A Calibrated Index for the Measurement of Evenness

Abstract

Until now, Alatalo's modified Hill's ratio F2,1 has been the most adequate evenness index for general application, because: (a) it is little affected by sampling bias and chance variations in the number of species appearing in the samples; and (b) its values depend only and unambiguously upon evenness. In this paper, it is postulated that only for two-species communities it is always possible to know a priori the exact expected evenness values, and a simulated gradation of two-species communities showing all possible species-abundance relationships is used to evaluate F21. The evaluation showed that F2,1 has two major shortcomings, namely: (1) the index markedly overvalues evenness; and (2) the index's values show a decidedly nonlinear relationship to evenness. Therefore, it is proposed that F2r1 be replaced by a calibrated version of the same index, to be named G2 1, that is written as G2,I (arcsin F2,1/90)F2 1, when F2,1>V/1/2; and as G2,1 = F213, when F2,1 Vl/2; where F2,1 = (N2-1)1(Nl-1), where N2 = 1// and N1 -= exp H', where A = 2p2 and H' = -Epi In Pi, where Pi = proportional abundance of species i. G2,1 retains the advantages of F2 ,1, but lacks its two major shortcomings. Because G2,1 is independent of species richness, the calibration based on two-species communities holds valid for communities of more species. Applied to gradations of species-richer communities, G2,1 also shows a superior behavior. In addition, for those needing very accurate values of G2,1, an algorithm to accomplish such an objective is provided.