Article | Published:

# Plant spatial patterns identify alternative ecosystem multifunctionality states in global drylands

Nature Ecology & Evolution volume 1, Article number: 0003 (2017) | Download Citation

## Abstract

The response of drylands to environmental gradients can be abrupt rather than gradual. These shifts largely occur unannounced and are difficult to reverse once they happen; their prompt detection is of crucial importance. The distribution of vegetation patch sizes may indicate the proximity to these shifts, but the use of this metric is hampered by a lack of large-scale studies relating these distributions to the provision of multiple ecosystem functions (multifunctionality) and comparing them to other ecosystem attributes, such as total plant cover. Here we sampled 115 dryland ecosystems across the globe and related their vegetation attributes (cover and patch size distributions) to multifunctionality. Multifunctionality followed a bimodal distribution across our sites, suggesting alternative states in the functioning of drylands. Although plant cover was the strongest predictor of multifunctionality when linear analyses were used, only patch size distributions reflected the bimodal distribution of multifunctionality observed. Differences in the coupling between nutrient cycles and in the importance of self-organizing biotic processes characterized the two multifunctionality states observed. Our findings support the use of vegetation patterns as indicators of ecosystem functioning in drylands and pave the way for developing effective strategies to monitor desertification processes.

The development of early warning signals to detect the onset of regime shifts in marine and terrestrial ecosystems has received increasing attention during the last decade1,2. Although rarely validated in natural ecosystems3, theoretical models suggest that drylands, which occupy over 41% of the Earth’s surface and host 38% of the world’s human population4, are prone to regime shifts5,6 (for example, from functional to desertified states). The early detection of these regime shifts is particularly important in these ecosystems, as desertification is a major environmental issue that affects more than 250 million people, especially in the developing world7.

Dryland perennial vegetation commonly forms isolated patches interspersed with bare soil; the size distributions of these patches are often characterized by heavy-tail distributions (that is, there are many small and a few very large patches8,​9,​10,​11). Such heavy-tail distributions commonly fit a power law function and have been suggested to be a consequence of plant–plant interactions and plant–soil feedback mechanisms5,9. Mathematical models predict that patch size distributions would deviate from a pure power law function with increasing external disturbances9,12. Thus, these deviations could indicate that an ecosystem is close to a regime shift, leading to drastic declines in its functioning9,12,13. However, empirical data showing how patch size distributions reflect ecosystem functioning in drylands is lacking. Most attempts to evaluate patch size distributions in the field have spanned a limited range of sites and environmental conditions10,12,14. Additionally, few studies have linked patch size distributions to ecosystem functioning or have compared their performance as indicators of ecosystem functioning with attributes such as vegetation cover14,​15,​16. These knowledge gaps raise doubts about which of the currently recommended management and monitoring tools (for example, plant cover17 or patch size distributions) are more suitable for detecting losses in ecosystem functioning, such as those caused by desertification18.

We used remote sensing and field data from a survey conducted in 115 drylands spanning four continents. We measured vegetation cover, patch size distribution and multifunctionality14,15, calculated as the average Z score of 16 soil variables (functions hereafter) related to carbon (C), nitrogen (N) and phosphorus (P) cycling (see Methods). The functions used are major determinants of soil fertility and plant productivity19,20 and are good indicators of ecosystem functioning21. First, we developed a continuous and general metric that can be used to characterize any heavy-tailed distribution and its adjustment to a power law function. Second, we identified two main types of patch size distributions in our data, on the basis of thresholds in their shape that compromise the scale-invariance of the distributions (a fundamental property of power law functions). Third, we evaluated the importance of aridity, plant cover and plant–plant interactions as drivers of these two types of patch size distributions across the sites studied. Finally, we compared the ability of plant patch size distributions and cover as predictors of multifunctionality in global drylands.

## Results

Image analyses (Methods, Supplementary Section 1) showed that the patch size distributions of all 115 sites were heavy-tailed with varying levels of curvature (Supplementary Fig. 1). In curved distributions, only a range of the patch sizes fits a power law. This range is hereafter referred to as the power law range (PLR) and was used as a proxy for the shape of the distribution (Supplementary Fig. 2) and to determine how well the distribution considered fitted a power law (Fig. 1b). The relationship between the PLR and the slope (α) of the power law (that is, the rate of decline in the number of patches with their sizes) of the fitted functions revealed the presence of two types of patch size distributions in the 115 sites studied (Fig. 1a): (i) sites where a large proportion of the distribution fitted a power law (PLR > 0.57, ‘PL-like sites’) and where α and the PLR were unrelated, as theoretically expected13,22 (Methods, Supplementary Section 3); and (ii) sites where distributions deviated strongly from pure power law functions (PLR < 0.57, ‘non-PL-like sites’) and where α and the PLR were significantly related. The threshold in the PLR identified was consistent when using other approaches, such as a comparison of the relative fit of the patch size distribution to pure power law versus lognormal functions (Fig. 1b) or the use of piecewise regressions to detect thresholds in the PLR–α relationship (Supplementary Section 3).

To disentangle the potential mechanisms underlying the differences between PL-like and non-PL-like sites, we developed structural equation models using the PLR and α as response variables and a number of covariates known to affect vegetation patterns in drylands, including perennial vegetation cover, aridity19 (defined as 1 − (precipitation/potential evapotranspiration)) and the frequency of positive plant–plant interactions8,13. In the PL-like sites, patch size distributions were driven by variations in plant–plant interactions and cover (Fig. 2b,d); in contrast, in the non-PL-like sites, patch size distributions were mainly driven by aridity (Fig. 2a,c).

We tested the relationships between patch size distribution or plant cover and multifunctionality using linear regressions. Total plant cover was a better predictor of multifunctionality than patch size distribution (Supplementary Table 1, Supplementary Figs 3a and 4). However, ecosystem attributes do not always vary linearly along environmental gradients1,23. Indeed, drylands are iconic examples of ecosystems whose response to environmental gradients can be abrupt rather than gradual, thereby shifting from one ecosystem state to another6,24,25. We therefore tested for the possible occurrence of several multifunctionality states on the basis of the frequency of the multifunctionality values in our data (assuming the most frequent to be more stable3). This analysis revealed a bimodal distribution of multifunctionality values in our sites (the Akaike information criterion (AIC) and Bayesian information criterion (BIC) values with one mode (respectively 173.5 and 179.3) were greater than with two modes (respectively 165.6 and 178.9, Fig. 3a), which can be interpreted as the existence of two multifunctionality alternative states in global drylands3.

To investigate to what extent plant cover and the PLR were related to the bimodal distribution of multifunctionality observed, we obtained a map depicting the trend in the number and value of estimated alternative states (local minima, as in Fig. 3a) along the aridity gradient studied (Fig. 4; Methods). Cover and the PLR showed only one mode for this gradient. However, although there was a smooth decrease in cover with aridity, the PLR showed an abrupt decrease that preceded the co-occurrence of the two multifunctionality states observed (Fig. 4). This drop in the PLR concurs with the shift in patch size distributions observed from the PL-like to non-PL-like sites and reflects contrasting drivers of plant spatial patterns (Fig. 2). Indeed, the type of patch size distribution was marginally associated with the two multifunctionality states observed (χ2 = 3.70, P = 0.05) and this association was significant at aridity levels preceding the two multifunctionality states (Supplementary Fig. 9). These results were robust to the approach used to estimate multifunctionality (Supplementary Figs 5 and 6) and to the number of sites considered (Supplementary Section 5); they were not confounded by the effects of aridity on both the PLR and multifunctionality (Supplementary Figs 7–9).

To further understand the mechanisms driving the two multi­functionality states observed, we calculated the correlations between all pairs of ecosystem functions examined. In the high multifunctionality sites, these functions were strongly correlated and phosphorus functions were loosely linked to other functions (Fig. 3b). In the low multifunctionality sites, organic C and total N contents were the main drivers of multifunctionality and phosphorus functions were strongly linked to other functions (Fig. 3b).

## Discussion

Our results indicate that the PL-like and non-PL-like patch size distributions (Fig. 2) were driven by biotic (plant–plant interactions, cover) versus abiotic (climate) drivers, respectively8,9,12,13. These findings provide empirical evidence linking plant–plant interactions to patch size distributions in drylands, as predicted by theoretical models8,9,12. Additionally, the plant cover of PL-like sites showed a strong negative relationship with aridity (Fig. 2b), as expected in drylands26, whereas these variables were unrelated in non-PL-like sites (Fig. 2a). The uncoupling between cover and aridity found in the non-PL-like sites suggests that plant productivity at these sites may be driven by factors other than water (for example, soil nutrients, grazing or fire regimes).

When using linear statistical models, cover explained multifunctionality metrics better than the shape of patch size distributions (measured as the PLR), extending previous findings14,15 to drylands worldwide. However, the bimodal nature of multifunctionality found in our study (Fig. 3) reveals the need for metrics that are able to detect these alternative states; these states may influence the relationship between ecosystem functioning and monitoring metrics, such as vegetation cover or patch size distribution. Indeed, cover was associated with multifunctionality in the low, but not in the high, multifunctionality state (Supplementary Fig. 3a), which casts doubts about the suitability of plant cover to reflect alternative functional states. The fact that the PLR exhibited an abrupt drop in the range of aridity values where the two multifunctionality states co-occur (Fig. 4), together with the association between the type of patch size distribution and the multifunctionality states, shows that vegetation spatial organization might reflect multifunctionality states. Changes in patch size distributions are not only related to the different drivers of ecosystem dynamics, but also indicate a spatial reorganization of the existing plant cover. This spatial reorganization is directly linked to the processes influencing ecosystem functioning in drylands, such as soil erosion27, and can reflect important variations in the structure of plant communities unrelated to variations in vegetation cover. For example, a replacement in the dominant plant functional traits28 can affect nutrient cycling and the patch size distribution via litter contributions to the soil and species interactions29. However, these functional changes might not be associated with changes in plant cover. We also found that the PLR was negatively related with aridity for the sites within the high multifunctionality state, but cover did not respond to increases in aridity in these cases (Supplementary Fig. 3b,c). This result further supports the potential of patch size distributions to anticipate discontinuous changes in ecosystem functioning, if these changes are triggered by increases in aridity or related disturbances (for example, a higher sensitivity to grazing or changes in the importance of fires). Regardless of the mechanisms involved, our results clearly show that although plant cover is the best linear predictor of multifunctionality in drylands, patch size distribution is better at identifying alternative states of this variable.

Contrasting correlation patterns of soil nutrients in low and high multifunctionality states observed allowed us to gain insights on the functional changes that occur between them. In low multifunctionality sites, total organic C and total N were the main drivers of the rest of soil nutrients and multifunctionality itself (Fig. 2b). As changes in soil organic C and total N contents in drylands are largely driven by the activity and abundance of plants19,30, our results suggest an increasing importance of biotic components as the drivers of biogeochemical cycling in the low multifunctionality sites19. Indeed, in the high multifunctionality sites, organic C and total N may be less limiting due to the relatively high inputs from biological activity, in accordance to the biotic control observed in their associated PL-like patch size distributions. Therefore, non-biotically driven functions, such as available P, become important drivers of functioning in the high multifunctionality sites. The aridity value at which both multifunctionality states co-occur is around 0.7 (range 0.6–0.8; Fig. 4a), which matches a shift from positive to negative net N inputs into the soil found in Chinese drylands30. Our findings extend this result by showing that discontinuities in multifunctionality states might be related to the uncoupling of processes related to the cycling of major elements and that these discontinuities are reflected by variations of plant spatial patterns.

Our results have important implications for the study of dryland responses to climate change. They suggest that ecosystems with aridity levels between 0.75 and 0.80 (in the transition zone between semi-arid and arid drylands) may undergo different multifunctionality states, with large contrasts in soil fertility, nutrient capture and nutrient cycling. A key result of our study is that these states are associated with different distributions of vegetation patch sizes, which are related to important changes in the way dryland ecosystems are organized. By providing an empirical link between plant spatial patterns and multifunctionality, our study suggests that spatial patterns might be used as indicators of drastic variations in ecosystem functioning9,12,13. Additional studies evaluating temporal trends in both the spatial structure of vegetation and multifunction­ality are needed to further investigate the role of patch size distributions as early warning signals of regime shifts in terrestrial ecosystems. Our results pave the way for developing effective indicators to detect such shifts and new restoration tools that consider the nonlinear nature of multifunctionality in drylands.

## Methods

### Study site and data collection

We used a database that contains vegetation and soil data of 224 drylands20, as well as data from six additional dryland sites surveyed during 2013 in Botswana using the same methodology. We retained the sites that we could source Google Earth (https://earth.google.com/) or VirtualEarth (http://www.bing.com/maps) images with enough resolution to allow visual identification of vegetation patches. The 115 sites used were grasslands or shrublands with discontinuous perennial plant cover and were located in 13 countries. The sites differed widely in their abiotic (elevation, temperature and precipitation) and biotic (cover and number of species) attributes.

At each site, we established a 30 m × 30 m plot representative of the vegetation present in the area and estimated plant cover using the line intercept method31 (more details in refs 19,20). We measured the frequency of positive plant–plant interactions as the proportion of all species present in the community that were more associated with a given nurse than expected by chance32,​33,​34,​35. We took five soil cores (0–7 cm depth) in areas devoid of perennial vegetation during the dry season. Finally, we obtained values of the aridity index36 (AI = precipitation/potential evapotranspiration), which was derived using data interpolations provided by Worldclim37. To facilitate the interpretation of the results, we calculated the aridity level19 of each site (1 − AI); higher values of this aridity level indicate drier conditions.

It must be noted that we use a space-by-time substitution approach, which has been shown to reflect changes in biotic attributes and ecosystem functions such as those studied here38. However, the approach should not be considered as evidence of more dynamic processes, such as desertification.

### Assessing multifunctionality

We measured 16 soil variables related to the C (organic C, β-glucosidase activity, pentoses, hexoses, aromatic compounds and phenols), N (nitrate, ammonium, total N, potential N transformation rate, amino acids and proteins) and P (available P, phosphatase activity, inorganic P and total P) cycles. The variables are ecosystem functions39 (for example, the potential N transformation rate) or variables related to key properties/processes40 (for example, organic C, total N and soil enzymes). The variables have been used in previous studies of ecosystem functioning and multifunctionality41,​42,​43,​44,​45 and are considered to be critical determinants of soil fertility and ecosystem functioning in natural and semi-natural drylands26. Most of these functions are also considered to support other ecosystem services, such as the production of plant biomass and livestock4,21,46. Additionally, variables such as those used here have been recommended for studying long-term ecosystem changes and resource collapses, because they have long turnover times7 and, therefore, are less sensitive to interannual variations in climate. For simplicity, all of the soil variables measured are called ‘functions’42. After field collection, the soil samples were sieved (2 mm mesh), air-dried for one month and stored for laboratory analyses19,20. To standardize soil analyses, dried soil samples from all the countries were shipped to Spain, where they were analysed following the same protocols and in the same laboratories (described in refs 19,20).

We calculated multifunctionality using the M index20, obtained as the average Z score across functions. This index has good statistical properties20 and is increasingly used in multifunctionality studies47,​48,​49,​50,​51,​52. The index is an averaging method and attempts to summarize multifunctionality so that high values of M mean high values of many of, but not necessarily all, the functions included. Thus, high values of all our functions have been associated with more functional ecosystems; because more functional ecosystems may depend on the ecosystem or function considered, we also report results on each individual function to ease interpretation of our findings (Supplementary Figs 4 and 6). It must be noted that M cannot distinguish between (i) two functions with similar values; and (ii) one function with high values and another function with low values (suggesting trade-offs between two given functions)53. To account for this issue, we also estimated multifunctionality using a multiple-threshold approach53; this evaluated the number of functions that simultaneously exceed multiple critical thresholds, calculated as a proportion from the highest (top 5%) performing sites for each function. Results using this approach were very similar to those obtained using M (Supplementary Figs 4 and 6) and thus are not further discussed here.

### Characterizing the patch size distributions

In most cases, the 30 m × 30 m plot surveyed in the field did not contain enough plant patches to obtain a reliable estimation of their distribution54. Therefore, we used satellite images to extract plant patches from the study sites. As we could only use data for sites from which good quality images could be obtained (resolution ≤ 0.3 m per pixel; with no cloud and a homogeneous surrounding landscape; see details in Supplementary Information), the number of sites for this study was reduced from 230 to 127. For each study site, we collected information from three 50 m × 50 m plots that were extracted from the aerial images; one of these plots was centred on the 30 m × 30 m field plot surveyed in the field and the other two plots were located nearby. This allowed us to validate cover estimates obtained from remote sensing with those measured in the field.

We used the k-mean classification approach55,​56,​57 implemented in Matlab58, which partitions the pixels of the picture in clusters according to their luminance intensity (using a monochromatic version of the image). We used 30 clusters, ordering them from 1 (darkest pixels only) to 30 (the entire image). We classified the images by selecting the luminance threshold (from 1 to 30) able to detect all the vegetation pixels of the image by using the graythresh and im2bw functions from Matlab (Supplementary Information). We then visually assessed whether the identified threshold was appropriate; if not (17.4% of the images), the threshold was adjusted according to expert knowledge. The cover estimated from the image was then compared with the cover measured in the field. We analysed the correlation between estimated (images) and measured (field) cover; to obtain a Pearson’s correlation of r > 0.7 (a threshold commonly used for assuming strong correlation between variables59), we sequentially discarded the sites for which the estimated cover deviated most from that measured in the field. This reduced the total number of sites to 115 for further analyses.

For each site, we extracted all the patches and their sizes in each of the 50 m × 50 m image plots after classification, pooled all the patches for a given site and fitted a power law to their distributions. We obtained the two main parameters of power law distributions according to the equation60,61: $(1)p(x)=α−1xmin(xxmin)−α$

where x represents the patch size and p(x) describes the frequency of patches of a certain size. This equation represents the probability density function (PDF) of a power decay. The parameters of the distribution are xmin, the minimum patch size from which the fit to a power law starts (below that point data are discarded from the fitting procedure) and α, the rate of decay of frequency with patch sizes. When p(x) and x are log-transformed, the inverse cumulative distribution (that is, the frequency of patches larger than a certain size as a function of size) of a pure power law would appear as a straight line with a negative slope (Supplementary Fig. 1). The approach used here calculates α using a maximum likelihood approach60 and estimates xmin by comparing differences in the relative fitting of cumulative distribution functions (using the Kolmogorov–Smirnoff statistic62, KS) of subsets of data with increasing xmin. The KS statistic allows such comparison, which is possible even with samples of the same patch size original distribution that differ in their N (caused by a different xmin depending on the function adjusted). This statistic simply needs to be minimized for a given combination of xmin and α, which happens in the combination that best minimizes both statistical fluctuations (estimated xmin > real xmin) and model deviations from proper fitting (estimated xmin < real xmin). The method allows the comparison of samples with different numbers of patches, provided that the function to be fitted is the same in the different subsamples. The approach allows fitting a power law function to all heavy-tail distributions, including lognormal or truncated power laws, as even in these cases a fraction of the distributions follow a power law. Sometimes the range of data remaining after discarding patch sizes lower than xmin is not representative of the observed patch size distribution, especially when the patch size distribution is curved and best fits a lognormal function. We called this range of patch sizes (where power laws can be fitted within a given distribution) the power law relative range (PLR). To obtain an estimation of this metric, we used the following equation: $(2)PLR=1−log10[xmin]−log10[xsmallest]log10[xmax]−log10[xsmallest]$

where, xsmallest is the size of the smallest patch and xmax the size of the largest patch in the image. The PLR theoretically varies from 1 (all data fitted to a power law function) to 0 (no data fit a power law function). The PLR is related to the shape of the distribution (understood as the level of curvature, Supplementary Fig. 2) and thereby to the goodness of fit to a power law (Fig. 1b), but is not exclusive to power law distributions. That is, it may be used for other heavy-tailed distributions as well; for example simulated lognormal distributions fitted using this methodology had a PLR of around 0.3–0.4. The use of the PLR allowed us to: (i) compare all patch size distributions among our sites, which varied from power law to lognormal, using a standard methodology for all of them (see Supplementary Information, Supplementary Fig. 1); and (ii) produce general descriptors of all the patch size distributions evaluated, independent of whether they fitted better a power law or a lognormal function.

### Statistical analyses

#### Types of patch size distribution

The estimated α of the patch size distributions was found to be very similar across a number of sites in our data set (Fig. 1a). Because of theoretical predictions9 and the relative constancy of the values of α estimated in previous field studies8,​9,​10,​11, we did not expect α to a priori vary much between sites, most probably because the emergence of power laws is favoured by plant–plant facilitation mechanisms that underlie the processes of vegetation pattern formation in drylands8,13,22 (Supplementary Information). However, in a subset of sites characterized by low PLR values, we found a strong relationship between the PLR and α (Fig. 1a). Moreover, in those sites, the PLR was the strongest driver of α (see Fig. 2), meaning that the slope (α) was (almost exclusively) a consequence of how much the distribution deviates from a pure power law. These results suggest that two ranges of the PLR are defining two types of distribution. To split the data set in two subsets according to the relationship found between the PLR and α, we performed linear regressions to subsets of the data by sequentially discarding the sites with a lower PLR. When the relationship between the PLR and α became non-significant (P > 0.05), we interpreted it as the separation between these two subsets of data. The threshold identified by this methodology was very similar to that found when comparing the relative fitting of pure power laws (without xmin, that is, fitted to all the patches of the data) versus the lognormal distribution (Fig. 1b). Other methods to subset our data into two types of patch size distribution, on the basis of piecewise regressions of the PLR versus α, also yielded consistent thresholds to the one found here (Supplementary Information).

#### Drivers of patch size distributions

Modifications in the scale invariant properties of the patch size distribution might be linked to changes in the ecological processes driving them. To test this, we evaluated the responses of patch size distribution to changes in total plant cover and aridity using structural equation models63 (SEM). We built a model accounting for direct and indirect effects of aridity and cover (known to relate with9,14,64 or drive26 plant spatial patterns in drylands) on the PLR and α. Since we found a strong relationship between the PLR and α (Fig. 1a), we introduced a link between these variables. We performed a second set of models with the same structure, but also including the frequency of facilitative interactions (as these were not measured in all sites). Theoretically, facilitation is a major mechanism generating power law-like distributions13,22,65, although its role has never been empirically tested before in drylands at the global scale. To do this we used the subset of sites from which this information was available (70 sites; 30 for PL-like sites and 40 for non-PL-like sites). SEM analyses were performed using AMOS v.18 (SPSS, AMOS Development Corporation).

#### Relationships between PLR, cover and multifunctionality

Both the PLR and cover can be good indicators of changes in ecosystem functioning14,15. To test which one is a better indicator of multifunctionality in our data, we first performed a simple correlation between all functions and M versus the PLR and cover separately. Then, we calculated a partial correlation for each function versus the PLR controlled by cover (see Supplementary Table 1, Supplementary Fig. 4).

#### Bimodality of multifunctionality

To test whether multifunctionality showed multiple modes in the sites studied, we used Gaussian mixture models analysis66. This technique calculates the BIC and AIC metrics for either one or two mode distributions fitted to the data. The minimum AIC/BIC value corresponds to the most probable number of modes (that is, Gaussian distributions within the data) of the distribution. We performed this analysis using the gmdistribution.fit function in Matlab.

If we consider the observable system to be dynamically coherent (that is, to always tend into a steady state over time), a collection of snapshots of this system will reveal less frequent values of non-stable states, although values close to stability will appear more often3,67. This implies that a surrogate of the dynamic potential of the system (interpretable as the ‘odds’ of change of the system as a function of the state variable) might be derived directly from the PDF of the variable of interest (that is, multifunctionality), as: $(3)U′=−σ22log(PDF)$

being, U′ the estimated potential and sigma the level of noise of the system and where the PDF is empirically derived from the data set. By calculating the scaled potential (U/σ2), we do not need to estimate the level of noise of the system. We obtained the PDF using the Matlab function ksdensity, with a standard bandwidth (h = 1.06  s/n0.2, where s is the standard deviation of the data and n is the number of data points). We used equation (3) to obtain the potential (Fig. 3a). This potential represents an analogy of dynamical stability in the system, in which local minima are often interpreted as stable states (see details in Supplementary Section 4).

To test the robustness of our results regarding the two alternative states in multifunctionality, we performed three additional sensitivity analyses (Supplementary Section 5, Supplementary Figs 5–8). These analyses confirmed that the bimodal pattern of multifunctionality was: (i) consistent regardless of the approach used for measuring multifunctionality; (ii) not a consequence of the subset of sites for which we could find good quality images; and (iii) not confounded by the distribution of aridity or any other predictor.

#### Structure of relationships between functions by multifunctionality state

We assessed the linear correlations between each individual function and between the functions and our overall multifunctionality metric, in each one of the two multifunctionality states found (see Supplementary Section 6 for rationale) (Fig. 3b). This allowed us to examine the most important (linked) components of ecosystem functioning and their relative contribution to the variation of M in the two multifunctionality states.

#### Stability landscapes of multifunctionality, PLR and cover

The evidence of a bimodal pattern in the sites studied (Fig. 3a) points to the presence of two alternate multifunctionality states in the drylands. Thus, a good predictor of multifunctionality needs to account for these discontinuous changes other than linearly and continuously predict multifunctionality. We evaluated the response of plant cover and patch size distribution to changes in aridity and compared their responses to the two multifunctionality alternative states observed. We first investigated if aridity was the trigger for such discontinuous changes in multifunctionality by sequentially obtaining the potentials of multifunctionality throughout the transformation of its PDFs into potential dynamical curves67. We took the 40 least arid sites and plotted their dynamical energy potential curve. Then, we sequentially changed the subset of plots by adding the next more arid plot and discarding the least arid one (total number of transits = 76). Our analyses show how the potential of multifunctionality changes throughout aridity in a tri-dimensional space, which is a reconstruction of the theoretical potential landscape through aridity. In observing this tri-dimensional space from above, in two dimensions, we obtained Fig. 4a, which represents a map of the expected trends of the alternative states through aridity. This figure is a reconstruction of the way multifunctionality would change along an increasing aridity gradient, if it was constrained to move only through stable states (understood as local minima in the derived potential); it illustrates a possible regime shift from one alternative state to another when aridity ranges between 0.6–0.8. In this range of aridity values, both states coexist. We conducted the same analyses using the PLR and cover, which allowed us to evaluate nonlinear and discontinuous trends in these relationships.

#### Associations between patch size distribution types and multifunctionality states

We wanted to assess whether the two major classes of patch size distributions identified (PL-like and non-PL-like sites; Fig. 1) were related to the multifunctionality states (M) found (Fig. 3a). We first classified our sites according to these states, considering high and low functional sites as those in which M was higher and lower than the unstable state (M ≈ −0.06; understood as the maximum in the potential between the two alternative states, see Fig. 3a), respectively. Second, we performed a χ2 test using SPSS v. 20 (IBM Corporation) between patch size distribution type (PL-like/non-PL-like) and multifunctionality type (high/low multifunctionality). We evaluated the association between these two variables across different levels of aridity. We performed the same χ2 test described above using a moving window through aridity. The sensitivity analyses discarded any confounding effects of aridity in this association, since the ability of the type of patch size distribution to identify the multifunctionality state peaked in the aridity levels corresponding to the shift between high and low multifunctionality (Supplementary Fig. 9, Supplementary Section 7).

### Data availability

The data generated and analysed in the current study are available from figshare (http://dx.doi.org/10.6084/m9.figshare.2751904) as are the Matlab and R scripts (http://dx.doi.org/10.6084/m9.figshare.3486164), with an additional document explaining how they were used in the manuscript.

How to cite this article: Berdugo, M., Kéfi, S., Soliveres, S. & Maestre, F. T. Plant spatialpatterns identify alternative ecosystem multifunctionality states in global drylands. Nat. Ecol. Evol. 1, 0003 (2017).

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## Acknowledgements

We thank D. Eldridge, E. Allan and M. Boer for comments and inputs on earlier versions of this manuscript, C. Xu for discussions during the processing of the images and all the members of the EPES-BIOCOM network for the collection of field data. This work was funded by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013) and ERC grant agreement no. 242658 (BIOCOM). M.B. was supported by a FPU fellowship from the Spanish Ministry of Education, Culture and Sports (ref. AP2010-0759). F.T.M. acknowledges support from a Humboldt Research Award from the Alexander von Humboldt Foundation during writing of the manuscript. S.K. received funding from the European Union’s Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 283068 (CASCADE).

## Affiliations

1. ### Departamento de Biología y Geología, Física y Química Inorgánica, Escuela Superior de Ciencias Experimentales y Tecnología, Universidad Rey Juan Carlos, C/Tulipán s/n, Móstoles 28933, Spain

• Miguel Berdugo
•  & Fernando T. Maestre

• Sonia Kéfi
3. ### Institute of Plant Sciences, University of Bern, Altenbergrain 21, 3013 Bern, Switzerland

• Santiago Soliveres

## Authors

### Contributions

F.T.M. designed the study and coordinated field data acquisition. Data analyses were done by M.B., assisted by S.K. and S.S. The paper was written by M.B. and all authors substantially contributed to subsequent drafts.

### Competing interests

The authors declare no competing financial interests.

## Corresponding author

Correspondence to Miguel Berdugo.

## PDF files

1. 1.

### Supplementary information

Supplementary Figures 1–9, Supplementary Table 1, Supplementary Methods, Supplementary References