1. Spatial patterns of and competition for resources by territorial carnivores are typically explained by two hypotheses: 1) the territorial defence hypothesis and 2) the searching efficiency hypothesis.

2. According to the territorial defence hypothesis, when food resources are abundant, carnivore densities will be high and home ranges small. In addition, carnivores can maximise their necessary energy intake with minimal territorial defence. At medium resource levels, larger ranges will be needed, and it will become more economically beneficial to defend resources against a lower density of competitors. At low resource levels, carnivore densities will be low and home ranges large, but resources will be too scarce to make it beneficial to defend such large territories. Thus, home range overlap will be minimal at intermediate carnivore densities.

3. According to the searching efficiency hypothesis, there is a cost to knowing a home range. Larger areas are harder to learn and easier to forget, so carnivores constantly need to keep their cognitive map updated by regularly revisiting parts of their home ranges. Consequently, when resources are scarce, carnivores require larger home ranges to acquire sufficient food. These larger home ranges lead to more overlap among individuals’ ranges, so that overlap in home ranges is largest when food availability is the lowest. Since conspecific density is low when food availability is low, this hypothesis predicts that overlap is largest when densities are the lowest.

4. We measured home range overlap and used a novel method to compare intraspecific home range overlaps for lions Panthera leo (n = 149) and leopards Panthera pardus (n = 111) in Africa. We estimated home range sizes from telemetry location data and gathered carnivore density data from the literature.

5. Our results did not support the territorial defence hypothesis for either species. Lion prides increased their home range overlap at conspecific lower densities whereas leopards did not. Lion pride changes in overlap were primarily due to increases in group size at lower densities. By contrast, the unique dispersal strategies of leopards led to reduced overlap at lower densities. However, when human-caused mortality was higher, leopards increased their home range overlap. Although lions and leopards are territorial, their territorial behaviour was less important than the acquisition of food in determining their space use. Such information is crucial for the future conservation of these two iconic African carnivores.