Rain forests exhibit enormous species diversity, but the mechanisms for establishing and maintaining such diversity are unknown. Models involving both exploitative and pre-emptive competition have been proposed. We examine two of these models mathematically and show that neither can exhibit species diversity. The inclusion of random fruiting events, together with seedling population decay, can result in both models exhibiting long-term coexistence of many species. However, the parameter values required to simulate such behaviour are more realistic for the pre-emptive competition model than for the exploitative competition model. Our analysis has general implications for all tropical rain forests in that it suggests that a competition-colonisation type trade-off is not a sufficient condition for species coexistence. © 2005 Elsevier B.V. All rights reserved.