A dynamic whole-stand growth model, derived from allometric relationships

Abstract

A dynamic whole-stand growth model, derived from allometric relationships Stankova T.V. (2016). A dynamic whole-stand growth model, derived from allometric relationships. Silva Fennica vol. 50 no. 1 article id 1406. 21 p. Highlights• A dynamic whole-stand model was derived from simple allometries and biological rationale.• The state-space modelling approach was applied, suggesting several novelties to overcome scarcity of longitudinal data.• The model consists of a three-dimensional state vector, defined by dominant stand height, stand density and mean stem volume, and three transition functions.• It was tested with data from Scots pine plantations. AbstractGrowth and yield tables are constrained by a standard production regime and the stand-level dynamic models are an attractive alternative for the even-aged monospecific stands. The objective of this study is to derive a parsimonious and biologically sound whole-stand dynamic growth model and to validate its consistency and relevance for prediction of stand growth and yield. The state-space modelling approach was employed, introducing several novelties in comparison with its current usage. The model consists of a three-dimensional state vector, defined by dominant stand height, number of trees per hectare and mean stem volume, and three transition functions. A site index model was incorporated for height growth projection and transition functions for stand density and mean stem volume with respect to dominant height increase were derived from simple allometries and biological rationale. The model was examined with data from 79 permanent sample plots in Scots pine plantations. Nonlinear Seemingly Unrelated Regression was used to account for cross-equation correlations, and the Base-Height-Invariant dummy variable method was employed to estimate dynamic-form equations. Model consistency was validated in terms of accuracy of predictions and applicability to both thinned and unthinned stands. The new dynamic growth model is a parsimonious biometric whole-stand model that simulates the expected stand development for a broad spectrum of potential management alternatives and can be incorporated in a computer program for further use. It may be especially useful for application when a scarcity of longitudinal data prevents the use of more complicated modelling approaches.

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

“…For Pinus radiata D. Don plantations in Galicia [9] explained 99.3% of the total variance. For the new developed mixed effects scenario stand density models the predictive ability accessed by statistical indexes such as the mean prediction bias (percentage), 0.352 (−0.06%), the root mean squared error of predictions (percentage), 45.173 (3.36%), the mean absolute prediction bias (percentage), 32.305 (3.32%), exceeds the results in previous studies [45].…”

“…(M2) mixed effects scenario for the second stand; (M3) mixed effects scenario for the third stand; (F) fixed effects scenario for all stands; black solid line-stand volume prediction curve; black dot line-stand volume forecast curve; black circles-estimation dataset, red circles-validation (forecast) dataset. According to the results presented by Stankova [45] for Scots pine stands, the best performing stand volume prediction model achieved prediction bias, −0.480 m 3 ha −1 (-1.89%), the root mean squared prediction error, 41.81 m 3 ha −1 , and the coefficient of determination, 0.919. The Growfor (GF) dynamic empirical stand-level model based on the state-space framework [54] used to model stand volume of Sitka spruce (lodgepole) pine attained the relative mean prediction bias, −0.01-16.91% (−2.65-10.60%), the relative root mean squared error, 14.32-23.91% (14.33-29.13%), and the coefficient of determination, 0.62-0.92 (0.59-0.86).…”

“…For the fixed effects scenario, all forecast relationships attained lower values of statistical indexes and p-values of tests than the mixed effects scenario models (compare Table 2; Table 3). For Scots pine stands the number of trees per hectare dynamic over dominant height was examined by Stankova (2016) [45] and attained the bias value −11.0 (−0.37%), the root mean square error value 403 and the coefficient of determination value 0.948. The transition functions method for the stand density predictions, using dataset from teak forests in southern India [46], produced coefficient of determination, 0.985, and root mean square error, 43.15.…”

Deriving a tree growth model from any existing stand growth model

“…Whole-stand models are relatively simple models that provide information for the entire stand. The predicted stand attributes can be stand survival (Zhang et al 1993, Diéguez-Aranda et al 2005, Tewari et al 2014, Stankova 2016, basal area per unit area (Cao and Durand 1991, Barrio Anta et al 2006, Naing 2020, or both (Somers and Farrar 1991, Erikäinen 2002, Garcia 2011, Dean et al 2013.…”

Predicting future diameter distributions given current stand attributes

“…Whole-stand models are the simplest type of models that provide information for the entire stand. The outputs can be stand survival (Zhang et al 1993, Diéguez-Aranda et al 2005, Tewari et al 2014, Stankova 2016, basal area per unit area (Cao and Durand 1991, Barrio Anta et al 2006, Naing 2020, or both stand survival and basal area (Somers and Farrar 1991, Erikäinen 2002, Garcia 2011, Dean et al 2013.…”