P.M.J. Berghuis^1,2, K. Siteur³, V.C. Reijers², A.G. Mayor⁴, T. van der Heide^1,5, J. van de Koppel^1,5, M. Rietkerk²

¹NIOZ, The Netherlands; ²Utrecht University, The Netherlands; ³RIVM, The Netherlands; ⁴University of Alicante, Spain; ⁵University of Groningen, The Netherlands

^* Corresponding author: paul.berghuis@nioz.nl

Introduction

Coastal ecosystems can display striking spatial patterns, from bands in seagrass meadows and mussel beds to branching marsh networks and patchy coral and dune landscapes. These patterns emerge through biogeomorphological feedbacks, in which habitat-forming organisms both respond to and modify hydrodynamic or aeolian flows, thereby shaping the environment in ways that feed back on their own growth (Corenblit et al., 2015). Collectively, such interactions can generate spatial self-organization at the landscape scale.

The most widely studied mechanism underlying self-organization are scale-dependent feedbacks (Rietkerk & van de Koppel, 2008), in which local facilitation is coupled to longer-range inhibition, often producing regular spatial patterns with a characteristic patch size and inter-patch spacing. More recently, an alternative mechanism has been proposed: density-dependent aggregation (Siteur et al., 2023). In this framework, pattern formation is governed by redistribution of a limiting component within the system, leading to phase-separation-like dynamics and coarsening through time rather than convergence to a fixed wavelength. Distinguishing between these mechanisms is important because they imply different resilience properties and may therefore require different restoration and conservation strategies (Siteur et al., 2023; Couteron, 2023).

Objective and Methods

Although spatial patterning can be very distinctive in some biogeomorphic coastal systems, in many others the mechanisms underlying spatial self-organization remain unresolved. One such system are coastal dunes. Dune-building grasses trap airborne sand and promote burial-driven growth, creating a strong local positive feedback that initiates embryo dunes and drives their expansion into mature dune systems (Bonte et al., 2021). Yet the dominant mechanism governing spatial self-organization of dunes on a landscape scale remains unclear.

Here, we ask whether developing coastal dune systems are better explained by scale-dependent feedbacks or by density-dependent aggregation. To test this, we compared spatial signatures observed in real world systems with those predicted for both mechanisms from theory (Siteur et al., 2023). Using high-resolution aerial imagery and elevation maps, we analysed (i) temporal changes in dune-grass patch spacing and size, (ii) vegetation density coupled to annual elevation gain, and (iii) dune-body size dynamics.

Results

Across three developing coastal dune systems along the Dutch coast, dune-grass patches showed a consistently broad and skewed patch-size distribution and lacked a clear characteristic spacing. This pattern points to irregularity and coarsening, rather than the emergence of a fixed wavelength as expected under scale-dependent feedbacks. A time-series analysis at our focal site (Texel) supported this interpretation: through time, dune-grass patches did not converge toward a dominant patch size or inter-patch distance.

Moreover, annual sand deposition was disproportionately concentrated in areas with high grass density, indicating density-dependent sediment capture and redistribution, a pattern that persisted and amplified through time. Finally, dune-body size distributions also showed coarsening behaviour, with growth towards fewer and larger dunes. Together, these results indicate that developing coastal dunes self-organize more closely through density-dependent aggregation than through scale-dependent feedbacks. Although translating theoretical pattern signatures to real-world systems requires caution, this distinction may provide important insights into the intrinsic resilience of coastal dune systems.

References

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