Diversity in complex systems: measuring parts of the distribution to the whole

Abstract

Abstract Despite the utility of the Hill numbers, measuring diversity within complex systems and complex datasets, particularly regarding parts of a distribution to the whole—that is, different portions of diversity types to the entire system or dataset—is a challenging issue. In this paper, we attempt to relate the diversity of a part (or parts) of a distribution to the diversity of the whole. We derive this relationship for the Hill numbers q D , and use these results to further examine the effect of a freely varying type on the diversity of the whole distribution.