Modelling the Growth and Yield of Tropical Forests

Jerome K. Vanclay

Submitted for the degree of Doctor of Science in Forestry
University of Queensland, June 1991.


Section 1. Information Needs and System Design

1. Vanclay, J.K., Henry, N.B., McCormack, B.L. and Preston, R.L. (1986) Interim Report of the Native Forest Resources Task Force. Queensland Department of Forestry, Brisbane.

2. Vanclay, J.K., Henry, N.B., McCormack, B.L. and Preston, R.L. (1987) Report of the Native Forest Resources Task Force. Queensland Department of Forestry, Brisbane.

3. Vanclay, J.K. (1990) Integrated Resource Monitoring and Assessment: An Australian Perspective of Current Trends and Future Needs. In: Global Natural Resource Monitoring and Assessments: Preparing for the 21st century, Proceedings of the international conference and workshop, Sept 24-30, 1989, Venice, Italy. American Society for Photogrammetry and Remote Sensing, USA. Pages 650-658.

4. Vanclay, J.K. (1988) Yield Regulation in Native Forests. In: Leech, J.W., McMurtrie, R.E West, P.W., Spencer, R.D. and Spencer, B.M. (eds) Modelling Trees, Stands and Forests. Proceedings of a Workshop in August 1985 at the University of Melbourne. School of Forestry, University of Melbourne, Bulletin No. 5. Pages 501-508.

5. Vanclay, J.K. (1990) Design and Implementation of a State-of-the-art Inventory Reporting and Yield Forecasting System for Indigenous Forests. In: Global Natural Resource Monitoring and Assessments: Preparing for the 21st century, Proceedings of the international conference and workshop, Sept 24-30, 1989, Venice, Italy. American Society for Photogrammetry and Remote Sensing, Pages 1072-1078.

6. Vanclay, J.K. (1988) Native forest inventory system users guide. Queensland Department of Forestry, Brisbane. Selected parts.

Section 2. Evolution of a Growth Modelling Approach

7. Vanclay, J.K. (1981) Report on a Joint Project with the Western Australian Forests Department under the Officer Interchange Program of the Queensland Public Service, 2 February to 15 May, 1981. Queensland Department of Forestry, Brisbane. Unpublished Report No. 2. Pages 20-41.

8. Vanclay, J.K. (1985) Strategy for Developing a Cypress Pine Growth Model. Queensland Department of Forestry, Brisbane, Cypress Pine Modelling Project Interim Report No 3.

9. Vanclay, J.K. (1988) A Stand Growth Model for Cypress Pine. In: Leech, J.W., McMurtrie RE., West, P.W., Spencer, R.D, and Spencer, B.M. (eds) Modelling Trees, Stands and Forests. Proceedings of a Workshop in August 1985 at the University of Melbourne. School of Forestry, University of Melbourne, Bulletin No. 5. Pages 310-332.

10. Vanclay, J.K. (1988) A Stand Growth Model for Yield Regulation in North Queensland Rainforests. In: Ek, A.R., Shifley, S.R, and Burk, T.E. (eds) Forest Growth Modelling and Prediction. Proceedings of IUFRO Conference, August 23-27, 1987, Minneapolis, Minnesota. USDA Forest Service Gen. Tech. Rep. NC-120. Pages 928-935.

11. Vanclay, J.K. (1989) A Growth Model for North Queensland Rainforests. Forest Ecology and Management 27:245-271.

12. Vanclay, J.K. (1989) A Stand Growth Model for Yield Prediction in Rainforests: Design, Implementation and Enhancements. In: Wan Razali Mohd., H.T. Chan and S. Appanah (eds) Proceedings of the Seminar on Growth and Yield in Tropical Mixed/Moist Forests, 20-24 June 1988, Kuala Lumpur. Forest Research Institute Malaysia. Pages 21-34.

Section 3. Assessment of Site Productivity

13. Vanclay, J.K. (1988) Precision in Modelling Native Forests. In: Leech, J.W., McMurtrie, R.E., West, P.W., Spencer, R.D. and Spencer, B.M. (eds) Modelling Trees, Stands and Forests. Proceedings of a Workshop in August 1985 at the University of Melbourne. School of Forestry, University of Melbourne, Bulletin No. 5. Pages 94-97.

14. Vanclay, J.K. and Henry, N.B. (1988) Assessing Site Productivity of Indigenous Cypress Pine Forest in Southern Queensland. Commonwealth Forestry Review 67(1):53-64.

15. Vanclay, J.K. (1989) Site Productivity Assessment in Rainforests: An Objective Approach Using Indicator Species. In: Wan Razali Mohd., H.T. Chan and S. Appanah (eds) Proceedings of the Seminar on Growth and Yield in Tropical Mixed/Moist Forests, 20-24 June 1988, Kuala Lumpur. Forest Research Institute Malaysia. Pages 225-241.

16. Vanclay, J.K. and Preston, R.A. (1990) Utility of Landsat Thematic Mapper Data for Mapping Site Productivity in Tropical Moist Forests. Photogrammetric Engineering and Remote Sensing 56(10):1383-1388.

17. Vanclay, J.K. (1990) Use of Remote Sensing. In: Natural Forest Rehabilitation Study Malaysia. Annex 3, Asian Development Bank, Manilla.

Section 4. Components of a Growth Model: Growth, Death & Harvesting

18. Vanclay, J.K. (1991) Data Requirements for Developing Growth Models for Tropical Moist Forests. Commonwealth Forestry Review 70(3):248-271.

19. Vanclay, J.K. (1985) Seasonal Growth Pattern of Cypress Pine. Queensland Department of Forestry, Brisbane, Cypress Pine Modelling Project Interim Report No 4.

20. Vanclay, J.K. (1985) Diameter Increment of Cypress Pine Stems: The Maximum Attainable Increment. Queensland Department of Forestry, Brisbane, Cypress Pine Modelling Project Interim Report No 6.

21. Vanclay, J.K. (1991) Aggregating tree species to develop diameter increment equations for  tropical rainforests. Forest Ecology and Management 42:143-168.

22. Vanclay, J.K. (1991) Compatible Deterministic and Stochastic Predictions by Probabilistic Modeling of Individual Trees. Forest Science 37:1656-1663.

23. Vanclay, J.K. (1991) Mortality Functions For North Queensland Rain Forests. Journal of Tropical Forest Science 4:15-36.

24. Vanclay, J.K. (1991) Modelling Changes in the Merchantability of Individual Trees in Tropical Rainforest. Commonwealth Forestry Review 70(2):105-111.

25. Vanclay, J.K. (1989) Modelling Selection Harvesting in Tropical Rain Forests. Journal of Tropical Forest Science 1(3):280-294.

Section 5. Applications and Implications for Management

26. Preston, R.A. and Vanclay, J.K. (1988) Calculation of Timber Yields From North Queensland Rainforests. Qld Dep. For. Tech. Pap. No. 47.

27. Vanclay, J.K. (1990) Effects of Selection Logging on Rainforest Productivity. Australian Forestry 53(3):200-214.

28. Vanclay, J.K. and Preston, R.A. (1989) Sustainable Timber Harvesting in the Rainforests of North Queensland. In: Forest Planning for People, Proceedings of 13th biennial conference of the Institute of Foresters of Australia, Leura, NSW, 18-22 September 1989. Pages 181-191.

29. Vanclay, J.K. (1991) Tropical Rainforest Logging in North Queensland: Was it Sustainable? Invited paper to Colloquium on Sustainability in Natural Tropical Forest Management, World Resources Institute, Washington D.C., March 21-22 1991.

30. Vanclay, J.K. (1990) Growth Modelling. In: Natural Forest Rehabilitation Study Malaysia. Annex 5, Asian Development Bank, Manilla.

31. Preston, R.A., Vanclay, J.K., Gibson, G. and Dale, G. (1989) Planning for World Heritage: Experiences and Future Directions for Use of Geographical Information Systems Presented at 13th biennial conference of the Institute of Foresters of Australia, Leura, NSW, 18-22 Sep 1989.

32. Vanclay, J.K. (1990) Research Needs for Sustained Forest Resources. Invited paper at Institute of Tropical Rainforest Studies Workshop on Rainforest Research and Management, Townsville, 4-6 May 1990.

Section 6. Book on Forest Growth Modelling

33. Vanclay, J.K. (1994) Modelling the Growth and Yield of Tropical Moist Forests. Manuscript, limited circulation.

Section 7. Other Contributions

34. Beck, R.D., Vanclay, J.K. and Others (1985) Plantation Timber Production and Utilization System (PLATIPUS) Feasibility Study. Queensland Department of Forestry, Brisbane. Pages 7-25.

35. Vanclay, J.K. (1986) Simulation models and information systems: their costs and benefits  Presented to Conversion Modelling Workshop, West Pennant Hills, Sydney, 7-8 October 1986.

36. Vanclay, J.K. (1988) PLATIPUS Physiology: Design of a Plantation Growth and Conversion Simulator Incorporating Silviculture and Wood Quality. In: Ek, A.R., Shifley, S.R. and Burk, T.E. (eds) Forest Growth Modelling and Prediction. Proceedings of IUFRO Conference, August 23-27, 1987, Minneapolis, Minnesota. USDA Forest Service Gen. Tech. Rep. NC-120. Pages 998-1005.

37. Vanclay, J.K. and Shepherd, PJ. (1983) Compendium of Volume Equations for Plantation Species used by the Queensland Department of Forestry. Queensland Department of Forestry, Technical Paper No. 36.

38. Vanclay, J.K. (1980) Small Tree Stem Volume Equations for Three Plantation Species. Queensland Department of Forestry, Research Note No. 32.

39. Vanclay, J.K. (1991) Tree Volume Equations for Slash Pine. Queensland Forest Service, Research Note No 43.

40. Vanclay, J.K. (1982) Volume to Any Utilization Standard for Plantation Conifers in Queensland. Queensland Department of Forestry, Research Note No. 36.

41. Vanclay, J.K. (1982) Stem Form and Volume of Slash Pine Thinnings in South East Queensland. Queensland Department of Forestry, Technical Paper No. 34.

42. Vanclay, J.K. (1982) Optimum Sampling of Sample Trees for Volume Equations. Queensland Department of Forestry, Research Note No. 35.

43. Vanclay, J.K. and Anderson, T.M. (1982) Initial Spacing Effects on Thinned Stem Volumes of Slash Pine in South East Queensland. Queensland Department of Forestry, Research Note No. 34.

44. Vanclay, J.K. (1986) Design for a Gene Recombination Orchard. Silvae Genetica 35:1-3.

45. Vanclay, J.K. (1991) Seed Orchard Designs by Computer. Silvae Genetica 40:89-91.

Introductory Statement

One of the current paradigms of forest management embraces the concept of sustained yield. This concept involves two fundamental components: 1) good land husbandry to prevent forest degradation and ensure continued productivity, and 2) scheduling the harvest to maintain continuity of supply. The former requires a knowledge of the ecology and silviculture of the forest, whilst the latter requires information regarding the extent, nature and growth of the resource. However, these are interrelated, as silviculture may influence growth, and the construction of realistic growth models requires a sound knowledge of silviculture and ecology.

Most Forest Services are good at collecting inventory data, but not so good at turning this data into information. Typical information needs include the ability to prepare tables showing stocking and volume by tree size and species for individual plots, selected strata and regions, as at the date of measure or simulated to some future date. The reliability of the information should also be indicated.

Efficient provision of such information requires an integrated system which facilitates the gathering of data and its transfer to computer, which enables the manipulation of area, inventory and growth data, and which allows reporting in a variety of forms to suit the needs of the forest manager. These basic information needs exist in all forests, both natural and planted, but are compounded in the tropical moist forests where there are many species, all sizes and unknown ages. My research has focussed on formulating and providing suitable information systems and numerical procedures to redress these deficiencies, particularly the development of growth models for the tropical moist forests.

Whilst information reporting is comparatively straight forward, the growth model required to prepare forecasts is complex. Many different modelling approaches are available, but most were developed for monospecific plantations and are unsuited to natural forests. A suitable approach for the tropical moist forest was developed by modifying the tree list approach to accommodate many species and integrating it with other components of the information system. Most of the papers submitted herein demonstrate the formulation, implementation and application of such a system. Others demonstrate the application of systems analysis and forest mensuration in information systems for plantation management. These papers are collated to emphasize some common themes, but many of the papers address more than one   theme. The themes used to collate papers include:

1. Information needs and system design,

2. Evolution of a growth modelling approach,

3. Site quality assessment,

4. Components of a growth model: growth, death and harvesting,

5. Applications and implications for management,

6. Book on forest growth modelling, and

7. Other papers on plantation growth modelling, volume equations, and seed orchard design.

All these topics are interrelated, and should not be viewed as ends in themselves, but rather as a means to provide useful resource information for forest management, and to enable the informed study of management implications.

Information Needs and System Design

Provision of information for forest managers, even for computer-literate individuals, requires more than providing access to inventory data and a growth model on a computer. Efficient provision of information requires a system, designed to facilitate the gathering, processing and reporting of data to satisfy the forest manager's needs. Only then do the data become information. Provision of such an integrated system requires an understanding of the needs of existing and potential users. Data collection procedures, databases and computer programs should be designed and implemented accordingly to satisfy these needs and to allow efficient transfer of data between the various components of the system.

The six papers in Section 1 illustrate the appraisal of the needs of forest managers and the design and implementation of a system to fulfill these needs. Surveying needs and designing a system accordingly sounds easy, but the track record of many forestry enterprises suggests otherwise. A forest manager who has, for a lifetime, relied on rules of thumb and gut reaction is not going to provide pearls of wisdom which concisely and explicitly describe his information needs from a computer. When asked for their information needs, many foresters respond "In our inventory, we measure .....", reflecting a data-oriented rather than an information needs outlook. When new yield forecasts are required, most foresters will commence more inventory (something tangible that they like doing), even though this is rarely the weakest component in the calculation. Thus a reliable assessment of information needs requires not only good rapport and an understanding of forest management, but also involves the production of a number of prototypes for evaluation under a range of scenarios (Paper 1). Although forest inventory is superficially analogous to supermarket stocktaking, forest management involves diverse objectives and interest groups, and information needs are correspondingly diverse. Thus standard reports are of little utility, and flexible reporting systems are essential (Paper 2).

Forest inventory (i.e. measurement of plots) satisfies only some of the information needed, namely the trees-per-hectare details. Additional information required but often overlooked includes the area data to give total rather than per-hectare data, estimates of sampling error to indicate the reliability of the data and strata in which more sampling is required, and a growth model to enable updating of data and forecasts of future conditions (Paper 4). Thus an information system should accommodate all these components, facilitate calculations and enable reporting in a range of different formats. Too often the end product of yield studies has been restricted to presentation of results rather than interpretation of results. The information system should make it easy to get results, so that users can concentrate on interpreting the results rather than just getting the results (Papers 5 & 6). The system should also indicate the reliability of the information (i.e. standard errors) so that forest managers and other interested parties can argue on the basis of facts, rather than about the ‘facts’.

Evolution of a Growth Modelling Approach

Most published growth models are for plantations and assume monocultures of known age. Other models for natural forests in temperate regions also require few species or known ages. These modelling techniques cannot be used in the tropical moist forest where there are many species, a wide range of tree sizes and where the ages of trees are not known and cannot be determined reliably. Several techniques (e.g. matrix models - see Section 6) involve assumptions which are untenable for yield prediction, and few approaches have proved useful for modelling the growth and yield of tropical moist forest.

The papers in Section 2 demonstrate the development, implementation and evaluation of several approaches suited to natural forests, and the evolution of a sufficiently flexible approach to provide a framework for modelling all the indigenous forests in Queensland. A modification of the traditional approach of stand table projection eliminated several unsatisfactory assumptions by fitting spline curves to the stand table to allow a non-uniform distribution within each class, and explicitly modelling the distribution of diameter increments to provide more reasonable growth estimates (Paper 7). Whilst this approach gave good results, it involved considerable mathematical complexity and could not be readily adapted to stands with many species (Paper 8). The cohort or tree list approach offered greater flexibility, and was progressively modified to enable all forest types in Queensland to be simulated within the same conceptual framework and single suite of computer programs (Papers 9-12). The current version of the simulation framework is conceptually the same as described in Paper 11, but incorporates the improvements suggested in Papers 12, 22 and 28. Individual species identities are retained throughout, and flexibility is provided through a look-up table which indicates for each species the growth and volume equations (Paper 6).

Site Quality Assessment

One of the biggest obstacles hindering reliable yield forecasts for tropical moist forests is the difficulty of assessing the site productivity - the capacity of the site to support biomass production. Whilst sophisticated methods for site assessment in plantations have evolved, few reliable procedures exist for uneven-aged forests. Most research in uneven-aged forests has ignored site differences, or has resorted to relatively crude estimates of stand height or log length.

The papers in Section 3 demonstrate the importance of site assessment in growth and yield forecasting (Paper 13), and the development of some suitable procedures for site quality assessment in uneven-aged forests comprising one (Paper 14) or many species (Paper 15) using the height-diameter relationship and the growth index respectively. Direct estimates of the growth index require permanent sample plots to be established and remeasured for several years, but there are indications that the growth index can also be determined indirectly from the presence or absence of certain indicator species (Paper 15), or from digital remote sensing data such as Landsat Thematic Mapper (Paper 16). Digital analysis of remotely sensed data may also be useful for other forms of site assessment, including the detection and mapping of areas degraded through logging or shifting agriculture (Paper 17).

Components of a Growth Model

The growth model requires functions to enable the prediction of diameter increment, deterioration, mortality and recruitment. A harvesting model is also required to predict the stand fraction removed in selection harvesting. The quality of these functions depends partly upon the quality of the data used, and partly on the form of the functional relationships used. The papers in Section 4 examine data needs and discuss the development of functional relationships.

Trees in tropical forests are characterized by an absence of annual growth rings, by buttressing, and by slow and/or variable growth rates, so that permanent plots with long remeasurement intervals are required to obtain reliable growth data (Papers 18 and 19). Seasonal fluctuations in growth rate and stem dimensions mean that plots should be remeasured on the anniversary of the previous measurement (Paper 19). These data provide the foundation for growth modelling and yield forecasting, and their importance cannot be overstated (Paper 18).

Diameter increment of individual trees can be predicted in many ways. One robust way for monospecific stands is to predict stand basal area increment and apportion this between the individual trees (Paper 9). However, it is prudent to determine the maximum attainable individual tree increment to provide a check on this approach. Several researchers have employed the greatest increments or the upper confidence interval of an increment function to provide this check, but these approaches may give a biased result. I favour the use of trees subjectively determined in the field to be free of competition (Paper 20). Whilst this approach gives good results in monospecific stands, it becomes complex to apportion stand increments in stands with many species, where it is more efficient to predict individual tree increments directly. However, where there are very many species, there are additional problems, which can best be overcome by amalgamating species into a reasonable number of groups for estimating equations (Papers 21 and 23).

The format of the diameter increment function is also important, and should be inherently constrained to provide realistic estimates and to be asymptotic to some reasonable maximum size, either explicitly (Paper 20) or implicitly (Paper 21). Predicting the probability of some specified movement rather than the actual increment offers several advantages, including the ability to include data otherwise rejected as outliers, and the ability to provide compatible deterministic and stochastic predictions (Paper 22).

Several other functions are required for a growth model. Functions are necessary to predict mortality (Paper 23), deterioration of merchantable trees (Paper 24) and to simulate selection harvesting (Paper 25). Simulation of harvesting includes several components: predicting those trees felled in harvesting, the proportion of these which are defective and yield no useful volume, and the incidence of damage to the residual stand (Paper 25). Equations are also required to predict recruitment of regeneration in the model. Several possible approaches are discussed in Paper 33. The most suitable approach is to use a two-stage model, using a logistic equation to predict the probability that any recruitment occurs in a given year, and a conditional linear regression to predict the amount given that some recruitment is known to occur (Paper 28).

Applications and Implications for Management

A growth model, or a yield prediction system, should not be an end in itself, but should be merely a means to an end, that end being the informed management of forests. Section 5 examines some of the applications of growth models and information systems for forest management.

The major applications of growth models include the preparation of yield forecasts, the estimation of sustainable yields (Papers 26 and 28), and the determination of impacts of repeated harvesting (Papers 27 and 29). However, growth models have other uses.

Even when derived subjectively, growth models enable simulations to investigate implications not able to be resolved otherwise. Thus even if subjective, they enable repeatable analyses to be performed for a range of alternatives enabling comparisons to be made (Paper 30).

Papers 31 and 32 look at land use planning needs in tropical rainforest, and considers needs for, and applications of inventory, remote sensing, geographic information systems and growth models in the broader aspects of forest management.

Book on Forest Growth Modelling

Growth models do not exist for most tropical forests, and the information to assist the development of models is not generally available. Journal articles have become complex and specialized whilst most general forest mensuration textbooks give growth models rather superficial treatment. Section 6 presents the manuscript of a textbook soon to be published. It provides a comprehensive introduction to growth model development, and draws together journal contributions relevant to tropical moist forest, identifies gaps in existing knowledge, and examines the relative merits of alternative methodologies.

Other Contributions

Section 7 reports contributions in the area of plantation forestry, including the design for a silvicultural growth model, taper and volume equations for plantation species, and computer programs for the design of seed orchards. All these contributions concern the application of quantitative methods to forest management. Two papers report the design and initial development of an advanced plantation growth model, several papers address conifer volume and taper equations, and two papers discuss seed orchard design.

Plantation forestry in Queensland has become increasingly intensive, with comprehensive site preparation, low initial stockings, weed control, fertilizer applications and high pruning with only one and sometimes no thinnings. These procedures incur high costs at establishment which are not recouped until harvesting, and forest managers need to know if these and other silvicultural alternatives such as mid-rotation fertilizing are warranted, how they influence wood characteristics and tree form as well as volumes, and how these affect veneer and sawn timber production. Most wood characteristics can be reliably predicted by modelling branches and three-dimensional growth ring patterns within individual trees. Computer technology and data available from plantation silviculture experiments enable such a model to be constructed, and Papers 34, 35 and 36 examine the design, costs and benefits of such a model.

Volume estimation is one of the most important aspects of forest mensuration. The Australian equation is the prevailing equation for tree volume estimation in plantations (Paper 37), and whilst it may provide reliable estimates for a broad range of merchantable tree sizes, it provides inferior predictions for small trees and is thus unsuitable for early appraisal of experiments. The product of basal area and tree height is probably the most robust simple index of early performance, but a volume equation based on the same relationship provides more meaningful units (Paper 38).

Other volume equations provide consistent and comparable estimates for a wide range of tree sizes (Paper 39). Utilization standards change with technology and demand, and the ability to predict volume to different specifications (e.g. small end diameter, minimum log length) provides great flexibility (Papers 40 and 41). Sample trees are necessary for the estimation of both volume and taper equations, but as they are expensive to measure, it is desirable to know how many and what sizes are necessary to achieve a specified precision. Paper 42 investigates these aspects. Paper 43 examines possible bias in volume estimates as a result of tree spacing and thinning.

Papers 44 and 45 consider optimal seed orchard design. Paper 44 considers the minimum orchard necessary to achieve all possible adjacencies between a specified number of clones so as to maximize natural cross-pollination between clones. Paper 45 derives an optimal design for a specified area and number of trees, which maximizes panmixis between unrelated clones. The latter program has been used to design all the Queensland Forest Service seed orchards during the past seven years.