A functional approach to Hill's numbers for assessing changes in species variety of ecological communities over time

Humans are dependent on a large number of species of animals, plants, fungi, and microbes that provide indispensable ecosystem functions and produce essential goods. Apart from the economic valuation of the direct and indirect benefits of biodiversity, people place existence values on biodiversity, i.e. they consider the existence of particular species, regardless of the services they provide. There is also a general recognition that species diversity indicates the status of the ecosystem or community, and thus the quality of the living environment; hence, both at academic and institutional level, there is a lively discussion about how to properly measure and monitor biodiversity. Although many candidates have been proposed, nowadays, no scientific consensus measure exists, and this is mainly due to three motivations: the large number of properties that an indicator of biodiversity should meet, the definition of biodiversity, and the specific interests of policymakers or stakeholders that indicators should satisfy. Because most existing indices neglect the multivariate nature of biodiversity, we address this drawback by proposing a functional approach to Hill's numbers for assessing changes in species variety of ecological communities over time. New functional tools are developed, both analytical and graphical: we present “the biodiversity surface”, “the volume under the biodiversity surface”, and some indicators which have been derived from them. This functional multivariate approach provides additional tools to the existing biodiversity monitoring techniques, and allows us to address biodiversity by considering both richness and evenness, and all of their possible shades. The goal of this research is to provide policymakers, stakeholders, and scholars with additional tools for improving the understanding of biodiversity dynamics within ecological communities.