Investigations of Pattern Formation in Dryland VegetationPublic Deposited
Vegetation in dryland environments is often patchy in response to water limitation. This patchiness can take the form of periodic patterning at length scales much larger than that of an individual plant. Instances of patterns resembling leopard spots and tiger stripes are widespread in dry regions of Africa, Australia, and North America. Mathematical modeling efforts over the past two decades have sought to account for dryland vegetation patterning via a self-organizing interaction between vegetation and water resources. These efforts have led to predictions for the response of the vegetation to environmental variation, and have generated speculation that the morphology of the patterns encodes information about the fragility of the environment. For a class of patterns that occurs on flat terrain, we use a bifurcation-theoretic framework to analyze the sequence of morphologically distinct patterns that are predicted by models to occur in a scenario of increasing aridity. Applying insights from the analysis of an idealized problem, we find a strong indication that a specific sequence of patterns occurs in the ecologically-relevant parameter space of a widely-studied dryland vegetation model. This finding is a step towards establishing credibility for a specific pattern sequence as a signal of dryland ecosystem fragility. For a class of patterns that occurs on gradually sloping terrain, we use aerial imagery over the Horn of Africa to assess the nature of change in the vegetation over six decades. We observe that the most substantial vegetation change is associated with human impact rather than climatic pressure, and that a signature of this impact appears in a readily measurable property of the pattern. These findings illuminate time scales of patterned vegetation dynamics, and suggest a focus on human impacts for future observations and theoretical explorations.