Abstract The coexistence of tree species in tropical forests has remained challenging to explain, characterise and predict with simple theoretical models. To address this phenomenon researchers have focused on processes and factors omitted in simple competition models. Meantime, theoretical considerations of simple models have sought out conditions for stable coexistence of many species. Here we show that a simple competition model parameterised using repeated forest tree inventory data can estimate the stable coexistence of numerous tree species and predict their biomass abundance and productivity in equilibrium communities. We apply a simple Lotka–Volterra competition model to describe species aboveground biomass, and employ leaf biomass as a proxy for exploitative competition among species. In such systems a globally stable multispecies equilibrium arises when, for every species, susceptibility of biomass growth to conspecific (same species) leaf biomass exceeds that to heterospecific leaf biomass. We applied this approach to tree species in the Pasoh 50‐ha plot of Malaysian lowland mixed dipterocarp forest. We parameterised species aboveground biomass productivity by tree growth, by recruitment, and losses from tree mortality. Biomass gains minus losses yields the biomass growth of each species population. Using variation in leaf biomass among quadrat subplots, we estimated the susceptibility of productivity by tree growth to conspecific and heterospecific leaf biomass. Our model analyses with plot census data predicted the stable coexistence of 351 of the 487 tree species assessed. Susceptibility to conspecific versus heterospecific leaf biomass was greater across all species (median: 95 times). The implied effect of conspecific competition appears to reflect ontogeny, that is declining relative tree growth with tree size. The equilibrium biomasses for predicted persistent species were broadly similar to observations. Removal of species indicates that ecosystem biomass and productivity at equilibrium increases asymptotically with species richness. Synthesis. Our analyses with a simple model provide a range of non‐trivial insights into tree species coexistence, community structure and ecosystem stability within a species‐rich rainforest. The insights available from such simple models provide references for a reassessment of the insights from more complex models and approaches.