In this review, we examine two new trait-based models of community assembly that predict the relative abundance of species from a regional species pool. The models use fundamentally different mathematical approaches and the predictions can differ considerably. Maxent obtains the most even probability distribution subject to community-weighted mean trait constraints. Traitspace predicts low probabilities for any species whose trait distribution does not pass through the environmental filter. Neither model maximizes functional diversity because of the emphasis on environmental filtering over limiting similarity. Traitspace can test for the effects of limiting similarity by explicitly incorporating intraspecific trait variation. The range of solutions in both models could be used to define the range of natural variability of community composition in restoration projects.