Old-growth forests are spatially heterogeneous among local stands with varied per-area biomass and tree species composition. How such stand-by-species heterogeneity influences forest primary productivity remains a challenging question in linking forest ecosystem functions and biodiversity. We quantified aboveground woody productivity versus aboveground biomass relationships among stands and among species by power-law models. We analyzed inventory data of the Pasoh 50-ha plot representing lowland mixed dipterocarp forest of Peninsular Malaysia. We divided the plot into 200 stands of 0.25 ha each. Relative (per-biomass) productivity decreased with biomass across local species populations. Stand-aggregated, plot level interspecific power law of relative productivity against biomass showed the exponent of about –0.1, whereas species-aggregated, among-stand exponent was around –0.7. High relative productivity in stands with low biomass was mainly determined by the community structure effect —high interspecific biomass variation in high-biomass stands— at 91%, more than the species response effect —low species productivity in high-biomass stands— at 9%. The contrast between interspecific (–0.2) and among-stand exponents (–0.7) was also observed for widely scattered 41 temperate forest plots (1 ha each as stand) across the Japanese archipelago (ranging 30N–45N). Analysis of the species-by-stand structure of biomass and woody productivity implies common roles of interspecific and among-stand variation in forest ecosystem functions.