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When comparing the diversity of samples it is important to consider if the relative diversity changes with the diversity index used. If it does, then it is clear that any arguments based on relative magnitude of the index might not be robust. This method allows the relative magnitude across a range of indices to be compared.
where α is the order (α≥0, α≠0), pi the proportional abundance of the ith species and log the logarithm to a base of choice - often e.
Hill (1973) used an almost identical index Na which is related to Hα by the equality
He demonstrated that Na for a = 0, 1, 2 gives the total species number, Shannon-Wiener, H and Simpson's D respectively. Thus by varying α, or 'a' we may generate a range of diversity measures. To test for non-comparability of communities Hα is calculated for a range of α values and the results presented graphically. If a community is always greater it can be considered to be more diverse. If two communities cross over they are non-comparable.