We quantify the expected demographic benefit to a seabird of conservation concern, the ashy storm‐petrel Oceanodroma homochroa, from the proposed eradication of introduced house mice Mus musculus on the South Farallon Islands, California. A key objective of the eradication is to reduce storm petrel predation by burrowing owls Athene cunicularia, which stopover on the island during their fall migration. Mouse trapping and field surveys of both owls and depredated storm petrel carcasses conducted during 2000–2012 reveal a strongly seasonal, inter‐related pattern among the three species: When owls arrive during the fall, mice are super‐abundant and the overwhelming choice of prey for those owls that remain. In the winter, the mouse population crashes just as storm petrels begin to arrive in large numbers; owls that remain on the island switch to preying upon storm petrels until May, when they depart to breed. Capture–recapture analyses of storm petrels showed (1) annual adult survival was inversely related to owl abundance, especially during January–April, and (2) storm petrels demonstrated a declining trend in abundance 2006–2012. The latter was associated with low rates of adult survival, high abundance of overwintering burrowing owls, and high incidence of depredated storm petrels. To evaluate projected impacts to storm petrels of a change in owl predation, we developed a Leslie matrix model, incorporating environmental stochasticity. We modeled future storm petrel population trajectories, allowing for different levels of owl‐mediated predation. Our results suggest that a reduction in owl abundance, a projected consequence of the elimination of mice, has the potential to substantially reduce overall storm petrel mortality, thereby reducing storm petrel declines and increasing the likelihood of stable trends in the future. While long‐term benefits to storm petrels of mouse eradication are apparent, the risk of increased predation due to prey‐switching by owls also needs to be addressed. This study highlights uncertainty of outcomes, which must be considered in evaluating management impacts. This study demonstrates the value of concurrent, continuous, long‐term datasets in providing a quantitative basis for management to aid the conservation of species of concern.