Multistability of model and real dryland ecosystems through spatial self-organization
- aMathematical Institute, Leiden University, 2300 RA Leiden, The Netherlands;
- bInternational Institute of Tropical Agriculture, BP 2008 (Messa), Yaounde, Cameroon;
- cCenter for Tropical Research, Institute of the Environment and Sustainability, University of California, Los Angeles, CA 90095;
- dDepartment of Environmental Sciences, Copernicus Institute, Utrecht University, 3508 TC Utrecht, The Netherlands;
- eDepartment of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research and Utrecht University, 4401 NT Yerseke, The Netherlands;
- fShanghai Key Laboratory for Urban Ecological Processes and Eco-Restoration, School of Ecological and Environmental Science, East China Normal University, 200241 Shanghai, China;
- gCenter for Global Change and Ecological Forecasting, School of Ecological and Environmental Science, East China Normal University, 200241 Shanghai, China;
- hInstitute for Mathematics, Carl von Ossietzky University Oldenburg, 26111 Oldenburg, Germany;
- iCentre d’Etudes Spatiales de la Biosphère, Université Toulouse III Paul Sabatier, Centre National d’Etudes Spatiales, Centre National de la Recherche Scientifique, Institut de Recherche pour le Développement, 31401 Toulouse, France
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Edited by Alan Hastings, University of California, Davis, CA, and approved September 18, 2018 (received for review March 19, 2018)

Significance
Today, vast areas of drylands in semiarid climates face the dangers of desertification. To understand the driving mechanisms behind this effect, many theoretical models have been created. These models provide insight into the resilience of dryland ecosystems. However, until now, comparisons with reality were merely visual. In this article, a systematic comparison is performed using data on wavenumber, biomass, and migration speed of vegetation patterns in Somalia. In agreement with reaction–diffusion models, a wide distribution of regular pattern wavenumbers was found in the data. This highlights the potential for extrapolating predictions of those models to real ecosystems, including those that elucidate how spatial self-organization of vegetation enhances ecosystem resilience.
Abstract
Spatial self-organization of dryland vegetation constitutes one of the most promising indicators for an ecosystem’s proximity to desertification. This insight is based on studies of reaction–diffusion models that reproduce visual characteristics of vegetation patterns observed on aerial photographs. However, until now, the development of reliable early warning systems has been hampered by the lack of more in-depth comparisons between model predictions and real ecosystem patterns. In this paper, we combined topographical data, (remotely sensed) optical data, and in situ biomass measurements from two sites in Somalia to generate a multilevel description of dryland vegetation patterns. We performed an in-depth comparison between these observed vegetation pattern characteristics and predictions made by the extended-Klausmeier model for dryland vegetation patterning. Consistent with model predictions, we found that for a given topography, there is multistability of ecosystem states with different pattern wavenumbers. Furthermore, observations corroborated model predictions regarding the relationships between pattern wavenumber, total biomass, and maximum biomass. In contrast, model predictions regarding the role of slope angles were not corroborated by the empirical data, suggesting that inclusion of small-scale topographical heterogeneity is a promising avenue for future model development. Our findings suggest that patterned dryland ecosystems may be more resilient to environmental change than previously anticipated, but this enhanced resilience crucially depends on the adaptive capacity of vegetation patterns.
Footnotes
- ↵1To whom correspondence should be addressed. Email: r.bastiaansen{at}math.leidenuniv.nl.
Author contributions: K.S., E.S., A.D., and M.R. initiated research; R.B., O.J., V.D., M.B.E., K.S., E.S., A.D., and M.R. designed research; S.M. and A.B. provided biomass data; V.D. performed remote sensing data analysis and statistical test; R.B. and O.J. analyzed data; R.B. and E.S. created model figures; R.B., V.D., M.B.E., and K.S. wrote the paper; and O.J., E.S., A.D., and M.R. provided feedback on draft versions of the manuscript.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1804771115/-/DCSupplemental.
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