The assertion that the spatial location of different species is independent of each other is fundamental in major ecological theories such as neutral theory that describe a stochastic geometry of biodiversity. However, this assertion has rarely been tested. Here we use techniques of spatial point pattern analysis to conduct a comprehensive test of the independence assertion by analysing data from three large forest plots with different species richness, a species-rich tropical forest at Barro Colorado Island (Panama), a tropical forest in Sinharaja (Sri Lanka) and a temperate forest in Changbaishan (China). We hypothesize that stochastic dilution effects owing to increasing species richness overpower signals of species associations, thereby yielding approximate species independence. Indeed, the proportion of species pairs showing (i) no significant interspecific association increased with species richness, (ii) segregation decreased with species richness and (iii) small-scale interspecific interaction decreased with species richness. This suggests that independence may indeed be a good approximation in the limit of very species-rich communities. Our findings are a step towards a better understanding of factors governing species-rich communities and we propose a hypothesis to explain why species placement in species-rich communities approximates independence.