Abstract. Palaeoecologists have shown that trees migrated at rates of 100–1000 m/yr in response to post-glacial warming. In order to predict the impact of forecast anthropogenic climate changes upon forest ecosystems we need to simulate how trees may migrate in response to the changes predicted for the next 1–2 centuries. These predictions must take account of the impacts upon migration of human land-use and habitat fragmentation. We have developed a spatially-explicit mechanistic model (MIGRATE) able to simulate the migration of a single species across a realistically heterogeneous landscape. MIGRATE uses biological parameters that readily may be estimated from data in the literature or from field studies, and represents the landscape as a grid of cells, each with an associated carrying capacity. A one-dimensional version of MIGRATE has been compared both with Skellam's (1951) diffusion model and with the more recent analytical models of van den Bosch et al. (1990, 1992); despite its fundamentally different approach, MIGRATE provides comparable estimates of migration rates, given equivalent input parameters. An example is described that demonstrates the ability of the two-dimensional version of MIGRATE to simulate the likely pattern of spread of a species across a heterogeneous landscape. It is argued that MIGRATE, or models like it, will play a central role in a spatially-hierarchic modelling strategy that must be developed if we are to achieve the goal of simulating the likely response of trees, and other organisms, to both global climate change and the increasing pressures of human land-use.