Models of Tree and Stand Dynamics: Theory, Formulation and Application

Preface.- List of symbols.- 1. Introduction.- 1.1. Introduction.- 1.2. Focus of this book.- 1.3. Dynamic models.- 1.4. Raison d'être.- 1.5. Hierarchy.- 1.6. Model resolution.- 1.7. Modeling approaches.- 1.8. Growth.- 1.8.1. Tree growth.- 1.8.2. Stand growth.- 1.8.3. Instantaneous rates of change.- 1.9. Carbon-balance models.- 1.10. Solving a model with R.- 1.10.1. Documentation & brief model description.- 1.11. Exercises.- 1.12. Suggested reading.- 2. Descriptive Models.- 2.1. Descriptive growth models.- 2.1.1. Gompertz model.- 2.1.2. Logistic model.- 2.1.3. Bertalanffy model.- 2.1.4. Similarities of the classic models.- 2.2. Garcia's general model.- 2.2.1. Solution.- 2.2.2. Scaling.- 2.3. Saturating responses.- 2.3.1. Mitscherlich model.- 2.3.2. Hyperbolas.- 2.3.3. Numerical switch.- 2.4. An empirical crown model.- 2.4.1. Crown rise.- 2.4.2. Height growth.- 2.4.3. Change in spacing and stand density.- 2.4.4. R script.- 2.5. Exercises.- 2.6. Suggested reading.- 3. Carbon Balance.- 3.1. Photosynthesis is the source of growth.- 3.2. Basic carbon balance of trees and stands.- 3.3. Stand-level feedbacks.- 3.3.1. Shading and photosynthesis.- 3.3.2. Nitrogen limitation.- 3.4. Tree-level feedbacks.- 3.4.1. Allocation.- 3.4.2. Self-shading.- 3.4.3. Hydraulic limitation.- 3.4.4. Respiration.- 3.4.5. Summary.- 3.5. Problems.- 4. Tree Structure.- 4.1. Introduction.- 4.2. Allometry.- 4.2.1. Allometry of trees.- 4.3. Pipe model.- 4.3.1. Basic definitions.- 4.3.2. Pipe model for tree-level variables.- 4.3.3. Fine roots.- 4.3.4. Biomass of active pipes.- 4.3.5. Disused pipes.- 4.3.6. Biomass estimation using the pipe model.- 4.4. Height-to-diameter ratios: Greenhill scaling.- 4.4.1. Vertical biomass density.- 4.4.2. Greenhill scaling.- 4.5. Fractal trees.- 4.5.1. Menger's sponge.- 4.5.2. Branching patterns and fractal foliage.- 4.5.3. Allometry and fractals.- 4.5.4. Allometry in pipe model trees with fractal foliage.- 4.6. Models of crown geometry.- 4.6.1. Models of foliage distribution for light interception.- 4.6.2. Crown architecture models.- 4.7. Summary.- 4.8. Exercises.- 5. Carbon Balance and Structure.- 5.1. Combining the carbon balance and structure.- 5.1.1. Results from the pipe model.- 5.2. Model of tree dynamics.- 5.2.1. Production and loss.- 5.2.2. Height growth rate and allocation fractions.- 5.2.3. Net growth rates.- 5.3. Cross-sectional growth.- 5.4. Summary of the model.- 5.5. R script.- 5.5.1. Setup.- 5.5.2. Solution.- 5.5.3. The stem profile.- 5.5.4. Response variables and graphs.- 5.5.5. Results.- 5.5.6. Sensitivity.- 5.6. Redux and reuse.- 5.7. Exercises.- 6. Competition.- 6.1. Introduction.- 6.2. Setting the scene: Effects of competition on growth on and mortality.- 6.2.1. Resource acquisition.- 6.2.2. Acclimations.- 6.2.3. Suppression and self-thinning.- 6.2.4. Implications for modelling competition.- 6.3. Simple stand-level approaches to competition.- 6.3.1. The Yoda rule.- 6.3.2. The Reineke rule.- 6.3.3. Summary.- 6.4. Models with competition for light.- 6.4.1. Competition for light in gap models.- 6.4.2. Models with photosynthesis.- 6.4.3. Summary.- 6.5. Models with structural plasticity.- 6.5.1. A crown-length rule.- 6.5.2. A mean-tree model with crown rise and self-thinning.- 6.5.3. A tree-level model with crown rise and self-thinning.- 6.5.4. Summary.- 6.6. Spatial approaches.- 6.6.1. Spatial crown-rise model.- 6.6.2. Perfect aggregation.- 6.6.3. Perfect Plasticity Approximation.- 6.7. Exercises.- 7. Tree structure revisited: Eco-evolutionary models.- 7.1. Introduction.- 7.2. Rationale for optimization.- 7.3. Crown structure.- 7.3.1. The evolutionary significance of crown architecture for carbon allocation.- 7.3.2. Crown allometry.- 7.3.3. Optimal crown shape and foliage density.- 7.3.4. Crown structure: Summary.- 7.4. Stem form.- 7.5. Co-allocation of carbon and nitrogen.- 7.5.1. Functional balance.- 7.5.2. Functional balance during exponential growth.- 7.5.3. Optimal canopy density and N supply.- 7.5.4. Co-allocation of carbon and nitrogen in closed canopies.- 7.5.5. Dynamic co-allocation of carbon and nitrogen.- 7.5.6. Summary.- 7.6. Evolutionary games.- 7.6.1. Evolutionarily stable strategies.- 7.6.2. Differential games.- 7.6.3. Height growth as a differential game.- 7.6.4. Adaptive system dynamics.- 7.7. Summary and outlook.- 8. Predicting stand growth: parameters, drivers and modular inputs.- 8.1. Introduction.- 8.2. Linkages between models and data.- 8.3. Empirical estimation of the core model.- 8.3.1. Considerations for _tting.- 8.4. Estimating structural parameters.- 8.5. Environment-sensitivity of metabolic parameters.- 8.5.1. Photosynthesis.- 8.5.2. Respiration.- 8.5.3. Tissue life span.- 8.5.4. Effects of growth site.- 8.6. Adaptive adjustment of structural parameters.- 8.7. Summary.- 8.8. Exercises.- 9. Calibration.- 9.1. Introduction.- 9.2. Basics of sensitivity and uncertainty analysis.- 9.2.1. Sensitivity.- 9.2.2. Uncertainty.- 9.3. Filtering methods.- 9.3.1. Gap-filling data streams.- 9.4. Bayesian calibration.- 9.4.1. Calibration of gas exchange model PRELES.- 9.4.2. Calibration of tree growth model PREBAS.- 10. Applications and future outlook.- 10.1. Introduction.- 10.2. Stand-scale growth and production as affected by management.- 10.3. Regional variability of growth and carbon sequestration.- 10.4. Climate change impacts.- 10.4.1. Climate scenarios.- 10.4.2. Incorporating climate impacts in OptiPipe.- 10.4.3. Sensitivity screening of OptiPipe.- 10.4.4. Analysis of climate change impacts with OptiPipe.- 10.4.5. Some uncertainties in analysing climate change impacts.- 10.5. Quo vadis?.- Solutions to Exercises.- References.- Author Index.- Index.