In comparison to former versions For-mind1.0(K¨ohler & Huth 1998a) and For-mind1.1 (K¨ohler et al. 2001) all submod-els of the model were revised and improved on the basis of current understanding of the ecological processes in tropical rain forests. Tree physiology was formulated in more general functional relationships and parametrised on the basis of new field data available only recently. Assumptions in the mortality submodel were simplified and a density dependent self-thinning rule was im-plemented. The recruitment submodel was enlarged with an alternative site-dependent approach, whose development and influence on general model behaviour play a major role in model analysis. Respiration was modelled in greater detail, and a concept was developed to validate it on the basis of available field data. Photosynthesiswas re-vised slightly. Finally, a simply dependency of tree growth on potential dry periods was implemented and thus the range of applica-tions was enlarged.
In the end, only the concepts of spa-tial resolution and general formulations of photosynthesis and respiration were taken from previous versions and from the Formix3-models, the latter especially from Formix3-Q (Ditzer 1999).
The main conceptual difference to Formix3 is the individual-oriented ap-proach. Formix3 so far works with a sim-ple concept of matrix models incl. tran-sition rates between different size classes, which are difficult to parametrise. With its more general formulation of processes For-mind2.0 differs from its predecessors also in its basic concept of species grouping, on which the whole parametrisation is based.
This allows a relatively fast model applica-tion to different forest sites.
Discussion
The modelling approach used in For-mind2.0 enables the developer or user to change each submodel and replace it with a currently more practical one. Sometimes research and new available field data for a certain site will suggest such modifications.
We discuss each submodel on its own.
The size of the model area in which trees compete with each other is important, as the dynamics of succession processes de-pend on it. The impact of one dominant tree on the light climate in the patches is too strong in too small areas. Thus, all other plants are repressed more than in re-ality. Only after the death of the domi-nant tree does growth in the recruitment take place. In too large simulated areas, leaf area in relation to patch area is too small. Death of even large trees will change the light climate only slightly. In both cases the real dynamic of succession in forest gaps will not be met with acceptable accuracy.
From these considerations it emerges that the most appropriate size of a patch used in models should be that of the crown of a typical large-canopy dominant tree of the stand. Typical sizes lie between 400 m2 and 800 m2. In forests of the tropical regions patch size can be chosen at the lower end of the range. This may be due to the fact that the steeper sun angles at low latitudes allow light to reach the forest floor in rela-tively small gaps (Shugart 1998). The patch size of 400 m2 chosen inFormind2.0lies in the given range taken from those theoretical considerations.
A large number of forest growth models calculate forest dynamics only in one patch that is why they are called gap models (Liu
& Ashton 1995). Most of them emerged from Jabowa (Botkin et al. 1972; Botkin 1993) and use age dependent growth func-tions. From our point of view a single patch can never be representative of a whole rain forest. Normally, areas in different phase of succession exist beside each other. This is
especially the case if secondary succession or external disturbances (e.g. logging of trees) are of interest.
In contrast, the model used in this study is able to simulate an area of any size, restricted only by computing capabilities.
This is useful for various reasons. First, the fraction of patches at the border of the simulated area will decrease with increasing size if the shape of area remains quatratic (from 6 4 % at 1 ha to 15 % at 25 ha). Bor-der areas are sensitive as assumptions on boundary conditions (e.g interactions leav-ing the simulation area) will affect them strongly. Furthermore, results are more in-dependent of stochasticity, included in mor-tality and recruitment, the larger the area is.
The individual-oriented cohort-approach is coupled with the chosen spatial resolu-tion of 20 m × 20 m. Only the non-explicit spatial position causes an aggrega-tion of individuals into cohorts. The res-olution of available data at the time of the model development was the main reason for that approach. Until now only a few re-search plots with explicit tree positions for each individual larger than 1 cm in stem diameter have been inventorised (Condit et al. 2000; Smithsonian-Tropical-Research-Institute 2000). In a few cases data are freely available, e.g. for a neo-tropical rain forest in Costa Rica (Clark & Clark 2000).
The gap-model approach, used for spatial resolution and calculation of competition situations in single patches, has been proven practical in various case studies (overview in Liu & Ashton 1995). Tropical (Shugart et al. 1980; Doyle 1981; K¨urpick et al. 1997) and temperate forests (Botkin et al. 1972;
Shugart 1984, 1998; Botkin 1993) have been modelled, and influences of climate and el-evation gradients were analysed (Bugmann 1996b, 1997). All gap-models known to the author calculate so-called potential natural vegetation (PNV), which reflects the steady-state of a model at current parametrisation, if simulation was started from a clear-cut
area. Thus, tendencies in species composi-tion as a response to assumed changes in en-vironmental conditions can be analysed, but a comparison of simulated dynamics with field data of long term observation areas was missing. This comparison is an important validation method (Vanclay & Skovsgaard 1997), whose results, together with an es-timate about the quality of the model, are more important than technical details, e.g.
which modelling approach has been chosen.
The few available data sets with explicit tree position raise the question if an appli-cation ofFormind2.0to those sites is only possible and meaningful after considerable model improvements. In this context only the vertical light competition needs to be discussed. In tests with Formind (K¨ohler 1996) we analysed whether we gain any fur-ther information of reducing temporal res-olution from steps of one year to months, days or even hours. A case study for French Guiana uses a spatial-explicit forest growth model (Chave 1999b). Complex interac-tions of individual trees with a three dimen-sional (3D) field vector of irradiance were calculated. As a result a detailed distribu-tion of irradiance in each part of the canopy can be calculated. This study and our own investigations have shown that computation time mainly depends on calculation of this irradiance field. Thus, Chave was using highly parallel computer systems available only in large research institutes to perform his study in an acceptable time frame. It is questionable if the detailed field vector gets the model closer to the real system, as ele-vation on the forest floor or daily variations in light climate have not been considered so far. Modelling of sun spots, important for the germination of seeds (Hammond et al.
1999), would be possible with daily varia-tions. Influence of sun spots on growth of seedlings inFormind was already analysed (K¨ohler 1996, p. 31) and can be neglected.
As recruitment rates work with the concept of reproductive success covering also seed and seedling predation, a more detailed
con-cept for germination is not needed. For temperate forests detailed models of light climate are available which can be used in spatial-explicit models (Brunner 1998). In this context, an error propagation analy-sis undertaken in the spatial-explicit model Sortie has to be discussed (Deutschmann et al. 1999). It was analysed how model dynamics depend on a more detailed reso-lution of incoming light (in 1, 16, 48, or 216 light rays). It transpires that most results (e.g. succession of tree species) achieved with one ray of light do not significantly differ from those of a more detailed descrip-tion. Differences between 16and 216are always negligible.
Comparisons of model results with diam-eter increment data from permanent sam-pling plots without explicit tree positions have proven our light competition model to be of acceptable quality (K¨ohler et al. 2001).
Formulations concerning tree physiog-nomy are at the current state of re-search. The available data sets for South-East Asia verified the used functional re-lationships between different tree variables (e.g. Forestal-International-Limited 1973;
Yamakura et al. 1986; Ashton & Hall 1992;
Poker 1993). Currently, research activities in rain forests are concentrated on the neo-tropics (Condit 1995; Cook 1998; Holl &
Kappelle 1999; Peres 1999). Thus, pub-lished field data for South America will be improved in the near future. This will enable us to specify some of assumptions, where regional differences were not cap-tured so far (see applications in Chapter 6-8). Site-dependent relationships of sev-eral physiognomic variables in South-East Asia has improved parametrisation (Ditzer 1999). The broadening of this approach to the sites in South America was so far not possible because of a lack of field data. In particular, analysis of leaf area or biomass partitioning was only undertaken in a few sites in South-East Asia. A verification of the upper boundary of individual tree’s leaf area index LAIM (Eq. 4.7) is of special
in-terest. This boundary is, so far, caused by model comparison with data from photo-synthesis production. Self-shading in tree crowns with high values of LAI leads to higher production rates of mid successional species compared to early successionals for trees of the same size and for high light in-tensities. This is inconsistent with observa-tions. In this context parametrisation of the light response curve (Eq. 4.14) does not dis-tinguish different values for the light use effi-ciencyαs, as differences in field data are sta-tistically weak (Eschenbach 1994; Eschen-bach et al. 1998), but results are sensitive to differences in αs. Other field studies use different regression functions, where αs is not calculable, or determine only maximum photosynthesis PM (e.g. Bazzaz & Pickett 1980; Oberbauer & Strain 1984; Ellsworth
& Reich 1996; Barker et al. 1997). However, the principal differences in photosynthetic characteristics of tropical trees along suc-cessional gradients were confirmed (Strauss-Debenedetti & Bazzaz 1996), and were par-tially correlated with tree height (Davies 1998; Thomas & Bazzaz 1999).
The main improvements of the tree growth submodel were the size-dependent growth limitation and splitting of tion into maintenance and growth respira-tion. Limitation of tree growth has been found in field datas (Koch et al. 1994;
Maruyama et al. 1997) and was already used in forest grwoth modelling (Valentine 1988 1990; Landsberg & Waring 1997). Thus, growth is limited, even if there is evidence that large emerging trees do not stop grow-ing (Chambers et al. 1998). Species richness is aggregated in PFTs inFormind2.0 and only the growth of average trees is modelled.
Limitation is a very useful and proper con-cept.
Respiration in tropical trees is one of the processes of which very little is under-stood (Kira 1978; Medina & Klinge 1983;
Yoda 1983; Oberbauer & Strain 1984; Ryan et al. 1997). The work of Ryan and co-authors mark important progress in this
subject. The splitting of respiration and a more detailed description of the processes was only possible with the process-based ap-proach used in the model. Ditzer (1999) has highlighted the importance of these details, which can not be incorporated in simpler approaches, where tree growth is modelled with one diameter growth function based on regressions.
We considered light conditions as most important for determining tree growth, an approach used in other studies before (Bartelink 1998a, 1998b). One obstacle in including below-ground processes is the dif-ficulty in measurement design and imple-mentation. However, there are research ac-tivities in this direction in tropical forests (Denslow et al. 1998; Hall & Matson 1999;
Chambers et al. 2000) or on a global scale (Jackson et al. 2000). In temperate for-est growth models nutrient or water cy-cles were considered already (Aber et al.
1982; Jansen et al. 1995; Bossel 1996b;
Endejan 1997; Friend et al. 1997; Kim-mins et al. 1999; Thornley & Cannell 2000).
Analysing corelations between soil nuitri-ents and forest stockings led to corrections factors of tree growth in the rain forest model Formix3-Q (Glauner 1999; Ditzer et al. 2000). We are therefore aware of the effects and the dependency of the tree growth on soil matters. Nevertheless, for average site conditions measured diameter growth was matched with simulation results (Chapter 5).
A main improvement of the mortality submodel is to model tree death with-out growth dependent mortality, which was used in a former version or the Formix3 model. Some field data (Swaine & Whit-more 1988) give a hint of that relation-ship. But as tree size was not consid-ered in their analysis it is difficult to gen-eralise results. Otherwise it would promote higher mortality in large trees, which nat-urally grow slower than smaller ones. This is in contradiction with observations. The-oretical considerations concerning the
prod-uct ω of growth rate g, maximum diameter dM and mortality rate M (ω = dM/g ·M) support our thesis. The number of large trees would be over- (ω << 1) or under-estimated (ω >> 1) if ω is very different from one (Chave 1999b). Enhanced mortal-ity of young trees is the only effective regu-lation of ingrowing trees. This effect is well known, but confirmed by only a few stud-ies (Clark & Clark 1992; Kennedy & Swaine 1992; Okuda et al. 1997). Sensitivity analy-sis of size-dependent mortality and compar-ison of tree densities with field census make a site-dependent parametrisation possible.
Density regulation through self-thinning is a known phenomenon in forests of dif-ferent latitude (White 1981; Westoby 1987;
Valentine 1988; Clark 1992a, 1992b; Pen-fold & Lamb 1999; Silva-Matos et al.
1999). Increasing basic mortality rates in dense patches, as done in previous ver-sions (K¨ohler & Huth 1998a; Ditzer 1999;
Huth & Ditzer 2000a) is far less restric-tive. In Formix3 density regulation might work this way, as transition rates from one layer to the other limit the growth of saplings, and thus, residence times in lower layers are prolonged. Adaptive changes in tree physiognomy (Wirtz 1998), espe-cially crown shape, are not considered in the model. Thus, in self-thinning an instant extraction of trees with overlapping crowns was included inFormind.
In experimental ecology, natural regener-ation and all processes concerning recruit-ment as main mechanisms determining fu-ture forest compositions were of central in-terest in the last years. Research can be distinguished in
• seed production (Putz 1979; Garwood 1983, 1989; Charles-Dominique 1993),
• seed dispersal (Fox 1972; Hubbell et al. 1991; Kennedy 1991; Wunderle 1997; Clark 1998; Clark et al. 1998a, 1998b; Higgins & Richardson 1999;
Martinez-Garza & Gonz´alez-Montagut 1999; Robinson et al. 1999),
• establishment of seedlings (Lang &
Knight 1983; Whitmore 1983; Ri´era 1985; Hubbell & Foster 1986a, b;
Schupp et al. 1989; Hartshorn 1989; Ve-blen 1989; Manokaran & Swaine 1994;
Milton et al. 1994; Phillips & Gen-try 1994; Pinard et al. 1996; Poorter et al. 1996; Sheil & May 1996; Powers et al. 1997; Okuda et al. 1997; Tucker
& Murphy 1997; van Gardingen et al.
1998; Diaz et al. 1999; Hammond et al.
1999; Hubbell et al. 1999; Kyereh et al.
1999; Xiong & Nilsson 1999),
• and photosynthesis and growth of seedlings (Chim & On 1973; Enright 1978; Manokaran & Kochummen 1987;
Brown 1990, 1993, 1996; Condit et al.
1995a; Lee et al. 1996; Press et al.
1996; Barker et al. 1997; Lee et al.
1997; Zipperlen & Press 1997; Ko-hyama & Takada 1998; Agyeman et al.
1999; Kobe 1999b; Nicotra et al. 1999;
d’Oliveira 2000).
Thus, it is important to incorporate de-tailed submodels of recruitment in forest growth models. Besides a theoretical ver-ification of field data on recruitment, the simulations of temporal dynamics of forests will be improved.
It is one of the main improvements of the model to be able to model explicit seed dis-persal depending on mother trees compared to only constant input of seedlings. How-ever, it is certainly true that the establish-ment of individual trees of the huge number of tree species in tropical forests follow more complex patterns. A controversial study concerning recruitment on Barro Colorado Island, a nature reserve on an island in the Panama Canal (Hubbell et al. 1999; Chaz-don et al. 1999; Hubbell 1999; Kobe 1999a;
Brokaw & Busing 2000) found that ”being at the right place at the right time” is more important for recruitment success than any individual strategy. Hubbell et al. (1999) did not find significant differences in the re-cruitment of different successional groups
in closed forest and canopy gaps. Fur-thermore, the limiting number of available seedlings determined success more than any other environmental conditions. So far, it is not possible with the model to verify stud-ies which identify tree specstud-ies diversity as function of different impacts (Cannon et al.
1998, 1999; Sheil et al. 1999). Enhancing Formind2.0 in a way that each individ-ual tree is correlated with one specific tree species while still modelling forest growth with a reduced set of plant functional types might address these questions in the future.
In particular, recruitment could be coupled to trees of individual species.
A more detailed description of recruit-ment than done so far does not seem to be useful. Necessary assumptions and data concerning seed predators, wind direction and seed etc. would be highly speculative, and parameters difficult to determine.
Interactions of disturbed animal, bird, or insect populations, which act as seed dis-persers and are important for future forest development, are in the focus of current eco-logical interest (Redford 1992; Curran et al.
1999; Law & Lean 1999; Lynam & Billick 1999; Price et al. 1999; Cullen et al. 2000;
da Silva & Tabarelli 2000). As dispersal agents of trees are complex, and mostly not depending on one species, the effects of ex-tinction of a single animal species on plant dynamics is difficult to estimate. However, it is definitely correct that hunting pressure and the collection of seed bearing fruits in now intact forest communities will alter re-cruitment capabilities of these in the future (Redford 1992). We take this into account through scenario analysis, where those in-teractions are considered as main effects (Chapter 8).