The complex spatial structure and dynamics of ecological communities continue to defy explanation by simple principles despite decades of attention from ecologists and theoreticians. For example, the relationship between plant spatial distributions and species coexistence is often challenging to resolve in empirical settings. By analysing the spatial patterns of trees in 21 large forest plots we find a general and strong latitudinal gradient in the relationship between conspecific aggregation and abundance of tree species, with stronger negative abundance-dependency as latitude increases. To derive theoretical expectations for how interactions between multiple spatial pattern and processes can impact species coexistence, we incorporate the observed spatial patterns together with neighbourhood crowding competition into a mathematical model to estimate the local extinction risk of species. Strikingly, we find simple relationships that predict species local extinction risk from their demography and spatial distribution. Compared to a corresponding non-spatial analysis, accounting for spatial patterns reduces the 1000-year extinction risk on average by 52% when species invade from low abundances of 50 individuals. Additionally, based on their current abundances, only 8% of the species had an extinction risk greater than 5%. Our approach opens up new avenues for integrating observed spatial patterns with multiple ecological processes into mathematical theory. Our results demonstrate that emerging spatial patterns can contribute substantially to coexistence in species-rich forests, emphasizing the need to understand the interacting multiple processes underpinning spatial patterns in greater detail than has previously been appreciated.