Alpha species diversity measured by Shannon’s H-index: Some misunderstandings and underexplored traits, and its key role in exploring the trophodynamic stability of dynamic multiscapes

Abstract

The spectrum of species diversity (SDi) can be broken down into αSDi (taxocene level), βSDi (community level), and γSDi (metacommunity level). Species richness (S) and Shannon's index (H) are well-known SDi measures. The use of S as a surrogate for SDi often neglects evenness (J). Additionally, there is a wide variety of indicators of SDi. However, there are no reliable theoretical criteria for selecting the most appropriate SDi index despite the undeniable empirical usefulness of this parameter. This situation is probably due to the analytical gap still existing between SDi and trophodynamics. This article contributes to closing that gap by analyzing why S as a single surrogate for SDi is inconsistent from the trophodynamic point of view, so that an index combining S and J, such as H or HB (Brillouin's index), are the most appropriate choices in the context of a new theoretical framework (organic biophysics of ecosystems, OBEC) based on the well-known classical links between ecosystem ecology and thermodynamics. Exploration of data from reef fish surveys under stationary and non-stationary conditions corroborated the existence of the ecological equivalent of Boltzmann's constant (keτ(e)) at the worldwide scale. This result substantiates the usefulness of the ecological equivalent of the compressibility factor as an indicator of environmental impact. keτ(e) stablishes an analytical linkage between ecology, information theory, and statistical mechanics that allowed us to propose a new measure of total negative entropy (a.k.a. syntropy) per survey (SeτT) that is easy to calculate and displayed a highly significant correlation with total standing biomass per survey (meTs). According to the slope of the regression equation SeτT, meTs there is a large portion of SeτT that leaks into the environment and/or is captured by numerous ecological degrees of freedom independent of standing biomass. According to the changing value of the exponent of keτ(e), even among coexisting taxocenes, it would have been impossible to obtain the results discussed in this article if the analysis had been carried out at the βSDi or γSDi level. This establishes αSDi as the most appropriate level of analysis to obtain empirically useful results about the key functional connections on which trophodynamic stability depends in dynamic multispaces. The results summarized here are based on the careful selection and intertwining of a few key variables, which indicates the importance of developing models as simple as possible in order to achieve the reliability necessary for successful biological conservation.