NOTE ON BIOLOGICAL DIVERSITY, EVENNESS, AND HOMOGENEITY MEASURES

This paper is concerned with the measurement of diversity of a biological or ecological sample of individuals belonging to various species. Using the concept of statistical odds, an alternative diversity measure with an appealing interpretation is formulated as a simple modification of the popular Simpson index. If SIGMA-p(i)2 denotes the sum of the squared proportions of individuals belonging to the different species in the sample, the new odds measure of diversity is simply defined by OD = (SIGMA-p(i)2)-1-1 and has the following interpretation: OD is the odds that two individuals selected at random (with replacement) from the sample are of different species. The same modification is also applied to a couple of other measures in use, providing them with convenient odds interpretations. These measures are all members of the same parameterized family, which represents a slight modification of the Hill's family. The inverse of OD is proposed as an odds measure of species homogeneity. Also, some properties of the different measures are outlined, and the measurement of evenness is discussed. Finally, some new indices of individual species dominance and surprise are briefly mentioned.