• Key message
Parametric indirect models derived from stem analysis of dominant trees were more robust than rule-based machine learning techniques for predicting Site Index of Scots pine stands as a ...function of climate.
• Context
The uncertainties derived from climate change make it necessary to develop new methods for representing the relationships between site conditions and forest growth.
• Aims
To compare parametric vs nonparametric approaches for modeling site index (
SI
) of Scots pine stands using bioclimatic variables.
• Methods
We used Random Forest, Boosted Trees, and Cubist techniques for directly predicting the
SI
of 41 research plots of Scots pine stands, and six parametric models for indirectly predicting
SI
using stem analysis data. As predictors, we used raster maps of 19 bioclimatic variables.
• Results
The fitted models explained up to
∼
80% of the
SI
variability, using from five to nine bioclimatic predictors. Though the apparent performance of the parametric models was lower than the rule-based, their bootstrap validation statistics were noticeably higher.
• Conclusion
Parametric indirect models seemed to be the most robust modeling alternative.
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•We combined a State-Space model with a Stand Density Management Diagram (SDMD).•Stand specificities are captured by local-model parameters in distinct dynamic SDMDs.•Tree-size ...distributions are estimated from mean and cumulative stand variables.•Dynamic Structural SDMD is applicable for state prediction and growth projection.•Management alternatives can be optimized for any particular stand using its DSSDMD.
A forest stand model that is able to account for individual stand characteristics and uses this information for state prediction, growth and yield projection and for management decisions at individual-stand level can be expected to possess the best properties and be of the highest utility. The aim of our study was to combine the advantages of the graphically presented whole-stand models called Stand Density Management Diagrams (SDMDs) with those of the state-space models to develop an improved, stand-specific density management model and to examine its performance with data from even-aged natural stands and plantations.
A dynamic, structural Stand Density Management Diagram (DSSDMD) consisting of a whole-stand model and distribution sub-models was developed. The whole-stand model is composed of a state vector and transition functions and is presented diagrammatically by four sets of isolines on a density-total volume/biomass chart. The state, developmental scenarios and thinning schedules of any stand are simulated on its individual DSSDMD and are characterized by three principal local model parameters, two of which are stand-specific and the third is common to a range of stands of the species under the same environmental conditions.
Dynamic Structural Stand Density Management Diagrams (DSSDMDs) were constructed for plantations of two pine species (Pinus radiata D. Don and P. sylvestris L.) and for natural even-aged stands of Quercus robur L. and Betula pubescens Ehrh. The goodness-of-fit tests revealed that, in most cases, regression equations explained more than 95% of the variation in the modelled variable and yielded a Root Mean Square Error <15% and bias <2% from the mean experimental variable values. When used for predicting or projecting total stand volume or biomass, the models performed acceptably well, in terms of the critical error estimate, within the observed range of ages and projection intervals. Management alternatives, according to specified objective, can be optimized for any particular stand using its DSSDMD, and the model can be incorporated into a simulator to ensure its most efficient usage.
A generalized height–diameter model was developed for
Eucalyptus globulus Labill. stands in Galicia (northwestern Spain). The study involved a variety of pure stands ranging from even-aged to ...uneven-aged. Data were obtained from permanent circular sample plots in which trees were sampled within different radii according to their diameter at breast height. A combination of weighted regression, to take into account the unequal selection probabilities of such an inventory design, and mixed model techniques, to accommodate local random fluctuations in the height–diameter relationship, were applied to estimate fixed and random parameters for several models reported in the relevant literature. The models that provided the best results included dominant height and dominant diameter as fixed effects. These models explained more than 83% of the observed variability, with mean errors of less than 2.5
m. Random parameters for particular plots were estimated with different tree selection options. Height–diameter relationships tailored to individual plots can be obtained by calibration of the height measurements of the three smallest trees in a plot. An independent dataset was used to test the performance of the model with data not used in the fitting process, and to demonstrate the advantages of calibrating the mixed-effects model.
•Climate change - anthropogenic origin interaction modifies site productivity model.•Gompertz function - based polymorphic model of multiple asymptotes was derived.•Random model parameter was best ...localized at stand level.•Site illumination level and heat-moisture index were relevant geocentric predictors.•Model parameterized with 20th century data was validated with 21st century subset.
The consequences of climate change on forest growth can be exacerbated for the forest ecosystems of anthropogenic origin, especially for the populations at the margins of the species range. The productivity-environment relationships are a methodological approach for modeling growth at whole-stand level, which although empirical is applicable under changing climatic conditions. Some peculiarities of the Scots pine plantations in Bulgaria, and namely a distribution range spreading outside the species areal and high stocking rates, made it challenging to derive an adequate productivity-environment model for this type of stands, which was the main objective of our study.
Dynamic phytocentric model, based on the function by Gompertz and fitted in a generalized algebraic difference equation form was derived at the first step of the analyses. The model is polymorphic, with variable, well-differentiated among the site quality classes asymptotes, a reflection of the large variety of sites of different carrying capacity where the man-made stands of Scots pine are grown in Bulgaria. Two classifications of the Scots pine plantations, based on assessment of stand fit to its environment, were tested to specify the site quality model at a lower hierarchical level. The random parameter component was better localized at stand level, rather than at ecosystem fit category or stand-within-ecosystem fit category level and three groups of environmental factors, were examined to calibrate the mixed-effects model parameter. The most adequate climate-sensitive dynamic growth model considered the level of site illumination and the annual heat-moisture index as geocentric predictors. In order to assess how successfully the derived site-productivity relationship makes realistic prediction of the species productivity levels under the changing climate, the data were divided into 20th and 21st century subsets for validation. The validation statistics revealed unbiased estimates of small relative error magnitude, with the predictions being more adequate when the 20th century data were used for parameterization.
Stem taper data are usually hierarchical (several measurements per tree, and several trees per plot), making application of a multilevel mixed-effects modelling approach essential. However, ...correlation between trees in the same plot/stand has often been ignored in previous studies. Fitting and calibration of a variable-exponent stem taper function were conducted using data from 420 trees felled in even-aged maritime pine (Pinus pinaster Ait.) stands in NW Spain. In the fitting step, the tree level explained much more variability than the plot level, and therefore calibration at plot level was omitted. Several stem heights were evaluated for measurement of the additional diameter needed for calibration at tree level. Calibration with an additional diameter measured at between 40 and 60% of total tree height showed the greatest improvement in volume and diameter predictions. If additional diameter measurement is not available, the fixed-effects model fitted by the ordinary least squares technique should be used. Finally, we also evaluated how the expansion of parameters with random effects affects the stem taper prediction, as we consider this a key question when applying the mixed-effects modelling approach to taper equations. The results showed that correlation between random effects should be taken into account when assessing the influence of random effects in stem taper prediction.
This paper presents a model for optimizing the management of single-species, even-aged stands. The model comprises a number of state variables, given by functions initially differentiable with ...respect to time, which cease to be due to the discontinuities that cause instant silvicultural treatments. Nevertheless, the proposed model maintains its differentiability with respect to the decision variables (timing, type, and intensity of each thinning, and rotation age). This allows for formulation of the problem of optimal management of this type of stands as a linearly constrained smooth optimization problem, which can be efficiently solved by any derivative-based optimization method. The effectiveness of this formulation is shown by using a sequential quadratic programming (SQP) algorithm to design the optimal management of Pinus pinaster Ait. in Asturias (northwestern Spain) from an economic perspective. These results are compared with those obtained using two methods that do not require derivatives. The SQP, as representative of gradient-type methods, proved robust and much more efficient than the derivative-free methods.
In this study we present several multi-objective models for forest harvest scheduling in forest with single-species, even-aged stands using a continuous formulation. We seek to maximize economic ...profitability and even-flow of timber harvest volume, both for the first rotation and for the regulated forest. For that, we design new metrics that allow working with continuous decision variables, namely, the harvest time of each stand. Unlike traditional combinatorial formulations, this avoids dividing the planning horizon into periods and simulating alternative management prescriptions before the optimization process. We propose to combine a scalarization technique (weighting method) with a gradient-type algorithm (L-BFGS-B) to obtain the Pareto frontier of the problem, which graphically shows the relationships (trade-offs) between objectives, and helps the decision makers to choose a suitable weighting for each objective. We compare this approach with the widely used in forestry multi-objective evolutionary algorithm NSGA-II. We analyze the model in a Eucalyptus globulus Labill. forest of Galicia (NW Spain). The continuous formulation proves robust in forests with different structures and provides better results than the traditional combinatorial approach. For problem solving, our proposal shows a clear advantage over the evolutionary algorithm in terms of computational time (efficiency), being of the order of 65 times faster for both continuous and discrete formulations.
•A new metric for measuring forest regulation using continuous decision variables is designed.•Continuous multi-objective models for forest harvest scheduling are formulated.•A scalarization technique plus a gradient-type method is used to obtain the Pareto frontier.•An intuitive graphical tool for forest decision making is proposed.
Maritime pine (Pinus pinaster Ait.) is one of the most important timber species in Asturias and more generally in northwest Spain. A dynamic growth model has recently been developed for this species ...and region, allowing computation of the merchantable volume by two alternative methods: a disaggregation system and a stand volume ratio function. The model enables optimization of the management schedule for the species by modifying the rotation age and the number, intensity, and timing of thinning operations. The two methods of volume estimation were compared in optimization by using the depth-first search (DFS) method, and both were found to provide similar results. Because the stand volume ratio function is computationally much more efficient, it was used in the next step, in which five direct search methods were tested: Hooke and Jeeves method (HJ); differential evolution (DE); particle swarm optimization (PS); evolution strategy (ES); Nelder and Mead method (NM); the last four are population-based methods. The HJ and DE methods yielded the highest values of the objective function, slightly outperforming the results of DFS in most cases, which proved to be about 100 times slower than HJ and 30 times slower than DE. DE was more stable than HJ (standard deviation was â¬30.6·haâ»Â¹ for HJ and â¬8.8·haâ»Â¹ for DE) and was therefore used for subsequent evaluation of the effects of site quality, stem density, and discount rate on the optimal management schedule. Rotation age and timing of thinnings both decreased as site quality and discount rate increased. The optimal management schedules often included three heavy thinning operations. The pseudo-code of the optimization methods tested is provided in an Appendix.
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•We modelled the natural thinning process with a system of three dynamic equations.•It comprises a density decrease model and two dynamic size-density models.•Model systems were ...tested with data from even-aged natural stands and plantations.•Polymorphic curves with multiple asymptotes describe stand self-thinning and growth.•Model incorporation into dynamic Stand Density Management Diagram is envisaged.
Our investigation aims (1) to derive a dynamic model for mean volume and biomass growth projection over time, considering the competition-induced tree mortality (dynamic size-density model), (2) to design a compatible two-component modelling system composed of the dynamic size-density model and an appropriate density decrease function, and (3) to examine the applicability of this composite natural thinning model to describe the growth dynamics of even-aged coniferous and broadleaved stands.
The stand growth projection system was formulated to include three dynamic equations: a density decrease model expressing the reduction in tree number with dominant height growth, and two dynamic size-density models, for mean stem volume and tree biomass respectively. Two size-density formulations (M1 and M2) were derived, each including one local (site- or stand-specific) and three global (common to all stands of the species) parameters. Model M1 suggests a polymorphic set of size-density curves, while model M2 describes size-density curves with variable asymptotes. The goodness-of-fit statistics showed that for radiata pine (Pinus radiata D. Don) and Scots pine (Pinussylvestris L.) datasets the three-model-system based on M1 performed better than the one based on M2. The growth trajectories of downy birch (Betula pubescens Ehrh.) and English oak (Quercus robur L.) stands were described only by model M2. The systems of projection equations explained more than 95% of the variation in most cases.
The two-component modelling system is implicitly defined by the stand density and mean tree size (biomass and/or volume) values for a given dominant stand height and set of global model parameters; it does not require any additional stand variables, constants of contested universality or standard-base variable values. It uses stand dominant height as a proxy for time, and inclusion of this growth stage indicator enables the bidirectional dependence between stand density and tree size to be reflected. The composite natural thinning model estimates sets of polymorphic curves with multiple asymptotes. Together with the stand-specific rate of density decrease, this also yields the stand-specific rate of size increase over time and the reduction in tree number, thus enabling prediction of contrasting individual growth patterns of stands of similar initial densities. It accounts for the isometric relationship between plant volume and biomass and can be considered for incorporation as a principal component of a dynamic Stand Density Management Diagram.
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