Environmental monitoring through functional biodiversity tools

The foundational concept for our research, which is largely shared by statisticians and ecologists, is thatbiodiversity is one of the most important indicators for environmental assessment. Because this indicatordecreases in relation to ecosystem stressors, its measurement is essential for predicting future biologicalimpacts of environmental damages. Although many indices have been proposed, no universally acceptedmeasure for biodiversity has yet been established. In this context, the use of diversity profiles allows theanalyst to display a family of indices in a single graph. However, this approach presents two critical lim-itations: first, a community composition is not always interpretable; second, the diversity profiles couldlead to ranking issues when the curves intersect each other. The aim of this paper is to resolve theselimitations by introducing functional biodiversity tools. In particular, three functional measures are pro-posed: the derivatives, the radius of curvature and the curve length. The analysis of derivatives and ofthe radius of curvature addresses the first limitation and highlights the characteristics, the differencesand the similarities among communities. Arc length addresses the second limitation, providing a scalarmeasure that leads to a unique communities ranking for a given pattern of richness even if profiles inter-sect. The proposed functional models are applied to a real data set involving lichen biodiversity in theprovince of Genoa, Italy. Our approach allowed us to analyze the characteristics of lichen communities andto identify the biodiversity ranking. The combined use of these tools provides a useful method for iden-tifying areas of high environmental risk, with the potential to address the monitoring of environmentalpolicies.