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 characteri zed by banded vegetation patterns (i.e. tiger bush). 2 The propagation-inhibition (PI) model suggests that a periodic pattern ch aracterized by a dominant wavelength can theoretically establish itself thr ough a Turing-like spatial instability depending only on a trade-off betwee n facilitative and competitive interactions among plants. Under strictly is otropic conditions, spotted and banded patterns are distinct outcomes of a unique process, whereas anisotropy leads to a banded structure. The model p redicts that spotted patterns will have a lower dominant wavelength than ba nds. 3 We test some outcomes of the PI model against vegetation patterns observa ble in aerial photographs from West Africa. Two sites with rainfall of c. 5 00-600 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 subjecte d 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 do minant wavelengths (30-50 m) was similar at two sites more than 500 km apar t. The PI model suggests that spots may occur as a hexagonal lattice but th ere is little evidence of such patterning in the field. A dominant waveleng th was far quicker to establish in simulations (c. 10(2)-10(3) years for an nual grasses) than a hexagonal symmetry (e. 10(5) years), and observed patt erns 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 i n semi-arid vegetation and may be of a broader ecological application.