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An Exergy-Based Model for Population Dynamics: Adaptation, Mutualism, Commensalism and Selective Extinction
Department of Mechanical & Aerospace Engineering, University of Roma La Sapienza, Via Eudossiana 18, 00184 Roma, Italy
School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK
* Author to whom correspondence should be addressed.
Received: 3 August 2012; in revised form: 23 September 2012 / Accepted: 2 October 2012 / Published: 15 October 2012
Abstract: Following the critical analysis of the concept of “sustainability”, developed on the basis of exergy considerations in previous works, an analysis of possible species “behavior” is presented and discussed in this paper. Once more, we make use of one single axiom: that resource consumption (material and immaterial) can be quantified solely in terms of exergy flows. This assumption leads to a model of population dynamics that is applied here to describe the general behavior of interacting populations. The resulting equations are similar to the Lotka-Volterra ones, but more strongly coupled and intrinsically non-linear: as such, their solution space is topologically richer than those of classical prey-predator models. In this paper, we address an interesting specific problem in population dynamics: if a species assumes a commensalistic behavior, does it gain an evolutionary advantage? And, what is the difference, in terms of the access to the available exergy resources, between mutualism and commensalism? The model equations can be easily rearranged to accommodate both types of behavior, and thus only a brief discussion is devoted to this facet of the problem. The solution space is explored in the simplest case of two interacting populations: the model results in population curves in phase space that can satisfactorily explain the evolutionistic advantages and drawbacks of either behavior and, more importantly, identify the presence or absence of a “sustainable” solution in which both species survive.
Keywords: exergy; population dynamics; species interaction; sustainability
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Sciubba, E.; Zullo, F. An Exergy-Based Model for Population Dynamics: Adaptation, Mutualism, Commensalism and Selective Extinction. Sustainability 2012, 4, 2611-2629.
Sciubba E, Zullo F. An Exergy-Based Model for Population Dynamics: Adaptation, Mutualism, Commensalism and Selective Extinction. Sustainability. 2012; 4(10):2611-2629.
Sciubba, Enrico; Zullo, Federico. 2012. "An Exergy-Based Model for Population Dynamics: Adaptation, Mutualism, Commensalism and Selective Extinction." Sustainability 4, no. 10: 2611-2629.