Degrees of freedom: Definitions and their minimum and most meaningful combination for the modelling of ecosystem dynamics with the help of physical principles

There is a neglected old schism in ecosystem ecology (EE): the foundations of crucial concepts and principles of EE lie in thermodynamics, but the current mainstream of ecological thought is significantly biased towards contingent mathematical models disconnected from physics. Frequently, these models have weak theoretical support in ecology itself, as well as a limited empirical validation. This situation emerged when some ecologists became aware that, seemingly, thermodynamics (devoted to study the dynamics of closed systems in equilibrium) should be useless to understand ecosystems (far-from-equilibrium open systems). The solution was, either developing a sort of new physics weakly linked to the principles and methods of conventional physics, or a direction change towards an astonishing diversification of analytical ways. In practice, both things have happened simultaneously. One of the many expressions of this controversial decision was a sort of rigmarole in the use of the concept of degrees of freedom. This article, based on a recent proposal (organic biophysics of ecosystems, OBEC): (i) contributes to resolve the dilemma physics vs. non-physics in EE; (ii) proposes a plausible and empirically-backed approach to the meaning, interaction and use of the concept of degrees of freedom in EE by reducing them to an inseparable triad of indicators (species diversity, dispersal intensity, and fresh biomass or body weight per individual) valid for any kind of ecosystem (non-contingency) and backed by six essential traits (simplicity, universality, evolvability, empirical manageability, inter-model inclusivity, and interdisciplinary scope); and (iii) explores the aftermaths of the aforementioned approach to propose a,complementary explanation to the metabolic theory of ecology, as well as the cornerstone of an analytical framework commonly shared by economics and EE, in order to develop a new way of getting reliable results in regard to the interaction between society and nature. In summary, the results included in these three analytical axes (from i to iii) are based on previous publications including empirical field data from 12 different kinds of taxocenes involving a total of 1649 plots and 8.874 x 10(7) individuals belonging to 1280 species. Besides, this article includes in itself additional data from 638 species of mammals, 97 samples of ruderal vegetation, 26 samples of zooplankton, as well as data in reference to a significant fraction of the U.S.A. population as a whole (x) over bar= 2.973 x 10(8) +/- 8.657 x 10(6) S.D. - individuals per year) in combination with abiotic environmental data (mean temperature and emission of greenhouse gases at the country level) over 12 consecutive years.