• Geometric constraints;
  • mid-domain effects;
  • null models;
  • range size frequency distribution;
  • species richness gradients


Recent null models that place species ranges randomly within a bounded domain have produced controversial results. Many such geometric constraint models predict a peak in species richness in the centre of domains in the absence of underlying environmental gradients or interspecific interactions. We used two-dimensional simulation models to explore different ways that species ranges could interact with the domain boundary. In the rejection model, a randomly generated range that overlaps a domain boundary is removed from the simulation. In the reshaping model, a range that overlaps the domain boundary is reshaped so that the entire range is placed within the domain. The truncation model allows potential ranges to extend across the boundary, but only that portion of the range within the domain is included in the realized range. Both rejection and reshaping models produced a drop in species richness near domain boundaries, though the effect was less pronounced in the reshaping model. Our truncation model did not produce any spatial pattern in species richness. Thus the random placement of species ranges within a bounded domain does not necessarily lead to a mid-domain effect.

 Range truncation is consistent with bioclimate envelope models, which can successfully predict a species range in response to the availability of appropriate climate conditions. We argue that such flexible range sizes are more realistic than the assumption that range size is an unvarying characteristic of a species. Other range characteristics, including size and shape, can change near domain boundaries in the null models, including the truncation model. A broader consideration of range characteristics near domain boundaries could be productive.