Understanding the mechanisms that shape animal population dynamics is of fundamental interest in ecology, evolution and conservation biology. Food supply is an important limiting factor in most animal populations and may have demographic consequences. Optimal foraging theory predicts greater consumption of preferred prey and less diet diversity when food is abundant, which may benefit key fitness parameters such as productivity and survival. Nevertheless, the correspondence between individual resource use and demographic processes in populations of avian predators inhabiting large geographic areas remains largely unexplored, particularly in complex ecosystems such as those of the Mediterranean basin. Based on a long-term monitoring program of the diet and demography of Bonelli's eagle Aquila fasciata in western Europe, here we test the hypothesis that a predator's diet is correlated to its breeding productivity and survival at both the territorial and population levels, and ultimately to its population growth rate. At the territorial level, we found that productivity increased with greater consumption of European rabbits Oryctolagus cuniculus, the Bonelli's eagle's preferred prey, and pigeons, an important alternative prey for this predator. The survival of territorial pairs was negatively affected by higher diet diversity, which probably reflected the inability to find sufficient high quality prey. Diet effects at the population level were similar but more noticeable than at the territorial level, i.e. a greater consumption of rabbits, together with lesser consumption of small-to-medium avian species (‘other birds’; non-preferred prey), increased productivity, while greater diet diversity and lower consumption of rabbits was associated with reduced survival and population growth rate. Overall, our study illustrates how the diet of a predator species can be closely related to key individual vital rates, which, in turn, leave a measurable fingerprint on population dynamics within and among populations across large spatial scales.