I present a model of stochastic community dynamics in which death occurs randomly in the community, propagules disperse randomly from a regional pool, and recruitment of new individuals of a species is proportional to the species local abundance multiplied by its local competitive ability. The competitive ability of a species is assumed to be determined by a function of one trait of the species, and I call this function the environmental filtering function. I show that information on local species abundances in a network of plots, together with trait data for each species, enables the inference of both the immigration rate and the environmental filtering function in each plot. I further study how the diversity patterns produced by this model deviate from the neutral predictions, and how this deviation depends on the characteristics of the environmental filtering function. I show that this inference framework is more powerful at detecting trait-based environmental filtering than existing statistical approaches based on trait distributions, and discuss how the predictions of this model could be used to assess environmental heterogeneity in a plot, to detect functionally meaningful trade-offs among species traits, and to test the assumption that there exists a simple relationship between species traits and local competitive ability.