In semi-arid ecosystems, vegetation self-organizes into striking spatial patterns — tiger bush stripes, labyrinths, and spots — as rainfall decreases. The Klausmeier model captures the key feedback: vegetation facilitates water infiltration (local positive feedback) while competing for water at a distance (long-range inhibition), exactly the Turing mechanism in an ecological setting.
Uniform vegetation
Biomass W (green=high, tan=bare)
1D transect (horizontal slice)
Phase diagram: rainfall vs pattern
1.80
0.45
100
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Klausmeier model (dimensionless): ∂W/∂t = A − W − WN² (water dynamics) ∂N/∂t = d·∇²N + WN² − BN (biomass dynamics)
W = soil water, N = plant biomass. Plants uptake water (WN²) and lose it to evaporation (W). Biomass grows via water uptake and dies at rate B.
Pattern regime: As rainfall A decreases below a threshold, the uniform state destabilizes (Turing instability) into spatial patterns. The sequence with decreasing A: uniform cover → labyrinths → stripes → spots → bare soil. This pattern sequence has been observed in aerial photography of the Sahel, Horn of Africa, and Australia.