The stability of ecological communities depends strongly on quantitative characteristics of population interactions (type-II vs. type-III functional responses) and the distribution of body masses across species. Until now, these two aspects have almost exclusively been treated separately leaving a substantial gap in our general understanding of food webs. We analysed a large data set of arthropod feeding rates and found that all functional-response parameters depend on the body masses of predator and prey. Thus, we propose generalised functional responses which predict gradual shifts from type-II predation of small predators on equally sized prey to type-III functional-responses of large predators on small prey. Models including these generalised functional responses predict population dynamics and persistence only depending on predator and prey body masses, and we show that these predictions are strongly supported by empirical data on forest soil food webs. These results help unravelling systematic relationships between quantitative population interactions and large-scale community patterns.