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Understanding the formation of feeding links provides insights into processes underlying food webs. Generally, predators feed on prey within a certain body‐size range, but a systematic quantification of such feeding niches is lacking. We developed a size‐constrained feeding‐niche (SCFN) model and parameterized it with information on both realized and non‐realized feeding links in 72 aquatic and 65 terrestrial food webs. Our analyses revealed profound differences in feeding niches between aquatic and terrestrial predators and variation along a temperature gradient. Specifically, the predator–prey body‐size ratio and the range in prey sizes increase with the size of aquatic predators, whereas they are nearly constant across gradients in terrestrial predator size. Overall, our SCFN model well reproduces the feeding relationships and predation architecture across 137 natural food webs (including 3878 species and 136,839 realized links). Our results illuminate the organisation of natural food webs and enables novel trait‐based and environment‐explicit modelling approaches. [ABSTRACT FROM AUTHOR]