Before revision:  Successful convergence depends crucially on network topology and is most efficient for scale-free connectivity. Convergence to an adapted phenotype in this class of networks is achieved without fine tuning of initial conditions or other model parameters, thus making it plausible for biological implementation . Experimental results have indeed shown that gene regulatory networks are characterized by this type of topology, suggesting a structural basis for exploratory adaptation .
After revision:  We find that successful convergence (adaptation) in high dimensions requires outgoing network hubs and is enhanced by their auto-regulation. The ability of these empirically-validated features of gene regulatory networks to support exploratory adaptation without fine-tuning, makes it plausible for biological implementation . Experimental results have indeed shown that gene regulatory networks are characterized by this type of topology, suggesting a structural basis for exploratory adaptation .