Spatial analysis of semi-arid patchy vegetation by the cumulative distribution of patch boundary spacings and transition probabilities

The vegetative cover in semi-arid lands typically occurs as patches of individual species more or less separated from one another by bare ground. We have adapted two methods to quantify the spatial pattern of such cover from measurements across patches on transects. Transects were laid in several directions across digital maps of the land surface or across the land itself, and the distances between successive patch boundaries were measured. The distances were ranked in order, and their cumulative distributions were computed and modeled with gamma functions. The parameters of the model provided estimates of the mean distance across patches. The means for different directions were further tested for anisotropy. Transitions between classes on the transects estimate the probabilities with which the different species occur next to others (and to bare ground) and so describe the arrangement of the patches occupied by the different species. The methods were tested with data from mosaic patterns at three semi-arid sites dominated by the tussock grass Stipa tenacissima. The differences in the estimated mean boundary spacings from site to site accorded with prior qualitative assessment, as did the estimated anisotropy. The transition matrices and the estimated proportions of cover showed the dominance of the bare soil with which all the individual species are intimately associated. The transitions also suggest the presence of both positive and negative relations among the main species. Those between Stipa tenacissima and Brachypodium retusum seem to be facilitative, as do those between this grass and the shrub Anthyllis cytisoides. In contrast, Globularia alypum seems to inhibit the other species. We also estimated transition probabilities geostatistically by summing the indicator variograms of the individual species. Standard variogram models were then fitted to describe the ordered series of values, and these again produced results that accorded with visual impressions.