In tropical rainforests, 30-65% of tree species grow at densities of less than one individual per hectare. At these low population densities, successful cross-pollination relies on synchronous flowering. In rainforests with low climatic seasonality, photoperiodic control is the only reliable mechanism for inducing synchronous flowering. This poses a problem because there is no variation in day length at the Equator. Here we propose a new mechanism of photoperiodic timekeeping based on the perception of variation in sunrise or sunset time, which explains and predicts the annually repeated, staggered, synchronous and bimodal flowering of many tree species in Amazonian rainforests near the Equator.