Adaptation of communities to environmental fluctuations can emerge from different facets of biodiversity, which may impact ecosystem functioning differently. Previous work in the field of biodiversity–ecosystem functioning (BEF) examined how ecosystem functions can be influenced by two sources of adaptive potential: sorting – i.e. changes in community composition due to fitness differences – can occur when multiple species or groups are present (richness), and trait adaptability – i.e. trait adjustments within species or functional groups – can emerge from genetic or phenotypic diversity. However, their effect is typically studied separately, and often in the context of only one trophic level. Therefore, we used a trait‐based, multispecies predator–prey model to investigate how sorting and trait adaptability, at one or two trophic levels, separately or jointly shape ecosystem functions and properties, such as total biomass, production, biomass‐weighted mean trait, relative top–down control and synchrony. We found that the adaptive potential emerging from any facet of diversity induced changes in trophic interactions, in turn affecting biomass distributions within and across trophic levels, dynamical behaviour, and synchrony of biomass dynamics within a trophic level. Particularly, sorting and trait adaptability could contribute to a similar degree and at a similar time to temporal changes in ecosystem functions, but their respective contribution depended on the speed of trait adaptation, the trait range between similar functional groups and trophic interactions. We thus suggest to consider multiple facets of diversity and their corresponding sources of adaptive potential to deepen our mechanistic understanding of BEF relationships, especially in the context of rapid biodiversity change.