While having the basic aims in common, the traditional Braun-Blanquet approach and numerical approaches differ in some respects. Indeed, no approach produces an objective or 'the correct' classification. In spite of the high degree of formalization involved in numerical classification, the numerous choices concerning the data set composition, cover-abundance transformation, numerical coefficients, classification algorithms, or number of vegetation units to be accepted result in the fact that numerical methods, like the traditional expert-based approaches, may suggest many different partitions of the same data.
Unlike the expert-based classifications, which often use unclear classification criteria, numerical classification methods consistently use explicit information on species occurrence and cover-abundance and apply it consistently across vegetation types. However, while experts often implicitly incorporate in the classification process knowledge of species behavior in a broad geographical and environmental range, numerical methods only use information contained in the particular data set, which often results in rather idiosyncratic classifications. It is therefore difficult to combine different numerical classifications into a single system of syntaxa, which would be valid over large areas and different habitats, without relying on expert judgment.
To avoid these problems, supervised classification methods have gained importance recently. They take traditional syntaxa that are widely recognized by phyto-sociologists as given and assign new releves to these syntaxa by numerical procedures. Such an approach supports both the stability of the traditional phytosociological system, which has already received wide acceptance, and the application of formal, unequivocal classification procedures. A simple approach is to calculate an index of similarity of species composition between new releves and constancy columns of synoptic tables (see the section entitled 'Phytosociological tables') that summarize the traditional classification and subsequent matching of each new releve to the vegetation unit to which it has the highest similarity. More sophisticated methods of supervised classification include quadratic discriminant analysis, multinomial log-linear regression, classification trees, and artificial neural networks. The latter, for example, can establish a classifier based on the previous knowledge of what the releves belonging to a certain vegetation unit look like. When new releves are submitted, the classifier assigns them, with some degree of uncertainty, to the correct vegetation unit.
Another method of supervised classification is COCKTAIL, which was specifically designed to imitate traditional Braun-Blanquet classification. It uses the external information on species behavior, extracted from large phytosociological databases, and forms sociological groups of species with statistical tendency of co-occurrence in the releves of the database. Then, unequivocal definitions of syntaxa are created that involve decision rules, postulating which of the sociological species groups must be present or absent for a particular releve to be assigned to the target syntaxon. COCKTAIL definitions can be created to fit the meaning of the syntaxa of traditional phytosociology. In such a way, traditional syntaxa can be defined formally and applied in the computer expert systems, which automatically assign newly encountered releves to syntaxa.
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