The latitudinal gradient of species diversity remains the most important unexplained pattern in ecology. A variety of neutral (or null) models have been proposed that predict certain features of diversity gradients without including any ecological processes related to competition or niche partitioning. One of these is the Mid-Domain Effect (MDE) model, which produces a unimodal diversity pattern between boundaries such as continental margins simply by assuming that species ranges are placed randomly with regard to location and size, with no interactions with either the environment or other species. The non-biological mechanism producing the patterns is described as “geometric constraints” (Colwell and Hurtt, 1994). We have recreated and examined the original variants of the MDE, as well as other related models and conclude that geometric constraints are likely to make only a minor contribution to actual diversity patterns, rather than being a primary cause of the patterns. The original MDE models have conceptual and methodological problems that produce an extreme pattern that drops to zero at the boundaries. Alternative null models eliminate this effect and allow quantification of the consequences of geometric constraints. The original theoretical work on the MDE used uniform random distributions of range size and location. Use of typical right-skewed range size frequency distributions in place of uniform distributions eliminates most of the diversity gradient produced by MDEs. We conclude that the MDE, as originally proposed, is not a valid null model for species richness patterns.