Evol Ecol Res 11: 355-370 (2009)     Full PDF if your library subscribes.

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

Robert K. Colwell1, Nicholas J. Gotelli2, Carsten Rahbek3, Gary L. Entsminger4, Catherine Farrell5 and Gary R. Graves6

1Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, Connecticut, USA,  2Department of Biology, University of Vermont, Burlington, Vermont, USA,  3Center of Macroecology and Evolution, Department of Biology, University of Copenhagen, Copenhagen, Denmark,  4Acquired Intelligence Inc. and Rocky Mountain Biological Laboratory, Montrose, Colorado, USA,  5Essex High School, Essex Junction, Vermont, USA and  6Department of Vertebrate Zoology, National Museum of Natural History, Smithsonian Institution, Washington, DC, USA

Correspondence: R.K. Colwell, Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, CT 06269-3043, USA.
e-mail: colwell@uconn.edu


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.

Keywords: biogeography, boundary effects, doughnut, geographical range, geometric constraints, null models, spatial scale, species richness gradients, stochastic models.

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