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Living systems operate in a critical dynamical regime -- between order andchaos -- where they are both resilient to perturbation, and flexible enough toevolve. To characterize such critical dynamics, the established 'structuraltheory' of criticality uses automata network connectivity and node bias (to beon or off) as tuning parameters. This parsimony in the number of parametersneeded sometimes leads to uncertain predictions about the dynamical regime ofboth random and systems biology models of biochemical regulation. We derive amore accurate theory of criticality by accounting for canalization, theexistence of redundancy that buffers automata response to inputs -- a knownmechanism that buffers the expression of traits, keeping them close to optimalstates despite genetic and environmental perturbations. The new 'canalizationtheory' of criticality is based on a measure of effective connectivity. Itcontributes to resolving the problem of finding precise ways to design orcontrol network models of biochemical regulation for desired dynamicalbehavior. Our analyses reveal that effective connectivity significantlyimproves the prediction of critical behavior in random automata networkensembles. We also show that the average effective connectivity of a largebattery of systems biology models is much lower than the connectivity of theiroriginal interaction structure. This suggests that canalization has beenselected to dynamically reduce and homogenize the seemingly heterogeneousconnectivity of biochemical networks.

Effective connectivity determines the critical dynamics of biochemical networks