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Canalization is a classic concept in Developmental Biology that is thought tobe an important feature of evolving systems. In a Boolean network it is a formof network robustness in which a subset of the input signals control thebehavior of a node regardless of the remaining input. It has been shown thatBoolean networks can become canalized if they evolve through a frustratedcompetition between nodes. This was demonstrated for large networks in whicheach node had K=3 inputs. Those networks evolve to a critical steady-state atthe boarder of two phases of dynamical behavior. Moreover, the evolution ofthese networks was shown to be associated with the symmetry of the evolutionarydynamics. We extend these results to the more highly connected K>3 cases andshow that similar canalized critical steady states emerge with the sameassociated dynamical symmetry, but only if the evolutionary dynamics is biasedtoward homogeneous Boolean functions.

Canalization in the Critical States of Highly Connected Networks of Competing Boolean Nodes