Thermostatistical distribution of a trophic energy proxy: Extension for modelling energy pyramids at the inter-taxocene scale and under non-stationary conditions

- A previous equation (PE) to model energy pyramids from physics has three limitations.
- Ecological state equation (ESE) was transformed for non-stationary conditions (NSEC).
- The change applied in previous item was also applied to PE to surpass its limitations.
- The usefulness of this change was tested by using a significant amount of field data.
- An equation to model inter-taxocene energy pyramids under NSEC was obtained.

The theory of food chains, and therefore the assembly and modifications of trophic pyramids depending on environmental influences, is an essential part of modern ecosystem ecology. A general model of energy pyramids based on a fruitful but simple analytical connection between ecology and conventional physics has been proposed by Rodríguez et al. (2015a). However, this model has several drawbacks. Among them: it has only been tested for isolated taxocenes and under stationary ecological conditions (SEC). Besides, it has not been tested if the internal distribution of typical species groups within the obtained pyramids follows the expected pattern according to the well-known trophic habits of these typical groups of species. This article starts with a brief summary of the most relevant drawbacks of our conventional point of view about trophic pyramids in order to highlight the differences, as well as the advantageous coincidences, of the above-mentioned new model in comparison with our orthodox point of view about trophic pyramids. This summary connects with a description of the obstacles that should be surpassed in order to develop a more general model (i) valid at the inter-taxocene scale and (ii) fully useful to model systems under non-stationary ecological conditions (NSEC). The article proposes two simple mathematical modifications of the original model in order to achieve items (i) and (ii). In subsequent sections, the effectiveness of these modifications is tested by using field data from 25 samplings belonging to 6 different taxocenes, by including a majority of zooplankton data from a human-made highly eutrophic reservoir (Acton Lake; Hueston Woods State Park, Ohio, U.S.A.) with frequent and contingent episodes of NSEC. According to our results, it is not possible to reject either the hypothesis about the validity of modifying the original equation to model ecosystems as a whole under NSEC or the hypothesis that typical species groups follow a distribution within their respective pyramid in agreement with the expected pattern according to their trophic habits. In summary, this article is an additional step in favor of the usefulness of rescuing and expanding the original epistemological roots of ecosystem ecology in connection with conventional physics.