Environmental monitoring through functional biodiversity tools

The foundational concept for our research, which is largely shared by statisticians and ecologists, is that biodiversity is one of the most important indicators for environmental assessment. Because this indicator decreases in relation to ecosystem stressors, its measurement is essential for predicting future biological impacts of environmental damages. Although many indices have been proposed, no universally accepted measure for biodiversity has yet been established. In this context, the use of diversity profiles allows the analyst to display a family of indices in a single graph. However, this approach presents two critical limitations: first, a community composition is not always interpretable; second, the diversity profiles could lead to ranking issues when the curves intersect each other. The aim of this paper is to resolve these limitations by introducing functional biodiversity tools. In particular, three functional measures are proposed: the derivatives, the radius of curvature and the curve length. The analysis of derivatives and of the radius of curvature addresses the first limitation and highlights the characteristics, the differences and the similarities among communities. Arc length addresses the second limitation, providing a scalar measure that leads to a unique communities ranking for a given pattern of richness even if profiles intersect. The proposed functional models are applied to a real data set involving lichen biodiversity in the province of Genoa, Italy. Our approach allowed us to analyze the characteristics of lichen communities and to identify the biodiversity ranking. The combined use of these tools provides a useful method for identifying areas of high environmental risk, with the potential to address the monitoring of environmental policies.