Phase switching in population cycles

Oscillatory populations may exhibit a phase change in which, for example, a high-low periodic pattern switches to a low-high pattern. We propose that phase shifts correspond to stochastic jumps between basins of attraction in an appropriate phase space which associates the different phases of a periodic cycle with distinct attractors. This mechanism accounts for two-cycle phase shifts and the occurrence of asynchronous replicates in experimental cultures of Tribolium.