Unsupervised classification of ecological communities ranked according to their biodiversity patterns via a functional principal component decomposition of Hill’s numbers integral functions

Biodiversity is recognized as one of the corner-stones of healthy ecosystems, thus its conservation is increasingly becoming one of the most important targets of environmental management. Despite there is a general recognition that it indicates the status of ecosystems, no consensus measure exists because biodiversity is a very complex concept that is intrinsically multidimensional and multivariate. Limiting the attention on the concept of biodiversity as variety, recent studies have highlighted that both the classical indices and biodiversity profiles suffer of some limitations because the former neglect the multivariate nature of biodiversity whereas the latter can not provide precise rankings among ecological communities when profiles intersect. For this reason, each attempt of comparing, ranking, or clustering ecological communities according to their variety is influenced by the limitations of the specific metric that is used to assess biodiversity. To overcome this problem, we propose a new approach that takes advantage of Hill’s numbers and functional data analysis for ranking and clustering ecological communities according to their variety. Specifically, we introduce three ecological indicators. The first is the “Hill’s numbers integral function” for considering the multivariate nature of biodiversity and ranking diversity profiles. Afterwards, a functional principal component decomposition is suggested for interpreting “Hill’s numbers integral functions” and computing their distance. Finally, an unsupervised classification of ecological communities is proposed by using a functional k-means algorithm based on a semi-metric distance that is computed considering the functional principal component decomposition of the “Hill’s numbers integral functions”. This last indicator provides ranked groups of ecological communities according to their variety by considering the multivariate nature of biodiversity, i.e. both richness and evenness, and all their possible shades. The goal of this research is to provide Ecologists, policymakers, and scholars with additional tools for ranking and detecting areas with high environmental risk and clustering ecological communities with similar biodiversity patterns according to their internal variety.