Multilevel Nonlinear Mixed-Effect Crown Ratio Models for Individual Trees of Mongolian Oak (Quercus mongolica) in Northeast China

Constructing two-level nonlinear mixed-effects crown width models for Moso bamboo in China

Bamboo crown width (CW) is a reliable index for evaluating growth, yield, health and vitality of bamboo, and light capture ability and carbon fixation efficiency of bamboo forests. Based on statistical results produced from fitting the eight basic growth functions using data from 1374 Phyllostachys pubescens in Yixing, Jiangsu Province, China, this study identified the most suitable function (logistic function) to construct a two-level mixed effects (NLME) CW model with the forest block and sample plot-level effects included as random effects in the model. Four methods for selecting sample bamboos per sample plot (largest bamboo, medium-sized bamboo, smallest bamboo, and randomly selected bamboos) and eight sample sizes (1-8 selected bamboos per sample plot) were evaluated to calibrate our NLME CW model. Using diameter at breast height (DBH), height to crown base (HCB), arithmetic mean diameter at breast height (MDBH), and height (H) as predictor variables, the model produced the best fit statistics (Max R², min RMSE, and TRE). This model was further improved by introducing random effects at two levels. The results showed a positive correlation of CW with HCB and DBH and a negative correlation with H. The smallest two bamboo poles per sample plot used to estimate the random effects of the NLME model provided a satisfactory compromise regarding measurement cost, model efficiency, and prediction accuracy. The presented NLME CW model may guide effective management and carbon estimation of bamboo forests.

Simultaneous Compatible System of Models of Height, Crown Length, and Height to Crown Base for Natural Secondary Forests of Northeast China

Individual trees are characterized by various sizes and forms, such as diameter at breast height, total height (H), height to crown base (HCB), crown length (CL), crown width, and crown and stem forms. Tree characteristics are strongly related to each other, and studying their relationships is very important. The knowledge of the compatibility and additivity properties of the major tree characteristics, such as H, CL, and HCB, is essential for informed decision-making in forestry. H can be used to represent site quality and CL represents biomass and photosynthesis of crown, which is the performance of individual tree vigor and light interception, and the longer the crown length (or shorter HCB) is, the more vigorous the tree would be. However, none of the studies have uncovered their inherent relationships quantitatively. This study attempts to explore such relationships through the application of appropriate modeling approaches. We applied seemingly unrelated regression, such as nonlinear seemingly unrelated regression (NSUR), which is commonly used for exploring the compatibility and additivity properties of the variables, for the proposes. The NSUR involves the variance and covariance matrices of the sub-models that are used for the interpretation of the correlations among the variables of interest. The data set acquired from Mongolian oak forest and spruce-fir forest in the Jingouling forest farm of the Wangqing Forest Bureau in the Northeast of China were used to construct two types of model systems: a compatible model system (the model system of H, CL, and HCB can be estimated simultaneously) and an additive model system (the sum of HCB and CL is H, the form of the H sub-model equals the sum of the HCB and CL sub-models) from the individual models of H, CL, and HCB. Among the various tree-level and stand-level variables evaluated, D (diameter at breast), Dg (quadratic mean diameter), DT (dominant diameter), CW (crown width), SDI (stand density index), and BAS (basal area of stand) contributed significantly highly to the variations of the response of the variables of interest in the model systems. Modeling results showed the existence of the compatibility and additivity of H, CL, and HCB simultaneously. The additive model system exhibited better fitting performance on H and HCB but poorer fitting on CL compared with the simultaneous model system, indicating that the performance of the additive model system could be higher than that of the simultaneous model system. Model tests against the validation data set also confirmed such results. This study contributes a novel approach to solving the compatibility and additivity of the problems of H, CL, and HCB models through the application of the robust estimating method, NSUR. The results and algorithm presented will be useful for constructing similar compatible and additive model systems of multiple tree-level models for other tree species.

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.

Individual Tree Attribute Estimation and Uniformity Assessment in Fast-Growing Eucalyptus spp. Forest Plantations Using Lidar and Linear Mixed-Effects Models

Fast-growing Eucalyptus spp. forest plantations and their resultant wood products are economically important and may provide a low-cost means to sequester carbon for greenhouse gas reduction. The development of advanced and optimized frameworks for estimating forest plantation attributes from lidar remote sensing data combined with statistical modeling approaches is a step towards forest inventory operationalization and might improve industry efficiency in monitoring and managing forest resources. In this study, we first developed and tested a framework for modeling individual tree attributes in fast-growing Eucalyptus forest plantation using airborne lidar data and linear mixed-effect models (LME) and assessed the gain in accuracy compared to a conventional linear fixed-effects model (LFE). Second, we evaluated the potential of using the tree-level estimates for determining tree attribute uniformity across different stand ages. In the field, tree measurements, such as tree geolocation, species, genotype, age, height (Ht), and diameter at breast height (dbh) were collected through conventional forest inventory practices, and tree-level aboveground carbon (AGC) was estimated using allometric equations. Individual trees were detected and delineated from lidar-derived canopy height models (CHM), and crown-level metrics (e.g., crown volume and crown projected area) were computed from the lidar 3-D point cloud. Field and lidar-derived crown metrics were combined for ht, dbh, and AGC modeling using an LME. We fitted a varying intercept and slope model, setting species, genotype, and stand (alone and nested) as random effects. For comparison, we also modeled the same attributes using a conventional LFE model. The tree attribute estimates derived from the best LME model were used for assessing forest uniformity at the tree level using the Lorenz curves and Gini coefficient (GC). We successfully detected 96.6% of the trees from the lidar-derived CHM. The best LME model for estimating the tree attributes was composed of the stand as a random effect variable, and canopy height, crown volume, and crown projected area as fixed effects. The %RMSE values for tree-level height, dbh, and AGC were 8.9%, 12.1%, and 23.7% for the LFE model and improved to 7.3%, 7.1%, and 13.6%, respectively, for the LME model. Tree attributes uniformity was assessed with the Lorenz curves and tree-level estimations, especially for the older stands. All stands showed a high level of tree uniformity with GC values approximately 0.2. This study demonstrates that accurate detection of individual trees and their associated crown metrics can be used to estimate Ht, dbh, and AGC stocks as well as forest uniformity in fast-growing Eucalyptus plantations forests using lidar data as inputs to LME models. This further underscores the high potential of our proposed approach to monitor standing stock and growth in Eucalyptus—and similar forest plantations for carbon dynamics and forest product planning.

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

In the context of uneven-aged mixed-species forest management, an individual-tree basal area increment model considering forest structural diversity was developed for oaks (Quercus spp.) using data collected from 11,860 observations in 845 sample plots from the 7th (2004), 8th (2009), and 9th (2014) Chinese National Forest Inventory in Hunan Province, south-central China. Since the data was longitudinal and had a nested structure, we used a linear mixed-effects approach to construct the model. We also used the variance function and an autocorrelation structure to describe within-plot heteroscedasticity and autocorrelation. Finally, the optimal mixed-effects model was determined based on the Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood (Loglik) and the likelihood ratio test (LRT). The results indicate that the reciprocal transformation of initial diameter at breast height (1/DBH), relative density index (RD), number of trees per hectare (NT), elevation (EL) and Gini coefficient (GC) had a significant impact on the individual-tree basal area increment. In comparison to the basic model developed using least absolute shrinkage and selection operator (LASSO) regression, the mixed-effects model performance was greatly improved. In addition, we observed that the heteroscedasticity was successfully removed by the exponent function and autocorrelation was significantly corrected by AR(1). Our final model also indicated that forest structural diversity significantly affected tree growth and hence should not be neglected. We hope that our final model will contribute to the scientific management of oak-dominated forests.

Generalized Nonlinear Mixed-Effects Individual Tree Crown Ratio Models for Norway Spruce and European Beech

Tree crowns are commonly measured to understand tree growth and stand dynamics. Crown ratio (CR—crown depth-to-total height ratio) is significantly affected by a number of tree- and stand-level characteristics and other factors as well. Generalized mixed-effects CR models were developed using a large dataset (measurements from 14,669 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica (L.)) acquired from permanent research plots in various parts of the Czech Republic. Among several tree- and stand-level variables evaluated, diameter at breast height, height to crown base, dominant height, basal area of trees larger in diameter than a focal tree, relative spacing index, and variables describing the effects of species mixture and canopy height differentiation significantly contributed to CR variation. We included sample-plot-level variations caused by randomness in the data and other stochastic factors into the CR models using the mixed-effects modeling approach. The logistic function, which predicts the values between 0 and 1, was chosen to develop the generalized CR mixed-effects model. A large proportion of the CR variation (R2adj ≈ 0.63 (Norway spruce); 0.72 (European beech)) was described by generalized mixed-effects model without significant residual trends. Testing the CR model against a part of the model fitting dataset confirmed its high prediction precision. Our CR model can be useful for growth simulation using inventory databases that lack crown measures. Other potential implications of our CR models in forest management are mentioned in the article.

Research on Roles of Mongolian Medical Warm Acupuncture in Inhibiting p38 MAPK Activation and Apoptosis of Nucleus Pulposus Cells

Background

Mongolian medical warm acupuncture has a desirable therapeutic effect on sciatica. Apoptosis of the nucleus pulposus cells is considered to play an important role in sciatica. Evidence has demonstrated that oxidative stress and its induced activation of the signaling pathways play important roles in sciatica. However, further research is expected to reveal whether Mongolian medical warm acupuncture can inhibit the apoptosis of nucleus pulposus cells and oxidative stress.

Objective

To study the effect of the p38 MAPK pathway activated by the generated ROS on apoptosis and the expression of the genes related to the balance of the extracellular matrix metabolism during treatment of sciatica with Mongolian medical warm acupuncture.

Method

The volume of the active oxygen generated in the nucleus pulposus cells was detected following intervention of Mongolian medical warm acupuncture. The p38 MAPK phosphorylation level was detected with Western blot. The genes are related to the metabolism of the nucleus pulposus extracellular matrix.

Result

Mongolian medical warm acupuncture reduced the active oxygen within the nucleus pulposus cells and inhibited the activation of the p38 MAPK pathway (P=0.013). Meanwhile, it upregulated the gene expression of Type II collagen, aggrecan, Sox-9, and tissue matrix metalloproteinase reagent 1 (P-0.015; P=0.025; P=0.031; P=0.045) and downregulated the gene expression of matrix metalloproteinase 3 (P=0.015).

Conclusion

Mongolian medical warm acupuncture may inhibit apoptosis of nucleus pulposus cells and activation of the extracellular matrix decomposition metabolism pathway and promote its anabolism. This process may rely on the oxidative stress matrix of the p38 MAPK pathway.

Modelling individual tree height to crown base of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.)

Height to crown base (HCB) of a tree is an important variable often included as a predictor in various forest models that serve as the fundamental tools for decision-making in forestry. We developed spatially explicit and spatially inexplicit mixed-effects HCB models using measurements from a total 19,404 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) on the permanent sample plots that are located across the Czech Republic. Variables describing site quality, stand density or competition, and species mixing effects were included into the HCB model with use of dominant height (HDOM), basal area of trees larger in diameters than a subject tree (BAL- spatially inexplicit measure) or Hegyi’s competition index (HCI—spatially explicit measure), and basal area proportion of a species of interest (BAPOR), respectively. The parameters describing sample plot-level random effects were included into the HCB model by applying the mixed-effects modelling approach. Among several functional forms evaluated, the logistic function was found most suited to our data. The HCB model for Norway spruce was tested against the data originated from different inventory designs, but model for European beech was tested using partitioned dataset (a part of the main dataset). The variance heteroscedasticity in the residuals was substantially reduced through inclusion of a power variance function into the HCB model. The results showed that spatially explicit model described significantly a larger part of the HCB variations [R²_adj = 0.86 (spruce), 0.85 (beech)] than its spatially inexplicit counterpart [R²_adj = 0.84 (spruce), 0.83 (beech)]. The HCB increased with increasing competitive interactions described by tree-centered competition measure: BAL or HCI, and species mixing effects described by BAPOR. A test of the mixed-effects HCB model with the random effects estimated using at least four trees per sample plot in the validation data confirmed that the model was precise enough for the prediction of HCB for a range of site quality, tree size, stand density, and stand structure. We therefore recommend measuring of HCB on four randomly selected trees of a species of interest on each sample plot for localizing the mixed-effects model and predicting HCB of the remaining trees on the plot. Growth simulations can be made from the data that lack the values for either crown ratio or HCB using the HCB models.