Climate variability has strong effects on marine ecosystems, with repercussions that range in scale from those that impact individuals to those that impact the entire food web. Climate-induced changes in the abundance of species in lower trophic levels can cascade up to apex predators by depressing vital rates. However, the characteristics and predictability of predator demographic responses remain largely unexplored. We investigated the detectability, limits, and nonlinearity of changes in Antarctic fur seal pup production at South Georgia over a 20-year period in response to environmental autocorrelation created by global climate perturbations; these were identified in time series of monthly averaged sea surface temperature (SST). Environmental autocorrelation at South Georgia was evident with frequent SST anomalies between 1990 and 1999, during a decade of warm background (time-averaged) conditions. SST anomalies were preceded by, and cross-correlated with, frequent El Niño-La Niña events between 1987 and 1998, which was also a decade of warm background conditions in the tropical Pacific Ocean. Nonlinear mixed-effects models indicated that positive anomalies at South Georgia explained extreme reductions in Antarctic fur seal pup production over 20 years of study. Simulated environmental time series suggested that the effect of anomalies on Antarctic fur seals was only detectable within a narrow range of positive SST, regardless of the distribution, variance, and autocorrelation structure in SST; this explained the observed nonlinearity in responses in pup production, which were observed only under persistent high SST levels. Such anomalies at South Georgia were likely associated with low availability of prey, largely krill, which affected Antarctic fur seal females over time scales longer than their breeding cycle. Reductions in Antarctic fur seal pup production could thus be predicted in advance by the detection of large-scale anomalies, which appeared to be driven by trends in global climate perturbation.