The search for simple principles that underlie the spatial structure and dynamics of plant communities is a long-standing challenge in ecology^1,2,3,4,5,6. In particular, the relationship between species coexistence and the spatial distribution of plants is challenging to resolve in species-rich communities^7,8,9. Here we present a comprehensive analysis of the spatial patterns of 720 tree species in 21 large forest plots and their consequences for species coexistence. We show that species with low abundance tend to be more spatially aggregated than more abundant species. Moreover, there is a latitudinal gradient in the strength of this negative aggregation–abundance relationship that increases from tropical to temperate forests. We suggest, in line with recent work¹⁰, that latitudinal gradients in animal seed dispersal¹¹ and mycorrhizal associations^12,13,14 may jointly generate this pattern. By integrating the observed spatial patterns into population models⁸, we derive the conditions under which species can invade from low abundance in terms of spatial patterns, demography, niche overlap and immigration. Evaluation of the spatial-invasion condition for the 720 tree species analysed suggests that temperate and tropical forests both meet the invasion criterion to a similar extent but through contrasting strategies conditioned by their spatial patterns. Our approach opens up new avenues for the integration of observed spatial patterns into ecological theory and underscores the need to understand the interaction among spatial patterns at the neighbourhood scale and multiple ecological processes in greater detail.