1 Forest Dynamics, Growth, and Yield: A Review, Analysis
of the Present State, and Perspective ........................ 1
1.1 System Characteristics of Trees and Forest Stands ....... 1
1.1.1 Differences in the Temporal and Spatial Scale
Between Trees and Humans ......................... 2
1.1.2 Forest Stands are Open Systems ................... 6
1.1.3 Forests are Strongly Structurally Determined
Systems .......................................... 8
1.1.4 Trees, Forest Stands, and Forest Ecosystems
are Shaped by History ........................... 11
1.1.5 Forests are Equipped with and Regulated by
Closed Feedback Loops ........................... 12
1.1.6 Forest Ecosystems are Organised
Hierarchically .................................. 14
1.1.7 Forest Stands are Systems with Multiple
Output Variables ................................ 20
1.2 From Forest Stand to Gene Level: The Ongoing Spatial
and Temporal Refinement in Analysis and Modelling
of Tree and Forest Stand Dynamics ...................... 21
1.2.1 Experiments, Inventories, and Measurement
of Structures and Rates ......................... 22
1.2.2 From Proxy Variables to "Primary" Factors for
Explanations and Estimations of Stand and Tree
Growth .......................................... 24
1.2.3 From Early Experience Tables to
Ecophysiologically Based Computer Models ........ 26
1.3 Bridging the Widening Gap Between Scientific Evidence
and Practical Relevance ................................ 29
1.3.1 Scale Overlapping Experiments ................... 29
1.3.2 Interdisciplinary Links Through Indicator
Variables ....................................... 31
1.3.3 Link Between Experiments, Inventories, and
Monitoring by Classification Variables .......... 32
1.3.4 Model Development ............................... 33
1.3.5 Link Between Models and Inventories: From
Deductive to Inductive Approaches ............... 35
Summary ..................................................... 37
2 From Primary Production to Growth and Harvestable Yield
and Vice Versa: Specific Definitions and the Link Between
Two Branches of Forest Science .............................. 41
2.1 Link Between Forest Growth and Yield Science and
Production Ecology ..................................... 41
2.2 General Definitions and Quantities: Primary
Production, Growth and Yield ........................... 42
2.2.1 Gross and Net Primary Production ................ 44
2.2.2 Gross and Net Growth ............................ 46
2.2.3 Gross and Net Yield ............................. 47
2.3 Specific Terminology and Quantities in Forest Growth
and Yield Science ...................................... 48
2.3.1 Growth and Yield of Individual Trees ............ 50
2.3.2 Growth and Yield at the Stand Level ............. 56
2.4 Stem and Merchantable Volume Growth as a Percentage
of Gross Primary Production ............................ 64
2.4.1 From Standing Volume or Stem or Merchantable
Wood Volume to Total Biomass .................... 66
2.4.2 Ephemeral Turnover Factor torg, for Estimation
of NPP .......................................... 72
2.4.3 Deriving Harvested Volume Under Bark from
Standing Volume over Bark ....................... 76
2.4.4 Conversion of Merchantable Wood Volume to GPP ... 78
2.5 Dead Inner Xylem ....................................... 81
2.6 Growth and Yield and Nutrient Content .................. 84
2.6.1 From Total Biomass to the Carbon Pool ........... 85
2.6.2 Nutrient Minerals ............................... 85
2.7 Efficiency of Energy, Nitrogen, and Water Use .......... 89
2.7.1 Energy Use Efficiency (EUE) ..................... 90
2.7.2 Nitrogen Use Efficiency (NUE) ................... 93
2.7.3 Water Use Efficiency (WUE) ...................... 94
Summary ..................................................... 95
3 Brief History and Profile of Long-Term Growth and Yield
Research ................................................... 101
3.1 From Rules of Thumb to Sound Knowledge ................ 101
3.2 Foundation and Development of Experimental Forestry ... 104
3.3 From the Association of German Forest Research
Stations to the International Union of Forest
Research Organizations (IUFRO) ........................ 105
3.4 Growth and Yield Science Section of the German Union
of Forest Research Organisations ...................... 105
3.5 Continuity in Management of Long-Term Experiment
Plots in Bavaria as a Model of Success ................ 107
3.6 Scientific and Practical Experiments .................. 110
3.7 Establishment and Survey of Long-Term Experimental
Plots ................................................. 112
3.7.1 Establishment of Experimental Plots and Trial
Plots .......................................... 112
3.7.2 Measuring Standing and Lying Trees ............. 115
Summary .................................................... 118
4 Planning Forest Growth and Yield Experiments ............... 121
4.1 Key Terminology in the Design of Long-Term
Experiments ........................................... 121
4.2 The Experimental Question and its Four Component
Questions ............................................. 123
4.2.1 Which Question Should Be Answered? ............. 123
4.2.2 With What Level of Accuracy Should the
Question be Answered? .......................... 124
4.2.3 What Level of Spatial-Temporal Resolution is
Wanted in the Explanation? ..................... 124
4.2.4 Why and for What Purpose Should the Question
be Answered? ................................... 124
4.3 Biological Variability and Replicates ................. 125
4.3.1 Total Population and Sample .................... 125
4.4 Size of Experimental Plot and Trial Plot Number ....... 126
4.5 Block Formation and Randomisation: Elimination of
Systematic Error ...................................... 128
4.6 Classical Experimental Designs ........................ 129
4.6.1 One-Factor Designs ............................. 130
4.6.2 Two-Factor or Multifactor Analysis ............. 133
4.6.3 Split-Plot and Split-Block Designs ............. 137
4.6.4 Trial Series and Disjunct Experimental Plots ... 139
4.7 Special Experimental Designs and Forest Growth
Surveys ............................................... 141
4.7.1 From Stand to Individual Tree Experiments ...... 141
4.7.2 Experiments and Surveys of Growth
Disturbances ................................... 144
4.7.3 Artificial Time Series or Growth Series ........ 145
Summary .................................................... 148
5 Description and Quantification of Silvicultural
Prescriptions .............................................. 151
5.1 Kind of Thinning ...................................... 154
5.1.1 Thinning According to Social Tree Classes
by Kraft (1884) ................................ 154
5.1.2 Thinning According to Combined Tree and Stem
Quality Classes from the Association of
German Forest Research Stations (1902) ......... 156
5.1.3 Thinning After the Selection of Superior or
Final Crop Trees ............................... 160
5.1.4 Thinning Based on Diameter Class or Target
Diameter ....................................... 164
5.2 Severity of Thinning .................................. 166
5.2.1 Thinning Based on a Target Stand Density
Curve .......................................... 167
5.2.2 Approaches for Regulating Thinning Severity
and Stand Density .............................. 167
5.2.3 Selection of Density Classes ................... 170
5.2.4 Management of Stand Density in Fertilisation
and Provenance Trials .......................... 171
5.2.5 Individual Tree Based Thinning Prescriptions ... 172
5.3 Intensity of Thinning ................................. 175
5.4 Algorithmic Formulation of Silvicultural
Prescriptions for Forest Practice and Growth and
Yield Models .......................................... 177
Summary .................................................... 178
6 Standard Analysis of Long-Term Experimental Plots .......... 181
6.1 From Measurement to Response Variables ................ 183
6.2 Importance of Regression Sampling for Standard
Analysis .............................................. 184
6.2.1 Principle of Regression Sampling ............... 184
6.2.2 Linear Transformation .......................... 184
6.3 Determination of Stand-Height Curves .................. 186
6.3.1 Function Equations for Diameter-Height
Relationships .................................. 187
6.3.2 Selection of the Most Suitable Model
Function ....................................... 188
6.4 Diameter-Height-Age Relationships ..................... 189
6.4.1 Method of Smoothing Coefficients ............... 191
6.4.2 Growth Function Methods for Strata Mean
Trees .......................................... 193
6.4.3 Age-Diameter-Height Regression Methods ......... 195
6.5 Form Factors and Volume Calculations for Individual
Trees ................................................. 196
6.5.1 Form Factors ................................... 197
6.5.2 Volume Calculations for Individual Trees ....... 199
6.6 Stand Mean and Cumulative Values at the Time of
Inventory and for the Periods Between Inventories ..... 199
6.6.1 Reference Area ................................. 199
6.6.2 Tree Number .................................... 199
6.6.3 Mean Diameter and Mean Diameter of the Top
Height Tree Collective ......................... 200
6.6.4 Mean and Top Height ............................ 201
6.6.5 Slenderness hq/dq and h100/d100 .................. 203
6.6.6 Stand Basal Area and Volume .................... 203
6.6.7 Growth and Yield Characteristics ............... 204
6.7 Results of Standard Analysis .......................... 205
6.7.1 Presentation in Tables ......................... 205
6.7.2 Stand Development Diagrams ..................... 211
Summary .................................................... 220
7 Description and Analysis of Stand Structures ............... 223
7.1 Structures and Processes in Forest Stands ............. 225
7.1.1 Interaction Between Structures and Processes ... 225
7.1.2 Effect of Initial Structure on Stand
Development .................................... 227
7.2 Descriptions of Stand Structure ....................... 229
7.2.1 Tree Distribution Maps and Crown Maps .......... 230
7.2.2 Three-Dimensional Visualisation of Forest
Growth ......................................... 234
7.2.3 Spatial Occupancy Patterns ..................... 239
7.3 Horizontal Tree Distribution Patterns ................. 242
7.3.1 Poisson Distribution as a Reference for
Analysing Stand Structures ..................... 243
7.3.2 Position-Dependent Distribution Indices ........ 246
7.3.3 Distribution Indices Based on Sample
Quadrats ....................................... 252
7.3.4 K-Function ..................................... 256
7.3.5 L-Function ..................................... 260
7.3.6 Pair Correlation Functions for Detailed
Analysis of Tree Distribution Patterns ......... 261
7.4 Stand Density ......................................... 266
7.4.1 Stocking Density ............................... 266
7.4.2 Percentage Canopy Cover (PCC) .................. 267
7.4.3 Mean Basal Area, mBA, by Assmann (1970) ........ 269
7.4.4 Quantifying Stand Density from the Allometry
Between Mean Size and Plants per Unit Area ..... 270
7.4.5 Crown Competition Factor CCF ................... 273
7.4.6 Density of Spatial Occupancy and Vertical
Profiles ....................................... 274
7.5 Differentiation ....................................... 276
7.5.1 Coefficient of Variation of Tree Diameters
and Heights .................................... 276
7.5.2 Diameter Differentiation by Füldner (1995) ..... 276
7.5.3 Species Richness, Species Diversity, and
Structural Diversity ........................... 279
7.6 Species Intermingling ................................. 284
7.6.1 Species Intermingling Index by Fuldner
(1996) ......................................... 284
7.6.2 Index of Segregation from Pielou (1977) ........ 285
Summary .................................................... 287
8 Growing Space and Competitive Situation of Individual
Trees ...................................................... 291
8.1 The Stand as a Mosaic of Individual Trees ............. 292
8.2 Position-Dependent Competition Indices ................ 292
8.2.1 Example of Competitor Identification and
Competition Calculation ........................ 293
8.2.2 Methods of Competitor Identification ........... 295
8.2.3 Quantifying the Level of Competition ........... 299
8.2.4 Evaluation of Methods .......................... 302
8.3 Position-Independent Competition Measures ............. 305
8.3.1 Crown Competition Factor ....................... 305
8.3.2 Horizontal Cross-Section Methods ............... 306
8.3.3 Percentile of the Basal Area Frequency
Distribution ................................... 307
8.3.4 Comparing Position-Independent with Position-
Dependent Competition Indices .................. 308
8.4 Methods Based on Growing Area ......................... 311
8.4.1 Circle Segment Method .......................... 311
8.4.2 Rastering the Stand Area ....................... 312
8.4.3 Growing Area Polygons .......................... 313
8.5 Detailed Analysis of a Tree's Spatial Growth
Constellation ......................................... 315
8.5.1 Spatial Rastering and Dot Counting ............. 315
8.5.2 Calculation of Spatial Distances ............... 318
8.5.3 Crown Growth Responses to Lateral
Restriction .................................... 320
8.6 Hemispherical Images for Quantifying the Competitive
Situation of Individual Trees ......................... 321
8.6.1 Fish-Eye Images as a Basis for Spatial
Analyses ....................................... 321
8.6.2 Methodological Principles of Fish-Eye
Projection in Forest Stands .................... 323
8.6.3 Quantifying the Competitive Situation of
Individual Trees in a Norway Spruce-European
Beech Mixed Stand .............................. 325
8.7 Edge Correction Methods ............................... 326
8.7.1 Edge Effects and Edge Correction Methods ....... 326
8.7.2 Reflection and Shift ........................... 327
8.7.3 Linear Expansion ............................... 328
8.7.4 Structure Generation ........................... 332
8.7.5 Evaluation of Edge Correction Methods .......... 333
Summary .................................................... 334
9 Effects of Species Mixture on Tree and Stand Growth ........ 337
9.1 Introduction: Increasing Productivity with Species
Mixtures? ............................................. 337
9.1.1 Fundamental Niche and Niche Differentiation .... 338
9.1.2 Maximizing Fitness isn't Equivalent to
Maximizing Productivity ........................ 340
9.1.3 The Balance Between Production Promoting
and Inhibiting Effects is Important ............ 341
9.2 Framework for Analysing Mixing Effects ................ 343
9.2.1 Ecological Niche ............................... 343
9.2.2 Site-Growth Relationships ...................... 344
9.2.3 Risk Distribution .............................. 344
9.2.4 Comparison of Mixed Stands with Neighbouring
Pure Stands: Methodological Considerations ..... 348
9.3 Quantifying Effects of Species Mixture at Stand
Level ................................................. 351
9.3.1 Cross-Species Diagrams for Visualising
Mixture Effects ................................ 351
9.3.2 Nomenclature, Relations and Variables for
Analysing Mixture Effects ...................... 352
9.3.3 Mixture Proportion ............................. 354
9.3.4 Examining Effects of Species Mixture on
Biomass Productivity in Norway Spruce-
European Beech Stands: An Example .............. 356
9.3.5 Examining Mean Tree Size in Norway Spruce-
European Beech Stands: An Example .............. 360
9.4 Quantifying Mixture Effects at the Individual Tree
Level ................................................. 363
9.4.1 Efficiency Parameters for Individual Tree
Growth ......................................... 363
9.4.2 Application of Efficiency Parameters for
Detecting Mixture Effects ...................... 365
9.5 Productivity in Mixed Forest Stands ................... 371
9.5.1 The Mixed Stands Issue: A Central European
Review and Perspective ......................... 371
9.5.2 Benchmarks for Productivity of Mixed Stands
Compared to Pure Stands ........................ 372
9.5.3 Spatial and Temporal Niche Differentiation as
a Recipe for Coexistence and Cause of Surplus
Productivity ................................... 375
9.5.4 Crown Shyness .................................. 376
9.5.5 Growth Resilience with Structural and Species
Diversity ...................................... 377
Summary .................................................... 378
10 Growth Relationships and their Biometric Formulation ....... 381
10.1 Dependence of Growth on Environmental Conditions and
Resource Availability ................................. 381
10.1.1 Unimodal Dose-Effect-Curve ..................... 381
10.1.2 Dose-Effect-Rule by Mitscherlich (1948) ........ 383
10.1.3 Combining the Effects of Several Growth
Factors ........................................ 386
10.2 Allometry at the Individual Plant Level ............... 387
10.2.1 Allometry and Its Biometric Formulation ........ 387
10.2.2 Examples of Allometry at the Individual Plant
Level .......................................... 389
10.2.3 Detection of Periodic Changes in Allometry ..... 391
10.3 Growth and Yield Functions of Individual Plants ....... 393
10.3.1 Physiological Reasoning and Biometrical
Formulation of Growth Functions ................ 393
10.3.2 Overview Over Approved Growth and Yield
Functions ...................................... 394
10.3.3 Relationship Between Growth and Yield .......... 397
10.4 Allometry at the Stand Level: The Self-Thinning
Rules from Reineke (1933) and Yoda et al. (1963) ...... 399
10.4.1 Reineke's (1933) Self-thinning Line and Stand
Density Index .................................. 400
10.4.2 -З/2-Power Rule by Yoda et al. (1963) .......... 402
10.4.3 Link Between Individual Tree and Stand
Allometry ...................................... 405
10.4.4 Allometric Scaling as General Rule ............. 406
10.5 Stand Density and Growth .............................. 407
10.5.1 Assmann's Concept of Maximum, Optimum and
Critical Stand Density ......................... 409
10.5.2 Biometric Formulation of the Unimodal Optimum
Curve of Volume Growth in Relation to Stand
Density and Mean Tree Size ..................... 411
10.6 Dealing with Biological Variability .................. 415
10.6.1 Quantifying Variability ........................ 416
10.6.2 Reproduction of Variability .................... 418
Summary .................................................... 420
11 Forest Growth Models ....................................... 423
11.1 Scales of Observation, Statistical and Mechanistic
Approaches to Stand Dynamics .......................... 425
11.1.1 Scales of Forest Growth and Yield Research
and Models ..................................... 425
11.1.2 From the Classical Black-Box to White-Box
Approaches ..................................... 426
11.1.3 Тор-Down Approach vs Bottom-Up Approach ........ 428
11.2 Model Objectives, Degree of System Abstraction,
Database .............................................. 429
11.2.1 Growth Models as Nested Hypotheses About
Systems Behaviour .............................. 430
11.2.2 Growth Models as a Decision Tool for Forest
Management ..................................... 430
11.3 Growth Models Based on Stand Level Mean and
Cumulative Values ..................................... 432
11.3.1 Principles of Yield Table Construction ......... 432
11.3.2 From Experience Tables to Stand Simulators ..... 437
11.4 Growth Models Based on Tree Number Frequencies ........ 445
11.4.1 Representing Stand Development by Systems of
Differential Equations ......................... 445
11.4.2 Growth Models Based on Progressing
Distributions .................................. 446
11.4.3 Stand Evolution Models - Stand Growth as a
Stochastic Process ............................. 449
11.5 Individual Tree Growth and Yield Models ............... 450
11.5.1 Overview of the Underlying Principles of
Individual-Tree Models ......................... 451
11.5.2 Growth Functions as the Core Element of
Individual-Tree Models ......................... 453
11.5.3 Overview of Model Types ........................ 455
11.6 Gap and Hybrid Models ................................. 456
11.6.1 Development Cycle in Gaps ...................... 457
11.6.2 JABOWA - Prototype Model from Botkin et al.
(1972) ......................................... 458
11.7 Matter Balance Models ................................. 462
11.7.1 Increasing Structural and Functional
Accordance of Models with Reality .............. 462
11.7.2 Modelling of the Basic Processes in Matter
Balance Models ................................. 465
11.7.3 Overview of Matter Balance Model Approaches .... 476
11.8 Landscape Models ...................................... 478
11.8.1 Application of Landscape Model LandClim ........ 481
11.9 Visualisation of Forest Stands and Wooded
Landscapes ............................................ 482
11.9.1 Visualisation Tools TREEVIEW and L-VIS ......... 484
11.10 Perspective .......................................... 488
Summary .................................................... 490
12 Evaluation and Standard Description of Growth Models ....... 493
12.1 Approaches for Evaluation of Growth Models and
Simulators ............................................ 494
12.1.1 Suitability for a Given Purpose ................ 494
12.1.2 Validation of the Biometric Model .............. 496
12.1.3 Suitability of the Software .................... 499
12.1.4 Customising Models and Simulators for End-
Users .......................................... 500
12.2 Examples of Model Validation .......................... 503
12.2.1 Validation on the Basis of Long-Term Sample
Plots and Inventory Data ....................... 503
12.2.2 Comparison with Growth Relationships ........... 508
12.2.3 Comparison with Knowledge from Experience ...... 510
12.3 Standards for Describing Models and Simulators ........ 510
Summary .................................................... 512
13 Application of Forest Simulation Models for Decision
Support in Practice ........................................ 515
13.1 Model Objective and Prediction Algorithm .............. 516
13.1.1 Model Objective ................................ 516
13.1.2 Prediction Algorithm ........................... 516
13.1.3 Database ....................................... 519
13.2 Site-Growth Model ..................................... 519
13.2.1 The Principles of Controlling Individual Tree
Growth by Means of Site Factors ................ 520
13.2.2 Modelling the Potential Age-Height Curve in
Dependence on Site Conditions .................. 520
13.3 Generation of Initial Values for Simulation Runs ...... 525
13.3.1 Stand Structure Generator STRUGEN .............. 526
13.4 Spatially Explicit Modelling of the Growth
Arrangement of the Individual Trees ................... 528
13.4.1 Index KKL as the Indicator of the Crown
Competition .................................... 528
13.4.2 Index NDIST as the Indicator for Competition
Asymmetry ...................................... 528
13.4.3 Index KMA for the Species Mixture in the
Neighbourhood of Individual Trees .............. 529
13.5 Application for Scenario Analysis at the Stand
Level: A Pure Norway Spruce Stand vs a Norway Spruce
- European Beech Mixed Stand .......................... 530
13.5.1 Growth and Yield at the Stand Level ............ 530
13.5.2 Growth and Yield on Tree Level ................. 532
13.5.3 Modelling Structural Diversity ................. 532
13.5.4 Multi-Criteria Considerations .................. 534
13.6 Growth Models for Dynamic Enterprise Planning ......... 535
13.6.1 Simulation at the Enterprise Level for Long-
Term Strategic Planning ........................ 536
13.6.2 Application of Models for Decision Support ..... 537
13.6.3 Application of the Munich Forestry Enterprise
Forest Management Plan ......................... 540
13.7 Estimation of Growth and Yield Responses to Climate
Change ................................................ 543
13.7.1 Dependence of Response Patterns on Site and
Tree Species ................................... 544
13.7.2 Sensitivity Analysis at the Regional Level ..... 545
13.7.3 Development of Silvicultural Measures for
Mitigation and Adaptation to Climate Change .... 548
Summary .................................................... 549
14 Diagnosis of Growth Disturbances ........................... 553
14.1 Growth Models as Reference ............................ 556
14.1.1 Comparison with Yield Table .................... 556
14.1.2 Dynamic Growth Models as Reference ............. 557
14.1.3 Synthetic Reference Curves ..................... 559
14.2 Undisturbed Trees or Stands as a Reference ............ 560
14.2.1 Increment Trend Method ......................... 560
14.2.2 Pair-Wise Comparison ........................... 565
14.2.3 Reference Plot Comparison ...................... 566
14.2.4 Reference Plot Comparison by Indexing .......... 570
14.2.5 Regression-Analytical Estimation of Increment
Decrease ....................................... 572
14.3 Growth Behaviour in Other Calendar Periods as
Reference ............................................. 576
14.3.1 Individual Growth in Previous Period as
Reference ...................................... 576
14.3.2 Long-Term, Age-Specific Tree Growth as
Reference (Constant Age Method) ................ 579
14.3.3 Growth Comparison of Previous and Subsequent
Generation at the Same Site .................... 580
14.3.4 Diagnosis of Growth Trends from Succeeding
Inventories .................................... 582
14.4 Dendro-Chronological Time Series Analysis ............. 585
14.4.1 Elimination of the Smooth Component ............ 586
14.4.2 Indexing ....................................... 587
14.4.3 Response Function .............................. 588
14.4.4 Quantification of Increment Losses ............. 589
Summary .................................................... 590
15 Pathways to System Understanding and Management ............ 593
15.1 Overview of Knowledge Pathways in Forest Growth and
Yield Research ........................................ 594
15.1.1 Observation, Measurement, and Collection of
Data ........................................... 595
15.1.2 Description .................................... 597
15.1.3 Formulation of Hypotheses for Elements of
Individual System Elements ..................... 597
15.1.4 Test of Hypotheses ............................. 599
15.1.5 Models as a Chain of Hypotheses ................ 602
15.1.6 Test of Model Hypothesis by Simulation ......... 603
15.1.7 Application of the Model in Research,
Practice, and Education ........................ 604
15.1.8 Relationships, Rules, Laws, and Theories ....... 604
15.2 Transfer of Knowledge from Science to Practice ........ 611
15.2.1 Concept of Forest Ecosystem Management ......... 611
15.2.2 Long-Term Experiments and Models for Decision
Support ........................................ 613
Summary .................................................... 615
References .................................................... 619
Index ......................................................... 655
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