Subsistence hunting provides a crucial food source for rural populations in tropical forests but is often practiced unsustainably. We use the empirical observation that subsistence hunters are central-place foragers to develop three 'biodemographic' hunting models of increasing complexity and realism for assessing the sustainability of hunting of an indicator species. In all our models, we calculate the spatial pattern of depletion of an indicator species (here, a large-bodied primate) across a landscape. Specifically, we show how to identify the area surrounding a human settlement that is expected to suffer local extinction. Our approach is an improvement over well-known sustainability indices of hunting, which are error-prone and do not provide clear links to policy prescriptions. Our first approach models the long-term effect of a single settlement and (1) can be parameterized with easily obtainable field data (such as settlement maps and knowledge of the major weapon used), (2) is simple enough to be used without requiring technical skill, and (3) reveals the asymptotic relationship between local human density and the level of game depletion. Our second model allows multiple settlements with overlapping hunting zones over large spatial scales. Our third model additionally allows temporal changes in human population size and distribution and source-sink dynamics in game populations. Using transect and hunting data from two Amazonian sites, we show that the models accurately predict the spatial distribution of primate depletion. To make these methods accessible, we provide software-based tools, including a toolbox for ArcGIS, to assist in managing and mapping the spatial extent of hunting. The proposed application of our models is to allow the quantitative assessment of settlement-stabilization approaches to managing hunting in Amazonia.