# Which properties define primary producers

Ecosystems are usually probabilistic, i.e. stochastic systems. They are because, on the one hand, they depend on a large number of different parameters, the most important of which can be captured, but never all, and, on the other hand, because they are always open. Your most important members, the organisms, are dependent on a constant supply of energy. There are therefore two conceptually different methods of obtaining information about communities and ecosystems.

Inventories have a long tradition. Here they should only be characterized in advance by keywords such as vegetation mapping and plant geography, more on this in the topic of plant communities.

The systems analysis approach is more recent. With the advent of cybernetics in the mid-forties, tools were developed to mathematically define systems and system properties and to design suitable models for forecasting.

Both approaches - inventory and systems theory - complement each other, and only by taking into account the results of both can an attempt be made to understand an ecosystem and to describe its behavior, its equilibrium and sensitivity to disturbances, and to recognize future developments.

The basics of system theory are discussed in the topic of cybernetics, here are some additions and an illustration using an example.

Simplified model of an energy and material flow in an ecosystem. The material flow (blue lines) is a cycle, the energy flow (red lines) a linear one.

The system elements (here producers, first-order consumers, second-order consumers, decomposers) are arranged one behind the other. The arrangement is hierarchical. The individual hierarchical levels are referred to as trophic levels.

There is an energy and a material flow between the system elements. The flow of energy is a linear process; the material flow represents a cycle.

Only plants (and a few microorganisms) can convert light energy into chemical energy. They are therefore called producers (primary producers, P). All other organisms are consumers (1st, 2nd, 3rd order) or decomposers (saprophytes). The way of life of the producers is called autotrophic, that of the consumer is called heterotrophic (autotrophy, heterotrophy). Four basic elements are now required for a mathematical description of an ecosystem:

1. System variable (v

_{i}): This is a group of values (v, v_{2}... v), which describe the state of a system at a given point in time. This includes, for example, information on the biomass (expressed in g, kg or t dry weight per unit area or volume). The producer (P) would therefore have the value v_{1}, the consumers of the 1st order the value v_{2}, the consumers of the 2nd order (Carnivoren der Wert v_{3}etc. too.

2. Transfer or transition functions (F

_{i}): These are equations that describe the metabolic rate in the system. Among other things, it records the proportion of biomass that is lost through respiration or that which is required to feed the individuals at a higher trophic level (see following section). The changes in a system variable as a function of time should therefore be described by the following differential equation

dv _{i}/ dt = f (v_{1}, v_{2}.......... vn, F_{1}, F_{2}... F_{n})

where f stands here quite generally for function.

3. Drive functions (inputs): This refers to the amount of energy and material available to a system, for example the amount of irradiated, usable solar energy, the limiting amount of nutrients (minerals) in the soil, the temperature as a reaction-determining factor, etc. If one only wants to consider the transfer function from one trophic level to the next higher, the corresponding F

_{i}to the drive function. For the amount of carnivores, for example, that of herbivores (and carnivores) is decisive.

4. Proportionality factors (c

_{i}), constant parameters: This category includes invariable quantities, for example the amount of vegetable food that an individual animal needs per unit of time.

The mathematical model of a system is now to be written as a set of equations that describe the flow of energy and material between the individual levels (stages). Nowadays, matrix calculations are used to calculate data sets and equations. First of all, a matrix is nothing more than a list of data in which each value is identified by its coordinates i and j. Matrices can be multiplied with one another, with the result that a matrix is created. Such a representation can be used, for example, to show which group (system component) has a direct influence on another. In relation to our generalized ecosystem, a picture emerges from which it can be seen that each system component has an effect on itself, but that the carnivores, for example, have no direct influence on the plants.

Large amounts of data are always generated in ecological research. It therefore makes sense to process them in a computer-friendly way, i.e. to arrange them in matrices from the outset in such a way that they are suitable for input into the computer. When assessing natural ecosystems, it must be taken into account that reality often deviates from idealized models. Exact data records cannot be obtained for many of the required parameters. As a rule, the drive functions are subject to large fluctuations, for example unpredictable weather conditions. The number of interactions in a natural ecosystem is usually greater than in the model. To go back to our example, it should be noted that animals can by no means be clearly divided into herbivores and carnivores, because many are known to be omnivores (omnivores). But if you know such complications, they can easily be integrated into an existing model. However, there is often a lack of the necessary information. On the other hand, there are also relationships that are quantitatively negligible. It therefore makes sense to neglect them in order not to burden yourself with unnecessary arithmetic work.

So far, only very few ecosystems have been known that have exemplified the properties of the system. There is a lake in Germany, the Plußsee near Plön / Holst., Which can be cited as an example of an almost completely researched ecosystem (edited by the Max Planck Institute for Limnology in Plön). As an example of a terrestrial system, the "Solling Project" can be mentioned, a forest area that is being investigated by scientists from the University of Göttingen.

The majority of ecologically working biologists mostly have the necessary knowledge of the plant and / or animal species, but very few know anything about soil bacteria and fungi (decomposers). There is therefore hardly any data on their species composition, population density and rate of reproduction in their natural environment. Propagation kinetics that were measured under laboratory conditions are only of limited use because the growth conditions there are usually more favorable and the rate of propagation is thus higher than in nature.

However, systems analysis approaches can often be perfected in such a way that one can make relatively accurate predictions with only a little, and also quite incomplete, information. For illustration, reference is made to the projections after federal and state elections, the first forecasts of which are usually very close to the official final result. In ecology, too, one is dependent on comparable optimization processes, because all data lists, no matter how extensive they may appear, only ever represent a relatively small sample of the actually available but not recorded data. As the complexity of a mathematical model increases, its accuracy increases, as the complexity of an ecosystem increases - as already mentioned - its stability also increases. We know from statistics that a systematic error (s) is inversely proportional to the square root of the number of individual measurements (1 / square root n). The larger the figures, the lower the error rate.

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