A New Index Measuring Evenness

Abstract

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 N_a of the oth, 1st and 2nd order coincide with three important diversity measures which have been frequently used, N_o = S, N₁ = e^H and N² = 1/SI, where S is the number of species, H is the shannon-Wiener information function –Σp_i In p_i 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 = e^H/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/H_max, with H_max = 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.