Significance: Pattern-formation theory predicts that vegetation gap patterns, such as the fairy circles of Namibia, emerge through the action of pattern-forming biomass–water feedbacks and that such patterns should be found elsewhere in water-limited systems around the world. We report here the exciting discovery of fairy-circle patterns in the remote outback of Australia. Using fieldwork, remote sensing, spatial pattern analysis, mathematical modeling, and pattern-formation theory we show that the Australian gap patterns share with their Namibian counterparts the same characteristics but are driven by a different biomass–water feedback. These observations are in line with a central universality principle of pattern-formation theory and support the applicability of this theory to wider contexts of spatial self-organization in ecology.

Gap distributions in forests reflect the spatial impact of man-made tree harvesting or naturally-induced patterns of tree death being caused by windthrow, inter-tree competition, disease or senescence. Gap sizes can vary from large (>100 m²) to small (<10 m²), and they may have contrasting spatial patterns, such as being aggregated or regularly distributed. However, very small gaps cannot easily be recorded with conventional aerial or satellite images, which calls for new and cost-effective methodologies of forest monitoring. Here, we used an unmanned aerial vehicle (UAV) and very high-resolution images to record the gaps in 10 temperate managed and unmanaged forests in two regions of Germany. All gaps were extracted for 1-ha study plots and subsequently analyzed with spatially-explicit statistics, such as the conventional pair correlation function (PCF), the polygon-based PCF and the mark correlation function. Gap-size frequency was dominated by small gaps of an area <5 m², which were particularly frequent in unmanaged forests. We found that gap distances showed a variety of patterns. However, the polygon-based PCF was a better descriptor of patterns than the conventional PCF, because it showed randomness or aggregation for cases when the conventional PCF showed small-scale regularity; albeit, the latter was only a mathematical artifact. The mark correlation function revealed that gap areas were in half of the cases negatively correlated and in the other half independent. Negative size correlations may likely be the result of single-tree harvesting or of repeated gap formation, which both lead to nearby small gaps. Here, we emphasize the usefulness of UAV to record forest gaps of a very small size. These small gaps may originate from repeated gap-creating disturbances, and their spatial patterns should be monitored with spatially-explicit statistics at recurring intervals in order to further insights into forest dynamics.

The spatial placement of recruits around adult conspecifics represents the accumulated outcome of several pattern-forming processes and mechanisms such as primary and secondary seed dispersal, habitat associations or Janzen–Connell effects. Studying the adult–recruit relationship should therefore allow the derivation of specific hypotheses on the processes shaping population and community dynamics. We analysed adult–recruit associations for 65 tree species taken from six censuses of the 50 ha neotropical forest plot on Barro Colorado Island (BCI), Panama. We used point pattern analysis to test, at a range of neighbourhood scales, for spatial independence between recruits and adults, to assess the strength and type of departure from independence, and its relationship with species properties. Positive associations expected to prevail due to dispersal limitation occurred only in 16% of all cases; instead a majority of species showed spatial independence (≈73%). Independence described the placement of recruits around conspecific adults in good approximation, although we found weak and noisy signals of species properties related to seed dispersal. We hypothesize that spatial mechanisms with strong stochastic components such as animal seed dispersal overpower the pattern-forming effects of dispersal limitation, density dependence and habitat association, or that some of the pattern-forming processes cancel out each other.

Aims: The fairy circles along the Namib Desert in southern Africa are round grassland gaps that have puzzled scientists for about 50 years. With the discovery of fairy circles in Australia in 2016, the debate on the origin of the circles has been extended to a new continent. Research interest on the topic has since then risen strongly but so has the use of the term “fairy circle”. This term has become more imprecise and, by analogy, has been applied to circular vegetation gaps or plant rings that are largely unrelated to fairy circles. For this reason, we define the concept of fairy circles by identifying their three main characteristics based on in situ field observations and soil excavations to larger‐scale spatial patterns, and regional‐scale distribution.Results: Following this approach, fairy circles are defined by: (a) being “empty gaps” in grassland without a central insect‐nest structure; (b) their ability to form spatially periodic patterns, which are regular hexagonal patterns with an extraordinary degree of spatial ordering; and (c) their strongly regional distribution confined within a narrow arid climatic envelope. In these combined traits, fairy circles differ from other common vegetation gaps which, for example, always have a central insect‐nest structure and may occur across broad climatic gradients on continents. Also plant rings have their own specific characteristics that largely differ from the combined attributes of genuine fairy circles.Conclusions: There are many other vegetation‐gap patterns in arid lands but if such gaps cannot jointly show the three characteristics defining the fairy circles, they should be carefully discussed on their own, rather than mixing them up with fairy circles. Our synthesis provides a new etymology for the different types of vegetation gaps and rings, aiming to guide the reader through various classes of circular plant patterns.

Regular spatial patterns of vegetation are a common sight in drylands. Their formation is a population-level response to water stress that increases water availability for the few via partial plant mortality. At the individual level, plants can also adapt to water stress by changing their phenotype. Phenotypic plasticity of individual plants and spatial patterning of plant populations have extensively been studied independently, but the likely interplay between the two robust mechanisms has remained unexplored. In this paper, we incorporate phenotypic plasticity into a multi-level theory of vegetation pattern formation and use a fascinating ecological phenomenon, the Namibian “fairy circles,” to demonstrate the need for such a theory. We show that phenotypic changes in the root structure of plants, coupled with pattern-forming feedback within soil layers, can resolve two puzzles that the current theory fails to explain: observations of multi-scale patterns and the absence of theoretically predicted large-scale stripe and spot patterns along the rainfall gradient. Importantly, we find that multi-level responses to stress unveil a wide variety of more effective stress-relaxation pathways, compared to single-level responses, implying a previously underestimated resilience of dryland ecosystems.