On the rather regional and detailed level of such local ecosystems, a description of the individual vegetation types can be produced by means of so-called plant formations. The description uses a physiognomic classification according to life forms (species), such as in the already discussed way in vegetation science. Schroeder  proposes 11 classes of formation for the description of vegetation. Richter , on the other hand, proposes only seven, although in the latter case the concept includes further sub classification. For example, a formation class is composed of formation groups, which again are made up of formations. Further subdivisions are classes and associations.
plant formation ^ As an example, the formation of the tropical rain forest belongs to the formation group of tropical evergreen forests, these in turn belong to the formation subclass of evergreen forests, which again is a part of the formation class of closed forests. In the scope of this overview we provide in the following a rough classification due to Schroeder, for a more detailed classification we refer to . Schroeder distinguishes:
■ Forest: Closed forest stand with tree crown cover (or equivalent stocking level) of more than 50% of the crown cover. Undergrowth covers a high proportion of the ground and is affected by shading conditions.
■ Open forest: Formations with discontinuous tree layers but with a coverage of at least 10% and less than 40%. The undergrowth is barely affected.
■ Shrubs: In the broader sense, shrubs and bushes are vegetation types where the dominant woody elements are shrubs, such as woody perennial plants, generally 2 – 5 m in height on maturity and without a definite crown.
■ Heath: Closed standing dwarf shrubs (predominantly calluna and erica) similar in being evergreen and microphyllous. Other growth forms are almost not present.
■ Grassland (Savannahs): Physiognomy characterized by grass-like plants, other growth forms are present but have little affect.
■ Perennial grassland: Consists mostly of grass-like, non woody perennials.
■ Annual grassland: Short-lived vegetation consisting of short-lived herbal and herbal-like (haulms) plants or grasses (monocarpic or hapaxanthic; perennial or annual; flowering and fruiting once, then dying).
■ Moss cover and lichens: Low-growth vegetation consisting of diverse mosses and lichens.
■ Semi desert: Plants evenly distributed on the ground; isolated; however, root systems touching.
■ Desert: Plant growth only in locally favorable areas.
■ Sweet water vegetation (aquatic vegetation): Underwater rooting or rootless, submerged vegetation.
The sense of this kind of subdivision compared with floristic divisions lies in the larger abstraction of individual plants. A tropical evergreen forest may consist in different regions of different plants; its characteristics, however, remain always the same.
On a rather local level, in areas with well-known flora, also a floristic division is possible in plant societies, and so the typology of formation can be more specific. The school of plant sociology, according to Braun-Blanquet , analyzes areals in different places, whereby the goal is to find characteristic colonization combinations, which result from a number of types with specific cover patterns. Such combinations, also called associations, can now be classified and ranked hierarchically to allow small-scale assessments of larger sites. Several associations form one alliance, several alliances constitute an order. A combination of orders make up a class, and several classes can represent a formation. Diagnostic criteria of plant societies (syntaxa) are the associated species. One distinguishes between character species, which are limited to certain vegetation units, and differential species, which include units of lower orders, and finally alliances, which can be defined as more generalized types that share some of the diagnostic species found in the associations.
There are several different approaches, at least for Europe, on the level of classes, how to systemize plant sociological classifications, and how to standardize them . Again, it is neither the goal of this book nor is there enough space to give a complete listing of the individual classes or the various methods. A small selection should suffice to give an approximate overview of the complexity of the material:
■ Clearcut and edge forest societies
Clearcut land societies Acid soil edge societies Thermophile edge societies
■ Cover and shrub societies
Subalpine high shrub and green alder societies
■ Forest societies
Continental sand and savannah heath-pine forest Acid soil moor forests Acid humus and coniferous forests Summergreen deciduous trees Greenweed oak forest-hickory societies Juniper-pine societies
Chapter 2 As an example of even further differentiation, we briefly introduce the societies Plants of the clearcut forest, which have settled in clearcut forests and clearings. There
are two orders : clearcut stands with acid soil and stands with high base saturation.
While Epilobium angustifolium (fireweed), Rubus idaeus (raspberry), and Cir – sium palustre (European swamp thistle) are found in all clearcuts, those with acid soil are mostly characterized by seven kinds of plants: Epilobium angusti – folium, senecio sylvaticus (heath groundsel), senecio viscosus (sticky groundsel), Rumex acetosella (common sheep sorrel), Avenella flexuosa (herbal grass only found in German forests), Agrostis capillaris (colonial bent grass) and Carex pilulifera (pill sedge).
At this point we can further subdivide into five societies, which are defined by a subset of the specified plants plus additional species. Such a society is, for example, the fireweed/thimbleberry society, which consists of two types and is to be found in acid soil stands, poorer soils of red beech forests and coniferous wood forests.
Similarly, six species are assigned to the clearcut forest stands of basic soils: Hypericum hirsutum (St. John’s wort), Fragaria vesca (wild strawberry), Fes – tuca gigantea (giant fescue), Galium odoratum (sweet woodruff), Bromus benekenii (forest grass) and Cirsium vulgare (bull thistle). These stands are again divided into three societies. For the different plant societies data is determined based on their quantitative composition. Very detailed analyses are made possible by manual counting out, whereby temporal changes are also recorded. Although such results are impressive in their detail, they are not very useful for computer-assisted modeling if there is not enough information available with regard to the appearance of individual plant populations and their interactions. Therefore, in the next chapter, after the mathematical description of branching structures, the spatial characteristics of different plant populations are mathematically described, and these are then later converted into distribution algorithms. For an accurate mathematical computation, the data of the individual population forms are combined with the data on vegetation covers, i. e., the respective plant societies.