Review
Regular pattern formation in real ecosystems

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Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through spatial self-organization. Possible mechanisms include oscillating consumer–resource interactions, localized disturbance-recovery processes and scale-dependent feedback. Despite abundant theoretical literature, studies revealing spatial self-organization in real ecosystems are limited. Recently, however, many examples of regular pattern formation have been discovered, supporting the importance of scale-dependent feedback. Here, we review these studies, showing regular pattern formation to be a general phenomenon rather than a peculiarity. We provide a conceptual framework explaining how scale-dependent feedback determines regular pattern formation in ecosystems. More empirical studies are needed to better understand regular pattern formation in ecosystems, and how this affects the response of ecosystems to global environmental change.

Section snippets

Spatial self-organization

Theoretical ecologists increasingly emphasize that ecosystems can reveal spatial self-organization. Spatial self-organization is the process where large-scale ordered spatial patterns emerge from disordered initial conditions through local interactions. This process is key to understanding ecological stability and diversity [1]. Causal mechanisms explaining spatial self-organization include oscillating consumer–resource interactions leading to spiral waves 2, 3, localized disturbance-recovery

Scale-dependent feedback

Ecosystems consist of organisms and the environment, which interact with each other. These interactions can impose various feedbacks upon the organisms and the environment. The feedback can be negative, for example when organisms deplete resources, leading to competition. Positive feedback can also occur, for example if organisms help others to survive through facilitation, by modifying the environment. If positive and negative feedbacks occur at different spatial scales (i.e. scale-dependent

Arid ecosystems

Regular pattern formation in arid ecosystems occurs in the form of stripes (‘tiger bush’), labyrinths, spots (‘leopard bush’) and gaps 15, 16, 17, 18, 19, 20, 21 (Figure 2a). Part of the mechanism is short-distance positive feedback between vegetation and soil water availability. Higher vegetation density enables higher water infiltration into the soil. The second part is subsequent redistribution of overland flow driven by differences in rainwater infiltration into the soil. The consequence of

Long-distance negative feedback

The study of the marsh tussocks makes it clear that long-distance negative feedback is essential for regular pattern formation in all of these ecosystems [46]. First, this means that short-distance positive feedback is not essential for regular pattern formation. Second, it implies that short-distance feedback alone, unaccompanied by long-distance feedback, will not be a sufficient condition for regular patterns to form (Figure 1). Indeed, the regularity of a pattern is determined by the

Ecosystem functioning

We reviewed studies from a wide range of ecosystems in which scale-dependent feedback is proposed to explain regular pattern formation. The mechanisms involved all correspond to Turing's scale-dependent activator–inhibitor principle and only differ in the details. The examples from arid ecosystems, wetland ecosystems, savanna ecosystems and coral reefs involve resource concentration in a so-called activator-depleted substrate system [14]. Here, the activation and inhibition mechanisms are

Acknowledgements

M.R. is supported by a personal VIDI grant from the Netherlands Organization of Scientific Research, Earth and Life Sciences (NWO-ALW). We thank David Bercovici, Wladimir Bleuten, Norbert Dankers, Chris Klausmeier, Brian Helmuth, David Jupp, Elena Lapshina, Olivier Lejeune, Roland Thar and Martin Wassen for sharing their photographs. Stefan Dekker, Maarten Eppinga, Jo Gascoigne, Erez Gilad, Frédéric Guichard and Sonia Kéfi provided comments and ideas that significantly improved the article.

Glossary

Localized disturbance-recovery processes
disturbance occurs primarily close to a site already disturbed (e.g. by wind) and recovery takes place primarily close to a site that is occupied by organisms (e.g. by local seed dispersal).
Long-distance negative feedback
ecological interactions resulting in a net negative feedback between organisms and their environment at a particular distance from the organisms.
Long-range competition
the process where organisms, by depleting resources, constrain the

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