Oscillatory populations may exhibit a phase change in which, for examp
le, a high-low periodic pattern switches to a low-high pattern. We pro
pose that phase shifts correspond to stochastic jumps between basins o
f attraction in an appropriate phase space which associates the differ
ent phases of a periodic cycle with distinct attractors. This mechanis
m accounts for two-cycle phase shifts and the occurrence of asynchrono
us replicates in experimental cultures of Tribolium.