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Although the existence of higher order associations has been proved, interspecific association is generally treated as a pair-wise phenomenon. Its possible reason is that although pair-wise association is only an imperfect description of the relationships among species, its methods are simple and well known. Unfortunately, the complexity of vegetation can not be described by such simplex methods. This paper shows two methods which enable detailed analysis of higher-order associations: Juhasz-Nagy's information theory functions and the log-linear contingency table analysis. From mathematical point of view, the two methods are closely related (both methods measure the non-randomness in the multi-way contingency tables). On the other hand, their theoretical backgrounds are different. The log-linear contingency table analysis was developed by statisticians to solve general statistical problems, while Juhasz-Nagy's approach was developed by a biologist to solve biological problems. The aim of this paper is to show how these two approaches decompose the total association, to point at the similarities and differences between the two approaches, and by this way to facilitate the analysis of higher order associations.

ANALYSING ASSOCIATIONS AMONG MORE THAN TWO SPECIES