Long-term time series of marine ecological indicators often are characterized by large-amplitude state transitions that can persist for decades. Understanding the significance of these variations depends critically on the underlying hypotheses characterizing expected natural variability. Using a linear autoregressive model in combination with long-term zooplankton observations off the California coast, we show that cumulative integrations of white-noise atmospheric forcing can generate marine population responses that are characterized by strong transitions and prolonged apparent state changes. This model provides a baseline hypothesis for explaining ecosystem variability and for interpreting the significance of abrupt responses and climate change signatures in marine ecosystems.