Significance Understanding how changes in climate will affect terrestrial ecosystems is particularly important in tropical forest regions, which store large amounts of carbon and exert important feedbacks onto regional and global climates. By combining multiple types of observations with a state-of-the-art terrestrial ecosystem model, we demonstrate that the sensitivity of tropical forests to changes in climate is dependent on the length of the dry season and soil type, but also, importantly, on the dynamics of individual-level competition within plant canopies. These interactions result in ecosystems that are more sensitive to changes in climate than has been predicted by traditional models but that transition from one ecosystem type to another in a continuous, non–tipping-point manner.