At this point it is necessary to clearly define a model. A model is reproduction of the reality with abstraction of redundant details. A model permits us to discern, comprehend and handle information without the knowledge about the whole background. The complexity of models is highly variable, depending on the degree of abstraction and naturally on the complexity of the part of the reality that it describes. The simplest models are mainly descriptive. A map provides us with different information about a landscape depending on its scale and on the number of details included. The more information we try to reproduce with the map, the more it becomes complex and difficult to read. A more complex form of description is for example, a chemical formula for a reaction, or a mathematical formula that describes a given set of
data. However, to satisfy the needs and questions of modern silviculture, it is necessary to go further. The description of complex dynamic processes in organisms (trees) or ecosystems (stands) is obtained through simulation, i.e. the virtual reproduction of the reality at a structural-functional level using a model. Simulation models serve to describe, analyse and validate theoretical and empirical data that led to the model formulation, and to generate prognoses under different (plausible) scenarios. The simulation models are thus a powerful research and decision making tool for the practice. However, it is important always to remember that a simulation is only a possible picture of the reality using a given set of boundary conditions and not the reality itself. Unfortunately, there is a tendency to overvalue the results of simulations.
A vast number of plant models have been developed using different approaches, depending on the goals of the respective project. In general, the modelling approaches for plant growth can be classified in three main categories, whose boundaries, however, can be vague. Thus, an exact assignation for each model to a category is not always possible without ambiguity.
First, process oriented models such as photosynthesis and C-allocation models. These models are based on the physical interaction between ecological compartments that can be defined on different time and space scales. One characteristic of this kind of models is that the definition of the spatial compartments used to delimit the process can be very abstract. These models often consist of a couple of mathematical formulas and rules that describe the given process.
This is given as the description of a state or a dynamic, especially equilibrium condition, threshold values, flow rates, uptake/loss rates, etc, or a combination of them (BASSOW ET AL. 1990; THORNLEY, 1976; BOSSEL, 1994).
Second, structural models based on the morphological architecture of the plant. Thus, these models are devoted to the observed growth topology of the plants without taking in con-sideration the interaction with the environment and the internal physiological processes of the plant. In this regard we have to distinguish between plant topology and plant morphology.
The term "plant topology" describes the relative relationship between the different elements of the plant - especially nodes and internodes - and their arrangement in space, while the term
"plant morphology" describes the general shape and form of the plant and its elements, along with their biological significance. Morphological models are generally based on empirical
botanical observation with abstraction from the physiological processes that control plant growth. Examples of this group are crown architecture models (HALLÉ AND OLDEMAN, 1970;
HALLÉ ET AL., 1978; KRANIGK, 1995) and basic Lindenmayer systems (PRUSINKIEWICZ, 1987;
PRUSINKIEWICZ ET AL., 1988; PRUSINKIEWICZ, 1994; KURTH, 1994; KURTH, 1997; KURTH, 1999). These models try to reproduce the observed or perceived reality without having to reproduce the processes or environmental conditions that led to a given state. A representative example for such models is the description of the crown morphology using length/diameter relationships to create new branches, and the general approach of the pipe model (DA VINCI, after RICHTER, 1970; SHINOZAKI ET AL., 1964) to simulate the secondary diameter growth.
At last, a new group of models has emerged, that increasingly unifies process modelling with more and more complex structural models (KELLOMÄKI AND KURTTIO, 1991; KELLOMÄKI AND STRANDMAN, 1995; KELLOMÄKI AND IKONEN, 1996; PERTTUNEN ET AL., 1996;
PERTTUNEN ET AL.,1998; SIEVÄNEN ET AL. 1995) where the structure is more than only the physical frame of the processes. Process and structure interact with each other and are thus interdependent. Thus, a direct description of plant growth in dependence on its physiological processes is made possible. This third category comprises the structural-functional models based on the reconstruction of the topological and/or morphological architecture of the plant, taking into account the dynamics of specific physiological and mechanical processes as well as the interaction of the plant with the environment and other plants (light, water, nutrients, and competition). In this context, we can also mention the model ECOPHYS (HOST ET AL., 1990), the AMAPpara software from CIRAD, France (DE REFFYE ET AL., 1995a; DE REFFYE ET AL., 1995b) and the advanced formalisms of the already mentioned L-systems.
For this category of models the differentiation in topological and morphological architecture is also important, because there exist models devoted to the reproduction and representation of tree stands, where the fine structure of single plants is ignored and only "raw"
morphological elements are used (i.e. cones, spheres or ellipsoids are used to represent single tree crowns, PFREUNDT AND SLOBODA, 1996; KAHN AND PRETZSCH, 1997; PRETZSCH, 1990a, PRETZSCH, 1990b; PRETZSCH, 1992a;PRETZSCH, 1992b).