Peaks, plateaus, canyons, and craters: the complex geometry of simple mid-domain effect models

Abstract

Background: Geographic ranges, randomly located within a bounded geographical domain, produce a central hump of species richness (the mid-domain effect, MDE). The hump arises from geometric constraints on the location of ranges, especially larger ones. Questions: (1) How do patterns of species richness in one- and two-dimensional MDE models change as a function of range size? (2) How does dispersal affect these patterns? Methods: We used a spreading dye algorithm to place assemblages of species of uniform range size in one-dimensional or two-dimensional bounded domains. In some models, we allowed dispersal to introduce range discontinuity. Results: As uniform range size increases from small to medium, a flat pattern of species richness is replaced by a pair of peripheral peaks, separated by a valley (one-dimensional models), or by a cratered ring (two-dimensional models) of species richness. With large range sizes, the peaks or rings fuse to form a central plateau (one-dimensional) or a flat-topped mound (two-dimensional) of highest species richness. Adding dispersal to the two-dimensional model weakens the peripheral ring and introduces complex patterns for long-distance dispersal. Conclusions: Heterogeneous range size distributions (whether theoretical or empirical) used in most MDE models produce species richness patterns dominated by wide-ranged species, hiding complex patterns formed by small- to medium-ranged species. These patterns, which are analogous for one and two dimensions, are complicated further by long-distance dispersal and discontinuous ranges. Although geometric constraints lead to classic mid-domain effects for large-ranged species and for mixed range-size frequency distributions, small- and medium-sized ranges of a uniform size generate more complex patterns, including peaks, plateaus, canyons, and craters of species richness.