  Robustness to mutations and noise has been shown to evolve through
stabilizing selection for optimal phenotypes in model gene regulatory networks.
The ability to evolve robust mutants is known to depend on the network
architecture. How do the dynamical properties and state-space structures of
networks with high and low robustness differ? Does selection operate on the
global dynamical behavior of the networks? What kind of state-space structures
are favored by selection? We provide damage propagation analysis and an
extensive statistical analysis of state spaces of these model networks to show
that the change in their dynamical properties due to stabilizing selection for
optimal phenotypes is minor. Most notably, the networks that are most robust to
both mutations and noise are highly chaotic. Certain properties of chaotic
networks, such as being able to produce large attractor basins, can be useful
for maintaining a stable gene-expression pattern. Our findings indicate that
conventional measures of stability, such as the damage-propagation rate, do not
provide much information about robustness to mutations or noise in model gene
regulatory networks.
