The existence of general characteristics of plant invasiveness is still debated. One reason we may not have found these characteristics is because we do not yet understand how processes underlying population dynamics contribute to community composition in invaded communities. Here I modify Ricker stock-recruitment models to parameterize processes important to community dynamics in an invaded grassland community: immigration, maximum intrinsic growth rate, self-regulation, and limitation by other species. I then used the parameterized models in a multi-species stochastic simulation to determine how processes affected long-term community dynamics. By parameterizing the models using the frequency of the 18 most common species in the grassland, I determined that life history and life form are stronger predictors of underlying processes than is native status. Immigration maintains exotic annual grasses and the dominant native perennial grass in the community. Growth rate maintains other perennial species. While the model mirrors the frequency of native species well, exotic species have lower observed than parameterized frequencies, suggesting that they are not reaching their potential frequency. These results, combined with results from past research, suggest that disturbance may be key to maintaining exotic species in the community. Here I showed that a continuous modified Ricker model fit discrete grassland frequency data well. This allowed me to model the dominant species in the community simultaneously and gain insight into the processes that determine community composition.