Species distribution models are a fundamental tool in ecology, conservation biology, and biogeography and typically identify potential species distributions using static phenomenological models. We demonstrate the importance of complementing these popular models with spatially explicit, dynamic mechanistic models that link potential and realized distributions. We develop general grid-based, pattern-oriented spread models incorporating three mechanisms--plant population growth, local dispersal, and long-distance dispersal--to predict broadscale spread patterns in heterogeneous landscapes. We use the model to examine the spread of the invasive Celastrus orbiculatus (Oriental bittersweet) by Sturnus vulgaris (European starling) across northeastern North America. We find excellent quantitative agreement with historical spread records over the last century that are critically linked to the geometry of heterogeneous landscapes and each of the explanatory mechanisms considered. Spread of bittersweet before 1960 was primarily driven by high growth rates in developed and agricultural landscapes, while subsequent spread was mediated by expansion into deciduous and coniferous forests. Large, continuous patches of coniferous forests may substantially impede invasion. The success of C. orbiculatus and its potential mutualism with S. vulgaris suggest troubling predictions for the spread of other invasive, fleshy-fruited plant species across northeastern North America.