life Article Evolving Always-Critical Networks Marco Villani 1,2,* , Salvatore Magrì 3, Andrea Roli 2,4 and Roberto Serra 1,2,5 1 Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, I-41125 Modena, Italy;
[email protected] 2 European Centre for Living Technology, 30123 Venice, Italy;
[email protected] 3 Department of Physics, University of Bologna, 40126 Bologna, Italy;
[email protected] 4 Department of Computer Science and Engineering, University of Bologna, 40126 Bologna, Italy 5 Institute for Advanced Study, University of Amsterdam, 1012 WX Amsterdam, The Netherlands * Correspondence:
[email protected] Received: 31 January 2020; Accepted: 1 March 2020; Published: 4 March 2020 Abstract: Living beings share several common features at the molecular level, but there are very few large-scale “operating principles” which hold for all (or almost all) organisms. However, biology is subject to a deluge of data, and as such, general concepts such as this would be extremely valuable. One interesting candidate is the “criticality” principle, which claims that biological evolution favors those dynamical regimes that are intermediaries between ordered and disordered states (i.e., “at the edge of chaos”). The reasons why this should be the case and experimental evidence are briefly discussed, observing that gene regulatory networks are indeed often found on, or close to, the critical boundaries. Therefore, assuming that criticality provides an edge, it is important to ascertain whether systems that are critical can further evolve while remaining critical. In order to explore the possibility of achieving such “always-critical” evolution, we resort to simulated evolution, by suitably modifying a genetic algorithm in such a way that the newly-generated individuals are constrained to be critical.