Null models that place species ranges at random within a bounded geographical domain produce hump-shaped species richness gradients (the "mid-domain effect," or MDE). However, there is debate about the extent to which these models are a suitable null expectation for effects of environmental gradients on species richness. Here, I present a process-based framework for modeling species distributions within a bounded geographical domain. Analysis of null models consistent with the mid-domain

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... sis shows that MDEs are indeed likely to be ubiquitous consequences of geographical domain boundaries. Comparing the probability distributions of range locations for the process-based and randomization-based models reveals that randomization models probably overestimate the contribution of MDEs to empirical patterns of species richness, but it also indicates that other testable predictions from randomization models are likely to be robust. I also show how this process-based framework can be extended beyond null models to incorporate effects of environmental gradients within the domain. This study provides a first step toward an ecological theory of species distributions in geographical space that can incorporate both "geometric constraints" and effects of environmental gradients, and it shows how such a theory can inform our understanding of species richness gradients in nature.