Plant spatial patterns identify alternative ecosystem multifunctionality ...

ARTICLES PUBLISHED: 9 JANUARY 2017 | VOLUME: 1 | ARTICLE NUMBER: 0003

Plant spatial patterns identify alternative ecosystem multifunctionality states in global drylands Miguel Berdugo1*, Sonia Kéfi2, Santiago Soliveres3 and Fernando T. Maestre1 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.

T

he 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 patches8–11). 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 cover14–16. 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’)

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. 2Institut des Sciences de l’Evolution, BioDICée team, Université de Montpellier, CNRS, IRD, EPHE, CC 065, Place Eugène Bataillon, Montpellier 34095, Cedex 5, France. 3Institute of Plant Sciences, University of Bern, Altenbergrain 21, 3013 Bern, Switzerland. *e-mail: [email protected] 1

NATURE ECOLOGY & EVOLUTION 1, 0003 (2017) | DOI: 10.1038/s41559-016-0003 | www.nature.com/natecolevol

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

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1.0 0.5 P 0.0

4

3

c With facilitation

2

1 Relative fitting to patch size distribution observed

b 600

R2 = 0.15 F1,113 = 20.02 P < 0.01

Best fitted to pure power law

300 0

Best fitted to lognormal

–300 –600 0.2

0.4

0.6

0.8

PLR

Figure 1 | Main types of patch size distribution found in global drylands. a, Relationship between α and the PLR in the 115 sites studied. Top: P value of the relationship (that is, linear regression) between the PLR and α, obtained by iteratively discarding sites with the lower PLR. The discontinuity point in the relationship between the PLR and α is indicated by the dashed red line (that is, where P > 0.05). b, Relative fit of patch size distributions to a power law versus a lognormal as a function of the PLR, measured as the differences of the log probability of a pure power law distribution (fitted on all patch sizes) and a lognormal distribution. The line represents the fitted linear regression, the statistics of which are shown. The dashed black line indicates no difference between the fit to a power law or lognormal function.

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 real xmin) and model deviations from proper fitting (estimated xmin 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:

(2)

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

U′ = −

σ2 log (PDF) 2

(3)

being, Uʹ 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).



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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.

Received 19 April 2016; accepted 11 October 2016; published 9 January 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).

Author 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.

Additional information

Supplementary information is available for this paper. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to M.B. How to cite this article: Berdugo, M., Kéfi, S., Soliveres, S. & Maestre, F. T. Plant spatial patterns identify alternative ecosystem multifunctionality states in global drylands. Nat. Ecol. Evol. 1, 0003 (2017).

Competing interests

The authors declare no competing financial interests.



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