Protected areas (PAs) play a vital role in wildlife conservation. Nonetheless there is concern and uncertainty regarding how and at what spatial scales anthropogenic stressors influence the occurrence dynamics of wildlife populations inside PAs. Here we assessed how anthropogenic stressors influence occurrence dynamics of 159 mammal species in 16 tropical PAs from three biogeographic regions. We quantified these relationships for species groups (habitat specialists and generalists) and individual species. We used long-term camera-trap data (1,002 sites) and fitted Bayesian dynamic multispecies occupancy models to estimate local colonization (the probability that a previously empty site is colonized) and local survival (the probability that an occupied site remains occupied). Multiple covariates at both the local scale and landscape scale influenced mammal occurrence dynamics, although responses differed among species groups. Colonization by specialists increased with local-scale forest cover when landscape-scale fragmentation was low. Survival probability of generalists was higher near the edge than in the core of the PA when landscape-scale human population density was low but the opposite occurred when population density was high. We conclude that mammal occurrence dynamics are impacted by anthropogenic stressors acting at multiple scales including outside the PA itself.