indices play a significant role in modeling individual-tree growth and survival. In this study, six distance-independent competition indices were evaluated using 200 permanent plots of loblolly pine (Pinus taeda L.). The competition indices were classified into three families: (1) size ratios, which include diameter ratio and basal area ratio; (2) relative position indices, which include basal area of larger trees (BAL) and tree relative position based on the cumulative distribution function (CDF); and (3) partitioned stand density index and relative density. Results indicated that different families of competition indices were suitable for different tree survival or diameter growth prediction tasks. The diameter ratio was superior for predicting tree survival, whereas the relative position indices (BAL and CDF) performed best for predicting tree diameter growth, with CDF receiving the highest rank.

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