1. Environmental variability, through interannual variation in food availability or climatic variables, is usually detrimental to population growth. It can even select for constancy in key life-history traits, though some exceptions are known. Changes in the level of environmental variability are therefore important to predict population growth or life-history evolution. Recently, several cyclic vole and lemming populations have shown large dynamical changes, that might affect rodent predator demography or life histories. 2. Skuas constitute an important case study among rodent predators, because of their strongly saturating breeding productivity (they lay only two eggs) and high degree of site fidelity, in which they differ from nomadic predators raising large broods in good rodent years. This suggests that they cannot capitalize on lemming peaks to the same extent as nomadic predators, and might be more vulnerable to collapses of rodent cycles. 3. We develop a model for the population dynamics of long-tailed skuas feeding on lemmings to assess the demographic consequences of such variable and nonstationary prey dynamics, based on data collected in NE Greenland. The model shows that populations of long-tailed skua sustain well changes in lemming dynamics, including temporary collapses (e.g. 10 years). A high floater-to-breeder ratio emerges from rigid territorial behaviour and a long life expectancy, which buffers the impact of adult abundance's decrease on the population reproductive output. 4. The size of the floater compartment is affected by changes in both mean and coefficient of variation of lemming densities (but not cycle amplitude and periodicity per se). In Greenland, the average lemming density is below the threshold density required for successful breeding (including during normally cyclic periods). Due to Jensen's inequality, skuas therefore benefit from lemming variability; a positive effect of environmental variation. 5. Long-tailed skua populations are strongly adapted to fluctuating lemming populations, an instance of demographic lability in the reproduction rate. They are also little affected by poor lemming periods, if there are enough floaters, or juveniles disperse to neighbouring populations. The status of Greenland skua populations therefore strongly depends upon floater numbers and juvenile movements, which are not known. This reveals a need to intensify colour-ringing efforts on the long-tailed skua at a circumpolar scale.