Similarity indices I: what do they measure

A method for estimating the effects of environmental effusions on ecosystems is described. The characteristics of 25 similarity indices used in studies of ecological communities were investigated. The type of data structure, to which these indices are frequently applied, was described as consisting of vectors of measurements on attributes (species) observed in a set of samples. A general similarity index was characterized as the result of a two-step process defined on a pair of vectors. In the first step an attribute similarity score is obtained for each attribute by comparing the attribute values observed in the pair of vectors. The result is a vector of attribute similarity scores. These are combined in the second step to arrive at the similarity index. The operation in the first step was characterized as a function, g, defined on pairs of attribute values. The second operation was characterized as a function, F, defined on the vector of attribute similarity scores from the first step. Usually, F was a simple sum or weighted sum of the attribute similarity scores. It is concluded that similarity indices should not be used as the test statistic to discriminate between two ecological communities