Modelling Forest Growth and Yield Applications to Mixed Tropical Forests Jerome K. Vanclay Professor of Tropical Forestry Royal Veterinary and Agricultural University Copenhagen Currently: Professor of Sustainable Forestry, Southern Cross University, Lismore NSW Australia Originally published in 1994 by CAB International, Wallingford UK as ISBN 0 85198 913 6 Note: for reasons best known to the WordPerfect people, this version has pagination similar, but not identical to the CABI edition. Dedicated to all those working toward the sustainable management of tropical forests, and especially to my daughter Erica, in the hope that she too may find the tropical forests as interesting, diverse and extensive as I have. Contents Figures ................................................ viii Tables................................................... xi Preface ................................................. xiii Foreword ................................................xv Acknowledgements ...................................... xvii 1. Introduction ........................................... 1 Role of Growth Models.................................. 2 What is a Growth Model? ................................ 4 Growth Modelling Approaches............................ 5 Components of a Model ................................. 8 Choosing a Model ...................................... 9 Examples ............................................ 10 Exercises ............................................ 13 2. Whole Stand Models ................................... 14 Growth and Yield Tables ............................... 14 Growth and Yield Equations............................. 16 More Detailed Whole Stand Approaches . 22 Synthesis ............................................ 31 Exercises ............................................ 32 3. Size Class Models ...................................... 34 Stand Table Approaches ................................ 34 Transition Matrices .................................... 43 Cohort Models ........................................ 50 Synthesis ............................................ 55 Exercises ............................................ 55 v vi Modelling Forest Growth and Yield 4. Single-tree and Tree List Models ......................... 57 Single-tree Spatial Models .............................. 58 Single-tree Non-spatial Models . 68 Tree List Models ...................................... 71 Synthesis ............................................ 77 Exercises ............................................ 77 5. Data Requirements .................................... 79 Differing Data Needs................................... 80 Data for Modelling .................................... 84 Data Collection ....................................... 91 Synthesis ........................................... 101 Exercises ........................................... 102 6. Constructing Growth Models ........................... 103 Model Design ....................................... 104 Regression Techniques ................................ 112 Statistical Assumptions ................................ 119 Strategies for Grouping Data............................ 127 Synthesis ........................................... 131 Exercises ........................................... 132 7. Forest Site Evaluation ................................. 134 Phytocentric Methods ................................. 136 Geocentric Methods................................... 145 Practical Considerations ............................... 151 Synthesis ........................................... 154 Exercises ........................................... 155 8. Diameter Increment .................................. 156 What to Model....................................... 156 Diameter Increment Functions . 162 Synthesis ........................................... 170 Exercises ........................................... 170 9. Mortality and Merchantability ......................... 172 Natural Mortality..................................... 173 Harvesting and other Human Factors . 182 Merchantability ...................................... 187 Synthesis ........................................... 190 Exercises ........................................... 190 10. Regeneration and Recruitment ........................ 192 Recruitment Models .................................. 193 Regeneration Models.................................. 201 Synthesis ........................................... 202 Exercises ........................................... 203 Contents vii 11. Model Evaluation and Re-calibration ................... 204 Model Criticism...................................... 205 Benchmark Tests ..................................... 211 Re-calibration ....................................... 219 Synthesis ........................................... 221 Exercises ........................................... 221 12. Implementation and Use .............................. 223 Implementing the Model ............................... 224 Resource Data for Simulation Studies . 225 Optimization Studies .................................. 229 Yield Prediction...................................... 234 Synthesis ........................................... 240 Exercises ........................................... 241 13. Future Directions .................................... 243 Models for all Forests ................................. 244 Different Management Needs ........................... 245 Environmental Changes ............................... 247 Integration with other Models ........................... 248 Model Construction and Use............................ 249 Presentation of Information............................. 249 Synthesis ........................................... 250 References ............................................. 252 Glossary .............................................. 275 Symbols ............................................ 275 Common and Botanical Species Names . 277 Terminology ........................................ 279 Solutions to Selected Exercises ............................ 285 Author Index .......................................... 298 Subject Index .......................................... 304 Figures Fig. 1.1. The role of growth models and complementary data in providing forest management information. 2 Fig. 1.2. The role of growth models in decision making, forest management and the formulation of forest policy. 3 Fig. 1.3. Yield table, curves and equation for Eucalyptus deglupta. 5 Fig. 1.4. Components of forest growth and the analogous representation in a stand growth model. 9 Fig. 2.1. Yield predictions for logged dipterocarp forest. 18 Fig. 2.2. Basal area increment curves for Callitris stands. 20 Fig. 2.3. Possible diameter distributions generated by the Weibull p.d.f........................................... 24 Fig. 2.4. Vector field illustrating a 2-dimensional state-space model. .............................................. 28 Fig. 2.5. Markov chain representation of a model. 29 Fig. 2.6. Markov matrix and its steady state. 30 Fig. 3.1. Stand table projection with movement ratio 0.25. 36 Fig. 3.2. Smoothing an uneven-aged stand table results in smaller estimates of upgrowth for a given movement ratio. 39 Fig. 3.3. Markov chain representation of Fig. 3.1 and Equation 3.1. .............................................. 44 Fig. 3.4. Single projection with a matrix model. 49 Fig. 3.5. Changes in tree rank in a pine stand. 50 Fig. 3.6. Tree record in cohort model represented by species, size and expansion factor. ............................ 52 Fig. 4.1. Competition indices include the competitive influence zone, area potentially available, size-distance, sky view and light interception approaches. 59 Fig. 4.2. Outputs from the PLATIPUS prototype included stem and branch profiles, and ring and knot patterns. 65 Fig. 4.3. Tree records representing a forest stand. 72 viii Fig. 4.4. Record tripling in the Prognosis model. 73 Fig. 4.5. Look-up tables can be used to find the coefficients to be used in equations to predict growth, mortality, recruitment, etc. ........................................... 75 Fig. 5.1. Interpolation is safer than extrapolation. 82 Fig. 5.2. Efficient placement of ten samples. 84 Fig. 5.3. Database weaknesses revealed by comparing dynamic and static inventory data. ............................. 87 Fig. 5.4. Recommended plot layout for permanent sample plots. 91 Fig. 5.5. Example of a field form for measuring PSPs. 98 Fig. 6.1. Concepts of precision and bias. 105 Fig. 6.2. Growth and yield forms of equations are analogous. 107 Fig. 6.3. Forms of the Bertalanffy equation. 111 Fig. 6.4. Dangers of extrapolating empirical models. 113 Fig. 6.5. Graphs for screening data and models. 114 Fig. 6.6. Interpreting residual plots. 115 Fig. 6.7. Principal component and least squares fit to data. 116 Fig. 6.8. Serial correlation may be minimized by modelling growth as a function of initial size. 120 Fig. 6.9. The R² does not indicate how well a model fits the data. 126 Fig. 6.10. Different species groupings based on growth trends. 129 Fig. 7.1. Site index of western larch estimated from the height–diameter relationship. 139 Fig. 7.2. Height–diameter curves used to estimate site productivity in Callitris stands in south-eastern Queensland. 140 Fig. 7.3. Growth index equation for Cardwellia sublimis. ...... 144 Fig. 8.1. Periodic increment may be a better predictor of growth at the mean diameter and competition