Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

Rupšys, Petras

doi:10.3390/math7080761

Cited by 13 publications

(17 citation statements)

References 47 publications

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“…However, the difficult challenge of forest growth and yield modeling is in tree species that differ from the idealized shape, size (diameter and height), age, and density. Previous SDE models have focused on bivariate (height and diameter) [12], trivariate (quadratic diameter, mean height, and density per hectare) [13], four-variate (height, diameter, crown base height, and crown width) [14][15][16], and five-variate (height, diameter, crown base height, crown width, and density per hectare) cases [17] for Scots pine trees in Lithuania. The main reason for developing SDE models is to gain the capacity to model highly nonlinear biological dynamics and their abnormalities [18].…”

Section: Introductionmentioning

confidence: 99%

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

2020

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This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are described by the mixed-effect parameters Vasicek, Gompertz, Bertalanffy, and the gamma-type bivariate stochastic differential equations (SDEs). The newly derived bivariate probability density function and its marginal univariate, as well as the conditional univariate function, can be applied for the modeling of population attributes such as the mean value, quantiles, and much more. The models presented here are the basis for further developments toward the tree diameter–height and height–diameter relationships for general purpose in forest management. The present study experimentally confirms the effectiveness of using bivariate SDEs to reconstruct diameter–height and height–diameter relationships by using measurements obtained from mountain pine tree (Pinus mugo Turra) species dataset in Lithuania.

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Section: Introductionmentioning

confidence: 99%

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

2020

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“…There is a general tendency in the population growth modeling literature to favor flexible techniques that represent features of multivariate data as well as possible [10,11]. Therefore, multivariate SDEs describing population growth models contain both the main effects and interaction effects involved in models using a variance-covariance matrix, improving the potential to interpret the data more informatively [12] and inferring the causality in a statistical sense as a type of dependence of the multivariate random variables [13].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Models to Qualify Stem Tapers

et al. 2020

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This study examines the performance of 11 tree taper models to predict the diameter of bark at any given height and the total stem volume of eight dominant tree species in the boreal forests of Lithuania. Here, we develop eight new models using stochastic differential equations (SDEs). The symmetrical Vasicek model and asymmetrical Gompertz model are used to describe tree taper evolution, as well as geometric-type diffusion processes. These models are compared with those traditionally used for four tree taper models by using performance statistics and residual analysis. The observed dataset consists of longitudinal measurements of 3703 trees, representing the eight dominant tree species in Lithuania (pine, spruce, oak, ash, birch, black alder, white alder, and aspen). Overall, the best goodness of fit statistics of diameter predictions produced the SDE taper models. All results have been implemented in the Maple computer algebra system using the "Statistics" and "VectorCalculus" packages.

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“…As a matter of fact, concrete choices of such exogenous factors lead to processes by which we may study patterns of behavior modeled by a wide range of growth curves (see Román-Román et al [6,7] and references therein). These references are related to the one-dimensional case, although there are extensions to multidimensionality such as the one proposed by Rupšys in [8], where a 4-variate Bertalanffy-type SDE is considered.…”

Section: Introductionmentioning

confidence: 99%

Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

2020

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Stochastic models based on deterministic ones play an important role in the description of growth phenomena. In particular, models showing oscillatory behavior are suitable for modeling phenomena in several application areas, among which the field of biomedicine stands out. The oscillabolastic growth curve is an example of such oscillatory models. In this work, two stochastic models based on diffusion processes related to the oscillabolastic curve are proposed. Each of them is the solution of a stochastic differential equation obtained by modifying, in a different way, the original ordinary differential equation giving rise to the curve. After obtaining the distributions of the processes, the problem of estimating the parameters is analyzed by means of the maximum likelihood method. Due to the parametric structure of the processes, the resulting systems of equations are quite complex and require numerical methods for their resolution. The problem of obtaining initial solutions is addressed and a strategy is established for this purpose. Finally, a simulation study is carried out.

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Understanding the Evolution of Tree Size Diversity within the Multivariate Nonsymmetrical Diffusion Process and Information Measures

Cited by 13 publications

References 47 publications

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

Stochastic Models to Qualify Stem Tapers

Two Stochastic Differential Equations for Modeling Oscillabolastic-Type Behavior

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