Problems with models assessing influences of tree size and inter-tree competitive processes on individual tree growth: a cautionary tale

In forest growing at any one site, the growth rate of an individual tree is determined principally by its size, which reflects its metabolic capacity, and by competition from neighboring trees. Competitive effects of a tree may be proportional to its size; such competition is termed ‘symmetric’ and generally involves competition below ground for nutrients and water from the soil. Competition may also be ‘asymmetric’, where its effects are disproportionate to the size of the tree; this generally involves competition above ground for sunlight, when larger trees shade smaller, but the reverse cannot occur. This work examines three model systems often seen as exemplars relating individual tree growth rates to tree size and both competitive processes. Data of tree stem basal area growth rates in plots of even-aged, monoculture forest of blackbutt (Eucalyptus pilularis Smith) growing in sub-tropical eastern Australia were used to test these systems. It was found that none could distinguish between size and competitive effects at any time in any one stand and, thus, allow quantification of the contribution of each to explaining tree growth rates. They were prevented from doing so both by collinearity between the terms used to describe each of the effects and technical problems involved in the use of nonlinear least-squares regression to fit the models to any one data set. It is concluded that quite new approaches need to be devised if the effects on tree growth of tree size and competitive processes are to be quantified and modelled successfully.

Managing Fuels, Tree, and Stand Growth Using Prescribed Fire and Alternatives in Young Mixed Conifer Stands

Background In the wake of increasingly frequent and severe wildfires in California, artificial regeneration and density management facilitate prompt reforestation and the rapid growth of large, fire-resistant trees. Young plantations are particularly prone to high-severity wildfire effects, suggesting the implementation of fuel reduction treatments in the early stages of stand development. The extent to which density management (i.e., thinning) and fuels management (i.e., prescribed fire) can work together is uncertain given their potentially conflicting effects on tree and stand level growth. We investigated how four different treatments – mastication, mastication plus herbicide, two prescribed burns, and mastication plus two burns – affected individual and stand-level growth versus fuel loads in mixed-conifer plantations during young stand development in the north-central Sierra Nevada, California, USA. Results The mastication plus herbicide treatment maximized individual tree growth, especially for white fir and incense-cedar, but fuel loads doubled after five years without the use of fire. The mastication only treatment resulted in a 151% increase in fuel loads over the same period, and individual tree growth was comparable to the burn only and mastication plus burn treatments. The burn only treatment greatly decreased fuel loads but also resulted in low relative stand growth. The mastication plus burn treatment prevented fuel accumulation and generally did not slow down individual tree growth. In addition, stand growth occurred at a rate similar to that of the mastication plus herbicide treatment. Conclusions Mastication followed by repeated prescribed burning could be a viable management strategy to reduce wildfire hazard without sacrificing growth in young mixed-conifer stands that are entering a vulnerable stage of fire risk. Mastication in combination with herbicide may grow trees to a large, fire-resistant size more quickly, but does not address fuel buildup. The use of fire alone can effectively reduce fuels while not substantially impacting individual tree growth, but stand growth may decline relative to mastication and herbicide.

Comparison of Spatially and Nonspatially Explicit Nonlinear Mixed Effects Models for Norway Spruce Individual Tree Growth under Single-Tree Selection

Background and Objectives: Continuous cover forestry is of increasing importance, but operational forest growth models are still lacking. The debate is especially open if more complex spatial approaches would provide a worthwhile increase in accuracy. Our objective was to compare a nonspatial versus a spatial approach for individual Norway spruce tree growth models under single-tree selection cutting. Materials and Methods: We calibrated nonlinear mixed models using data from a long-term experiment in Finland (20 stands with 3538 individual trees for 10,238 growth measurements). We compared the use of nonspatial versus spatial predictors to describe the competitive pressure and its release after cutting. The models were compared in terms of Akaike Information Criteria (AIC), root mean square error (RMSE), and mean absolute bias (MAB), both with the training data and after cross-validation with a leave-one-out method at stand level. Results: Even though the spatial model had a lower AIC than the nonspatial model, RMSE and MAB of the two models were similar. Both models tended to underpredict growth for the highest observed values when the tree-level random effects were not used. After cross-validation, the aggregated predictions at stand level well represented the observations in both models. For most of the predictors, the use of values based on trees’ height rather than trees’ diameter improved the fit. After single-tree selection cutting, trees had a growth boost both in the first and second five-year period after cutting, however, with different predicted intensity in the two models. Conclusions: Under the research framework here considered, the spatial modeling approach was not more accurate than the nonspatial one. Regarding the single-tree selection cutting, an intervention regime spaced no more than 15 years apart seems necessary to sustain the individual tree growth. However, the model’s fixed effect parts were not able to capture the high growth of the few fastest-growing trees, and a proper estimation of site potential is needed for uneven-aged stands.

Development of Individual Tree Growth and Yield Model Across Multiple Contrasting Species Using Non-parametric and Parametric Methods in the Hyrcanian Forests of Northern Iran

BackgroundThe Hyrcanian forests of Iran contain many species-rich communities that can only be maintained through an understanding of the renewal and development of these forests. Located in the Jojadeh section of the Farim forest in northern Iran, individual tree growth of five distinct species [(Oriental beech (Fagus orientalis Lipsky), chestnut-leaved oak (Quercus castaneifolia Coss. ex J.Gay), Persian maple (Acer velutinum Boiss.), common hornbeam (Carpinus betulus L.) and Caucasian alder (Alnus subcordata C.A.Mey.)] were measured on 313 permanent sample plots (0.1 ha) over a 10-year period (2003-2013). MethodsIn this analysis, various tree-level predictions were investigated using the available data with application of parametric models and two artificial neural networks (i.e., the multilayer perceptron (MLP) and radial basis function (RBF) networks). ResultsIndividual tree diameter growth models showed a robust negative relationship with basal area in larger trees (BAL), which was relatively consistent across species. A total height model indicated that the examined species did not differ for a given set of covariates. In the survival model, the survival probability of Oriental beech was lower than the other species, while the ingrowth model revealed sapling density of all species increased with the greater basal area. The artificial neural network based on the MLP was superior for all models and predicted more accurately than the RBF. Furthermore, the models based on the MLP were also superior to the parametric individual tree models developed using mixed-effect regression. ConclusionThe use of these developed models in forest planning and management is imperative, but assessment of long-term projection behavior across the contrasting statistical approaches used is warranted despite the general superiority of the non-parametric models.