Periodic spotted patterns in semi‐arid vegetation explained by a propagation‐inhibition model

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Abstract
Summary: Vegetation cover regularly punctuated by spots of bare soil is a frequent feature of certain semi‐arid African landscapes, which are also characterized by banded vegetation patterns (i.e. tiger bush). The propagation‐inhibition (PI) model suggests that a periodic pattern characterized by a dominant wavelength can theoretically establish itself through a Turing‐like spatial instability depending only on a trade‐off between facilitative and competitive interactions among plants. Under strictly isotropic conditions, spotted and banded patterns are distinct outcomes of a unique process, whereas anisotropy leads to a banded structure. The model predicts that spotted patterns will have a lower dominant wavelength than bands. We test some outcomes of the PI model against vegetation patterns observable in aerial photographs from West Africa. Two sites with rainfall ofc.500–600 mm year−1were studied: a 525‐ha plain in north‐west Burkina Faso and a 300‐ha plateau in southern Niger. Digitized photographs were subjected to spectral analysis by Fourier transform in order to quantify vegetation patterns in terms of dominant wavelengths and orientations. Spotted vegetation proved highly periodic. The characteristic range of dominant wavelengths (30–50 m) was similar at two sites more than 500 km apart. The PI model suggests that spots may occur as a hexagonal lattice but there is little evidence of such patterning in the field. A dominant wavelength was far quicker to establish in simulations (c. 102–103 years for annual grasses) than a hexagonal symmetry (c. 105 years), and observed patterns are therefore likely to be far from the asymptotic structure. Elongated and smudged spots that locally became flexuous bands have been observed in southern Niger. This pattern that had a dominant wavelength of 50 m but lacked any dominant orientation can be interpreted as a transition from spots to bands under fairly isotropic conditions. The PI model provides a framework for further investigation of patterns in semi‐arid vegetation and may be of a broader ecological application.