A new paradigm in modelling the evolution of a stand via the distribution of tree sizes

Rupšys, Petras; Petrauskas, Edmundas

doi:10.1038/s41598-017-16100-2

Cited by 15 publications

(11 citation statements)

References 26 publications

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“…The slenderness coefficient is an important characteristic for indexing tree resistance to wind throw and snow damage [20]. The evolution of the tree crown structure is affected by random processes that govern crown movements [21].…”

Section: Slendernessmentioning

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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Section: Slendernessmentioning

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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“…Fundamental SDE theory is defined on random variables. The universality of random processes accounts for the wide range of applications of the theory, including human population [2], forestry [3,4], biology [5], and epidemiology [6]. In biological systems, SDEs are used in place of deterministic models, obtained by including a noise term in the ordinary differential equation of the respective deterministic model [7].…”

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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“…More recently, mixed effects univariate SDE models have provided the means to quantify and distinguish additional sources of variability in an observed dataset [26]. In addition to the inter-individual variability, multivariate SDE models also consider the covariance structure between size components [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Modeling Dynamics of Structural Components of Forest Stands Based on Trivariate Stochastic Differential Equation

Rupšys

2019

Forests

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Research Highlights: Today’s approaches to modeling of forest stands are in most cases based on that the regression models and they are constructed as static sub-models describing individual stands variables. The disadvantages of this method; it is laborious because too many different equations need to be assessed and empirical choices of candidate equations make the results subjective; it does not relate to the stand variables dynamics against the age dimension (time); and does not consider the underlying covariance structure driving changes in the stand variables. In this study, the dynamical model defined by a fixed-and mixed effect parameters trivariate stochastic differential equation (SDE) is introduced and described how such a model can be used to model quadratic mean diameter, mean height, number of trees per hectare, self-thinning line, stand basal area, stand volume per hectare and much more. Background and Objectives: New developed marginal and conditional trivariate probability density functions, combining information generated from an age-dependent variance-covariance matrix of quadratic mean diameter, mean height and number of trees per hectare, improve stand growth prediction, and forecast (in forecast the future is completely unavailable and must only be estimated from historical patterns) accuracies. Materials and Methods: Fixed-and mixed effect parameters SDE models were harmonized to predict and forecast the dynamics of quadratic mean diameter, mean height, number of trees per hectare, basal area, stand volume per hectare, and their current and mean increments. The results and experience from applying the SDE concepts and techniques in an extensive whole stand growth and yield analysis are described using a Scots pine (Pinus sylvestris L.) experimental dataset in Lithuania. Results: The mixed effects scenario SDE model showed high accuracy, the percentage root mean square error values for quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare predictions (forecasts) were 3.37% (10.44%), 1.82% (2.07%), 1.76% (2.93%), 6.65% (10.41%) and 6.50% (8.93%), respectively. In the same way, the quadratic mean diameter, mean height, number of trees per hectare, stand basal area and stand volume per hectare prediction (forecast) relationships had high values of the coefficient of determination, R2, 0.998 (0.987), 0.997 (0.992), 0.997 (0.988), 0.968 (0.984) and 0.966 (0.980), respectively. Conclusions: The approach presented in this paper can be used for developing a new generation stand growth and yield models.

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A new paradigm in modelling the evolution of a stand via the distribution of tree sizes

Cited by 15 publications

References 26 publications

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

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

Stochastic Models to Qualify Stem Tapers

Modeling Dynamics of Structural Components of Forest Stands Based on Trivariate Stochastic Differential Equation

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