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

TY - JOUR

T1 - Peaks, plateaus, canyons, and craters: The complex geometry of simple mid-domain effect models

AU - Colwell, Robert K.

AU - Gotelli, Nicholas J.

AU - Rahbek, Carsten

AU - Entsminger, Gary L.

AU - Farrell, Catherine

AU - Graves, Gary R.

N1 - Keywords: biogeography, boundary effects, doughnut, geographical range, geometric constraints, null models, spatial scale, species richness gradients, stochastic models.

PY - 2009

Y1 - 2009

N2 - 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 arisesfrom 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 uniformWe 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, weallowed dispersal to introduce range discontinuity.Results: As uniform range size increases from small to medium, a flat pattern of speciesAs 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-dimensionalmodels), or by a cratered ring (two-dimensional models) of species richness. With large rangesizes, the peaks or rings fuse to form a central plateau (one-dimensional) or a flat-toppedmound (two-dimensional) of highest species richness. Adding dispersal to the two-dimensionalmodel weakens the peripheral ring and introduces complex patterns for long-distance dispersal.Conclusions: Heterogeneous range size distributions (whether theoretical or empirical) usedHeterogeneous 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 areanalogous for one and two dimensions, are complicated further by long-distance dispersal anddiscontinuous ranges. Although geometric constraints lead to classic mid-domain effects forlarge-ranged species and for mixed range-size frequency distributions, small- and medium-sizedranges of a uniform size generate more complex patterns, including peaks, plateaus, canyons,and craters of species richness.

AB - 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 arisesfrom 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 uniformWe 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, weallowed dispersal to introduce range discontinuity.Results: As uniform range size increases from small to medium, a flat pattern of speciesAs 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-dimensionalmodels), or by a cratered ring (two-dimensional models) of species richness. With large rangesizes, the peaks or rings fuse to form a central plateau (one-dimensional) or a flat-toppedmound (two-dimensional) of highest species richness. Adding dispersal to the two-dimensionalmodel weakens the peripheral ring and introduces complex patterns for long-distance dispersal.Conclusions: Heterogeneous range size distributions (whether theoretical or empirical) usedHeterogeneous 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 areanalogous for one and two dimensions, are complicated further by long-distance dispersal anddiscontinuous ranges. Although geometric constraints lead to classic mid-domain effects forlarge-ranged species and for mixed range-size frequency distributions, small- and medium-sizedranges of a uniform size generate more complex patterns, including peaks, plateaus, canyons,and craters of species richness.

M3 - Journal article

SN - 1522-0613

VL - 11

SP - 355

EP - 370

JO - Evolutionary Ecology Research

JF - Evolutionary Ecology Research

ER -