On population diversity measures in Euclidean space

In this paper we define a mathematical notion of ectropy for classifying diversity measures in terms of the extent to which they tend to penalize point collocation, we investigate the advantages and disadvantages of several known measures and we propose some novel ones. In particular, we introduce a measure based on Euclidean minimum spanning trees, a class of power mean based measures and three measures based on discrepancy from uniform distribution. All considered measures are tested and compared on a large set of random and structured populations. Special attention is also devoted to the complexity of computing the measures. The measure based on Euclidean minimum spanning trees turns out to be the most promising one in terms of the tradeoff between the computational complexity and the ectropic behavior.