The most important source of energy to tropical shallow water coral reefs is light, the transformation of which ultimately limits reef biomass and growth. Therefore, measurements of productivity (primary production, P) for benthic reef organisms and communities are critical to understand reef functioning. Short-term (minutes to hours) P measurements of reef photosynthesizers virtually always produce the classic hyperbolic tangent (or similar) P-E (irradiance) relationship, with P rapidly rising to a saturation point as E increases. Longer-term (days to weeks), larger-scale investigations of natural reef communities typically do not explore P-E relationships, but the few that do show no saturation of time-integrated P with high time-integrated E. In this paper we present a modeling study to reconcile this apparent contradiction. We used 52 published short-term (instantaneous) P-E curves of organisms (corals, algae) and communities (corals, mixed corals and algae) from different reefs in the Indo-Pacific and the Caribbean, each coupled with 928 diel light curves comprising a wide range of cloud cover scenarios. The diel light curves provided instantaneous E at 1-minute intervals, from which we calculated corresponding instantaneous P using the different published P-E relationships. We integrated both variables to calculate time-integrated E and P. Time-integrated E varied up to 18-fold due to changes in cloud cover and season. We found that, despite routine saturation of instantaneous P, day-scale P-E relationships were near linear in all cases, with slightly decreased linearity in cases where instantaneous light saturation occurred very early during the day. This indicates that the Functional Convergence Hypothesis (FCH) developed by terrestrial ecologists may also apply for reef photosynthesizers. The FCH states that despite short-term light saturation, plants on average do not absorb more light than they can use, since resource allocations are strictly coordinated and tailored towards an optimal use. Thus, there is no contradiction: At the growth time scale (≥ day), P should be expected to be a near linear function of E. One implication is that reef P can be estimated using rapid optical measurements, as opposed to traditional, laborious respirometry methods. The requirement going forward is to derive appropriate values for light-use efficiency, which is the rate at which the plant or community converts absorbed light into fixed carbon.