Vegetation in arid regions of Africa, America, Australia, and Asia reveals remarkable patterns, such as spotted vegetation, labyrinths, gap patterns, and regular bands (Brom-ley et al. 1997; Aguiar and Sala 1999; Klausmeier 1999; Leprun 1999; Couteron and Lejeune 2001; Von Hardenberg et al. 2001). Here, the term “arid” refers to environments characterized by an extended dry season, where yearly potential evaporation exceeds yearly rainfall, and where plant growth is limited by water availability. The two-phase mosaics of vegetation alternating with bare soil as observed in arid ecosystems differ in scale and shape, depending on slope gradient and rainfall. When slope gradient is !0.2% and mean annual rainfall ranges from 200 to 550 mm yr 1, observed vegetation patterns include spots with a diameter of 5–20 m, labyrinths with a vegetated band width of 10–50 m (fig. 1a), and gap patterns with bare spots in the vegetation with a diameter of 5–20 m (fig. 1b; Bromley et al. 1997; Aguiar and Sala 1999; Ludwig et al. 1999b; Valentin et al. 1999; Couteron and Lejeune 2001). On slopes steeper than 0.2% in arid regions, typical regular-banded vegetation patterns with a band width in the range of a few tens of meters are observed (Klausmeier 1999; Leprun 1999; Valentin et al. 1999; d’Herbes et al. 2001).
Scientists are still searching for possible unifying mechanisms to explain this range of spatial patterns (Tongway and Ludwig 2001), and an important question of this research is whether this range is the result of preexisting environmental heterogeneity, the result of spatial selforganization, or both (Klausmeier 1999; Couteron and Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg
et al. 2001). Here, we contribute to the ongoing debate about vegetation pattern formation in arid ecosystems by presenting novel, spatially explicit model analyses and results, extending on the work of HilleRisLambers et al. (2001). Our results show that these different vegetation
patterns observed in arid ecosystems might all be the result of spatial self-organization, caused by one single mechanism:
water infiltrates faster into vegetated ground than into bare soil, leading to net displacement of surface water to vegetated patches. This model differs from earlier model results (Klausmeier 1999; Couteron and Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg et al. 2001)primarily in two ways: it is fully mechanistic, and it treats the lateral flow of water above and below the soil as separate, not independent, variables. Although the current model greatly simplifies the biophysics of arid systems, it can reproduce the whole range of distinctive vegetation patterns as observed in arid ecosystems, indicating that the proposed mechanism might be generally applicable.
We further show that self-organized vegetation patterns can persist far into regions of high aridity, where plants would become extinct if homogeneously distributed, pointing to the importance of this mechanism for maintaining productivity of arid ecosystems (Noy-Meir 1973)
Our analyses are based on the model first developed in HilleRisLambers et al. (2001), which we now briefly review. Vegetation patterning is generally linked to the mechanism by which plants increase surface-water infiltration into the soil, in combination with low annual rainfall conditions (Bromley et al. 1997; Klausmeier 1999; Leprun 1999; Ludwig et al. 1999a; HilleRisLambers et al. 2001). During rain showers, some rainwater will infiltrate into the soil, while the remainder will run off as surface water to other areas. With increasing plant density, the rate of infiltration of surface water into the soil will asymptotically approach a maximum (Rietkerk and van de Koppel 1997). Lateral flow
of surface water is due to pressure differences measured by the slope of the thickness of the surface-water layer and can be described with a single diffusion term (Bear and Verruyt 1990; HilleRisLambers et al. 2001). Part of the infiltrated soil water subsequently evaporates or moves out of reach of plant roots by drainage and lateral subsurface flow due to capillary forces (Hills 1971; Lawrence Dingman 1994). Soil water uptake and plant growth are both assumed to be saturation functions of soil-water availability (de Wit 1958; Rietkerk et al. 1997). Plant dispersal, through seed or vegetative propagation, is approximated by a diffusion term (Okubo 1989; Cain 1990; HilleRisLambers et al. 2001).