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

Abstract

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.

OUP accepted manuscript

“…The model references that do exist also often have an empirical/statistical approach and do not express a clear intention to strive towards simplicity and few predictors. The distance-dependent model presented by Bianchi et al 2020b) serves as the most relevant reference, although it is a statistical model that depends on 10 predictor variables. They presented a lower RMSE from cross-validation (3.21 cm).…”

“…Regarding the few existing distance-dependent models, some rely on tree age as predictor Vettenranta 1999) and others are calibrated exclusively on even-sized stands (Pukkala 1989;Tham 1989;Pukkala and Kolström 1991;Pukkala et al 1994). An exception is Bianchi et al 2020b) who presented a distancedependent model for southern Finland and ITS. This model has a statistical polynomial structure, which makes it relatively complex in terms of number of predictor variables.…”

Individual-tree-selection in uneven-sized Norway spruce stands in southern Sweden: Developments of tools for simulation and optimization

“…The growth boost for individual trees in individual tree selection (Norway spruce) has been shown to be proportional to the intensity of release of the residual tree (Bianchi et al 2020b). This effect ceases at intensities above 50 % (Bianchi et al 2020a).…”

“…When the literature search includes tree-level growth models also from Norway and Finland, the list of models is extended with another 15 examples, of which at least six have been calibrated on uneven-sized stands (Andreassen and Tomter 2003, Pukkala et al 2009, Pukkala et al 2013, Bianchi et al 2020a, Bianchi et al 2020b, Pukkala et al 2021. However, none of these can be expected to cover growing conditions of southern Sweden.…”