Symmetric and Asymmetric Diffusions through Age-Varying Mixed-Species Stand Parameters

(1) Background: This paper deals with unevenly aged, whole-stand models from mixed-effect parameters diffusion processes and Voronoi diagram points of view and concentrates on the mixed-species stands in Lithuania. We focus on the Voronoi diagram of potentially available areas to tree positions as the measure of the competition effect of individual trees and the tree diameter at breast height to relate their evolution through time. (2) Methods: We consider a bivariate hybrid mixed-effect parameters stochastic differential equation for the parameterization of the diameter and available polygon area at age to ensure a proper description of the link between them during the age (time) span of a forest stand. In this study, the Voronoi diagram was used as a mathematical tool for the quantitative characterization of inter-tree competition. (3) Results: The newly derived model considers bivariate correlated observations, tree diameter, and polygon area arising from a particular stand and enables defining equations for calculating diameter, polygon-area, and stand-density predictions and forecasts. (4) Conclusions: From a statistical point of view, the newly developed models produced acceptable statistical measures of predictions and forecasts. All the results were implemented in the Maple computer algebra system.

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Comparison of ordinary least square and mixed-effect regression models for estimation of tree diameter increment

Proceedings of the 9th International Conference on Ubiquitous Information Management and Communication - IMCOM '15 ◽

10.1145/2701126.2701167 ◽

2015 ◽

Author(s):

Suriyati Harun ◽

Yasmin Yahya ◽

Nurashikin Saaludin ◽

Wan Suriyani Che Wan Ahmad

Keyword(s):

Regression Models ◽

Least Square ◽

Mixed Effect ◽

Ordinary Least Square ◽

Tree Diameter ◽

Diameter Increment ◽

Effect Regression

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A Multivariate Hybrid Stochastic Differential Equation Model for Whole-Stand Dynamics

Mathematics ◽

10.3390/math8122230 ◽

2020 ◽

Vol 8 (12) ◽

pp. 2230

Author(s):

Petras Rupšys ◽

Martynas Narmontas ◽

Edmundas Petrauskas

Keyword(s):

Differential Equation ◽

Stochastic Differential Equation ◽

Diffusion Processes ◽

Basal Area ◽

Equation Model ◽

Forest Stand ◽

Growth And Yield ◽

Stand Dynamics ◽

Mixed Effect ◽

Pine Tree

The growth and yield modeling of a forest stand has progressed rapidly, starting from the generalized nonlinear regression models of uneven/even-aged stands, and continuing to stochastic differential equation (SDE) models. We focus on the adaptation of the SDEs for the modeling of forest stand dynamics, and relate the tree and stand size variables to the age dimension (time). Two different types of diffusion processes are incorporated into a hybrid model in which the shortcomings of each variable types can be overcome to some extent. This paper presents the hybrid multivariate SDE regarding stand basal area and volume models in a forest stand. We estimate the fixed- and mixed-effect parameters for the multivariate hybrid stochastic differential equation using a maximum likelihood procedure. The results are illustrated using a dataset of measurements from Mountain pine tree (Pinus mugo Turra).

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Yields of Southwestern Pinyon-Juniper Woodlands

Western Journal of Applied Forestry ◽

10.1093/wjaf/3.3.70 ◽

1988 ◽

Vol 3 (3) ◽

pp. 70-74 ◽

Cited By ~ 1

Author(s):

Frederick W. Smith ◽

Thomas Schuler

Keyword(s):

Maximum Yield ◽

Stand Density ◽

Site Index ◽

Average Density ◽

Pinus Edulis ◽

Site Quality ◽

Mixed Species ◽

Growing Stock ◽

Highly Correlated ◽

Utah Juniper

Abstract Site quality and growth-growing stock relations were developed for southwestern woodlands of pinyon (Pinus edulis) and one-seed juniper (Juniperus monosperma) or Utah juniper (J. osteosperma). Anamorphic height-age site index curves for pinyon were developed from a regional sample of 60 woodlands. Site index was unaffected by variation in stocking and was correlated with woodland yield when used in conjunction with density. Pinyon and juniper PAI, when taken separately, were highly correlated with stand density and pinyon site index. Pinyon was twice as productive as juniper at similar stand densities. Pinyon and juniper yields in woodlands of average density and site index were estimated at 0.29 and 0.15 m3ha-1y-1. At high densities pinyon and juniper yields increased to 0.61 and 0.31 m3ha-1y-1 Pinyon and juniper yields appeared independent of the density of the other species in an individual woodland. Maximum yield of dense mixed species woodlands on average sites was 0.78 m3ha-1y-1, and occurred when pinyon constituted 65% of woodland density. West. J. Appl. For. 3(3):70-74, July 1988.

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Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

Symmetry ◽

10.3390/sym12010080 ◽

2020 ◽

Vol 12 (1) ◽

pp. 80 ◽

Cited By ~ 3

Author(s):

Martynas Narmontas ◽

Petras Rupšys ◽

Edmundas Petrauskas

Keyword(s):

Goodness Of Fit ◽

Diffusion Processes ◽

Parameters Estimation ◽

Data Set ◽

Mixed Effect ◽

Fit Statistics ◽

Stem Taper ◽

Longitudinal Measurements ◽

High Level ◽

Taper Models

In this work, we employ stochastic differential equations (SDEs) to model tree stem taper. SDE stem taper models have some theoretical advantages over the commonly employed regression-based stem taper modeling techniques, as SDE models have both simple analytic forms and a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stem taper models by developing an approximated maximum likelihood procedure and using a data set of longitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetric Gompertz-type diffusion processes used adequately describe stem taper evolution. The proposed SDE stem taper models are compared to four regression stem taper equations and four volume equations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parameters SDEs stem taper models. All results are obtained in the Maple computer algebra system.

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Incorporating intertree competition into an ecosystem model

Canadian Journal of Forest Research ◽

10.1139/x95-046 ◽

1995 ◽

Vol 25 (3) ◽

pp. 413-424 ◽

Cited By ~ 32

Author(s):

R.L. Korol ◽

S.W. Running ◽

K.S. Milner

Keyword(s):

Process Model ◽

Basal Area ◽

Stand Density ◽

Tree Height ◽

Ecosystem Model ◽

Growth And Yield ◽

Maintenance Respiration ◽

Tree Diameter ◽

Diameter Increment ◽

Individual Trees

Current research suggests that projected climate change may influence the growth of individual trees. Therefore, growth and yield models that can respond to potential changes in climate must be developed, TREE-BGC, a variant of the ecosystem process model FOREST-BGC, calculates the cycling of carbon, water, and nitrogen in and through forested ecosystems. TREE-BGC allocates stand-level estimates of photosynthesis to "each tree using a competition algorithm that incorporates tree height, relative radiation-use efficiency, and absorbed photosynthetically active radiation, TREE-BGC simulated the growth of trees grown in a dense and an open stand of interior Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) near Kamloops, B.C. The competition algorithm dynamically allocated stand estimates of photosynthesis to individual trees, and the trees were grown using an allometric relationship between biomass increment and height and diameter increment. Asymptotic height growth and the changes in the height–diameter relationship with competition were also incorporated in the model algorithms. Sapwood and phloem volume were used to calculate maintenance respiration. Predicted reductions in diameter growth with stand density were similar to those observed in the study stands. Although the carbon balance of individual trees was not tested, simulated tree diameter increments and height increments were correlated with the actual measurements of tree diameter increment (r2 = 0.89) and tree height increment (r2 = 0.78) for the 5-year period (n = 352). Although the model did not work well with trees that had diameters <5 cm, the model would be appropriate for a user who required an accuracy of ± 0.03 m3•ha−1 for volume, ± 0.02 m2•ha−1 for basal area, or ± 0.4 m for tree height over a 5-year period.

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Rapid Assessment of Relative Density in Mixed-Species Stands of the Northeastern United States

International Journal of Forestry Research ◽

10.1155/2010/212068 ◽

2010 ◽

Vol 2010 ◽

pp. 1-8

Author(s):

M. J. Ducey ◽

R. A. Knapp

Keyword(s):

United States ◽

Specific Gravity ◽

Rapid Assessment ◽

Basal Area ◽

Stand Density ◽

Sampling Technique ◽

Northeastern United States ◽

Mixed Species ◽

Stand Density Index ◽

Simple Tree

Basal area has shortcomings as a measure of stand density, but it is often preferred for operational assessments because it is easy to measure. Previous work has demonstrated that an additive version of Reineke's stand density index can be estimated by a simple tree count using a modified horizontal point sampling technique. We show that this technique can be extended further to estimate a mixed-species density measure that has been developed for complex stands in the northeastern United States, using wood specific gravity to harmonize the density contributions of different species. The sampling technique provides design-unbiased estimates of stand density from a weighted tree count, where the weights depend on specific gravity but not on diameter. Rounding the specific gravity values for different species in the calculation of estimates introduces a trivial amount of bias but streamlines the procedure for rapid use in the field.

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Rapid detection of stand density, tree positions, and tree diameter with a 2D terrestrial laser scanner

European Journal of Forest Research ◽

10.1007/s10342-014-0799-1 ◽

2014 ◽

Vol 133 (5) ◽

pp. 819-831 ◽

Cited By ~ 8

Author(s):

Andreas Brunner ◽

Belachew Gizachew

Keyword(s):

Rapid Detection ◽

Laser Scanner ◽

Stand Density ◽

Terrestrial Laser Scanner ◽

Tree Diameter

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Precommercial Thinning in a Ponderosa Pine Stand Affected by Armillaria Root Disease in Central Oregon: 30 Years of Growth and Mortality

Western Journal of Applied Forestry ◽

10.1093/wjaf/14.3.144 ◽

1999 ◽

Vol 14 (3) ◽

pp. 144-148 ◽

Cited By ~ 4

Author(s):

Gregory M. Filip ◽

Stephen A. Fitzgerald ◽

Lisa M. Ganio

Keyword(s):

Ponderosa Pine ◽

Tree Mortality ◽

Basal Area ◽

Stand Density ◽

Root Disease ◽

Diameter Growth ◽

Individual Tree ◽

Precommercial Thinning ◽

Tree Diameter ◽

Armillaria Root Disease

Abstract A 30-yr-old stand of ponderosa pine was precommercially thinned in 1966 to determine the effects of thinning on tree growth and mortality caused by Armillaria root disease in central Oregon. After 30 yr, crop tree mortality was significantly (P = 0.02) less in thinned plots than in unthinned plots. Tree diameter growth was not significantly (P = 0.17) increased by thinning. Crop-tree basal area/ac growth was significantly (P = 0.03) greater in thinned plots. Apparently, from a root disease perspective, precommercial thinning of pure ponderosa stands significantly decreases the incidence of crop-tree mortality after 30 yr and significantly increases basal area/ac growth but not individual tree diameter growth. Recommendations for thinning based on stand density index (SDI) are given. West. J. Appl. For. 14(3):144-148.

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