This dataset is associated with the manuscript Episodes of opposing survival and reproductive selection cause strong fluctuating selection on seasonal migration versus residence. Quantifying temporal variation in sex-specific selection on key ecologically relevant traits, and quantifying how such variation arises through synergistic or opposing components of survival and reproductive selection, is central to understanding eco-evolutionary dynamics but rarely achieved. Seasonal migration versus residence is one key trait that directly shapes spatio-seasonal population dynamics in spatially- and temporally-varying environments, but temporal dynamics of sex-specific selection have not been fully quantified. We fitted multi-event capture-recapture models to year-round ring resightings and breeding success data from partially-migratory European shags (Phalacrocorax aristotelis) to quantify temporal variation in annual sex-specific selection on seasonal migration versus residence arising through adult survival, reproduction, and the combination of both (i.e. annual fitness). We demonstrate episodes of strong, and strongly fluctuating, selection through annual fitness that were broadly synchronised across females and males. These overall fluctuations arose because strong reproductive selection against migration in several years contrasted with strong survival selection against residence in years with extreme climatic events. These results indicate how substantial phenotypic and genetic variation in migration versus residence could be maintained, and highlight that biologically important fluctuations in selection may not be detected unless both survival selection and reproductive selection are appropriately quantified and combined.