Every species on Earth fills a unique environmental niche that is driven, in part, by the process of environmental filtering, where the adaptive value of the functional traits of individuals determine their fitness within the given environmental conditions. Despite its long-standing importance in ecology, theoretical investigations of environmental filtering have lagged behind studies of species interactions and neutral dynamics. A new statistical model of trait-based environmental filtering can be a useful tool for exploring the logical consequences of this process while holding all other processes constant. The model uses the logic of objective Bayesian inference to compute the probabilities of species within different environments using two sources of information: the location and dispersion of species within functional trait space, and the statistical relationship between traits and environmental gradients. By varying key parameters in the model, we highlight several testable hypotheses for trait-based ecology. First, niche breadth decreases as intraspecific trait variation decreases, as the strength of the environmental filter increases, and if the trait values do not enhance fitness in any environmental condition in the landscape. Second, niche shape is determined by the form of the trait-environment relationships, where species with extreme trait values are predicted to dominate at the environmental extremes when traits are linearly related to the environment, species with intermediate trait values generally have a selective advantage across a broader environmental range, and bimodal species response curves can occur independently from negative species interactions. The generality of these modelling results can be tested using empirical data from any ecosystem.