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

1 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). 2 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. 3 We test some outcomes of the PI model against vegetation patterns observable in aerial photographs from West Africa. Two sites with rainfall of c. 500-600 mm year(-1) were 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. 4 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. 10(2)-10(3) years for annual grasses) than a hexagonal symmetry (e. 10(5) years), and observed patterns are therefore likely to be far from the asymptotic structure. 5 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. 6 The PI model provides a framework for further investigation of patterns in semi-arid vegetation and may be of a broader ecological application.