International audience 1. The disparity of the spatial domains used by predators and prey is a common feature of many terrestrial avian and mammalian predatory interactions, as predators are typically more mobile and have larger home ranges than their prey. 2. Incorporating these realistic behavioural features requires formulating spatial predator–prey models having local prey mortality due to predation and its spatial aggregation, in order to generate a numerical response at timescales longer than the local prey consumption. Coupling the population dynamics occurring at different spatial scales is far from intuitive, and involves making important behavioural and demographic assumptions. Previous spatial predator–prey models resorted to intuition to derive local functional responses from non-spatial equivalents, and often involve unrealistic biological assumptions that restrict their validity. 3. We propose a hierarchical framework for deriving generic models of spatial predator–prey interactions that explicitly considers the behavioural and demographic processes occurring at different spatial and temporal scales. 4. The proposed framework highlights the circumstances wherein static spatial patterns emerge and can be a stabilizing mechanism of consumer–resource interactions.