Background: Geographic ranges, randomly located within a bounded geographical domain,

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

(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

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

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

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.