Models of Tree and Stand Dynamics

Preface
	Acknowledgements
Contents
Symbols of the Core Model
1 Introduction
	1.1 Setting the Stage
	1.2 Focus of This Book
	1.3 Dynamic Models
	1.4 Raison D\'être
	1.5 Hierarchy
	1.6 Model Resolution
	1.7 Modelling 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
	Documentation—R script
	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 García\'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 Combining the Carbon Balance and Structure into a Core Model
	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 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: Geometrical-Empirical Approach
	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 Concluding Remarks on Competition in Process-Based Models
	6.5 Models with Structural Plasticity
		6.5.1 A Crown-Length Rule
		6.5.2 A Mean-Tree Model with Crown Riseand Self-Thinning
		6.5.3 A Tree-Level Model with Crown Riseand Self-Thinning
		6.5.4 Summary: Crown Rise and Space
	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 Optimisation
	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 Leaf 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 Nitrogen 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
	7.8 Exercises
8 Predicting Stand Growth: Parameters, Drivers, and ModularInputs
	8.1 Introduction
	8.2 Linkages Between Models and Data
	8.3 Empirical Estimation of the Core Model
		8.3.1 Considerations for Fitting
	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
	9.5 Exercises
10 Applications and Future Outlook
	10.1 Introduction
	10.2 Stand-Scale Growth and Production as Affectedby 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?
		10.5.1 Emerging Eco-Physiological Issues
		10.5.2 Trends in Mainstream Methods
		10.5.3 Trends in Application
Solutions to Exercises
	Exercises of Chapter 1
	Exercises of Chapter 2
	Exercises of Chapter 3
	Exercises of Chapter 4
	Exercises of Chapter 6
	Exercises of Chapter 7
	Exercises of Chapter 8
	Exercises of Chapter 9
References
Index