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Abstract

Regular spatial patterns, aka Turing patterns, where vegetated patches alternate with bare ground are encountered in many ecosystems. The formation of such patterns is intricately linked to hydraulic processes, like the redistribution of surface water in semi-arid environments or the turbulent mixing of seawater above mussel beds. These patterns are conceptually perceived as being periodic. This has been corroborated with statistical tests and deterministic models. However, natural patterns exhibit a considerable degree of spatial variation, as the size of patches and the distance between them varies. Therefore, we hypothesize that environmental spatial patterns are stochastic, and that conventional numerical models generate too regular patterns. First, we reveal shortcomings of previous statistical approaches and introduce a method for quantifying the regularity of spatial patterns. We then support our hypotheses in a metastudy comparing natural and model generated patterns. Second, we show that patterns similar to natural ones can be generated by introducing environmental heterogeneity (noise) into established deterministic models. We then take a new perspective on pattern formation, recognizing that patterns emerge through the filtration of environmental noise rather than through the perturbation of an unstable homogeneous state. We derive spectral processes for the pattern formation both in diffusion and advection dominated systems, and link our method for quantifying the regularity of spatial patterns based on their spectral density. We call for appreciating the stochasticity of environmental spatial patterns and for reexamination of the vulnerability of pattern-forming ecosystems to environmental pressure which has been predominantly studied with deterministic models.