A contribution to the systematic quantification of the resource flow needed to sustain a given population dynamics

In previous studies [1-5], we provided an analytical treatment of the evolution of a population numerosity in time. The method is based on one single axiom: that resource consumption (of any kind) can be quantified solely in terms of exergy flows. The results show that the dynamics of a population is ruled by the system complexity and is constrained by certain thresholds - expressed in terms of evolutionary competition parameters and individual resource consumption- below or beyond which the system exhibits trends that can be judged in terms of its ability to maintain itself (possibly through fluctuations), in a self-preserving , i.e., thermodynamically sustainable, state. The principle of analysis is simple, and its application shows that complexity, measured both by the number of interactions between the elements of the system and by the degree of nonlinearity of the transfer functions of these elements, plays a major role, and -even for the simplest cases- often leads to non-trivial solutions in phase space. Several sets of well-documented experimental results were used to benchmark the method, and the results were very satisfactory. Since the use of the concept of "sustainability" is enjoying an evermore widespread use in the analysis of energy and societal systems, it becomes important to assess the general "feasibility" of new strategies and new scenarios: on the basis of the results hitherto derived, it can be stated that the application of our method leads to the correct identification, among different possible solutions ("scenarios" or "configurations"), the one that promises a less unsustainable future for the population(s) under study. It is necessary to remark that the "sustainability" we are discussing here must be intended in a purely physical sense, since it is derived solely from thermodynamic principles and does not include other sides of the issue (equitable development, social justice, rational resource allocation) that may well retain their relevance outside of the conceptual boundaries of the present treatment. The study presented in this paper is an extension of the previous ones, and addresses a "reverse" problem: if the history of the population evolution is known, what is the necessary amount of primary resources required to reproduce the data? It is clear that an answer to this question is of the outmost importance for policy makers and energy planners alike, because it allows for the medium- and long range planning of "minimal exergy consumption". As in our previous papers, a comparison of our results with some of the available experimental evidence is provided.