Species loss can alter ecosystem function. Recent work proposes a general theoretical framework, the "Price Equation partition," for understanding how species loss affects ecosystem functions that comprise the summed contributions of individual species (e.g., primary production). The Price Equation partition shows how the difference in function between a pre-species-loss site and a post-loss site can be partitioned into effects of random loss of species richness (species-richness effect; SRE), nonrandom loss of high- or low-functioning species (species-composition effect; SCE), and post-loss changes in the functional contributions of the remaining species (context-dependence effect; CDE). However, the Price Equation partition is silent on the underlying determinants of species' functional contributions. Here we extend the Price Equation partition by using multiple regression to describe how species' functional contributions depend on species' traits. This allows us to reexpress the SCE and CDE in terms of nonrandom loss of species with particular traits (trait-based SCE), and post-loss changes in species' traits and in the relationship between species' traits and species' functional contributions (trait-based CDE). We apply this new trait-based Price Equation partition to studies of species loss from grassland plant communities and protist microcosm food webs. In both studies, post-loss changes in the relationship between species' traits and their functional contributions alter ecosystem function more than nonrandom loss of species with particular traits. The protist microcosm data also illustrate how the trait-based Price Equation partition can be applied when species' functional contributions depend in part on the traits of other species. To do this, we define "synecological" traits that quantify how unique species are (e.g., in diet) compared to other species. Context dependence in the protist microcosm experiment arises in part because species loss alters the diet uniqueness of the remaining species.