Investigating beta diversity by Kullback–Leibler information measures

Since its introduction in the early 1950s, information theory, thanks to the link among the concepts of information, entropy and complexity, has seemed to provide a theoretical basis and statistical tools for capturing some of the fundamental properties of complex living systems from the molecular to the community scale. Moreover, the flexibility of information analysis, which resides essentially in the fact that its applicability is not burdened by restrictive assumptions on the underlying probability distribution of data, which characterise conventional multivariate statistics, has facilitated its widespread use among biologists. In spite of their common root with Shannon's H′, which is probably the most widely used index of alpha diversity in ecology, the Kullback–Leibler information measures have received scant attention from ecologists as dissimilarity measures between communities. In this paper, after having illustrated the potentiality of applying them to this matter, we propose a similarity index based on the Kullback–Leibler divergence and on the concept of sample coverage, and test its effectiveness by applying it to the evaluation of beta diversity of phytoplankton along a water stability gradient in Lake Trasimeno (Umbria, Italy). The results show that the proposed indices are effective in revealing a community gradient which is consistent with the environmental gradient investigated and advise their use particularly when there are slight differences in the composition and structure of the communities being compared. The study also shows how the decomposition of the divergence function can offer a way for calculating and partitioning the total diversity of a pooled set of communities from the perspective of information theory.