Similarity indices, sample size and diversity

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Abstract
The effect of sample size and species diversity on a variety of similarity indices is explored. Real values of a similarity index must be evaluated relative to the expected maximum value of that index, which is the value obtained for samples randomly drawn from the same universe, with the diversity and sample sizes of the real samples. It is shown that these expected maxima differ from the theoretical maxima, the values obtained for two identical samples, and that the relationship between expected and theoretical maxima depends on sample size and on species diversity in all cases, without exception. In all cases but one (the Morisita index) the expected maxima depend strongly to fairly strongly on sample size and diversity. For some of the more useful indices empirical equations are given to calculate the expected maximum value of the indices to which the observed values can be related at any combination of sample sizes. It is recommended that the Morisita index be used whenever possible to avoid the complex dealings with effects of sample size and diversity; however, when previous logarithmic transformation of the data is required, which often may be the case, the Morisita-Horn or the Renkonen indices are recommended.