Interactions among neighboring individuals influence plant performance and should create spatial patterns in local community structure. In order to assess the role of large trees in generating spatial patterns in local species richness, we used the individual species-area relationship (ISAR) to evaluate the species richness of trees of different size classes (and dead trees) in circular neighborhoods with varying radius around large trees of different focal species. To reveal signals of species interactions, we compared the ISAR function of the individuals of focal species with that of randomly selected nearby locations. We expected that large trees should strongly affect the community structure of smaller trees in their neighborhood, but that these effects should fade away with increasing size class. Unexpectedly, we found that only few focal species showed signals of species interactions with trees of the different size classes and that this was less likely for less abundant focal species. However, the few and relatively weak departures from independence were consistent with expectations of the effect of competition for space and the dispersal syndrome on spatial patterns. A noisy signal of competition for space found for large trees built up gradually with increasing life stage; it was not yet present for large saplings but detectable for intermediates. Additionally, focal species with animal-dispersed seeds showed higher species richness in their neighborhood than those with gravity- and gyration-dispersed seeds. Our analysis across the entire ontogeny from recruits to large trees supports the hypothesis that stochastic effects dilute deterministic species interactions in highly diverse communities. Stochastic dilution is a consequence of the stochastic geometry of biodiversity in species-rich communities where the identities of the nearest neighbors of a given plant are largely unpredictable. While the outcome of local species interactions is governed for each plant by deterministic fitness and niche differences, the large variability of competitors causes also a large variability in the outcomes of interactions and does not allow for strong directed responses at the species level. Collectively, our results highlight the critical effect of the stochastic geometry of biodiversity in structuring local spatial patterns of tropical forest diversity.