A new measure of fidelity and its application to defining species groups

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Abstract
The first objective of this paper is to define a new measure of fidelity of a species to a vegetation unit, called u. The value of u is derived from the approximation of the binomial or the hypergeometric distribution by the normal distribution. It is shown that the properties of u meet the requirements for a fidelity measure in vegetation science, i.e. (1) to reflect differences of a species’relative frequency inside a certain vegetation unit and its relative frequency in the remainder of the data set; (2) to increase with increasing size of the data set. Additionally (3), u has the property to be dependent on the proportion of the vegetation unit's size to the size of the whole data set.The second objective is to present a method of how to use the value of u for finding species groups in large data bases and for defining vegetation units. A species group is defined by possession of species that show the highest value of u among all species in the data set with regard to the vegetation unit defined by this species group. The vegetation unit is defined as comprising all relevés that include a minimum number of the species in the species group. This minimum number is derived statistically in such a way that fewer relevés always belong to a species group than would be expected if the differential species were distributed randomly among the relevés. An iterative algorithm is described for detecting species groups in data bases. Starting with an initial species group, species composition of this group and the vegetation unit defined by this group are mutually optimized. With this algorithm species groups are formed in a data set independently of each other. Subsequently, these species groups can be combined in such a way that they are suited to define commonly known syntaxa a posteriori.