Underlying thermodynamic relations of a species diversity index: Freshwater crabs from Colombia

The goal of this paper is to apply the theoretical method described in Campos (2011) to the characterization of an ecological system represented by data corresponding to a collection of freshwater crabs consisting of 100 species and 6397 specimens recorded in Colombia between 1910 and 2010.The registers in the collection are translated into a set of probabilities (relative abundances) P={P1,P2,…,PN}P={P1,P2,…,PN}, where NN is the species richness. The index for species diversity is calculated as the product of a function of the species richness times a function of the Helmholtz free energy F(P,q)F(P,q), where the entropic parameter q allows the system to be considered under various hypothetical environmental conditions.

► An ecological system represented by a collection of freshwater crabs is considered. ► Hypothetical environmental conditions are described by an entropic parameter q. ► A geometrical species diversity index allows the characterization of the system. ► Geometrical index has some advantages over Shannon measure of ecological diversity.