Development of a Mixed-Effects Individual-Tree Basal Area Increment Model for Oaks (Quercus spp.) Considering Forest Structural Diversity

Developing the Additive Systems of Stand Basal Area Model for Broad-Leaved Mixed Forests

Stand basal area (SBA) is an important variable in the prediction of forest growth and harvest yield. However, achieving the additivity of SBA models for multiple tree species in the complex structure of broad-leaved mixed forests is an urgent scientific issue in the study of accurately predicting the SBA of mixed forests. This study used data from 58 sample plots (30 m × 30 m) for Populus davidiana × Betula platyphylla broad-leaved mixed forests to construct the SBA basic model based on nonlinear least squares regression (NLS). Adjustment in proportion (AP) and nonlinear seemingly unrelated regression (NSUR) were used to construct a multi-species additive basal area prediction model. The results identified the Richards model (M6) and Korf model (M1) as optimal for predicting the SBA of P. davidiana and B. platyphylla, respectively. The SBA models incorporate site quality, stand density index, and age at 1.3 m above ground level, which improves the prediction accuracy of basal area. Compared to AP, NSUR is an effective method for addressing the additivity of basal area in multi-species mixed forests. The results of this study can provide a scientific basis for optimizing stand structure and accurately predicting SBA in multi-species mixed forests.

Estimating the self-thinning boundary line for oak mixed forests in central China by using stochastic frontier analysis and a proposed variable density model

A suitable self-thinning model is fundamental to effective density control and management. Using data from 265 plot measurements in oak mixed forests in central China, we demonstrated how to estimate a suitable self-thinning line for oak mixed forests from three aspects, i.e., self-thinning models (Reineke's model and the variable density model), statistical methods (quantile regression and stochastic frontier analysis), and the variables affecting stands (topography and stand structure factors). The proposed variable density model, which is based on the quadratic mean diameter and dominant height, exhibited a better goodness of fit and biological relevance than Reineke's model for modeling the self-thinning line for mixed oak forests. In addition, the normal-truncated normal stochastic frontier model was superior to quantile regression for modeling the self-thinning line. The altitude, Simpson index, and dominant height-diameter ratio (H d /D) also had significant effects on the density of mixed forests. Overall, a variable density self-thinning model may be constructed using stochastic frontier analysis for oak mixed forests while considering the effects of site quality and stand structure on density. The findings may contribute to a more accurate density management map for mixed forests.

Machine Learning for the Estimation of Diameter Increment in Mixed and Uneven-Aged Forests

Estimating the diameter increment of forests is one of the most important relationships in forest management and planning. The aim of this study was to provide insight into the application of two machine learning methods, i.e., the multilayer perceptron artificial neural network (MLP) and adaptive neuro-fuzzy inference system (ANFIS), for developing diameter increment models for the Hyrcanian forests. For this purpose, the diameters at breast height (DBH) of seven tree species were recorded during two inventory periods. The trees were divided into four broad species groups, including beech (Fagus orientalis), chestnut-leaved oak (Quercus castaneifolia), hornbeam (Carpinus betulus), and other species. For each group, a separate model was developed. The k-fold strategy was used to evaluate these models. The Pearson correlation coefficient (r), coefficient of determination (R2), root mean square error (RMSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) were utilized to evaluate the models. RMSE and R2 of the MLP and ANFIS models were estimated for the four groups of beech ((1.61 and 0.23) and (1.57 and 0.26)), hornbeam ((1.42 and 0.13) and (1.49 and 0.10)), chestnut-leaved oak ((1.55 and 0.28) and (1.47 and 0.39)), and other species ((1.44 and 0.32) and (1.5 and 0.24)), respectively. Despite the low coefficient of determination, the correlation test in both techniques was significant at a 0.01 level for all four groups. In this study, we also determined optimal network parameters such as number of nodes of one or multiple hidden layers and the type of membership functions for modeling the diameter increment in the Hyrcanian forests. Comparison of the results of the two techniques showed that for the groups of beech and chestnut-leaved oak, the ANFIS technique performed better and that the modeling techniques have a deep relationship with the nature of the tree species.

Temporal Dynamics of Root Reinforcement in European Spruce Forests

The quantification of post-disturbance root reinforcement (RR) recovery dynamics is of paramount importance for the optimisation of forest ecosystem services and natural hazards risk management in mountain regions. In this work we analyse the long-term root reinforcement dynamic of spruce forests combining data of the Swiss National Forest Inventory with data on root distribution and root mechanical properties. The results show that root reinforcement recovery depends primarily on stand altitude and slope inclination. The maximum root reinforcement recovery rate is reached at circa 100 years. RR increases continuously with different rates for stand ages over 200 years. These results shows that RR in spruce stands varies considerably depending on the local conditions and that its recovery after disturbances requires decades. The new method applied in this study allowed for the first time to quantify the long term dynamics of RR in spruce stands supporting new quantitative approaches for the analysis of shallow landslides disposition in different disturbance regimes of forests.

Individual tree basal area increment model for sessile oak (Quercus petraea (Matt.) Liebl.) in coppice-originated stands

In this study, the basal area increment models were developed to be both age dependent and independent with a stepwise multiple regression analysis for coppice-originated pure sessile oak stands in the Marmara region, which is located in north-western Turkey. Data was obtained from a total of 73 sample trees, which were sampled from coppice-originated pure sessile oak stands over different growth periods and in different site conditions. The most suitable competition variable was determined by examining the correlations between the 24 competition index values and calculated using different approaches and the basal area increment. The individual tree basal area increment models were obtained as functions of tree size, competition, age, and site characteristics. The most important variables that affect the basal area increment in the age-dependent model were the diameter at breast height (DBH) (36.1%), competition index (26.4%), and age (10%). For the age-independent model, the variables are the competition index (32.6%), DBH (30.3%), and the site index (3%), according to the relative importance values. The age-dependent model explained the increased variation of 10% and predicted a 13% decrease in error in the basal area increment than the age-independent model.

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 Crown Ratio and Height to Crown Base Models for Masson Pine in Southern China

Crown ratio (CR) and height to crown base (HCB) are important crown characteristics influencing the behavior of forest canopy fires. However, the labor-intensive and costly measurement of CR and HCB have hindered their wide application to forest fire management. Here, we use 301 sample trees collected in 11 provinces in China to produce predictive models of CR and HCB for Masson pine forests (Pinus massoniana Lamb.), which are vulnerable to forest canopy fires. We first identified the best basic model that used only diameter at breast height (DBH) and height (H) as independent variables to predict CR and HCB, respectively, from 11 of the most used potential candidate models. Second, we introduced other covariates into the best basic model of CR and HCB and developed the final CR and HCB predictive models after evaluating the model performance of different combinations of covariates. The results showed that the Richards form of the candidate models performed best in predicting CR and HCB. The final CR model included DBH, H, DBH0.5 and height-to-diameter ratio (HDR), while the final HCB model was the best basic model (i.e., it did not contain any other covariates). We hope that our CR and HCB predictive models contribute to the forest crown fire management of Masson pine forests.

Pollen Production of Quercus in the North-Western Iberian Peninsula and Airborne Pollen Concentration Trends during the Last 27 Years

Natural forests are considered a reservoir of great biological diversity constituting one of the most important ecosystems in Europe. Quercus study is essential to assess ecological conservation of forests, and also of economic importance for different industries. In addition, oak pollen can cause high sensitization rates of respiratory allergies in pollen-allergy sufferers. This study sought to know the pollen production of six oak species in the transitional area between the Eurosiberian and Mediterranean Bioclimatic Regions, and to assess the impact of climate change on airborne oak pollen concentrations. The study was conducted in Ourense (NW Spain) over the 1993–2019 period. A Lanzoni VPPS 2000 volumetric trap monitored airborne pollen. A pollen production study was carried out in ten trees randomly selected in several Quercus forest around the Ourense city. Oak pollen represented around 14% of annual total pollen registered in the atmosphere of Ourense, showing an increasing trend during the last decade. Pollen production of the six studied oak species follow the proportions 1:1:2:5:90:276 for Q. ilex, Q. faginea, Q. rubra, Q. suber, Q. pyrenaica, and Q. robur respectively. We detected a significant trend to the increase of the annual maximum temperature, whereas a decrease of the maximum and mean temperatures during three previous months to oak flowering. This could be related with the detected trend to a delay of the oak Main Pollen Season onset of 0.47 days per year. We also found significant trends to an increase of the annual pollen integral of 7.9% pollen grains per year, and the pollen peak concentration of 7.5% pollen grains per year. Quercus airborne pollen monitoring as well as the knowledge of the reproductive behavior of the main oak species, bring us an important support tool offering a promising bio-indicator to detect ecological variations induced by climate change.

Evaluation of Different Calibration Approaches for Merchantable Volume Predictions of Norway Spruce Using Nonlinear Mixed Effects Model

Research Highlights: Determination of merchantable wood volume is one of the key preconditions for sustainable forest management. This study explores accuracy of calibrated predictions of merchantable wood volume of Norway spruce (Picea abies (L.) H. Karst.) using stem taper curves (STC) in a form of a mixed model. Background and Objectives: The study is devoted to the determination of merchantable wood volume (over bark) of individual standing stems based on the integration of an STC model calibrated using upper diameter measurements. Various options of upper diameter measurement were tested and their impact on the accuracy of merchantable wood volume prediction was evaluated. Materials and Methods: To model stem taper curves, a Kozak 02 function was applied in a form of a nonlinear, mixed effects model. Accuracies of calibrated merchantable wood volume predictions obtained through remote (optical) upper diameter measurements were compared to accuracies corresponding to contact measurements by a caliper. The performance of two alternative methods used in the Czech National Forest Inventory (NFI) and forestry practice, involving diameter at breast height and total tree height as the only predictors, were also tested. The contact measurements were performed at identical stem positions after felling the respective sample tree. The calibration was done in order to account for factors inherent in particular location, and, optionally, also in a particular sample stem (within the respective location). Input data was sourced as part of a dedicated survey involving the entire territory of the Czech Republic. In total, 716 individual spruce trees were measured, felled and analysed at 169 locations. Results: In general, the best merchantable volume predictions were obtained by integrating the STC fitted (and calibrated) by minimising errors of stem cross-sectional areas instead of diameters. In terms of calibrated predictions, using single-directional, caliper measurement of upper diameter at 7 m (after felling) led to the best accuracy. In this case, the observed mean bias of merchantable volume prediction was only 0.63%, indicating underestimation. The best optical calibration strategy involved upper diameter measurements at two heights (5 and 7 m) simultaneously. Bias of this volume prediction approach was estimated at 2.1%, indicating underestimation. Conclusions: Concerning the prediction of merchantable stem volume of standing Norway spruce trees, STC calibration using two optical upper diameter measurements (at 5 and 7 m) was found to be practically applicable, provided a bias up to 3.7% can be accepted. This method was found to be more accurate than the existing national alternatives using diameter at breast height and the total tree height as the only predictors.