Introduction

Emergent vegetation patterns are the products of causal mechanisms at lower levels of organization, but are primarily expressed at the larger landscape scale (Newman et al. 2019). Vegetation patterns are a prominent feature of many water-limited drylands worldwide and they are often characterized by highly regular, spatially periodic distributions (Deblauwe et al. 2008). Examples of self-organized vegetation patterns include tree stripes, also called ‘tiger bush’ (Lefever and Lejeune 1997), gaps in African shrubland (Barbier et al. 2008) or vegetation spots (Borgogno et al. 2009). These patterns result from scale-dependent ecohydrological feedbacks where short-range positive plant interaction leads to long-range water depletion and finally to emergent vegetation patterns (Meron 2018).

Since about twenty years, also the so-called “fairy circles” (FCs), which form a spatially periodic vegetation gap pattern in arid Namibia, have been suspected to be a self-organized pattern whose relative permanence is critical for the optimal functioning of the ecosystem to capture, store and recycle limited resources (van Rooyen et al. 2004). Limited resources like water are obviously critical for the FCs in Namibia because they are confined to a very narrow climatic rainfall belt where they mainly exist between 70 and 120 mm mean annual precipitation (MAP) but disappear under moister conditions at 150 mm MAP (Cramer and Barger 2013). Field evidence has shown that the scale-dependent facilitative and competitive interactions between the grasses are likely responsible for the formation of fairy circles in Namibia (Cramer et al. 2017; Ravi et al. 2017), as well as in Western Australia (Getzin et al. 2021a). In a recent study, it has also been demonstrated with continuous soil–water measurements that the grasses surrounding the FCs in Namibia likely deplete the soil moisture within the vegetation gaps and thereby outcompete the grasses that try to establish within the FCs (Getzin et al. 2022). This research has shown that the young but quickly dying grasses within FCs had significantly higher root-to-shoot ratios than the vital grasses outside in the matrix, which indicates a more resource-depleted and stressful environment. This study was questioned by Jürgens and Gröngröft (2023) because they argued that the hydraulic conductivity is only high above a volumetric moisture content of 8%, but soil water cannot move in sands when the moisture content is below a threshold of 6% to 8%. However, the data of Getzin et al. (2022, their Table 3) show that soil moisture within the FCs was at 20 cm depth not below that threshold during the time period when grasses strongly draw water from the FCs. In a detailed response, Getzin and Yizhaq (2024) show that during the first 20 days after rainfall, when grasses germinate and die within FCs, soil moisture was always between 18 to 8%, which allows a high hydraulic conductivity. The study of Getzin and Yizhaq (2024) demonstrated also that the grasses within FCs die due to desiccation in the uppermost topsoil because it is significantly drier than the surrounding matrix soil. With their 10 cm long roots and weak water-drawing ability, these young grasses cannot benefit from the existence of higher moisture that is only found in deeper soil layers.

Besides the plant self-organization hypothesis, also other causal theories about the origin of the fairy circles have been proposed such as the Euphorbia hypothesis (Meyer et al. 2020) or the sand termite hypothesis (Jürgens 2013). The Euphorbia hypothesis has been recently refuted based on detailed fieldwork and high-resolution image analysis, demonstrating that decaying Euphorbias did not inhibit grass growth and did not form FCs (Getzin et al. 2021b).

The sand termite hypothesis proposed by Jürgens (2013) claimed that in 80% to 100% of FCs, Psammotermes allocerus nests and underground tunnel-like galleries were found a few centimeters to decimeters underneath the bare patch. This study and subsequent studies of the same author such as Jürgens et al. (2015) proposed that the sand termites would kill the freshly germinated grasses by foraging on the roots. However, the Namibian termite expert Eugene Marais undertook an extensive survey in the Namib and has “not found such a ubiquitous presence of sand termites at fairy circles as was suggested by Juergens (2013) when carrying out ad hoc searches throughout the fairy circle range” (Ravi et al. 2017). The major shortcoming of the sand termite hypothesis is the fact that even 10 years after its first publication, it is not supported by systematic data evidence in the field (Jürgens et al. 2022). Such evidence would have to show, based on in-situ root measurements and many replicates from study sites in the entire Namib, that Psammotermes sand termites would systematically kill the freshly germinated green grasses within FCs, but such data do not exist. In a thorough discussion of the proposed termite-feeding mechanism, Getzin and Yizhaq (2024) concluded “that there is no single study to date that has demonstrated with systematic field evidence in the form of root measurements and data from several regions of the Namib that the green germinating grasses within the FCs would be killed by root herbivory of sand termites”. This is in line with previous research in the Namib that has shown that Psammotermes “selectively grazes the outer grey layer of the stems of perennial Stipagrostis species” (Jacobson et al. 2015). Recently, Getzin et al. (2022) conducted for the first time systematically root measurements of grasses across the southern to northern Namib to test the sand termite hypothesis. By excavating about 500 grasses and by comparing the roots of freshly germinated but dying grasses within FCs to neighboring vital green grasses in the matrix, the authors showed that termite herbivory did not cause the plant death. The measurements have shown that the roots of the dead grasses were as long or even longer than the roots of the vital matrix grasses, which excludes termite herbivory as a cause. Only when the grasses were already desiccated and dead for a relatively long time after rainfall, root herbivory by termites became more noticeable which confirms that sand termites are typical detritus feeders in the Namib (Crawford and Seely 1994; Jacobson et al. 2015).

As outlined above, water availability is a very critical factor for the grasses in the Namib Desert. For example, the Stipagrostis ciliata grasses that form FCs only start growing after a rainfall event of around 12 mm (Jacobson 1997) but they do not germinate when a rainfall event is below 10 mm. Additionally, where only one such rainfall event occurs, established grasses within fairy circles will complete their whole life cycle from germination to death within a few weeks and then disappear again quickly (Getzin et al. 2022). Therefore, studying the direct coupling of precipitation and grass growth in and around FCs will shed light on the extent to which water and the associated biomass-water feedbacks are a main driver of the FC-landscape phenomenon.

Until now, the spatio-temporal dynamics of FCs have hardly been investigated. So far, it was more the temporal dynamics of FC birth and death that have been the focus of some FC studies (Tschinkel 2012). In this regard, the study of Zelnik et al. (2015) revealed some important insights on the rainfall dependency of FCs. Based on satellite images, these authors showed for the NamibRand Nature Reserve in the southern Namib that FCs tend to shrink in diameter or fully disappear after above average rainfall, while FCs may enlarge in size after cumulative drought years (Zelnik et al. 2015). However, the spatial patterns where such FCs revegetate with grass, relative to the distance of neighboring FCs have never been thoroughly investigated. It is well known that FCs store water at soil depths particularly below 30 cm and thereby act as water reservoirs and sources of water (Albrecht et al. 2001; Picker et al. 2012). Hence, the distances and spatial patterns of FCs around revegetating FCs should matter because a higher density of surrounding FCs means more available water for grass growth in the vegetation matrix. This would also favor the closing and disappearance of FCs after above-average rainfall sequences. Indeed, the analysis of spatial patterns of the size distribution of FCs indicated already such an effect. For example, FC diameters in northern Namibia were below average when the FCs were closer than about 13 m because there was locally more water to enable more plant growth, which led to smaller FCs (Getzin et al. 2015a).

So far, spatial pattern analysis on FCs has been undertaken on static snap-shot distributions, which is an important first step in gathering information about the fairy circles within a framework of pattern-process inference (Getzin et al. 2015a,b, 2019, 2021a,b,c; Noy et al. 2023). However, the link between temporal rainfall effects during different years and the disappearance or re-opening of FCs has never been investigated in a spatially explicit context. But even snap-shot patterns in different landscapes across the southern to northern Namib have never been compared to each other using a large sample basis. This is important because environmental factors such as substrate heterogeneity or topographic variation may affect the patterns of FCs and induce more variation in their spacing and shape (Getzin and Yizhaq 2019; Noy et al. 2023). Fairy circles form a unique dryland vegetation gap pattern in that they have the ability to form spatially periodic patterns, which is a special case of regular patterns with an extraordinary degree of spatial ordering (Getzin et al. 2015b, 2016, 2019, 2021c; Maestre et al. 2021). There are many merely regular gap patterns in the global drylands which may resemble FCs (Guirado et al. 2023) but these are classified as “common vegetation gaps” because they do not show an ability to form spatially periodic patterns which is one of the key properties that define genuine FCs in the Namib Desert and in Western Australia (Getzin et al. 2019, 2021c). Nevertheless, in regions where the substrate is not very homogeneous or where environmental heterogeneity and noise may have an effect, deviations from a spatially periodic pattern will occur (Meyer et al. 2020; Getzin et al. 2021b).

Thus, to get an overview about the variation in spatial FC patterns, we drone-mapped 10 large plots with fairy circles across 1000 km from the southern to the northern Namib. Additionally, we mapped repeatedly three FC plots in the sandy southern Namib and assessed how the individual FCs revegetated with grass after rainfall, or on the contrary, opened up again in the next year. This second part of the research focuses on the spatio-temporal dynamics of the FCs and benefitted from two very good rainfall seasons in the years 2021 and 2022, as well as from poor rainfall years in 2020 and 2023.

In this research we investigate three main hypotheses:

  1. 1.

    The most regular FC patterns, which are spatially periodic, can be found on homogeneous deep aeolian sands where rain water percolates quickly, while less regular patterns are found on less homogeneous substrates.

  2. 2.

    After drought years and a subsequent season with ample rainfall, a large proportion of FCs revegetates with grass because water was the main determinant of the FC dynamics. In contrast, new FCs hardly form because fairy circles are primarily an expression that there is not enough water to sustain a continuous vegetation cover.

  3. 3.

    Revegetating FCs within large study plots should be located in areas where there is locally a higher density of FCs because the moisture reservoirs of nearby FCs support the revegetation with grass.

Material and methods

Study area and data collection

During the rainy seasons 2020 to 2023, we mapped 10 plots that are spread from the Marienfluss Valley in the northern Namib to Garub 1000 km further south (Supporting Information Fig. S1). Mean annual precipitation (MAP) for the study plots ranges from almost 120 mm in the Marienfluss Valley to less than 60 mm in the most southern region (Table 1). These rainfall data were assessed with WorldClim2, which provides MAP with a resolution of 1 km2 for Namibia (Fick and Hijmans 2017). The predominant plant species that form the FCs in these ephemeral grasslands are Stipagrostis ciliata, S. obtusa or S. uniplumis which all have laterally confined roots, hence they cannot grow far into the FCs (Cramer and Barger 2013). From north to south, the plots are located in the Marienfluss Valley (Mar-1), the Giribes Plains (Gir-3), at Brandberg (Bra-3), Rostock farm (Ros-1), Kamberg (Kam-2), the Tsondab Valley (Tso-1), at Jagkop in the NamibRand Nature Reserve (Jag-1, Jag-2, Jag-3), and at Garub (Gar-1). The naming of the plots is derived from Getzin et al. (2021b, 2022). Infiltration measurements were previously done in each plot, except for the Jag-2 and Jag-3 replicate plots, because these were near the Jag-1 plot (all plot centers < 1.5 km away from each other) and had the same sandy substrate. The time of 60 ml water infiltration was assessed with a mini-disc infiltrometer with each three measurements in three selected FCs per plot, and each three measurements in three matrix positions about 2–3 m away from the FC peripheries (see details in Getzin et al. 2021b, 2022). In Table 1 we summarize the mean infiltration time based on the 18 measurements for each plot, to provide an indication for the edaphic differences.

Table 1 Plot names and information on water infiltration and data acquisition
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Drone mapping

The FCs in the study areas are about 500 m × 500 m in extent and have been mapped with a DJI Mavic 2 Pro at 90 m flying altitude. The drone was flown at 5 m/s and the 20 megapixel images were taken with 80% forward and 40% sideward overlap. All RGB images were processed in OneButton software (www.icaros.us) to stitch a single orthorectified and geo-referenced aerial image for each plot. The image resolution was 3 cm/pixel.

The large mature FCs constitute the typical gap pattern in the Namib. In order to describe the mature FCs, we mapped nine study plots in the dry year 2020, when there was no green matrix vegetation but the large FCs were still visible via a conspicuous ring of dormant grasses (Fig. 1). Only the Mar-1 plot in the Marienfluss was mapped in 2021 because it was too far north to be included in the 2020 work program. This plot was as dry as the other ones mapped in 2020.

Fig. 1
figure 1

Examples of the study plot Jag-1 and the classification of mature (M), closing (C) and opening (O) FCs during different years. Due to the drought in 2020, only mature FCs were visible in 2020. Many FCs closed with grass cover after the good rains in 2021. Those closing FCs either remained in that state in the years 2022 (and 2023) or they opened up again. The image from 2022 shows two FCs that remained in the closing state with grass cover hiding much of the sand

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The three Jag-plots at NamibRand have been mapped continuously every rainy season from 2020 to 2023. Hence, these replicate plots near Mt. Jagkop were suitable to assess the vegetation dynamics, and thus the closing and opening of mature FCs in dependence on rainfall (Fig. 1). Annual rainfall at Jagkop occurs mainly from January to April and amounted to 8 mm, 81 mm, 122 mm, and 16 mm in the years 2020, 2021, 2022, and 2023, respectively (Weather data NamibRand). Table 1 summarizes the coordinates of all 10 study plots, the date of drone mapping, as well as the extracted features from drone imagery.

Image analysis and classification of fairy circle dynamics

As in previous remote-sensing studies, we used a minimum diameter of 2 m to define the “mature” FCs (Getzin et al. 2019). The FCs were manually delineated in each of the 10 plots. For each segmented FC we created a shapefile (a geospatial vector format, digitized with QGIS-3.10.5 software, https://qgis.org/en/site/) with geo-referenced information on the object’s x,y-coordinate, and the diameter.

For the repeatedly mapped Jag-plots, we additionally identified two major categories of vegetation dynamics—“closing” and “opening” FCs (Fig. 1). In the drought year 2020, only “mature” FCs were identified. In 2021, due to new grass growth within the circles after abundant rainfall, many of the mature FCs were classified as “closing”. This also occurred with a few FCs in 2022. Closing FCs were classified as such when they were covered with grass by at least 2/3 of the inner area. Some of the closing FCs even disappeared completely with 100% vegetation cover, which induced their temporal death (Fig. 1). In the years 2022 and 2023, a large proportion of FCs opened up again and showed a larger bare-soil area than in the previous year. In 2022 and 2023 the three categories “mature, “closing”, and “opening” were thus possible. As a minor category, we identified also “new” FCs which became only visible within the vegetation matrix in 2021 to 2022 but not in the sparse matrix in 2023. These new FCs have also not been visible in older Google satellite images from 2012. Due to their very low number, these new FCs were not analyzed with spatial statistics.

Spatial statistical analysis

We used three spatial statistics to analyze the univariate patterns of mature FCs: (1) the Clark-Evans R-index of dispersion; (2) the g-function; and (3) the L-function.

The R-index (Clark and Evans 1954) is defined as \(R = \overline{r}_{A} /\overline{r}_{E}\) where \(\overline{r}_{A}\) is the average distance from randomly selected points to their nearest neighbors, and \(\overline{r}_{E}\) is the theoretically expected average distance between nearest neighbors based on the Poisson distribution of complete spatial randomness (CSR). R = 1 for random patterns, whereas aggregated (clumped) patterns have values approaching R = 0, and perfect hexagonal patterns have a maximum value of R = 2.1491 (not achieved in ecological systems). For comparative reasons, the R-index is presented without edge correction because those have been primarily published in the past (Getzin et al. 2019). Also, for large data sets with > 100 points the importance of edge correction is diminished (Velázquez et al. 2016).

To describe the scale-dependent smaller-scale order in the pattern of mature FCs, we used the pair-correlation function g(r), which is the expected density of points at a given distance r of an arbitrary point, divided by the intensity λ of the pattern (Wiegand and Moloney 2004). Under CSR, g(r) = 1. Values of g(r) < 1 indicate regularity, while values of g(r) > 1 indicate aggregation.

In a third analysis, we used a summary statistic based on Ripley’s K-function, which is the cumulative counterpart to g(r). The L-transformation (L-function) of Ripley’s K-function, L(r) = (K(r)/π)0.5–r, is used to more accurately assess departures from CSR at larger scales (i.e. 50–200 m) than the non-cumulative g-function (Wiegand and Moloney 2014). For a random pattern, L(r) = 0 and values of L(r) < 0 indicate regularity, while values of L(r) > 0 indicate aggregation. Hence, if the L-function, after the first small-scale deviations from CSR, moves consistently into the null-model envelopes of the simulated random distributions, this indicates a pattern that is homogeneous at large scales. In contrast, significant departures from the CSR null model at these large scales indicate that a pattern is heterogeneously distributed on the landscape (Wiegand and Moloney 2004; Getzin et al. 2008).

The spatial patterns of “closing” and “opening” FCs, relative to the distances of surrounding FCs were analyzed with the bivariate pair-correlation function g12(r) and the null model of bivariate random labelling. Under random labelling, the pair-correlation functions are invariant with g12(r) = g21(r) = g11(r) = g22(r) = g1,1+2(r) = g2,1+2(r) (Wiegand and Moloney 2014). In order to reveal possible spatial dependencies in the revegetation of FCs in 2021 or their subsequent opening in the years 2022 and 2023, we applied the test statistic g1,1+2(r)–g2,1+2(r). This statistic is particularly suitable to detect density-dependent effects (Raventós et al. 2010) in the revegetation of FCs because it compares the density of a neighborhood composed of both closing and mature FCs (as indicated by the subscript 1 + 2) surrounding closing FCs (pattern 1, g1) with the neighborhood surrounding mature FCs (pattern 2, g2). Under random labelling, the test result of g1,1+2(r)–g2,1+2(r) would be zero and no density-dependent effects would occur. However, under density-dependent revegetation of FCs, we hypothesize closing FCs (pattern 1) to occur in areas with high overall densities of fairy circles (pattern 1 + 2), that is g1,1+2(r) > g2,1+2(r). Given that FCs are water reservoirs (Albrecht et al. 2001; Picker et al. 2012), such a test result would indicate that revegetation of FCs occurs in areas where there is overall more soil water in the immediate neighborhood. Conversely, a negative test result as indicated by g1,1+2(r) < g2,1+2 (r) would in principle be possible as well. This would show that closing FCs occur in areas of overall lower FC density.

For this analysis, we assessed the closing FCs versus the mature FCs for the first good rainfall year 2021. Given that these revegetating FCs started to open again in the years 2022 and 2023, we assessed the patterns of opening FCs (pattern 1, g1) only relative to the closing FCs (pattern 2, g2) because we wanted to primarily know which of the previously closing FCs opened up again.

The univariate summary statistics g(r) and L(r) were assessed against the Poisson null model (CSR) using the 5th-lowest and 5th-highest values of 199 Monte Carlo simulations to generate approximately 95% simulation envelopes. Similarly, the random labelling was assessed against the independent marking null model by randomly shuffling the mark “closing” for the year 2021 over the joint pattern of closing and mature FCs. For 2022 and 2023, the mark “opening” was shuffled over the joint pattern of opening and closing FCs. All analyses were done using R-software (packages spatstat and ecespa; http://www.R-project.org/).

Results

Spatial patterns of fairy circles across the Namib

The most regularly spaced FCs were found in the plots Mar-1, Jag-1, Jag-2, Jag-3, and Gir-3 with Clark-Evans R-indices attaining very high values of 1.67, 1.67, 1.65, 1.67 and 1.62, respectively. Less regular patterns were found in the plots Bra-3, Kam-2, Ros-1, and Tso-1 with R-indices of 1.51, 1.47, 1.39, and 1.16, respectively. All these patterns were significantly regular with p-values < 0.01. Only the plot Gar-1 with its low number of 113 FCs had a low R-index of 1.10 that did not differ significantly from a random Poisson distribution (p = 0.302).

These Clark-Evans indices correlated strongly negatively with the infiltration time of water. The R-square of 0.63 was significant at p = 0.018 and indicates that faster infiltration times in the soil lead to higher regularities of FC patterns (Fig. 2).

Fig. 2
figure 2

Pattern regularity of fairy circles (FCs) versus infiltration time of water. There is a significant negative relationship (p = 0.018) between the speed of water infiltration in FC and matrix soils and the spatial regularity of the FCs at the plot scale. The highest regularity is found on coarse homogeneous sands, the least regular patterns are found on more calcareous gravel-like substrates

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The extremely high FC regularities of the five study plots at Marienfluss, Jagkop, and Giribes are best reflected by the g-functions (Fig. 3). They showed not only a regular but a “spatially periodic” pattern, as indicated by the strong and significant fluctuation of the pair-correlation function around the null model envelopes (Getzin et al. 2015b, 2021a, b, c). At the same time the L-functions stayed at larger scales within the simulation envelopes and thereby revealed homogeneous distributions (Fig. 3). The g-functions of the FCs in the plots Bra-3, Kam-2, Ros-1, and Tso-1 did not show such periodic fluctuations and patterns were merely regular up to short neighborhood distances of 9.5 m to 16 m. The plot Gar-1 showed random patterns at very small scales and then regularity for some radii up to 15 m. The least regular plots Ros-1, Tso-1, and Gar-1 showed all heterogeneous FC distributions at larger scales, as indicated by their L-functions (Fig. 3).

Fig. 3
figure 3

Univariate analysis of the patterns of mature FCs using the g-function and the L-function. The pattern is regular or aggregated at circular neighborhood distances if the solid red line of the g-function or L-function is either below the lower or above the upper grey lines of the simulation envelopes, respectively. Strong and significant small-scale fluctuations of the g-function far above and below the null-model envelopes indicate a spatially periodic pattern. Large-scale deviations of the L-function indicate non-homogeneous distributions. Null model envelopes were constructed using the 5th‐lowest and 5th‐highest value of 199 Monte Carlo simulations of the randomly distributed Poisson point process. The dashed red line is the theoretical expectation based on the null model

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The dynamic closing and opening of fairy circles in response to rainfall

A large proportion of mature FCs revegetated with grass cover in the year 2021, when annual rainfall at Jagkop was with 81 mm double the amount compared to the average of 40 mm during the years 2012–2021. In the plots Jag-1, Jag-2 and Jag-3, 58%, 44% and 34% of all mature FCs closed, respectively (Fig. 4). Only 9 new FCs emerged in Jag-1, 0 new FCs emerged in Jag-2, and 6 new FCs emerged in Jag-3. During the second good rainfall year 2022, 30%, 26%, and 11% of FCs opened up in the plots Jag-1, Jag-2 and Jag-3, respectively. In that year 29, 11 and 18 new FCs emerged in Jag-1, Jag-2 and Jag-3, respectively. In the poor rainfall year 2023, the proportion of opening FCs increased further with 46%, 36%, and 21% in the plots Jag-1, Jag-2 and Jag-3, respectively.

Fig. 4
figure 4

Percentage of closing and opening FCs in the three study plots at Jagkop in the NamibRand Nature Reserve from one year to the next. Note the high percentage of closing FCs during the first good rainfall year in 2021 after many years of drought. Many of those closing FCs opened up again in the subsequent years

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In terms of dynamics, the highest proportion of closing and opening FCs was found in the plot Jag-1, the lowest proportion of changing FCs was found in Jag-3.

The spatio-temporal closing and opening of fairy circles

Analysis of the spatio-temporal patterns of closing and opening FCs revealed strong density-dependent effects and linkages to the proportion of those closing and opening FCs (Fig. 5). The closing FCs in 2021 showed in all three plots significant peaks of the g-function at neighborhood radii of about 14 m (Fig. 5). These strong peaks (red line) of the test statistic g1,1+2(r)–g2,1+2(r) far above the grey simulation envelopes of the null model indicate that the revegetating FCs occurred in areas with an overall higher local density of surrounding closing and mature FCs, relative to the FC densities that surround the mature FCs. There is also a clear order in the amplitude of the g-function: at r = 14.5 m, the Jag-1 plot had its highest g-value of 0.338. At r = 14.0 m, Jag-2 has its highest g-value of 0.317, and at r = 13.5 m, Jag-3 has a g-value of 0.290. This decline in the strength of density-dependent effects parallels the declining proportion of closing FCs from Jag-1 to Jag-3 (Fig. 4).

Fig. 5
figure 5

Bivariate analyses of closing (green dots) vs. mature (black) and opening (blue) FCs vs. closing FCs using random labelling and the function g1,1+2(r) – g2,1+2(r). If the test statistic (red line) is above the simulation envelopes, then closing or opening FCs (pattern 1) occurred in areas with a higher overall density of fairy circles (closing + mature FCs or opening + closing FCs). If the red line is below the lower simulation envelopes, then closing or opening FCs occurred in areas of overall lower FC density. Note that x,y-plots show only the two categories indicated above the respective plot, specifically, in 2022 and 2023 mature FCs are present in appreciable numbers but not shown

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Conversely, also the opening FCs revealed a related trend and partly density-dependent effects. Especially the plot Jag-1, which had the highest proportion of opening FCs, showed significant negative peaks in the g-functions in the years 2022 and 2023, as indicated by the red line being below the grey envelopes of the null model at distances of around 10 m radius (Fig. 5). This indicates that opening FCs occurred in areas where the surrounding local density of opening and closing FCs was lower than in areas where closing FCs occurred. Such a significant effect was also visible for the plot Jag-2 in 2022 but deviation from the random labelling null model was only marginal, and it disappeared in 2023 (Fig. 5). The least dynamically changing plot Jag-3 did not show significant density-dependent effects in 2022 and 2023 for the relatively low proportion of opening FCs, which is a result of the low proportion of initially closing FCs in that plot.

Discussion

Previous studies on Namibian fairy circles have focused on direct measurements of water flow in the sandy substrates, supporting the plant self-organization explanation for the emergence of these vegetation gaps (Cramer et al. 2017; Ravi et al. 2017; Getzin et al. 2022; Getzin and Yizhaq 2024). With the current research, we are extending these studies by relating the emergent fairy circle patterns to soil–water infiltration and variability in the amount of annual rainfall.

Spatial patterns of fairy circles across the Namib—Hypothesis 1

Our data show that FC patterns attain extremely regular, spatially periodic distributions when water infiltration into the substrate is very fast (Fig. 2). In the Namib, this occurs primarily on coarse-grained, deep aeolian sands such as in the NamibRand Nature Reserve (Fig. 1, Fig. S2), the Giribes Plains or in the Marienfluss Valley. In these regions, the sandy substrate is very homogeneous and, as our data show, rain water infiltrates quickly and is little affected by micro-topography or overland flow. This enables the Stipagrostis grasses with their laterally confined roots to form symmetrically spaced FCs. Consequently, these patterns spread evenly and homogeneously across the landscape, as also the analysis with the L-function demonstrates (Fig. 3). However, also within the same region such as in the southern Giribes, FCs may form less regular and less symmetric patterns when topography and directed overland water flow near mountains disrupt the homogeneity (Meyer et al. 2020; Getzin et al. 2021b). Then, even strongly elongated FCs may form within drainage channels (Getzin and Yizhaq 2019; Noy et al. 2023).

Less regular patterns occurred in the Bra-3 plot north of Brandberg, where soils are less sandy and overland water flow may impact the symmetry of the pattern (Fig. S2). Also in the interdune valley of the Kam-1 plot or at slightly undulating terrain of Ros-1 plot at Rostock farm, the sand layer was less deep or more stony and resulted in less regular and even heterogeneous patterns (Fig. 3, Fig. S2). Likewise, the plots Tso-1 and Gar-1 with their very slow infiltration times had the least regularly or even just randomly spaced FC patterns, respectively. These two plots also showed heterogeneous distributions at larger scales. It can be assumed that the Tso-1 plot in the Tsondab Valley with its hard calcareous layer 5 cm to 20 cm below the surface causes heterogeneous overland water flow during strong rainfall events, which is amplified by micro-topography (Getzin and Yizhaq 2019). Similar effects may work at Garub on undulating terrain (Fig. S2).

Another factor that may influence the regularity of the FC pattern is related to differences in the evaporation rate. Homogeneous substates are known to lose less soil water via evaporation than heterogenous substrates (Or et al. 2013). Consequently, more soil water is stored within FCs on homogeneous sands, which allows for more stable biomass around the FC edges and enables a space saturation of tightly packed, spatially periodic FC patterns.

Such abiotic processes have been little studied to date. This includes also the potential role of aeolian feedbacks and sand sorting within and around FCs. For example, the permanent winds along the Namib and the long-lasting presence of alive or dead grass stubbles around the FC edge may cause aeolian feedbacks and soil textural differences with coarser particles remaining within the FCs (Ravi et al. 2017; Yizhaq et al. 2024). Such processes may locally lead to a faster loss of soil water from the upper topsoil and thereby induce the desiccation and death of freshly germinated seedlings within the FCs (Getzin and Yizhaq 2024). However, this can only be a secondary effect for the cause of the FCs because such differences in water infiltration between FCs and the matrix do not occur consistently across the Namib Desert (Getzin et al. 2022).

Overall, our analysis of the static snap-shot patterns of FCs across 1000 km of the Namib confirms our first hypothesis because the most regular patterns are found on homogeneous deep sands where rain water percolates quickly.

The dynamic closing and opening of fairy circles in response to rainfall—Hypothesis 2

In our study, above average rainfall of 81 mm in 2021, relative to the previous mean of 40 mm during the years 2012 to 2021, led to a strong revegetation of mature FCs in the three plots at Mt. Jagkop. The 58%, 44% and 34% of closing FCs in these plots strongly supports the view that Namibia’s fairy circles are primarily a rainfall driven and soil–water driven phenomenon. These percentage values correspond to 409, 423, and 260 closing FCs in the plots Jag-1, Jag-2, Jag-3, respectively. In contrast, only 9, 0, and 6 new FCs emerged in these plots, respectively. Hence, these altogether 1092 closing FCs are 73 times more in number than the 15 new FCs that formed after the long drought in the good rainfall year 2021.

Our data are based on a high-resolution mapping of three large plots with altogether 2432 mature fairy circles (Table 1). These quantitative data strongly contradict the sand termite hypothesis and the notion of Jürgens et al. (2015) that “new FCs seem to be generated in wet years”. Jürgens et al. (2023) further stated that “after pulses of rainfall that trigger germination of seedlings, Psammotermes attacks and damages the root systems, causing the young plants to die”. Furthermore, they claim that all landscapes with FCs would have living and active colonies of sand termites and that “the mechanism directly responsible for the bare patch of fairy circles is the elimination of newly germinated seedlings” after rainfall. While this elimination of new grass seedlings by sand termites is not supported by any systematic field data (cf. Getzin and Yizhaq 2024), this statement is also contradicted by our new data, because the strong pulses of rainfall in 2021 caused 1092 FCs to close with healthy grass vegetation. Moreover, of the nine new FCs that formed in 2021 in the plot Jag-1, five were examined by us in detail using grass excavations and measurements on the roots and shoots. In these new FCs the majority of desiccated grasses had fully intact roots and they died due to plant-water stress and desiccation but not due to root herbivory induced by sand termites (Getzin et al. 2022). That study has also shown for other FC regions in the Namib that initial grass death after rainfall pulses was not due to root herbivory by sand termites because the roots of dying grasses were undamaged and partly even significantly longer than the roots of the vital matrix grasses outside of the FCs.

As our new data and personal observations in several regions of the Namib indicate, fairy circles revegetate with new grass only for a short time and mostly not longer than for one or two rainy seasons (Fig. 4, Fig. S3). Given that even the opening FCs in 2022 had still more grass cover than the bare mature FCs, this demonstrates that also in 2022 rainfall was causing the temporary vegetation coverage within the FCs (cf. Zelnik et al. 2015). We ascribe the opening of FCs and emergence of new FCs in the year 2022 to the plant-competitive interactions whereby competitively superior plants exert positive biomass-water feedbacks at small scales and thereby draw soil water from the neighborhood via lateral diffusion (Getzin et al. 2016; Cramer et al. 2017; Getzin and Yizhaq 2024).

The proposed uptake-diffusion feedback which is exerted by the Stipagrostis grasses is principally supported by the fact that the volumetric soil water content at 20 cm depth within the FCs was always between 8 to 18% during the first 20 days after rainfall (Getzin et al. 2022; Getzin and Yizhaq 2024). Given that the “hydraulic conductivity is strongly related to the water content of the soils” (Jürgens and Gröngröft 2023, their Fig. 3), such high values of soil moisture allow a very high hydraulic conductivity and lateral movement of water, which is further enhanced by the active suction of water via the grass roots and the accompanying concentration gradient in soil moisture. In particular, the perennial, rapidly greening large grasses around the periphery of the FCs suck up water strongly because of their competitive advantage and established bulk of roots at 20 to 30 cm depth. This causes rapid drying of the uppermost soil layer after ten to twenty days, where the young grasses with their only 10 cm long roots die in the topsoil of the FCs, which is significantly drier than the topsoil of the matrix (Getzin and Yizhaq 2024).

In the good rainfall year 2022, plant vitality was boosted from the previous good rainfall year and thus, especially the strengthened perennial edge plants around the FC periphery had strong water-drawing abilities. This has been also shown by Cramer et al. (2017) who found that the short-range positive feedback leads to a five times higher canopy volume per area of the peripheral edge plants, compared to the weaker matrix grasses. These strong water-drawing characteristics of the plants surrounding the FCs have been also revealed with continuous soil–water measurements in the Jag-1 plot at 20 cm depth (Getzin et al. 2022). In that in-situ study, the surrounding plants caused in 2021 and 2022 a strong decline in soil water within the FCs after rainfall. Our recording of soil moisture within and around FCs showed also that the grasses used up much more water in 2022 as compared to 2021. During the rainfall season 2021, the grasses re-established for the first time after a long drought. But in 2022, the rainy season caused another boost for the grasses and water uptake was then considerably stronger (Fig. S4). These stronger biomass-water feedbacks explain why FCs opened up again in 2022 and why some new FCs emerged in the matrix due to long-range negative feedbacks and soil–water depletion (Zelink et al. 2015; Cramer et al. 2017). As expected, the opening of FCs progressed further in the poor rainfall year 2023, because there was overall less moisture in the system to sustain vegetation coverage.

In summary, our statistical analysis based on 2432 mature FCs, monitored at NamibRand over four consecutive years, confirms our second hypothesis. Rainfall is a main driver of the revegetation of FCs, which supports the notion that fairy circles are an emergent vegetation gap pattern in water-limited environments. It explains also why FCs are confined to a very narrow climatic envelope and why they disappear when mean annual precipitation exceeds 150 mm (van Rooyen et al. 2004; Cramer and Barger 2013).

The spatio-temporal closing and opening of fairy circles—Hypothesis 3

Fairy circles are local water reservoirs that store soil moisture particularly below a depth of 30 cm (Picker et al. 2012; Jürgens 2013). These underground sources of moisture supply the surrounding vegetation matrix with water and they explain why FCs often have a more than 10 m wide halo around their edge with grass biomass declining with distance from the FCs (Getzin et al. 2015b; Getzin and Yizhaq 2024). It also explains why FC diameters become smaller than average in the landscape when FCs are located closer than 13 m to each other. This has been shown for study plots of the Marienfluss and Giribes (Getzin et al. 2015a) that have similar sandy substrates and fast infiltration rates as the Jagkop-plots at NamibRand (Fig. 2). FCs have smaller than average diameters because there is more soil moisture in the surrounding neighborhood up to a radius of 13 m, which enables more grasses to survive and causes the FCs to shrink. This is the same effect that causes FC diameters to enlarge, on the contrary, after drought years, when there is not enough water to sustain the grasses (Zelnik et al. 2015). With the spatio-temporal analysis of closing and opening FCs we are providing further support for this observation.

Indeed, the evidence for our third hypothesis is strong: revegetating FCs occurred in areas where there is locally a higher density of FCs. Hence, the grasses benefitted from that surrounding surplus water and they were able to even fully close the FCs in the good rainfall year 2021. The highly significant peak in the test statistic g1,1+2(r)–g2,1+2(r) was strongest for the Jag-1 plot, which also had the highest proportion of closing FCs (Fig. 5). The amplitude of the peak in the g-function was lowest for the Jag-3 plot, which also had the lowest proportion of closing FCs. This underlines the strong density-dependent effects whereby the surrounding density of FC water reservoirs determines which of the FCs in a plot revegetate and which remain bare-soil gaps.

Likewise, the spatial position of opening FCs in 2022 and 2023, relative to the position of closing FCs, showed a similar trend. Opening FCs occurred in areas with lower local density of opening and closing FCs and thus in areas where there was relatively less soil water in the neighborhood. This density-dependent effect was again strongest for the Jag-1 plot which also had the highest proportion of opening FCs (Fig. 5). The effect was weaker and only significant for the Jag-2 plot in 2022, and not significant for the plot Jag-3, which had the lowest proportion of opening FCs.

These results on the spatio-temporal dynamics show that rainfall and soil moisture are the main drivers of the FC landscape phenomenon because revegetating FCs were located in areas where there is overall a higher density of FCs and thus where there is more soil water. Similarly, a recent global-scale analysis of related gap patterns in arid grass vegetation underlines that these patterns were associated with narrow and specific values of soil and climatic conditions (Guirado et al. 2023).

Conclusion

In this study, we investigated the spatio-temporal patterns of the Namibian fairy circles with regard to rainfall variability and soil–water infiltration. We have shown that FCs attain extremely regular, spatially periodic patterns, when rain water infiltrates quickly in the homogenous coarse sands of the Namib Desert. Under these conditions, the small-scale positive biomass-water feedbacks of the grasses result in highly homogeneous and evenly spaced patterns at the landscape scale. The bare-soil gaps of the fairy circles occur only in strongly water-limited regions along the Namib where MAP is less than 150 mm (Cramer and Barger 2013). They are thus an expression that there is not enough water on the landscape scale to allow a continuous vegetation cover. But after a longer drought followed by ample rainfall, a large proportion of FCs revegetates while new FCs hardly form. Finally, we have shown that this revegetation and conversely, the opening of the FCs, is a highly density-dependent process, because soil–water diffusion from the FC water reservoirs to the surrounding areas determines which of the FCs revegetate and which open up again to become bare-soil gaps. Besides previous in-situ studies (Cramer et al. 2017; Ravi et al. 2017; Getzin et al. 2022) and remote sensing studies (Getzin et al. 2015a, 2019; Zelnik et al. 2015), this new research supports the view that the fairy circles of Namibia are induced by plant self-organization mediated by rainfall and soil properties whereby the grasses act as ecosystem engineers to form this emergent vegetation gap pattern.