Abstract Tree functional diversity can increase forest productivity by enhancing species interactions and providing greater growth stability. However, very few studies have examined the influence of tree community trait structure on survivor growth, recruitment and mortality simultaneously, which are the main drivers of forest population dynamics. Here, we explore the interactions among functional diversity, productivity and climate to investigate the role of the trait structure of communities on forest productivity and to determine under what circumstances functional diversity should be promoted to ensure forest adaptive capacity under future climate. Using random‐forest modelling and a network of permanent sample plots covering a broad gradient of climatic conditions, we isolated the effects of functional diversity—described as the distribution of trait values in a community—and climate variables on net forest productivity (NFP), survivor growth, recruitment and mortality. Based on our findings, community‐level trait structure affects forest productivity in different ways. NFP was influenced by three traits from three different plant strategy dimensions, whereas survivor growth and recruitment were strongly correlated with leaf and resource acquisition traits, and tree mortality with a mix of traits reflecting various plant strategies. We also observed climate interactions with the functional trait structure of tree communities. For instance, we observed an interaction between drought tolerance and mean annual temperature: At low temperatures, NFP biomass accumulation increased with the value of the drought tolerance trait; however, at higher temperatures, the opposite pattern was observed. However, we found contrasting patterns of population response to climate variability, depending on their functional diversity. Greater functional diversity does not necessarily increase biomass accumulation under different climatic conditions. Synthesis. As all components of forest productivity contribute to NFP, studies on forest productivity should consider not only survivor growth but also recruitment and mortality. Each component responds differently in terms of biomass changes in climatic variation, according to the trait structure of tree communities. This study provides a framework to identify the trait structure that should be targeted under different climate scenarios to anticipate change and help strengthen forest response capacity to climate change.