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A new model for vegetation patterns is introduced. The model reproduces a wide range of patterns observed in water-limited regions, including drifting bands, spots, and labyrinths. It predicts transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation, through intermediate states of spot, stripe, and hole patterns. It(More)
Habitat and species richness in drylands are affected by the dynamics of a few key species, termed "ecosystem engineers." These species modulate the landscape and redistribute the water resources so as to allow the introduction of other species. A mathematical model is developed for a pair of ecosystem engineers commonly found in drylands: plants forming(More)
A mathematical model for plant communities in water-limited systems is introduced and applied to a mixed woody-herbaceous community. Two feedbacks between biomass and water are found to be of crucial importance for understanding woody-herbaceous interactions: water uptake by plants' roots and increased water infiltration at vegetation patches. The former(More)
Ecosystem regime shifts are regarded as abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or by global disturbances. Spatially extended ecosystems, however, can also respond to local disturbances by the formation of small domains of the alternative state. Such a response can lead to gradual(More)
Vegetation patches in drylands are localized structures of biomass and water. We study these structures using a mathematical modeling approach that captures biomass-water feedbacks. Biomass-water structures are found to differ in their spatial forms and ecological functions, depending on species type, soil conditions, precipitation range, and other(More)
In this article, we develop a unifying framework for the understanding of spatial vegetation patterns in heterogeneous landscapes. While much recent research has focused on self-organised vegetation the prevailing view is still that biological patchiness is mostly due to top-down control by the physical landscape template, disturbances or predators. We(More)
Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result in desertification shifts from patterned vegetation to bare soil. Pattern formation theory suggests various scenarios(More)
Using a spatially explicit mathematical model for water-limited vegetation we show that spatial instabilities of uniform states can lead to species coexistence under conditions where uniformly distributed species competitively exclude one another. Coexistence is made possible when water-rich patches formed by a pattern forming species provide habitats for a(More)
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a(More)
Wavetrains of impulses in homogeneous excitable media relax during propagation toward constant-speed patterns. Here we present a study of this relaxation process. Starting with the basic reaction-diffusion or cable equations, we derive kinematics for the trajectories of widely spaced impulses in the form of ordinary differential equations for the set of(More)