Population dynamics of small mammals and predators in semi-arid Chile is positively correlated with rainfall associated with incursions of El Niño (El Niño Southern Oscillation: ENSO). However, the causal relationships between small mammal fluctuations, predator oscillations, and climatic disturbances are poorly understood. Here, we report time series models for three species of small mammal prey and two species of owl predators. The large differences in population fluctuations between the three small mammal species are related to differences in their respective feedback structures. The analyses reveal that per capita growth rate of the leaf-eared mouse is a decreasing function of log density and of log barn owl abundance together with a positive rainfall effect. In turn, per capita population growth rate (R-function) of the barn owl is a negative function of log barn owl abundance and a positive function of leaf-eared mouse abundance, suggesting a predator–prey interaction. The dramatic population fluctuations exhibited by leaf-eared mouse (Phyllotis darwini) are caused by climate effects coupled with a complex food web architecture.