  Living systems operate in a critical dynamical regime -- between order and
chaos -- where they are both resilient to perturbation, and flexible enough to
evolve. To characterize such critical dynamics, the established 'structural
theory' of criticality uses automata network connectivity and node bias (to be
on or off) as tuning parameters. This parsimony in the number of parameters
needed sometimes leads to uncertain predictions about the dynamical regime of
both random and systems biology models of biochemical regulation. We derive a
more accurate theory of criticality by accounting for canalization, the
existence of redundancy that buffers automata response to inputs -- a known
mechanism that buffers the expression of traits, keeping them close to optimal
states despite genetic and environmental perturbations. The new 'canalization
theory' of criticality is based on a measure of effective connectivity. It
contributes to resolving the problem of finding precise ways to design or
control network models of biochemical regulation for desired dynamical
behavior. Our analyses reveal that effective connectivity significantly
improves the prediction of critical behavior in random automata network
ensembles. We also show that the average effective connectivity of a large
battery of systems biology models is much lower than the connectivity of their
original interaction structure. This suggests that canalization has been
selected to dynamically reduce and homogenize the seemingly heterogeneous
connectivity of biochemical networks.
