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Positive feedbacks promote power-law clustering of Kalahari vegetation

Abstract

The concept of local-scale interactions driving large-scale pattern formation has been supported by numerical simulations, which have demonstrated that simple rules of interaction are capable of reproducing patterns observed in nature1,2. These models of self-organization suggest that characteristic patterns should exist across a broad range of environmental conditions provided that local interactions do indeed dominate the development of community structure. Readily available observations that could be used to support these theoretical expectations, however, have lacked sufficient spatial extent or the necessary diversity of environmental conditions to confirm the model predictions. We use high-resolution satellite imagery to document the prevalence of self-organized vegetation patterns across a regional rainfall gradient in southern Africa, where percent tree cover ranges from 65% to 4%. Through the application of a cellular automata model, we find that the observed power-law distributions of tree canopy cluster sizes can arise from the interacting effects of global-scale resource constraints (that is, water availability) and local-scale facilitation. Positive local feedbacks result in power-law distributions without entailing threshold behaviour commonly associated with criticality. Our observations provide a framework for integrating a diverse suite of previous studies that have addressed either mean wet season rainfall or landscape-scale soil moisture variability as controls on the structural dynamics of arid and semi-arid ecosystems.

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Figure 1: Satellite observations of tree canopies and cluster size distributions.
Figure 2: Observations and models of tree canopy clustering.

References

  1. 1

    Solé, R. V. & Manrubia, S. C. Are rainforests self-organized in a critical state? J. Theor. Biol. 173, 31–40 (1995)

    Article  Google Scholar 

  2. 2

    Wooten, J. Local interactions predict large-scale pattern in empirically derived cellular automata. Nature 413, 841–844 (2001)

    ADS  Article  Google Scholar 

  3. 3

    Levin, S. A. The problem of pattern and scale in ecology. Ecology 73, 1943–1967 (1992)

    Article  Google Scholar 

  4. 4

    Katori, M., Kizaki, S., Terui, Y. & Kubo, T. Forest dynamics with canopy gap expansion and stochastic Ising model. Fractals 6, 81–86 (1998)

    Article  Google Scholar 

  5. 5

    Condit, R. et al. Spatial patterns in the distribution of tropical tree species. Science 288, 1414–1418 (2000)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Asner, G. P. & Warner, A. S. Canopy shadow in IKONOS satellite observations of tropical forests and savannas. Rem. Sens. Environ. 87, 521–533 (2003)

    ADS  Article  Google Scholar 

  7. 7

    Cale, W. G., Henebry, G. M. & Yeakley, J. A. Inferring process from pattern in natural communities. Bioscience 39, 600–605 (1989)

    Article  Google Scholar 

  8. 8

    Aguiar, M. R. & Sala, O. E. Competition, facilitation, seed distribution and the origin of patches in a Patagonian steppe. Oikos 70, 26–34 (1994)

    Article  Google Scholar 

  9. 9

    Archer, S. Tree-grass dynamics in a Prosopis-thornscrub savanna parkland: reconstructing the past and predicting the future. Ecoscience 2, 83–99 (1995)

    Article  Google Scholar 

  10. 10

    Plotkin, J. B., Chave, J. & Ashton, P. S. Cluster analysis of spatial patterns in Malaysian tree species. Am. Nat. 160, 629–644 (2002)

    Article  Google Scholar 

  11. 11

    Koch, G. W., Scholes, R. J., Vitousek, P. M. & Walker, B. H. The IGBP terrestrial transects: Science plan, Report No. 36 (International Geosphere-Biosphere Programme, Stockholm, 1995)

    Google Scholar 

  12. 12

    Scholes, R. J. et al. Trends in savanna structure and composition along an aridity gradient in the Kalahari. J. Veg. Sci. 13, 419–428 (2002)

    Article  Google Scholar 

  13. 13

    Caylor, K. K., Shugart, H. H., Dowty, P. R. & Smith, T. M. Tree spacing along the Kalahari Transect in southern Africa. J. Arid Environ. 54, 281–296 (2003)

    ADS  Article  Google Scholar 

  14. 14

    Pascual, M. & Guichard, F. Criticality and disturbance in spatial ecological systems. Trends Ecol. Evol. 20, 88–95 (2005)

    Article  Google Scholar 

  15. 15

    Stauffer, D. & Aharony, A. Introduction to percolation theory (Taylor and Francis, London, 1985)

    Book  Google Scholar 

  16. 16

    Keitt, T. H. Spectral representation of neutral landscapes. Landscape Ecol. 15, 479–493 (2000)

    Article  Google Scholar 

  17. 17

    Halley, J. M. et al. Uses and abuses of fractal methodology in ecology. Ecol. Lett. 7, 254–271 (2004)

    Article  Google Scholar 

  18. 18

    Guichard, F., Halpin, P. M., Allison, G. W., Lubchenco, J. & Menge, B. A. Mussel disturbance dynamics: Signatures of oceanographic forcing from local interactions. Am. Nat. 161, 889–904 (2003)

    Article  Google Scholar 

  19. 19

    Manrubia, S. C. & Solé, R. V. On forest spatial dynamics with gap formation. J. Theor. Biol. 187, 159–164 (1997)

    Article  Google Scholar 

  20. 20

    Malamud, B. D., Morein, G. & Turcotte, D. L. Forest fires: An example of self-organized critical behavior. Science 281, 1840–1842 (1998)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Grassberger, P. On a self-organized critical forest-fire model. J. Phys. A 26, 2081–2089 (1993)

    Article  Google Scholar 

  22. 22

    Holdo, R. M. Stem mortality following fire in Kalahari sand vegetation: effects of frost, prior damage, and tree neighbourhoods. Plant Ecol. 180, 77–86 (2005)

    Article  Google Scholar 

  23. 23

    Scanlon, T. M., Albertson, J. D., Caylor, K. K. & Williams, C. A. Determining land surface fractional cover from NDVI and rainfall time series for a savanna ecosystem. Rem. Sens. Environ. 82, 376–388 (2002)

    ADS  Article  Google Scholar 

  24. 24

    Pascual, M., Roy, M., Guichard, F. & Flierl, G. Cluster size distributions: signatures of self-organization in spatial ecologies. Phil. Trans. R. Soc. Lond. B 357, 657–666 (2002)

    Article  Google Scholar 

  25. 25

    Yeomans, J. M. Statistical mechanics of phase transitions (Clarendon Press, Oxford, 1992)

    Google Scholar 

  26. 26

    Wang, G. L. & Eltahir, E. A. B. Biosphere–atmosphere interactions over West Africa. II: Multiple climate equilibria. Q. J. R. Metereol. Soc. 126, 1261–1280 (2000)

    ADS  Article  Google Scholar 

  27. 27

    Scholes, R. J. & Archer, S. R. Tree–grass interactions in savannas. Annu. Rev. Ecol. Syst. 28, 517–544 (1997)

    Article  Google Scholar 

  28. 28

    Nathan, R. et al. Mechanisms of long-distance dispersal of seeds by wind. Nature 418, 409–413 (2002)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Schlesinger, W. H., Reikes, J. A., Hartley, A. E. & Cross, A. F. On the spatial pattern of soil nutrients in desert ecosystems. Ecology 77, 364–374 (1996)

    Article  Google Scholar 

  30. 30

    Molofsky, J., Bever, J. D. & Antonovics, J. Coexistence under positive frequency dependence. Proc. R. Soc. Lond. B 268, 273–277 (2001)

    CAS  Article  Google Scholar 

Download references

Acknowledgements

Funding for this research was provided by grants to Princeton University from the NSF, the Mellon Foundation and the NSF National Center for Earth Surface Dynamics, and a grant to the University of Virginia from NASA IDS.

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Correspondence to Todd M. Scanlon.

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Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Supplementary information

Supplementary Information

The file contains Supplementary Discussion which provides background information on the development of the cellular automata model ands shows results of the model with alternative weighting schemes (exponential and linear weighting) applied to the calculation of local densities; Supplementary Figure S1 showing location of the six sites along the Kalahari Transect where high-resolution satellite images were acquired and analyzed for this study and Supplementary Tables S1-S3 which list parameter values fit to a more general expression describing the cluster size distributions. (PDF 189 kb)

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Scanlon, T., Caylor, K., Levin, S. et al. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature 449, 209–212 (2007). https://doi.org/10.1038/nature06060

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