25Reef-building coral assemblages are typically species-rich, yet the processes maintaining 26 coral biodiversity remain poorly understood. Disturbance has long been believed to promote 27 coral species coexistence by reducing the strength of competition. However, such 28 disturbance-induced effects have since been shown to be insufficient on their own to prevent 29 competitive exclusion. Nevertheless, Modern Coexistence Theory has revealed other 30 mechanisms by which disturbance and, more generally, environmental variation can favour 31 coexistence. Here, we formulate, calibrate, and analyze a size-structured, stochastic coral 32 competition model using field data from two common colony morphologies. These two coral 33 morphologies, tabular and digitate, differ in their size-dependent vulnerability to 34 dislodgement caused by wave action. We confirm that fluctuations in wave action can 35 promote coral species coexistence. However, using a recently proposed partitioning 36 framework, we show that, contrast to previous expectations, temporal variability in strength 37 of competition did not promote coexistence. Instead, coexistence was enabled by differential 38 fluctuations in size-dependent mortality among competitors. Frequent and intense 39 disturbances resulted in monocultures of digitate corals, which are more robust to wave 40 action than tabular corals. In contrast, infrequent or weak disturbances resulted in 41 monocultures of tabular corals. Coexistence was only possible under intermediate levels of 42 disturbance frequency and intensity. Given the sensitivity of coexistence to disturbance 43 frequency and intensity, anthropogenic changes in disturbance regimes are likely to affect 44 biodiversity in coral assemblages in ways that are not predictable from single population 45 models. 46 47 48 Reef-building coral assemblages are an example of the 'paradox of the plankton' 51 (Hutchinson 1961): they can be species-rich, even though species compete for a small 52 number of limiting resources, mainly space, light, and nutrients in the water column. 53