On the stripe width distribution of regular vegetation patterns

At hillslopes, arid ecosystems tend to form characteristic spatial patterns consisting of alternating vegetated and bare stripes. As such patterns form autogenously, they can potentially provide insight into the ecosystem functioning, health, and resilience. While the spectral properties of striped patterns are well understood, less is known about the stripe width. To fill this gap, I address several essential questions: 1) What is the general form of the stripe width distribution (SWD)? 2) How do exogenous random spatial heterogeneities modulate the SWD? 3) How can the regularity of patterns be measured based on the SWD? 4) What can the SWD reveal about the health and resilience of ecosystems? 5) What caveats complicate the estimation and interpretation of the SWD? To answer these questions, I first derive a theoretical SWD based on a parsimonious stochastic model for anisotropic patterns, and second, systematically explore the stripe width distributions of patterns generated with the more complex Rietkerk model which explicitly accounts for pattern forming processes. I ensure variation of the stripe width in the simulations by simulations by perturbing the infiltration capacity randomly in space. I find that the theoretical SWD agrees very well with the SWD of patterns generated in one-dimensional simulations, and after a small extension, also agrees reasonably well with that of patterns generated in two dimensions. Finally, I compare the theoretical SWD to that of natural striped vegetation patterns.