Unravelling the spatial structure of regular dryland vegetation patterns

Many resource-limited ecosystems exhibit spatial patterns where patches of biomass alternate with bare ground. Patterns can enhance ecosystem functioning and resilience, depending on their spatial structure. Particularly conspicuous are regular patterns, where patches are of similar size and spaced in similar intervals. The spatial structure of regular patterns is often described to be periodic. This has been corroborated by statistical testing of natural patterns and generation of periodic patterns with deterministic reaction–diffusion models. Yet, natural regular patterns appear conspicuously erratic compared to periodic patterns. So far, this has been attributed to perturbations by noise, varying patch size and spacing. First, we illustrate by means of an example that the spatial structure of regular vegetation patterns cannot be reproduced by perturbing periodic patterns. We then compile a large dataset of regular dryland patterns and find that their spatial structure systematically differs from periodic patterns. We further reveal that previous studies testing for periodicity overlook two aspects which dramatically inflate the number of false positives and result in the misclassification of patterns as periodic. We amend the test procedure by accounting for both aspects, finding that regular natural patterns have no significant periodic components. Lastly, we demonstrate that stochastic processes can generate regular patterns with similar visual appearance, spatial structure and frequency spectra as natural regular patterns. We conclude that new methods are required for quantifying the regularity of spatial patterns beyond a binary classification and to further investigate the difference between natural and model generated patterns.