Many African large carnivore populations are declining due to decline of the herbivore populations on which they depend. The densities of apex carnivores like the lion and spotted hyena correlate strongly with prey density, but competitively subordinate carnivores like the African wild dog benefit from competitive release when the density of apex carnivores is low, so the expected effect of a simultaneous decrease in resources and dominant competitors is not obvious. Wild dogs in Zambia's South Luangwa Valley Ecosystem occupy four ecologically similar areas with well-described differences in the densities of prey and dominant competitors due to spatial variation in illegal offtake. We used long-term monitoring data to fit a Bayesian integrated population model (IPM) of the demography and dynamics of wild dogs in these four regions. The IPM used Leslie projection to link a Cormack-Jolly-Seber model of area-specific survival (allowing for individual heterogeneity in detection), a zero-inflated Poisson model of area-specific fecundity and a state-space model of population size that used estimates from a closed mark-capture model as the counts from which (latent) population size was estimated. The IPM showed that both survival and reproduction were lowest in the region with the lowest density of preferred prey (puku, Kobus vardonii and impala, Aepyceros melampus), despite little use of this area by lions. Survival and reproduction were highest in the region with the highest prey density and intermediate in the two regions with intermediate prey density. The population growth rate ( ) was positive for the population as a whole, strongly positive in the region with the highest prey density and strongly negative in the region with the lowest prey density. It has long been thought that the benefits of competitive release protect African wild dogs from the costs of low prey density. Our results show that the costs of prey depletion overwhelm the benefits of competitive release and cause local population decline where anthropogenic prey depletion is strong. Because competition is important in many guilds and humans are affecting resources of many types, it is likely that similarly fundamental shifts in population limitation are arising in many systems.