Abstract
Biological diversity is a key concept in the life sciences and plays a fundamental role in many ecological and evolutionary processes. Although biodiversity is inherently a hierarchical concept covering different levels of organization (genes, population, species, ecological communities and ecosystems), a diversity index that behaves consistently across these different levels has so far been lacking, hindering the development of truly integrative biodiversity studies. To fill this important knowledge gap, we present a unifying framework for the measurement of biodiversity across hierarchical levels of organization. Our weighted, information-based decomposition framework is based on a Hill number of order q = 1, which weights all elements in proportion to their frequency and leads to diversity measures based on Shannon's entropy. We investigated the numerical behaviour of our approach with simulations and showed that it can accurately describe complex spatial hierarchical structures. To demonstrate the intuitive and straightforward interpretation of our diversity measures in terms of effective number of components (alleles, species, etc.), we applied the framework to a real data set on coral reef biodiversity. We expect our framework will have multiple applications covering the fields of conservation biology, community genetics and eco-evolutionary dynamics.