Savanna tree cover often exhibits sudden discontinuities across space. It has been proposed that local spatial processes imposed by variation in tree cover itself (as opposed to by external drivers such as edaphic variation) can reinforce such discontinuities. Despite this, we generally lack data on tree demography and the environmental drivers affecting the former as a function of tree neighborhoods in these systems. Given the importance of disturbance traps in savannas, spatial processes affecting the likelihood of escape from the seedling/sapling stage to the adult tree stage are likely to be critical. In a longitudinal survey of 800 saplings distributed along eight 1-km transects spanning woodland-grassland transitions in Serengeti National Park, we found a positive association between tree cover and sapling growth and survival, but no relationship with sapling abundance, maximum tree height, disturbance, or topkill. Based on microclimate and soil moisture dynamics data, we found no evidence to suggest that tree cover itself drives variation in growth. Based on a prior analysis of soil properties along these transects, we hypothesized that underlying edaphic conditions may be responsible for variation in growth. Regardless of the underlying mechanism, we used simulations to show that subtle growth rate gradients interacted with intense disturbance regimes to produce sharp discontinuities in tree cover, with strong demographic bottlenecks where growth is slowest, explaining the observed patterns of tree cover along the transects. Our results indicated that disturbance and herbivory are equally intense in areas of high and low tree cover, and that although trees have the potential to successfully establish and reach adulthood in open, grassy sites, they grow too slowly to escape disturbance traps there. Importantly, we showed that although herbivory and fire are fundamental for explaining savanna structural patterns, their effects are not necessarily reinforced by tree cover itself.