Divergence Measures as Diversity Indices

Abstract: Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices for short, suffer from three problems. First, when computing the diversity for samples withdrawn from communities with different structures, diversity indices can easily yield non-comparable and hard to interpret results. Second, diversity indices impose weighting schemes on the species distributions that unnecessarily emphasize low abundant rare species, or erroneously identified ones. Third, diversity indices do not allow for comparing distributions against each other, which is necessary when a community has a well-known species' distribution. In this paper we propose a new general methodology based on information theoretic principles to quantify the species diversity of a community. Our methodology, comprised of two steps, naturally overcomes the previous mentioned problems, and yields comparable and easy to interpret diversity values. We show that our methodology retains all the functional properties of any diversity index, and yet is far more flexible than entropy--based diversity indices. Our methodology is easy to implement and is applicable to any community of interest.