Sensitivity analysis (SA) is a useful tool to identify important parameters that affect model performance and it plays an important role in model parameterization, calibration, optimization, and uncertainty quantification. In this study, two popular global SA methods, the Morris and Sobol methods, are applied to an ecological competition model, which simulates the temporal dynamics of coral reef communities with 29 parameters. Both of the results obtained by the Morris and Sobol methods show that there are higher interactions in states 3 and 5 compared with other states. Moreover, the two methods provide very similar results for influential and non-influential model parameters. To achieve sufficient precision, the Sobol method requires 1000 repetitions, while the Morris method only requires 100 repetitions. Overall, the results of this study reveal that the Morris method is capable of producing a highly similar set of the most influential and non-influential parameters as that obtained by Sobol’s method but with less computation cost. For complex models with a large number of parameters or expensive computations, the method of Morris may be an efficient way to identify parameter sensitivities.