Ostwald ripening in dryland vegetation

Dryland landscapes self-organize to form various patterns of vegetation patchiness.Two major classes of patterns can be distinguished:regular patterns with characteristic length scales and scale-freepatterns. The latter form under conditions of global competitionover the water resource. In this paper we show that the asymptoticdynamics of scale-free vegetation patterns involve patch coarseningsimilar to Ostwald ripening in two-phase mixtures. We demonstrate itnumerically, using a spatially explicit model for water-limited vegetation,and further study it by drawing an analogy to an activator-inhibitor systemthat shares many properties with the vegetation system. Theecological implications of patch coarsening may not be highly significantdue to the long time scales involved. The reported results, however, raise aninteresting pattern formation question associated with the incompatibilityof mechanisms that stabilize vegetation spotsand the condition of global competition.