Modelling anthropogenic impacts on the growth of tropical rain forests
- using an individual-oriented forest growth model for analyses of logging and fragmentation in three case studies
Peter K¨ohler Der Andere Verlag, Osnabr¨uck, Germany, 2000 ISBN 3-934366-99-6 Zugl.: Kassel, Univ., Diss., 2000
Cover: Dawn in Danum Valley, Sabah (Borneo), Malaysia October 1997 taken by P. K¨ohler Modelling anthropogenic impacts on the growth of tropical rain forests
- using an individual-oriented forest growth model for analyses of logging and fragmentation in three case studies
Modellierung anthropogener Einflusse¨ auf das Wachstum tropischer Regenw¨alder - Analyse von Holznutzung und Fragmentierung in drei Fallstudien unter Verwendung eines individuen-orientierten Waldwachstumsmodells
Inaugural-Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) im Fachbereich Physik der Universit¨at Gesamthochschule Kassel
vorgelegt von Dipl.-Phys.
Peter K¨ohler
aus Kassel Kassel, den 01.11.2000 Als Dissertation vom Fachbereich Physik angenommen am 01.11.2000
Erster Gutachter: Prof. Dr. Hartmut Bossel Zweiter Gutachter: Prof. Dr. Burkhart Fricke Drittes Mitglied der Promotionskommission: Dr. habil. Andreas Huth Viertes Mitglied der Promotionskommission: Prof. Dr. Albrecht Goldmann
Tag der m¨undlichen Pr¨ufung: 01.11.2000 ”If everyone complains bitterness, then to whom is the world?”
Zainal Abidin Jaafar
Overview
For answering questions concerning anthropogeneous impacts on tropical forest develop- ment the individual-oriented and process-based forest growth model Formind2.0 was developed. It simulates the spatio-temporal dynamics of uneven-aged mixed forest stands in areas of one hectare to several km2. The model describes forest dynamics as a mosaic of interacting forest patches of 20 m2×20 m2 in size. Within these patches trees are not spatial-explicitly distributed, and thus all compete for light and space following the gap model approach. Tree species diversity is aggregated into 5-20 plant functional types (PFT) on the basis of species maximum tree height and successional status. The carbon balance of each individual tree incl. photosynthesis and respiration is modelled explicitly. Thus, we can match measured diameter increment for different PFT, size and light condi- tions accurately. Allometric relationships connect above-ground biomass, stem diameter, tree height and crown dimensions. Beside increasing mortality through self-thinning in dense plots one of the main processes of mortality is gap creation by falling of large trees. This process as well as seed dispersal from mature trees interlinks neighbouring plots with each other. The model was parametrised for three different sites in South-East Asia and south- America: Sabah (Malaysia), Venezuela, and French Guiana. Model accuracy is tested with growth data from permanent sampling plots in Sabah. Sensitivity of various result variables on variation of most parameter values is tested and gives important insights into general model behaviour. Two examples of anthropogeneous impacts on tropical forest dynamics are management practise and fragmentation, both of major concern. Following applications are performed: Growth and yield of Venezuelan rain forest under various logging methods, intensities and cycles are analysed for their sustainability. Effects of logging (methods and cycles), fragmentation and recruitment assumptions on forest dynamics in Sabah are discussed. Finally, fragmentation impacts on mortality and recruitment are simulated and their effects on forest dynamic and biomass loss are evaluated for a forest site in French Guiana.
Keywords: abandoned land; basal area; dipterocarp forest; edge effects; forest growth model; Formind; fragmentation; French Guiana; functional groups; individual-oriented model; logging impacts; logging scenarios; Malaysia; maximum height; model; mortal- ity; plant functional types; rain forest; recruitment; secondary succession; simulation; successional status; sustainable timber harvest; tropical rain forest.
Contents
1 Introduction 15
2 An introduction to tropical rain forests 21
3 Concepts for the aggregation of tropical tree species into functional types and the application to Sabah’s lowland rain forests 25
4 The model Formind2.0 35
5 Comparison of measured and simulated growth on permanent plots in Sabah’s rain forests 51
6 Sustainable timber harvesting in Venezuela: a modelling approach 65
7 The effects of logging, fragmentation and recruitment on growth of di- pterocarp forest 85
8 Long-term response of tropical rain forests to the effects of fragmenta- tion: a simulation study 111
Summary 133
Zusammenfassung 139
Bibliography 145
AInventory data 165
B Lists of tree species 171
Danksagung 215 Account
Chapters of this thesis have been published as follows:
Chapter 3:
K¨ohler, P., Ditzer, T., & Huth, A. 2000b. Concepts for the aggregation of tropical tree species into functional types and the application on Sabah’s lowland rain forests. Journal of Tropical Ecology, 16(4), 591-602.
Chapter 5:
K¨ohler, P., Ditzer, T., Ong, R. C., & Huth, A. 2001. Comparison of mea- sured and simulated growth on permanent plots in Sabah’s rain forests. Forest Ecology and Management, 142(1-3), in press.
Chapter 6:
Kammesheidt, L., K¨ohler, P., & Huth, A. 2000. Sustainable timber harvest- ing in Venezuela: a modelling approach. Journal of Applied Ecology, in press.
Chapter 7:
K¨ohler, P., Ditzer, T., & Huth, A. 2000c. The effects of logging, fragmen- tation and recruitment on growth of dipterocarp forest. Journal of Ecology, submitted.
Chapter 8:
K¨ohler, P., Chave, J., Riera, B., & Huth, A. 2000a. Long-term response of tropical rain forests to the effects of fragmentation: a simulation study. To be submitted. Other publications by the author related to the topics of this thesis:
Ditzer, T., Glauner, R., F¨orster, M., K¨ohler, P., & Huth, A. 2000. The process-based stand growth model FORMIX3-Q applied in a GIS-environment for growth and yield analysis in a tropical rain forest. Tree Physiology, 20, 367–381.
K¨ohler, P. 1996. Ein individuenbasiertes Wachstumsmodell zur Simulation tropischer Regenw¨alder. Diploma thesis, University of Kassel, Germany.
K¨ohler, P. 1997. An individual based rain forest model: Formind. in Hahn-Schilling, B. (editor), Forest management with growth models. Malaysian-German Technical Cooperation Project, Forest Department of Sarawak, Malaysia, Kuching, Malaysia.
K¨ohler, P. 1998. Parameter research for the tropical rain forest growth model FORMIX4. Research report P9801, Center for Environmental Systems Research, University of Kassel, Germany.
K¨ohler, P. & Huth, A. 1998a. The effect of tree species grouping in tropical rain for- est modelling - Simulation with the individual based model Formind. Ecological Modelling, 109, 301–321.
K¨ohler, P. & Huth, A. 1998b. An individual based rain forest model - concepts and sim- ulation results. In: Kastner-Maresch, A., Kurth, W., Sonntag, M., & Breckling, B. (editors), Individual-based structural and functional models in ecology, number 52 in Bayreuther Forum Okologie.¨ Bayreuther Institut f¨ur Terrestrische Okosystem-¨ forschung, Bayreuth, 35–51.
Chapter 1
Introduction
Introduction Goldammer 1999; Laurance & Fearnside 1999; Nepstad et al. 1999; Hashimotio et al. The use of natural resources change our en- 2000). vironment directly and indirectly through With 36000 000 km 2 of forests, cov- effects which are not fully understood so far. ering a quarter of the total land sur- Climate change and an increase in mean face on earth, beside the oceans forests global temperature, the amount of carbon- are the biggest ecosystems on our planet. dioxide in the atmosphere, or rising sea lev- About 475 to 825 billion tons of carbon els are some examples of occurring effects are bound in the forests and thus they are (Fan et al. 1998; Chavez et al. 1999; Malhi & the biggest above-ground carbon storages Grace 2000). These anthropogeneous influ- (Murphy 1975; Enquete-Kommission 1990; ences will change our environment for cen- Grace et al. 1995; Fan et al. 1998; Pren- turies. Plants might react adaptivly to their tice & Lloyd 1998; Alexandrov et al. 1999b, changing environment (Pastor & Post 1988; 1999b). A further reduction of woodland Friend 1997; Cao & Woodward 1998; Tian and, following this, an increasing release of et al. 1998; DeLucia et al. 1999; Pounds carbon in the form of carbondioxide would et al. 1999; Stil et al. 1999; Hashimotio et al. certainly intensify climate changing effects. 2000). Huge ecosystems like forests might Currently, annual release of carbon and its buffer changes, caused for example by ex- input in the atmosphere are estimated at traction of timber woods over a long period. seven billion tons. About 20 % of the release But if natural catastrophes occur in ecosys- is caused by global deforestation (Enquete- tems, which have already been weakened, Kommission 1994; Houghton et al. 2000). damage is more dramatic than ever thought There are various reasons which make before (Phillips & Gentry 1994; Laurance forests worth protecting and sustainable et al. 1997; Phillips et al. 1998; Peres 1999; management desirable. Forests produce Gascon et al. 2000). Thus, forest fires in timber, firewood and food, act as lo- the Amazonian rain forest and the Indo- cal climate regulator, prevent erosion, and Malayan archipelago in the years 1997/1998 are important water storages. Addition- spread very fast. El Ni˜no, the Great South- ally, tropical rain forests are remarkable ern Oscillation, caused serious dry periods for their enormous biological species diver- (Leighton & Wirawan 1986; Walsh 1996; sity (Tuomisto et al. 1995; Hubbell 1997; Hartshorn & Bynum 1999), in which human Tilman 1999). It is assumed that 50-75 % made fires for land clearing could spread of all existing species are found in the tropi- easily to adjacent areas. These forest were cal wet forests (Terborgh 1993). In a survey already highly disturbed through logging to identify global extinction threats tropi- and forest management, and available dead cal regions were endangered the most (Sisk wood fuelled the fires further (Brown 1998; et al. 1994). For the conservation of as Kellman et al. 1998; Cochrane et al. 1999; 16 Chapter 1 many different species as possible the ap- detailed planning effort it might be possi- proach of biodiversity hotspots is proposed ble to manage tropical forests in a way that (Myers 1989; 1990; Reid 1998 Myers et al. ecosystems have a realistic chance for sus- 2000; Cincotta et al. 2000). Thus, areas tainable regeneration. On the global scale with highest diversity are considered most this is especially of interest, as case stud- valuable for protection. ies have shown that forests under reduced- Tropical rain forests covered roughly impact management will act as a sink for 18 000 000 km2 in the year 1990, corre- carbondioxide, compared to those under sponding to 13 % of earth’s land surface. commercial logging (Putz & Pinard 1993; Characteristics of tropical climate are a con- Pinard & Putz 1996, 1997). However, stant high temperature with monthly aver- the most important motivation for sus- ages above 18 ◦C and high precipitation (> tainable management are economic profit 100 mm per month) with no, or only short, on a short time scale (Plumptre 1996). dry seasons. Areas with those climatic Economic studies have verified increasing conditions are found in a belt of 40◦ lati- profit in well planned management (Bar- tude around the equator (Whitmore 1998). reto et al. 1998). Certification of trop- There are three regions where tropical rain ical timber wood is one of the possibil- forests occur: South and Central America, ities to support sustainable management central Africa and South-East Asia. strategies (Hahn-Schilling et al. 1994; Boot & Gullison 1995). Non-governmental or- Logging of timber, land clearing, slash- ganisations like the World Wildlife Found and-burn cultivation, high population pres- for Nature (WWF) are promoting this ap- sure and ongoing forest fragmentation are proach (Liedeker 1999; Forest-Stewardship- threatening tropical forests (Aiken & Leigh Council 2000). The controversial discussion 1993; Cannon et al. 1998; Brown 1998; about criteria of sustainability is certainly Grainger 1998; Foster et al. 1999; Rosen- not finished (Johns 1985, 1997; F¨olster et al. zweig 1999; Hughes et al. 2000). Reduc- 1986; Brown & Lugo 1990, 1994; Bruenig ing those impacts and changing to sus- 1996; Ong et al. 1996; Putz & Viana 1996; tainable development is needed to stop Weidelt 1996; Rice et al. 1997; Bowles et al. the extinction of various animal and plant 1998). species (Terborgh 1993; Laurance et al. 1997; Bowles et al. 1998; Whitmore 1998). For an estimate of annual allowable cuts The Food and Agriculture Organisation of (AAC) knowledge on the main processes the United Nations (FAO) estimated the an- of forest dynamics is essential. In tem- nual loss of tropical forests at 169 000 km2 perate forests, management planning was in 1990 with increasing tendency (Riswan based on modelling and computer simula- & Hartanti 1995; Laurance 1999b). If these tions over some decades (e.g. Botkin et al. trends of deforestation continue most trop- 1972; Shugart 1984, 1998; Battaglia & ical forest will be destroyed within the 21st Sands 1998; Borgesa & Hoganson 2000). century. Thus, long-term tendencies of forest dynam- ics can be estimated under changing condi- From an ecological point of view it might tions. be desirable to declare as many forest ar- eas as possible as protection zones with a Modelling of tropical rain forests started total ban of timber logging (Whitmore & in the early nineties with models of various Sayer 1992). Very often those idealistic con- complexity (e.g. Adlard et al. 1989; Alvarez- servation ideas conform with public opin- Buylla & Garcia-Barrios 1991, 1993; Bossel ion and policy making in developed coun- & Krieger 1991, 1994; Alder 1992; Howard tries, but neglect local needs for fuel, tim- & Valerio 1992; Vanclay 1994; Osho ber for construction and labour. With a 1995, 1996; Albers 1996; Alder & Silva Introduction 17
2000). Available data sets from long- (e.g. the model Formal (K¨urpick et al. term ecological research plots, (Nakashizuka 1997) needs the maximum tree age as an in- et al. 1999; Smithsonian-Tropical-Research- put parameter, which can be estimated only Institute 2000) and simulation studies in roughly) others come up with elegant math- the context of international climate protec- ematical equations (Kaspar 1996). Models, tion programmes (IGBP 1990) led to an in- which are not only used for testing ecologi- creasing interest in rain forest models in re- cal hypothesis, but for model application in cent years (Liu & Ashton 1998, 1999; Chave forestal management planning are of special 1999a, b; Pinard & Cropper 2000). Another interest (Ditzer 1999; Ditzer et al. 2000). motivation for developing models for trop- Problems of these approaches arise be- ical forest growth was management plan- cause they are mostly based on an aggre- ning, very often with the cooperation of Eu- gation of tree species in a few (3-5) species ropean developing projects and local gov- groups, which are easy to parametrise, but ernmental institutes, e.g. the British gov- simplify ecological processes of rain forests ernment in Indonesia (van Gardingen & greatly. Concepts of species grouping in Phillips 1999) or the German Gesellschaft tropical rain forests based on a more sys- f¨ur Technische Zusammenarbeit (gtz) in tematic approach were developed only re- Malaysia (Ong & Kleine 1995, 1996; Ditzer cently (Gitay et al. 1999; K¨ohler et al. 1999; Ditzer et al. 2000; Huth & Ditzer 2000b; Phillips et al. 2000). They are 2000a,b). The focus of these schemes was in the most important for all further work of South-East Asia, where deforestation rates this thesis. Furthermore, analysis in Kas- were highest in the last decade (Plumptre sel showed the largest potential for data 1996). Current rates of forest loss in Latin- based model development in individual- −1 America (7.4 million ha y )arenearly based models (Huston et al. 1988; DeAn- twice as high as those in Asia (3.9 million ha gelis & Gross 1992; Judson 1994; Liu & −1 y ) (FAO 1997). Modelling approaches de- Ashton 1995), as computation time was not pend on available field data used for model a limiting factor anymore, because of im- Symfor development. Thus, the model provements in computer capabilities. was developed in tight cooperation with log- Formind ging companies and for instant application The model developed by the in forest management planning and depends author in previous studies (K¨ohler 1996; mainly on inventory data collected by the K¨ohler & Huth 1998a, 1998b) was the ba- companies (Young & Muezelfeldt 1998; van sis of the further research and development Formind Gardingen & Phillips 1999), while Chave presented in this thesis. is an and colleagues (Chave et al., unpublished individual-based model, while the parallel Formix3-Q manuscript) are interested in long-term de- development of (Ditzer et al. velopment of rain forest migration and try 2000) is still based on a simple matrix ap- to understand seed dispersal patterns found proach, incl. transition rates between classes in paleoecological research. of different tree size. As result of the chosen approach, the model structure of Formind Various projects of the research group was more flexible and an application with Ecosystem Modelling at the Center of En- different numbers of species groups was easy vironmental Research, University of Kassel, to perform (K¨ohler & Huth 1998a). Germany, for the Deramakot Forest Reserve showed dependency of simulation results Two main targets are the focus of on the chosen modelling approach (Haupt this work. First, no existing model of 1995; Kaspar 1996; K¨ohler 1996; K¨urpick rain forests growth was applied to tropical 1 et al. 1997; Ditzer 1999; Huth 1999). While forests in various regions . This work tries some models are difficult to parametrise 1Ditzer (1999) was developing a concept of site 18 Chapter 1 to show that, with a model structure cov- only Chapters 2 and 4 have not been pub- ering all main processes, sites in various re- lished or submitted for publication. The gions can be simulated. Second, most pre- Chapters are arranged in chronological or- vious work was based on a forest recruit- der to allow a comprehensible understand- ment module covering only simple princi- ing of model improvement. ples. Ongoing forest fragmentation will de- An introduction to rain forest dynamics termine recruitment as one limitating factor is given in Chapter 2. A general approach in rain forest dynamics (Ribbens et al. 1994; to tree species grouping, based on avail- da Silva & Tabarelli 2000). Thus, beside able data sets, follows thereafter (Chap- general model improvement and enhance- ter 3, K¨ohler et al. 2000b). The model For- ment the development of new approaches mind2.0 used in this thesis is completely for modelling of recruitment is one of the described in Chapter 4. Chapter 5 consists main focuses of this work. The resulting of a validation of the model in its version Formind2.0 new model will be used to an- Formind1.1 with field data from Sabah swer various questions: (K¨ohler et al. 2001). Additional analysis of the same data with current versions of the 1. Is there a general approach for clas- model close this Chapter. Besides an inten- sifing several hundred tree species in sive sensitivity analysis of model behaviour, different rain forest sites into a few various logging methods and intensities in groups? a Venezuelan rain forest are analysed in 2. Does simulated tree growth match Chapter 6(Kammesheidt et al. 2000). An measured data sets with acceptable ac- application of the model to a rain forest site curacy? in Sabah (Malaysia) is performed in Chap- ter 7. The influence of various recruitment 3. Which logging method and rotation modules and their impacts on timber log- length can be called sustainable de- ging are analysed in detail (K¨ohler et al. pending on the forest site? 2000c). The model application to French Guiana contains an analysis of the effects 4. How does recruitment determine forest of forest fragmentation on further forest dy- growth and yield? namics (Chapter 8, K¨ohler et al. 2000a). 5. Can tropical rain forests buffer the ef- Finally, the methods and most important fects of ongoing fragmentation? results related to questions posed are sum- marised incl. an outlook. This summary is For this purpose three different rain written in both German and English. forest sites, in South-East Asia (Sabah, Data collections (inventory data and lists Malaysia) and South-America (Venezuela of tree species), which were needed for sim- and French Guiana), were parametrised ulations, are found in the Appendix. (Fig. 1.1)2 Besides the introduction, this thesis con- sists of seven further chapters from which depending parametrisation, but was restricted to dipterocarp lowland rain forests in South-East Asia. 2At the time of planning this research project a cooperation with a project in Kenya (Africa) ex- isted.Thus, it seemed possible to apply the model to all three global rain forest regions.Unfortu- nately the leader of the gtz-project was shot dead two days before cooperation started and the project was closed thereafter. Introduction 19
Caparo Venezuela
Deramakot Sabah (Malaysia) Piste de Saint-Elie French Guiana
Figure 1.1: Global distribution of forests, including research plots used in this thesis.The map is based on data collected between 1980 and 1990 (from WWF 1997).
Chapter 2
An introduction to tropical rain forests
In the following chapter some fundamen- is based on systematic combination of infor- tal characteristics of tropical rain forests are mation on temperature and water availabil- described. I focus on processes which are ity (Terborgh 1993; Shugart 1998). Cur- important to understand growth dynamics rently, a framework for a worldwide com- of the forest trees and their species compo- parison of tropical woody vegetation types sition. A more detailed description of the is developed (Blasco et al. 2000). ecology of tropical forests is found in sev- Classically, the term rain forest describes eral informative text books (Richards 1952, evergreen tropical lowland wet forest up to 1996; Whitmore 1984, 1993, 1998; Jacobs an elevation of 750 m. Those are closed 1988; Lieth & Werger 1989; Terborgh 1993; large growing forests found in latitudes be- MacKinnon et al. 1996; Huth 1999). The tween 10◦ north and 10◦ south with high objective of the current chapter is not to go precipitations without seasonal dry peri- into the details of the ecological processes, ods. Evergreen tropical wet forests covered but to explain some basic facts about the about 7 million km2 of land surface in 1993, ecology of tropical rain forests. Thus, the mainly in the Amazon-Orinoco area (Amer- following introduction will be rather brief. ican rain forest formation), at the Gulf of Guinea and in the water catchment of the Congo river (African rain forest formation), Evergreen lowland rain forest in Sri Lanka, Western India, Thailand, In- dochina, on the Philippines, in Malaysia, In- The tropics are mostly defined by their cli- donesia, New Guinea (Indo-Malaysian rain mate conditions. In tropical regions daily forest formation), and on the east coast of temperature fluctuations exceed average an- Australia (Enquete-Kommission 1994). nual temperature variability. Thus, trop- ical regions are extended north and south Lowland rain forests are by far the most of the equator until daily and annual tem- diverse plant communities on earth. Up to perature variability match each other (Lam- 400 different tree species are found in one precht 1986; Enquete-Kommission 1990). hectare (Terborgh 1993). The largest trees reach heights of 45 to 60 m, in a few cases up The most important site factors for vege- to 70 m. The tree crowns of those large in- tation formations are temperature, precipi- dividuals, called emergents, rise above the tation, light, and soil conditions. For an ex- closed forest canopy, which reaches about plicit differentiation of several tropical for- 30 m in height. Depending on light condi- est formations, climate, soil water, soil qual- tions small trees and saplings are found be- ity and elevation are considered (see Ta- low the canopy. Ground vegetation is rare ble 2.1). In Central America vegetation is in dense closed forests and consists mainly classified after a scheme of Holdridge, which 22 Chapter 2. An introduction to tropical rain forests
Table 2.1: Classification of tropical wet forests (from Whitmore 1998).
Climate Soil water Soils Elevation Forest formation
Seasonally Strong annual shortage Monsoon forests (various dry formations) Slight annual shortage Semi-evergreen forest Everwet Dryland Zonal Lowlands Lowland evergreen (perhumid) (mainly rain forest oxisols, (750) 1200-1500 m Lower montane rain forest ultisols) (600) 1500-3000 m Upper montane rain forest 3000 m to tree line Subalpine forest Podzolized Mostly lowlands Heath forest sands Limestone Mostly lowlands Forest over limestone Ultrabasic Mostly lowlands Forest over ultrabasics rocks Water Coastal salt- Beach vegetation, Man- table water grove forest, Brackish wa- high ter forest (at least Inland fresh- Oligotrophic Peat swamp forest periodi- water peats cally) Eutrophic ±Permanently wet Freshwater swamp forest (muck and mineral Periodically wet Freshwater periodic soils) swamp forest of recruitment of young trees. Shrubs and into two or three ecological classes (Denslow bushes are found in single areas (Whit- 1987; Whitmore 1998; Thomas & Bazzaz more 1998). This sort of layer structure 1999). Pioneers and climax species are the is controversially discussed in the literature extreme positions in a more or less contin- (Richards 1936; Terborgh & Petren 1991). uous spectrum. While pioneers establish While a model for light distribution in for- early in succession of available areas, climax est canopies tries to explain the structure or late successional species follow last in a (Terborgh 1993), new mathematical analy- succession process. Most important charac- sis of different vertical forest structures for teristics of pioneers and climax species are tropical and temperate regions found no dif- summarised in Table 2.2. ferences between them and only a few dis- Seeds of climax species germinate and es- tinct layers in both regions (Baker & Wilson tablish in the shade of the own mature com- 2000). munity. Therefore, they are called shade- All other rain forest formations differ tolerant. They are the dominant plant from this type through simpler structures, species in undisturbed primary forests and lower species diversity and a smaller spec- contribute mainly to the main canopy of trum of life forms. For means of simplicity a rain forest. The largest individuals nor- we address evergreen tropical lowland rain mally belong to those species (Whitmore forest by the short term rain forest. 1998). The second category are the pioneers. Their seeds depend on light and can only Tree species germinate and establish in forest gaps. Height growth is fast, and thus shade- Tree species in rain forests can be distin- tolerant competitors are suppressed. Pio- guished, after their successional behaviour, neer tree species are seldom found in ma- 23
Table 2.2: Most important characteristics of pioneer and climax species in tropical rain forests (from Whitmore 1998).
Pioneers Climax
Common alter- Light-demander, (shade-) intolerant, sec- Shade-bearer, (shade-) tolerant, primary native names ondary Germination Only in canopy gaps open to the sky Usually below canopy which receive some full sunlight Seedlings Cannot survive below canopy in shade, Can survive below canopy, forming a never found there ”seedling bank” Seeds Usually small, produced copiously and Often large, not copious, often produced more or less continuously, and from early annually or less frequently and only on in life trees that have (almost) reached full height Soil seed bank Many species Few species Dispersal By wind or animals, often for a consider- By diverse means, including gravity, able distance sometimes only a short distance Dormancy Capable of dormancy commonly abun- Often with no capacity for dormancy, sel- dant in forest soil as a seed bank dom found in soil seed bank Growth rate Carbon fixation rate, unit leaf rate, and these rates lower relative growth rates high Light compensa- High Low tion point Height growth Fast Often slow Branching Sparse, few orders Often copious, often several orders Leaf life Short, one generation present, viz.high Long, sometimes several generations turn-over rate present so slow turn-over rate Wood Usually pale, low density Variable, pale to very dark, low to high density Longevity Often short Sometimes very long
ture primary forests, but are most domi- dynamic equilibrium, gap creation and re- nant in secondary forest following regrowth growth within them balance each other of abandoned land, or in highly disturbed (Shugart 1984, 1998; Brokaw 1985; Brokaw forests after logging or catastrophic events. & Scheiner 1989; Platt & Strong 1989; Bel- The canopy of those forests is not closed and sky & Conham 1994). light demanding plants dominate the sites. Gaps are first filled with pioneers. In Tree species of medium characteristics, a second growth cycle, climax seedlings es- called mid successional species, are also dis- tablish themselves underneath the pioneers. tinguished. They are neither pioneer, nor After the death of the short-living pioneer climax (Whitmore 1998). species, established climax trees grow and fill the gap. It takes between several decades and some centuries until trees of sizes simi- Succession and gap dynamics lar to mature forest dominate those former gap areas (Whitmore 1998). A forest gap is a not-fully-closed canopy within a mature forest. Gaps are created This growth cycle is called succession. It by the falling of large trees, often causing is essential for the simultaneous coexistence the destruction of several other, i.e. smaller of tree species with different successional trees. As mature forest stands are in a behaviour in forests. 24 Chapter 2. An introduction to tropical rain forests
In tropical rain forests annual mortal- show that even in areas with dry seasons ity rates of trees with a diameter ≥10 cm of a few months some small, but effective are about 1-3 % (Swaine 1989; Phillips & model improvements will lead to acceptable Gentry 1994). Mortality rates cover dead results (Chapter 6). It should be mentioned standing trees, fallen individuals and those that dry periods as caused regularly by the which were smashed by collapsing trees. Great Southern Oscillation, El Ni˜no, will The causes of tree falls are wind, heavy rain result in significantly higher tree mortality fall and others. Field data show that an- rates (Walsh 1996). nually up to 1.5 % of standing trees fall Soil investigations show that two thirds over and thus 90 % of mortality is connected of all tropical soils have average to very low with gap creating events (van der Meer & fertility. Generally, agriculture can only be Bongers 1996). performed for a very short period of a few In the literature the definition of a forest years before soils become infertile. It has gap is widely discussed (Vandermeer 1994; been shown that above-ground growth of van der Meer et al. 1994). For example, tropical forests depends little on soil fer- Brokaw (1982) defined a gap as a missing tility (F¨olster et al. 1986; Terborgh 1993). canopy, which reaches down to 2 m above Endemic species are very well adapted to the forest floor. Others (van der Meer & nutrient-poor conditions. Plant growth de- Bongers 1996) define it as a canopy gap pends on very effective and fast decompo- reaching down to 20 m above the floor. For sition processes in the top soil layer. Most comparing field studies, gap definition is nutrients are bound in the living biomass, crucial. Thus, the range of gap numbers and and only about 20 % are depleted and reen- gap sizes varies widely (Barden 1989; Run- ter through precipitation and mineral rock kle 1989). With the second definition given erosion. Heavy disturbances of those cycles above, a neo-tropical rain forest in Panama through clearing, erosion or damage of the would have a gap fraction of 34 % (Hubbell humus layer might lead to massive nutrient & Foster 1986a). depletion. Thus, in these soils forests might Disturbance of forests by gap creation not grow to their former complexity and size can be distinguished in three different areas. (Terborgh 1993). In the region of the roots of the falling tree, Dependence of forest dynamics on soil the forest floor is damaged. Light intensity conditions and slope was analysed in other is increased through the missing tree crown studies (Biehounek 1999; Clark et al. 1999a; above. Beside the trunk of the falling tree Ditzer 1999; Glauner 1999; Ditzer et al. the disturbance is weak. The crown of the 2000), and is not the subject of the current falling tree destroys most trees, especially in thesis. We assume in the following more or the understorey (Hubbell & Foster 1986a). less undisturbed nutrient cycles. Investiga- tions of nutrient inputs through air and rain on Borneo support this approach (Weidelt Water and nutrient cycles 1993). The implications of this simplifica- tion are discussed in Chapter 4. As precipitation in the tropics is high and regular (e.g. Sabah on Borneo, Malaysia: 3505 mm per year, Schlensog 1997) without distinct dry seasons, water is not a limit- ing factor in tree growth (Friend 1993). An explicit description of water cycles within the model is therefore not necessary for ac- curate modelling results. Applications will Chapter 3
Concepts for the aggregation of tropical tree species into functional types and the application to Sabah’s lowland rain forests
Peter K¨ohler, Thomas Ditzer and Andreas Huth
Center for Environmental Systems Research, University of Kassel Kurt-Wolters-Str. 3, D-34109 Kassel, Germany
Abstract
For analysing field data as well as for modelling purposes it is useful to classify tree species into a few functional types.In this paper a new aggregation of tree species of the dipterocarp rain forests in Sabah (Borneo), Malaysia, is developed.The aggregation is based on the two criteria successional status and potential maximum height.Three classes of successional status (early, mid and late successional species), five classes of potential maximum heights (≤5 m, 5–15 m, 15–25 m, 25–36 m, > 36 m) and their systematic crossing lead up to 15 functional types.The criteria of the developed classification are chosen to fit applications with process-based models, such as Formix3 and Formind, which are based on photosynthesis production as the main process determining tree growth.The concept is universal and can easily be applied to other areas.With this new method of grouping a more realistic parametrisation of process-based rain forest growth models appears possible.
Keywords: dipterocarp forest, Malaysia, maximum height, model, plant functional types, successional status, tropical rain forest Journal of Tropical Ecology (2000) 16(4), 591-602. 26 Chapter 3
Introduction (2) Classification based on differences in potential maximum height. Richards (1936) was the first to derive a grouping concept Tropical rain forests are known for their in tropical rain forest research when he de- great tree species diversity with up to sev- scribed the layering structure of rain forest eral hundred different tree species in one canopy and distinguished tree species ac- hectare (Groombridge 1992). Their ecology cording to potential canopy layers. This ap- and physiology have been increasingly stud- proach was developed further by various re- ied in the last decades (e.g. Bazzaz & Pick- searchers (Hubbell & Foster 1986a; Swaine ett 1980; Mooney et al. 1980; Leigh et al. & Whitmore 1988; Poker 1995; Condit et al. 1985; Mulkey et al. 1996; Whitmore 1988, 1996; Denslow 1996). 1995, 1998). For generalization of ecologi- cal results for single species as well as for (3) Intensive statistical data analysis of modelling purposes different concepts have diameter growth pattern, for a specific site been developed for aggregating tree species to derive groups with significant different diversity in tropical forests into few plant diameter increment behaviour (Host & Pre- functional types (PFTs). gitzer 1991; Vanclay 1991; Ong & Kleine 1995). The principles of species aggregation into PFTs have been discussed widely (Botkin (4) Approaches which combine several 1975; Smith et al. 1993, 1997; Box 1996; Gi- concepts together. Lieberman et al. (1985 tay & Noble 1997; Lavorel et al. 1997). As 1990) combine diameter growth analysis pointed out by Gitay & Noble (1997) there with maximum size, Acevedo et al. (1995), is no universal classification or concept for Condit et al. (1996) shade-tolerance with the development of PFTs, the type of classi- maximum height, Shugart (1984, 1997) gap fication depends on the context of the per- requirements for regeneration with maxi- formed aggregation. PFTs are often used mum size. Kammesheidt’s (2000) classifi- in global vegetation models (Cramer 1997; cation is based on all available data con- Leemans 1997) and climate change analy- cerning different criteria as growth form, es- sis (Bugmann 1996a). For forest ecosystems tablishment, phenology, etc. In single case the following conceptual approaches can be studies pioneer species are distinguished distinguished: from other tree species, which are fur- ther subdivided (Manokaran & Kochum- (1) Grouping based on physiological cri- men 1987; Manokaran & Swaine 1994; teria such as shade tolerance at different Bossel & Krieger 1991; K¨ohler & Huth life stages (Hubbell & Foster 1986b; Whit- 1998a, b). more 1988, 1989, 1998). This concept varies from the rough distinctions whether Within the context of modelling, group- species are early or late successional ones ing concepts become important for integrat- (Shugart 1997) to more exact differentia- ing field data in terms of parameter values tions of several aspects of plant behaviour in models and for comparing typical simu- and growth strategies for light demanding lation results with observations (Vanclay & pioneer species and shade-tolerant climax Skovsgaard 1997). Interpretation of results species (Whitmore 1989). While Swaine & is easier with a small number of functional Whitmore (1988) state that it is difficult to types, where by with increasing number of distinguish more than the mentioned two PFTs accuracy increases as well. groups, Kammesheidt (2000) distinguishes Approaches already published are unsat- early, mid and late successional species. isfactory for the purpose of process-based However, Swaine & Whitmore suggest to modelling for two reasons. First, the bal- subdivide the two major ecological groups ance between adequate and necessary ac- into further sub-groups. Plant functional types in Sabah’s rain forests 27
Table 3.1: Successional status (SS) of 468 Swaine & Whitmore 1988). In the context of Sabah’s lowland tree species.No: Num- of modelling we define different successional ber of species per SS.Ab: Abundance of trees status as (a) different light requirements for with diameter > 10 cm in forest inventories the establishment of seedlings, (b) different in Deramakot, Lingkabau, Kalabakan and Ulu growth rates in a given light regime for trees Segama. of similar size, and (c) differences in mortal- ity rates. While early successional species Successional status SS No Ab [%] grow fast they tend to build low-density stems, in contrast to the slow growing late successional species which have higher wood Early successional spp. 1 31 24.8 densities. Based on the correlation between Mid successional spp. 2 317 63.4 wood density and growth rate a data set Late successional spp. 3 120 11.9 of Ong & Kleine (1995) on wood density covering 468 tree species was used to de- rive species successional status. Apart from typical pioneers (classified as early succes- sional spp. in our context), Ong & Kleine curacy has so far not been dealt with sat- distinguish timber groups of light, medium isfactorily. Most approaches use very few and heavy hardwood species. We classify (e.g. five) or many (20–50) PFTs, where those light and medium hardwood species 10 to 20 PFTs seems to be more appropri- as mid-successional, and heavy hardwoods ate, if both interpretation and accuracy is as late successional species. In a few of concern. Second, no approach is generic cases (including an undefined group, called in its concept and easily applicable to differ- OTHERS), grouping differs due to addi- ent forest sites using available data to derive tional knowledge on successional behaviour the appropriate number of PFTs. We there- (Rundi, pers. comm.). The quality of fore develop a universal approach, based on the timber group classification is verified the systematic combination of well estab- through a literature survey on wood den- lished classifications into different succes- sity (Meijer & Wood 1964; Burgess 1966; sional status and maximum height at matu- rity to derive about 10–20 PFTs, and apply Table 3.2: Aggregation of 468 of Sabah’s low- the concept to tropical lowland rain forests land tree species into five height groups (HG). in Sabah, Malaysia. Corresponding canopy layer.H: Height range at maturity.No: Number of species per HG. Ab: Abundance of trees with diameter > 10 cm in forest inventories in Deramakot, Lingkabau, Methods Kalabakan and Ulu Segama.
Criteria for the development of Canopy layer H [m] HG No Ab [%] plant functional types
We choose as grouping criteria successional Shrubs 0- 5 1 15 5.7 status (as defined in detail below) and at- Understorey 5-15 2 97 13.5 tainable maximum height. Lower canopy 15-25 3 119 32.9 We distinguish early, mid and late suc- Upper canopy 25-364 117 21.9 cessional species. We are aware of several Emergents >365 120 26.0 different nomenclatures for these classes (e.g. pioneers, non-pioneers), but find this the most appropriate (for alternatives see 28 Chapter 3
Table 3.3: Autecological characteristics of 13 plant functional types (PFTs) of Sabah’s lowland tree species.Height at maturity.SS: related successional status (Table 3.1).HG:related height group (Table 3.2). No: number of species per PFT. Ab: Abundance of trees with diameter > 10 cm in forest inventories in Deramakot, Lingkabau, Kalabakan and Ulu Segama.
Plant functional type Height [m] PFT SS HG No Ab [%]
Shrub mid successional spp. 0-5 1 2 1 15 5.7
Understorey early successional spp. 5-15 2 1 2 5 0.4 Understorey mid successional spp. 5-15 3 2 2 28 4.7 Understorey late successional spp. 5-15 4 3 2 65 8.3
Lower canopy early successional spp. 15-25 5 1 3 14 19.0 Lower canopy mid successional spp. 15-25 62 3 92 13.6 Lower canopy late successional spp. 15-25 7 3 3 13 0.3
Upper canopy early successional spp. 25-368 1 4 10 4.1 Upper canopy mid successional spp. 25-369 2 4 89 16.0 Upper canopy late successional spp. 25-3610 3 4 18 1.8
Emergent early successional spp. >3611 1 5 3 1.2 Emergent mid successional spp. >3612 2 5 93 23.3 Emergent late successional spp. >3613 3 5 24 1.5
Fox 1970; Cockburn 1980; Keating & Bolza determined using the literature (Meijer & 1982; PROSEA 1994). Wood 1964; Burgess 1966; Fox 1970; Whit- more & Ng 1972; Cockburn 1980; Keat- The maximum potential height hmax of trees is grouped into five classes for Sabah’s ing & Bolza 1982; PROSEA 1994). In rain forests. The classes can be named some cases, where no data on maximum according to their canopy layers as emer- height were available maximum girth or di- ameter was used to determine maximum gents (hmax > 36m), upper main canopy height by using height-to-diameter func- (25 m
Table 3.4: Diameter increment rates [mm y−1] for different successional status SS (early (1), mid (2) and late (3) successional spp.). N: sample size. P-values of χ2-test.
Location SS N χ2 P 123
Garinono 3.3 4.1 2.8 7694 0.33 0.85 Sepilok 4.8 3.9 2.9 6435 0.43 0.81 Segaliud Lokan1 5.0 4.9 4.2 6132 0.11 0.95 Segaliud Lokan2 6.6 5.4 4.6 2213 0.47 0.79
Table 3.5: Average annual mortality rates [% y−1] for different successional status SS (A: early (1), mid (2) and late (3) successional spp.). Sample size see Table 3.4. P-values of χ2-test.B only distinguishes between early (1) and non-early (4) successional spp.
AB Location mean SG SG 123χ2 P4χ2 P
Garinono 2.6 3.8 1.9 2.7 0.75 0.69 3.2 0.68 0.41 Sepilok 5.1 6.6 4.7 7.5 1.6 0.45 5.0 2.68 0.10 Segaliud Lokan1 5.1 8.4 4.4 3.9 2.54 0.28 6.4 2.48 0.12 Segaliud Lokan2 6.3 9.8 3.4 2.9 5.15 0.08 4.8 2.24 0.13
mortality rates differ in the different PSPs tween mid- and late successional species (Garinono: 2.6% y −1; Segaliud Lokan1: easily. However, differences between early 5.1 % y−1; Segaliud Lokan2: 6.3 % y−1 and and non-early successional spp. are seen Sepilok: 5.1 % y−1) and over time, indi- clearly (Table 3.5B). Differences between cating changes with dry years as observed groups increase as analysis is focused on two in Sabah in 1982/83 (Walsh 1996). Mor- groups only. tality is unexpectedly high in all observa- The discussion (by Hubbell et al. (1999)) tions, compared to normally observed an- about recruitment limitations and abun- −1 nual mortality rates of 1–2 % y in tropi- dances of seedling in canopy gaps cannot cal rain forests (e.g. Manokaran & Swaine be broadened to include our concepts yet, 1994). Mortality rates decline from early because data available on recruitment pat- to late successional species in the two ar- terns (FMU inventories) lack information eas in Segaliud Lokan, whereas in Garinono on canopy structure. and Sepilok, beside highest mortality rates in early successional spp., mid-successionals have lowest rates (Table 3.5A). The group- ing might not resolve the differences be- 32 Chapter 3
Table 3.6: Average annual mortality rates [% y−1] of mid- and late successional spp.for different height groups (shrubs (1), understorey(2), lower main canopy (3), upper main canopy(4) and emergent (5)).N: sample size.P-values of χ2-test.
Location mean Height group N χ2 P 12345
Garinono 2.0 3.4 3.0 1.61.60.9 4867 2.28 0.68 Sepilok 5.0 9.2 7.0 4.1 4.4 4.3 5825 4.63 0.33 Segaliud Lokan1 4.4 6.2 3.7 2.9 3.4 4.9 4752 1.69 0.79 Segaliud Lokan2 3.3 6.3 3.6 2.7 3.5 2.9 952 38.05 0.56
Maximum potential height It should be noted finally that any PFTs defined lie on a continuum and dividing it up is a matter of convenience based on ar- Because the list underlying our classifica- bitrary divisions. tion concentrates on tree species it is not surprising to find very few shrub species in it. In our context, missing shrubs are Plant functional types unimportant. It might be necessary, how- ever, to consider those shrubs for analysis of In previous model applications (Huth et al. slash-and-burn-techniques practised by in- 1998; K¨ohler & Huth 1998a; Ditzer et al. digenous people (Whitmore 1998). 2000) the non-existence of a principal ap- The height limits chosen were al- proach to grouping has been a crucial ready used (with small differences) in the point. Thus, within only five groups, Formix3 model (Huth et al. 1998; Ditzer which were distinguished by maximum tree et al. 2000). Thus, model application and heights, one contained all early successional former data analysis have shown them to be species. This implied that all mid or late very practical. Nevertheless, one might de- successional species with similar maximum fine a different number of height groups at heights were grouped to slightly incorrect different height limits. height groups. From this experience, the optimal number of derived PFTs was be- As some verification of the height group tween 10 and 20. At the upper end, classification we again analyse trends in the parametrization already becomes difficult, mortality rates for different groups. We but modelling the complex system of the only consider differences between height tropical rain forest with less than ten PFTs groups of mid and late successional species, might include assumptions leading to biased knowing that early successional species have results. higher mortality rates. Taller-growing trees, in general, should have longer life-times than shorter-growing trees (Manokaran & Conclusions Swaine 1994). This tendency is found in their mortality rates (Table 3.6), although We presented a generic concept for the ag- differences from the average are not signif- gregation of tree species into plant func- icant (χ2 test; P > 0.3). Again the test tional types which can be applied to forests verifies our classification. in different regions. The concept was de- Plant functional types in Sabah’s rain forests 33 veloped in the context of process-based Additional remarks, not modelling of forest dynamics and therefore was focused on criteria which are essen- included in the article tially influencing tree growth in the models Formix3 and Formind: successional sta- We think that the aggregation of tree tus and potential height. In the application species to plant functional types is abso- for Sabah’s lowland rain forests successional lutely necessary in the modelling of tropical status was classified into three groups, po- forest dynamics. In the meantime a model Formosaic tential height into five groups. Thirteen called was developed (Liu & plant functional types in total were dis- Ashton 1998, 1999), which tried to quan- tinguished for this application, a number tify the dynamic of species richness for the which we consider as very practical for fur- large and long-term research area of Pa- ther forest growth analysis. Within this soh, Malaysia (50 ha, inventoried for now Formosaic concept it is and will be difficult to rely 15 years). The approach of was on published data sets for all species in to model the dynamic of individual species, this respect. In this case it is important but the abundance of many of these tree to test the classification with all available species was too low - even in this area of field data. We have shown different possibil- 50 ha - to gain statistically well supported ities for testing using field data on diameter results for recruitment, growth and mortal- increment, mortality rates, photosynthesis ity. production and wood densities. Simultaneously to the development of As a consequence of the final PFTs de- our grouping concept different approaches rived in this paper a new parametriza- were proposed for tropical rain forest in tion of the forest growth models Formix3 Ghana, Africa (Atta-Boateng & Moser and Formind will be elaborated. Simu- 1998), Australia (Gitay et al. 1999) and lations and model analysis with the new Kalimantan, Indonesian Borneo (Phillips parametrization will show whether and in et al. 2000). The first approach was fo- what ways the quality and accuracy of the cused on commercial tree species and based results are improved. on typical diameter increment rates with the emphasis on model construction. In the second case, various theoretical con- siderations about principle differences of Acknowledgements ecological characteristics, which might be used for the identification of plant func- We would like to thank all members of tional groups were discussed (Pillar 1999; the Malaysian–German Sustainable Forest Weiher et al. 1999). To identify timber Management Project, and the Forest Re- groups was the main targets in the species search Center, Sandakan, Sabah, Malaysia, grouping in Indonesia. However, applica- responsible for data collection, for their kind tion and validation possibilities of the con- cooperation, especially M. Rundi for shar- cepts were also of central interest (McIntyre ing his knowledge on the successional status et al. 1999b). More general considerations of trees, R. Ong and M. Kleine for making concerning different applications in global data available for us and R. Glauner for in- vegetation models and for analysing field formation on height-to-diameter-relations. data were found in a special issue of Jour- We also owe a debt of gratitude to D. New- nal of Vegetation Science (McIntyre et al. bery and an anonymous reviewer for very 1999a) and in the standard text book of helpful comments on a former version of the Smith and colleagues (Smith et al. 1997). manuscript. Thanks to L. Kammesheidt for critical reading.
Chapter 4
The model Formind2.0
Because model descriptions in articles with a model, which initially might be ver- need to be very brief, a complete descrip- bal describing main interactions. How- tion of the model used is contained in this ever, to obtain quantitative answers to ques- chapter. tions of interest, mathematical equations An individual-oriented cohort model are needed. From the first more general de- (Uchma´nski & Grimm 1996) is described, scription of interactions, qualitative conclu- which is able to simulate growth dynam- sions about modelled systems can be drawn. ics in mixed tropical rain forests. The Two general types of models can be distin- model includes all important growth pro- guished: Those describing behaviour and cesses. Thus, the model can be applied those explaining the system. Descriptive to different rain forest sites, if parametri- models try to match system behaviour with sation is adapted to specific conditions. Af- model behaviour. Very often regression ter some more general thoughts about mod- functions are used in this context. Explana- els, the principles of the modelling approach tory models try to extract essential struc- are described. Spatial and temporal resolu- tures of the system correctly and rebuild tions are described. Individual physiolog- them in the model. The advantage of the ical submodel and their mathematical im- latter approach is the possibility to study plementations are explained in detail. Fol- systems with different environmental con- lowing this, the main differences to a former ditions (Bossel 1992). version of Formind (K¨ohler 1996; K¨ohler Often models describe very complex sys- & Huth 1998a, 1998b) are discussed. Simi- tems. Thus, it is necessary to reduce the lar features of various versions of the model number of modelled processes. One in- Formix3 (Ditzer et al. 2000; Huth & Ditzer evitably has to make simplifying assump- 2000a) are also mentioned. A discussion of tions which will not enable all possible ques- the chosen model approach closes the chap- tions to be answered with the same mod- ter. elling approach. To gain an overview over the quality of a model, several criteria in respect to the aim General concepts about of modelling should be fulfilled. The dy- namic behaviour of the model should qual- models itatively fit to that of the real system. Nu- merical and logical model results should cor- One of the basic approaches in physics is respond to those of the original if environ- the description of physical phenomena with mental or boundary conditions are compa- mathematical models. rable. Differences should be explainable through assumptions made during model Modelling of ecological systems uses a building. Simulation results should be use- similar approach. A system is described 36 Chapter 4 ful with respect to potential applications of the model and with respect to the aim of modelling.
Basic structure of model ha Patch 100 m In the following section spatial and tempo- 20 m ral resolutions are described. Furthermore, the technical realisation of the model as Figure 4.1: Spatial resolution of simulated an individual-oriented cohort model is ex- area. plained. 4. the extent to which variability of indi- viduals of the same age is considered. The individual-oriented ap- proach Formind2.0 uses simple assumptions concerning nutrient and water cycles. For Individual-based modelling is one of the higher computing efficiency, small individu- main concepts in recent theoretical ecology als are packed together into cohorts. Thus, (DeAngelis & Gross 1992; Judson 1994; Liu models are highly flexible because cohorts & Ashton 1995; Grimm 1999; Lett et al. canbeaddedandremovedeasily.Accord- 1999; Haefner & Dugaw 2000). However, ing to Vanclay (1994) the three main com- there are various researchers who empha- ponents of tree growth are modelled in the size the importance of different modelling following way within a cohort model: approaches. Thus, it is desirable to combine the advantages of different concepts (Bolker 1. Diameter increment is modelled by in- et al. 1997; Uchma´nski & Grimm 1996). crementing the size of a representative Advantages of individual-based modelling tree; with those of the cohort approach (Vanclay 1994) are optimised and unified in the cur- 2. mortality is simulated by reducing the rent study. Thus, our approach is called expansion factor (the number of trees individual-oriented according to the rather represented by each cohort); and narrow definition of Uchma´nski & Grimm 3. recruitment is accommodated by initi- (1996). ating new cohorts from time to time. The biological criteria, which underlie this classification of different approaches are Within one cohort the growth of one tree is as follows (Uchma´nski & Grimm 1996): modelled, which interacts through complex functional relationships with trees of its own 1. the degree to which complexity of in- and the other cohorts. dividual’s life cycles is reflected in the A strict individual-based model corre- model; sponds to a cohort model with an expan- 2. whether or not the dynamics of the re- sion factor of one. Aggregating trees to sources (e.g. food, space) is explicitly cohorts is an effective optimisation of com- taken into account; puting time. For initialisation, trees of the same species group, same commercial status 3. the use of numbers of individuals or and within the same spatial subunit are ag- densities in representing the size of gregated into cohorts in diameter classes of populations; and 5 cm. Within the cohorts of the small trees The model Formind2.0 37