  The oft-observed persistence of symmetry properties in the face of strong
symmetry-breaking interactions is examined in the SO(5)-invariant interacting
boson model. This model exhibits a transition between two phases associated
with U(5) and O(6) symmetries, respectively, as the value of a control
parameter progresses from 0 to 1. The remarkable fact is that, for intermediate
values of the control parameter, the model states exhibit the characteristics
of its closest symmetry limit for all but a relatively narrow transition region
that becomes progressively narrower as the particle number of the model
increases. This phenomenon is explained in terms of quasi-dynamical symmetry.
