1. Reductions in resource availability, associated with land-use change and agricultural intensification in the UK and Europe, have been linked with the widespread decline of many farmland bird species over recent decades. However, the underlying ecological processes which link resource availability and population trends are poorly understood. 2. We construct a spatial depletion model to investigate the relationship between the population persistence of granivorous birds within the agricultural landscape and the temporal dynamics of stubble field availability, an important source of winter food for many of those species. 3. The model is capable of accurately predicting the distribution of a given number of finches and buntings amongst patches of different stubble types in an agricultural landscape over the course of a winter and assessing the relative value of different landscapes in terms of resource availability. 4. Sensitivity analyses showed that the model is relatively robust to estimates of energetic requirements, search efficiency and handling time but that daily seed survival estimates have a strong influence on model fit. Understanding resource dynamics in agricultural landscapes is highlighted as a key area for further research. 5. There was a positive relationship between the predicted number of bird days supported by a landscape over-winter and the breeding population trend for yellowhammer Emberiza citrinella, a species for which survival has been identified as the primary driver of population dynamics, but not for linnet Carduelis cannabina, a species for which productivity has been identified as the primary driver of population dynamics. 6. Synthesis and applications. We believe this model can be used to guide the effective delivery of over-winter food resources under agri-environment schemes and to assess the impacts on granivorous birds of changing resource availability associated with novel changes in land use. This could be very important in the future as farming adapts to an increasingly dynamic trading environment, in which demands for increased agricultural production must be reconciled with objectives for environmental protection, including biodiversity conservation.