Statistical determination of diagnostic species for site groups of unequal size

Abstract Aim: Concentration of species occurrences in groups of classified sites can be quantified with statistical measures of fidelity, which can be used for the determination of diagnostic species. However, for most available measures fidelity depends on the number of sites within individual groups. As the classified data sets typically contain site groups of unequal size, such measures do not enable a comparison of numerical fidelity values of species between different site groups. We therefore propose a new method of measuring fidelity with presence/absence data after equalization of the size of the site groups. We compare the properties of this new method with other measures of statistical fidelity, in particular with the Dufrêne-Legendre Indicator Value (IndVal) index. Methods: The size of site groups in the data set is equalized, while relative frequencies of species occurrence within and outside of these groups are kept constant. Then fidelity is calculated using the phi coefficient of association. Results: Fidelity values after equalization are independent of site group size, but their numerical values vary independently of the statistical significance of fidelity. By changing the size of the target site group relative to the size of the entire data set, the fidelity measure can be made more sensitive to either common or rare species. We show that there are two modifications of the IndVal index for presence/absence data, one of which is also independent of the size of site groups. Conclusion: The phi coefficient applied to site groups of equalized size has advantages over other statistical measures of fidelity based on presence/absence data. Its properties are close to an intuitive understanding of fidelity and diagnostic species in vegetation science. Statistical significance can be checked by calculation of another fidelity measure that is a function of statistical significance, or by direct calculation of the probability of observed species concentrations by Fisher's exact test. An advantage of the new method over IndVal is its ability to distinguish between positive and negative fidelity. One can also weight the relative importance of common and rare species by changing the equalized size of the site groups. Nomenclature: Ehrendorfer (1973).