Small heterogeneity has large effects on synchronization of ecological oscillators.

Heterogeneity in habitat plays a crucial role in the dynamics of spatially extended populations and is often ignored by both empiricists and theoreticians. A common assumption made is that spatially homogeneous systems and those with slight heterogeneity will behave similarly and, therefore, the results and data from studies of the former can be applied to the latter. Here, we test this assumption by deriving a phase model from two weakly coupled predator-prey oscillators and analyze the effect of spatial heterogeneity on the phase dynamics of this system. We find that even small heterogeneity between the two patches causes substantial changes in the phase dynamics of the system which can have dramatic effects on both population dynamics and persistence. Additionally, if the prey and predator time scales are similar, the effect of heterogeneity is much greater.