Simple models coupling the dynamics of single predators to single prey populations tend to generate oscillatory dynamics of both predator and prey, or extirpation of the prey followed by that of the predator. In reality, such oscillatory dynamics may be counteracted by prey refugia or by opportunities for prey switching by the predator in multi-prey assemblages. How these mechanisms operate depends on relative prey vulnerability, a factor ignored in simple interactive models. I outline how compositional, temporal, demographic and spatial heterogeneities help explain the contrasting effects of top predators on large herbivore abundance and population dynamics in species-rich African savanna ecosystems compared with less species-diverse northern temperate or subarctic ecosystems. Demographically, mortality inflicted by predation depends on the relative size and life history stage of the prey. Because all animals eventually die and are consumed by various carnivores, the additive component of the mortality inflicted is somewhat less than the predation rate. Prey vulnerability varies annually and seasonally, and between day and night. Spatial variation in the risk of predation depends on vegetation cover as well as on the availability of food resources. During times of food shortage, herbivores become prompted to occupy more risky habitats retaining more food. Predator concentrations dependent on the abundance of primary prey species may restrict the occurrence of other potential prey species less resistant to predation. The presence of multiple herbivore species of similar size in African savannas allows the top predator, the lion, to shift its prey selection flexibly dependent on changing prey vulnerability. Hence top-down and bottom-up influences on herbivore populations are intrinsically entangled. Models coupling the population dynamics of predators and prey need to accommodate the changing influences of prey demography, temporal variation in environmental conditions, and spatial variation in the relative vulnerability of alternative prey species to predation.