Punctuated equilibrium as an emergent process and its modified thermodynamic characterization

Abstract

We address evolutionary dynamics and consider under which conditions the ecosystem interaction network allows punctuated equilibrium (i.e., alternation between hectic and quasi-stable phases). We focus on the links connecting various species and on the strength and sign of those links. For this study we consider the Tangled Nature model, which allows considerable flexibility and plasticity in the analysis of interspecies interactions. We find that it is necessary to have a proper balance of connectivity and interaction intensities so as to establish the kind of mutual cooperation and competition found in nature. It suggests evolutionary punctuated equilibrium as an emergent process, thus displaying features of complex systems. To explicitly demonstrate this fact we consider an extended form of thermodynamics, defining (for the present context) relevant out-of-equilibrium "collective" functions. We then show how to characterize the punctuated equilibrium through entropy-like and free energy-like quantities. Finally, from a close analogy to thermodynamic systems, we propose a protocol similar to simulated annealing. It is based on controlling the species' rate of mutation during the hectic periods, in this way enhancing the exploration of the genome space (similar to the known behavior of bacteria in stressful environments). This allows the system to more rapidly converge to long-duration quasi-stable phases.

The evolutionary origins of Lévy walk foraging

“…The relations between a group of species in habitat A can be considerably distinct from those for the same species but in habitat B [ 170 ]. Also, trophic interactions (e.g., the predator-multiprey competition) can be modified by the presence of heterogeneities in the environment [ 171 , 172 ]. Hence, the implausibility of retaining Lévy strategies in complete distinct environments without any underlying evolutionary pressure has motivated the idea of a general Hierarchical Lévy Flight Foraging Hypothesis [ 50 ], of which examples in [ 60 ] and [ 79 ] are potential concrete cases.…”

Revisiting the complex adaptive systems paradigm: Leading perspectives for researching operations and supply chain management issues

“…Studies in complex systems have shown that such punctuated equilibrium does not occur in all instances and requires a specific network structure to manifest fully. Specifically, it requires some level of balance between the number and magnitude of agent interactions (Wosniack, da Luz, & Schulman, ). A deeper examination of situations within the OSCM domain that are characterized by this balance and those that are not is necessary to embrace the concept fully.…”

Tangled Nature: a model of emergent structure and temporal mode among co-evolving agents

“…The intermittency, or punctuated equilibrium, of the TaNa model was studied by Wosniack, da Luz and Schulman from the perspective of thermodynamics [67]. The authors define an energy, and entropy and a free energy and study how these behave differently in the q-ESS states and the hectic states separating the q-ESS sates.…”