Summary 1. In this paper we determine whether interspecific variation in entire photosynthetic light–response curves correlates with the leaf traits of the ‘leaf economics spectrum’ (LES) and the degree to which such traits can predict interspecific variation in light–response curves. This question is important because light–response curves are included in many ecosystem models of plant productivity and gas exchange but such models do not take into account interspecific variation in such response curves. 2. We answer this question using original observations from 260 leaves from 130 plants of 65 different species of herbaceous (25) and woody (40) angiosperms. Herbs were grown in growth chambers and gas exchange measurements were taken in the laboratory. Leaf traits and gas exchange measurements for the woody plants were taken in the field. Leaf traits measured were leaf mass per area (LMA), leaf nitrogen concentration (N) and leaf chlorophyll concentration (Chl). We fitted the Mitscherlich and Michaelis–Menten equations of the light–response curve separately for each leaf. This gave (for the Mitscherlich equation) the light compensation point (ϕ), the quantum yield at the light compensation point (q(ϕ)), and maximum net photosynthesis (Amax) and (for the Michaelis–Menten equation), the maximum gross photosynthesis (Gmax), the half saturation coefficient (k) and the dark respiration rate (Rd). 3. Amax and q(ϕ) were highly correlated with the measured leaf traits but ϕ was not. All three parameters of the Michaelis–Menten equations were correlated with the leaf traits. Allometric equations predicting the parameters of the Mitscherlich and Michaelis–Menten equations by N and LMA are presented. Replacing the leaf‐specific parameters by these general allometric equations based on leaf N and LMA gave good predictions of net photosynthetic rates over the entire range of irradiance (r = 0·79–0·98) but with a downward bias for the herbs when the most general allometric equations are used. 4. These results further extend the generality of the LES and may allow available information from large leaf trait data bases to be incorporated into ecosystem models of plant growth and gas exchange.