Identifying anomalous patterns in ecological communities’ diversity: leveraging functional boxplots and clustering of normalized Hill’s numbers and their integral functions

Diversity is fundamental in many disciplines, such as ecology, business, biology, and medicine. From a statistical perspective, calculating a measure of diversity, whatever the context of reference, always poses the same methodological challenges. For example, in the ecological field, although biodiversity is widely recognised as a positive element of an ecosystem, and there are decades of studies in this regard, there is no consensus measure to evaluate it. The problem is that diversity is a complex, multidimensional, and multivariate concept. Limiting to the idea of diversity as variety, recent studies have presented functional data analysis to deal with diversity profiles and their inherently high-dimensional nature. A limitation of this recent research is that the identification of anomalies currently still focuses on univariate measures of biodiversity. This study proposes an original approach to identifying anomalous patterns in environmental communities’ biodiversity by leveraging functional boxplots and functional clustering. The latter approaches are implemented to standardised and normalised Hill’s numbers treating them as functional data and Hill’s numbers integral functions. Each of these functional transformations offers a peculiar and exciting point of view and interpretation. This research is valuable for identifying warning signs that precede pathological situations of biodiversity loss and the presence of possible pollutants.