The use of diversity and evenness indices is well established in recent ecological literature. Many indices have been proposed, to such an extent that the choice of a suitable index became somewhat of a problem. Recently, however, Hill (1973) introduced a unifying notation where diversity numbers are denned in relation to Rényi's definition of a generalized entropy. Hill showed that his diversity numbers Na of the oth, 1st and 2nd order coincide with three important diversity measures which have been frequently used, No = S, N1 = eH and N2 = 1/SI, where S is the number of species, H is the shannon-Wiener information function –Σpi In pi and SI is Simpson's index . According to this notation, evenness should be calculated by dividing two of Hill's diversity numbers, e.g. N2/N1 = eH/S. This index was proposed by Sheldon (1969), but its use in ecological literature has been negligible. The most commonly used evenness index has been the one proposed by Pielou (1966), e = H/Hmax, with Hmax = lnS. Contrary to Hill's (1973) statement, it shares with Hill's continuum of evenness measures the property of remaining constant when the number of individuals of all species is multiplied with a constant factor. Intuitively, this seems to be a necessary property of an evenness index.