Abstract Tropical forests store and sequester large amounts of carbon in above‐ and below‐ground plant biomass and soil organic matter (SOM), but how these are driven by abiotic and biotic factors remains poorly understood. Here, we test the effects of abiotic factors (light variation, caused by logging disturbance, and soil fertility) and biotic factors (species richness and functional trait composition) on biomass stocks (above‐ground biomass, fine root biomass), SOM and productivity in a relatively monodominant Guyanese tropical rainforest. This forest grows on nutrient‐poor soils and has few species that contribute most to total abundance. We, therefore, expected strong effects of soil fertility and species’ traits that determine resource acquisition and conservation, but not of diversity. We evaluated 6 years of data for 30 0.4‐ha plots and tested hypotheses using structural equation models. Disturbance increased productivity but decreased above‐ground biomass stocks. Soil phosphorus (P) enhanced above‐ground biomass and productivity, whereas soil nitrogen reduced fine root biomass. In contrast to expectations, trait values representing acquisitive strategies (e.g. high leaf nutrient concentration) increased biomass stocks, possibly because they indicate higher nutrient absorption and thus higher biomass build‐up. However, under harsh conditions where biomass increase is slow, acquisitive trait values may increase respiration and vulnerability to hazards and therefore increase biomass loss. As expected, species richness did not affect productivity. We conclude that light availability (through disturbance) and soil fertility—especially P—strongly limit forest biomass productivity and stocks in this Guyanese forest. Low P availability may cause strong environmental filtering, which in turn results in a small set of dominant species. As a result, community trait composition but not species richness determines productivity and stocks of biomass and SOM in tropical forest on poor soils. A plain language summary is available for this article.