The presence of corridors and the way patches are arranged in a landscape are thought to be important for the long-term conservation of many species, and may determine whether species are able to recover from large-scale disturbances. Here we used individual-based models to investigate how population recovery was affected by landscape structure for four species in an agricultural landscape: skylark (Alauda arvensis), vole (Microtus agrestis), a ground beetle (Bembidion lampros) and a linyphiid spider (Erigone atra). We characterized population persistence based on equilibrium population sizes (K) and the time it took populations to recover from perturbations. We separated the effects of corridors and patch arrangement by comparing results from a real landscape with results from two virtual landscapes: One where linear corridors were removed by homogenizing patch shapes, while leaving the spatial arrangement of the patches unaltered, and one where patches were shuffled around, while still leaving the landscape composition unaltered. Patch arrangement and the presence of corridors had a large effect on population dynamics for species whose local success depended on the identity of the neighbouring patches. The short-dispersing beetle and vole recovered slowly from perturbations in landscapes where they had low K. Our study demonstrates that it is necessary to consider the dynamics of populations in a spatially explicit context when designing landscapes for conservation of species.