1. Gyrfalcon predation on ptarmigan during the breeding season was studied in north-east Iceland 1981–97. The ptarmigan population went through a complete 10-year cycle of numbers with a 4·3-fold difference in density between high and low years. The yearly number of occupied gyrfalcon territories was correlated with ptarmigan density with a 3-year time-lag. Total falcon numbers in late summer (territorial adults + fledglings) showed a 2-year lag with ptarmigan numbers. Variability in falcon density was significantly less than that of ptarmigan. It is suggested that the factors contributing to the time-lag between the two populations are the year-round residency of falcons on nesting territories, and late maturity (2- to 4-year-old). Mean brood size and the proportion of the territorial falcon population breeding successfully showed no relation to ptarmigan numbers.
2. Ptarmigan density in spring was an important factor determining composition and variability in the diet of gyrfalcons during the breeding season. Alternative prey for falcons included waterfowl, alcids and waders. Adult ptarmigan featured highly in gyrfalcon diet in all years. The functional response curve to changes in ptarmigan density was slightly convex or close to linear and showed relatively little change in the average number of ptarmigan killed per individual predator over the range of ptarmigan densities observed.
3. The impact of gyrfalcon predation on the ptarmigan population and ptarmigan density was in opposite phases, and the predation rate peaked during the decline and the low phase of the ptarmigan cycle. This suggests that gyrfalcons accelerate decline, accentuate the amplitude and affect the length of the low phase of the ptarmigan cycle. The following factors seem to promote the destabilizing effects of predation by gyrfalcons: they are resident specialist predators, they show a delayed numerical response to changes in ptarmigan density and a high utilization of this prey at all phases of the ptarmigan cycle.