@misc{KaestnerVijselCaviedesVoulliemeetal., author = {K{\"a}stner, Karl and Vijsel, Roeland C. van de and Caviedes-Voulli{\`e}me, Daniel and Hinz, Christoph}, title = {A scale-invariant method for quantifying the regularity of environmental spatial patterns}, series = {Ecological Complexity}, volume = {60}, journal = {Ecological Complexity}, publisher = {Elsevier BV}, issn = {1476-945X}, doi = {10.1016/j.ecocom.2024.101104}, pages = {13}, abstract = {Spatial patterns of alternating high and low biomass occur in a wide range of ecosystems. Patterns can improve ecosystem productivity and resilience, but the particular effects of patterning depend on their spatial structure. The spatial structure is conventionally classified as either regular, when the patches of biomass are of similar size and are spaced in similar intervals, or irregular. The formation of regular patterns is driven by scale-dependent feedbacks. Models incorporating those feedbacks generate highly regular patterns, while natural patterns appear less regular. This calls for a more nuanced quantification beyond a binary classification. Here, we propose measuring the degree of regularity by the maximum of a pattern's spectral density, based on the observation that the density of highly regular patterns consists of a narrow and high peak, while the density of highly irregular patterns consists of a low and wide lobe. We rescale the density to make the measure invariant with respect to the characteristic length-scale of a pattern, facilitating the comparison of patterns observed or modelled under different conditions. We demonstrate our method in a metastudy determining the regularity of natural and model-generated patterns depicted in previous studies. We find that natural patterns have an intermediate degree of regularity, resembling random surfaces generated by stochastic processes. We find that conventional deterministic models do not reproduce the intermediate regularity of natural patterns, as they generate patterns which are much more regular and similar to periodic surfaces. We call for appreciating the stochasticity of natural patterns in systems with scale-dependent feedbacks.}, language = {en} } @misc{KaestnerVijselCaviedesVoulliemeetal., author = {K{\"a}stner, Karl and Vijsel, Roeland C. van de and Caviedes-Voulli{\`e}me, Daniel and Frechen, Nanu T. and Hinz, Christoph}, title = {Unravelling the spatial structure of regular dryland vegetation patterns}, series = {CATENA}, volume = {247}, journal = {CATENA}, publisher = {Elsevier BV}, issn = {0341-8162}, doi = {10.1016/j.catena.2024.108442}, pages = {13}, abstract = {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.}, language = {en} }