Stochastic Mixed-Effects Parameters Bertalanffy Process, with Applications to Tree Crown Width Modeling

Rupšys, Petras

doi:10.1155/2015/375270

Cited by 13 publications

(9 citation statements)

References 20 publications

(24 reference statements)

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“…The direct effects of stand variables such as site index and management practices and thinning could be included in the new developed models (see [28], [29]); however, their indirect effect via mixed effects (see right side Fig 6) has been included in mixed effects tree mean volume models.…”

Section: Resultsmentioning

confidence: 99%

“…The solution, H i ( d ), of Eq 3 has a normal distribution with conditional probability density, mean, and variance, respectively [29]: and the solutions, H i ( d ), of Eqs 4–7 have lognormal distributions, with conditional probability density, means, and variance, respectively [28, 38]: …”

Section: Appendix Bmentioning

confidence: 99%

“…The conditional mean, m(d), and variance, v(d), functions of the tree height, H(d), for all the models (Eqs 14–17) are given by the following expressions [28], [29], [38]: …”

Section: Appendix Bmentioning

confidence: 99%

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New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

Rupšys

2016

PLoS ONE

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The aim of this paper is twofold: to introduce the mathematics of stochastic differential equations (SDEs) for forest dynamics modeling and to describe how such a model can be applied to aid our understanding of tree height distribution corresponding to a given diameter using the large dataset provided by the Lithuanian National Forest Inventory (LNFI). Tree height-diameter dynamics was examined with Ornstein-Uhlenbeck family mixed effects SDEs. Dynamics of a tree height, volume and their coefficients of variation, quantile regression curves of the tree height, and height-diameter ratio were demonstrated using newly developed tree height distributions for a given diameter. The parameters were estimated by considering a discrete sample of the diameter and height and by using an approximated maximum likelihood procedure. All models were evaluated using a validation dataset. The dataset provided by the LNFI (2006–2010) of Scots pine trees is used in this study to estimate parameters and validate our modeling technique. The verification indicated that the newly developed models are able to accurately capture the behavior of tree height distribution corresponding to a given diameter. All of the results were implemented in a MAPLE symbolic algebra system.

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Section: Resultsmentioning

confidence: 99%

Section: Appendix Bmentioning

confidence: 99%

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New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

Rupšys

2016

PLoS ONE

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“…The Gompertz, Verhulst, Bertalanffy, and Maltussian type SDEs were used to model the total tree height over age [10] and diameter [11,12], to model the stem taper [13], and to model tree crown width over diameter [14]. They found that the SDE models provided much more accurate predictions of individual tree height and crown width compared to nonlinear regression models.…”

Section: Introductionmentioning

confidence: 99%

A Linkage among Tree Diameter, Height, Crown Base Height, and Crown Width 4-Variate Distribution and Their Growth Models: A 4-Variate Diffusion Process Approach

Rupšys

Petrauskas

2017

Forests

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Abstract:The evolution of the 4-variate probability distribution of the diameter at the breast height, total height, crown base height, and crown width against the age in a forest stand is of great interest to forest management and the evaluation of forest resources. This paper focuses on the Vasicek type 4-variate fixed effect stochastic differential equation (SDE) to quantify the dynamic of tree size components distribution against the age. The new derived 4-variate probability density function and its marginal univariate, bivariate, trivariate, and conditional univariate distributions are applied for the modeling of stand attributes such as the mean diameter, height, crown base height, crown width, volume, and slenderness. All parameters were estimated by the maximum likelihood procedure using a dataset of 1630 Scots pine trees (12 stands). The results were validated using a dataset of 699 Scots pine trees (five stands). A newly developed 4-variate simultaneous system of SDEs incorporated covariance structure driving changes in tree size components and improved predictions in one tree size component given the other tree size components in the system.

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“…Crecente-Campo et al (2009) used both geometrical shapes and equations to model crown profile. Rupšys (2015) developed stochastic models of crown widths. Power et al (2012) proposed equations of crown length, profile, shape and surface area of black spruce (Picea mariana) and white spruce (Picea glauca) to characterize crown characteristics of these species.…”

Section: Introductionmentioning

confidence: 99%

Analytical approaches for modeling tree crown volume in black wattle (Acacia mearnsii De Wild.) stands

Guilherme¹,

Carlos²,

Sylvio³

et al. 2016

Afr. J. Agric. Res.

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In this paper, four strategies were proposed for modeling tree crown volume using as independent variable stem variables, crown variables, combination of stem and crown variables, and stem volume. We used a dataset comprised of 170 trees from 12 temporary plots located in forest stands in southern Brazil. Models composed of stem variables presented weaker predictive ability. The best model contained crown variables, which explained 78.95% of observed variability. However, implementation of such model is bounded by its independent variables, which are not often measured in forest inventories. The model composed by diameter at breast height and crown length proved to be an adequate modeling approach. The predictive capability was kept by model , which is composed by most easily measured variable in a forest -diameter at breast height, also by the most easily acquirable crown variable -crown length. In our suggested model, estimates of and are coefficients that convert volume of a regular geometric solid -RGS is dbh² times crown length) -into crown volume, whilst estimate of is an allometric constant.

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Stochastic Mixed-Effects Parameters Bertalanffy Process, with Applications to Tree Crown Width Modeling

Cited by 13 publications

References 20 publications

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

A Linkage among Tree Diameter, Height, Crown Base Height, and Crown Width 4-Variate Distribution and Their Growth Models: A 4-Variate Diffusion Process Approach

Analytical approaches for modeling tree crown volume in black wattle (Acacia mearnsii De Wild.) stands

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