Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A theoretical foundation for multi-scale regular vegetation patterns

Abstract

Self-organized regular vegetation patterns are widespread1 and thought to mediate ecosystem functions such as productivity and robustness2,3,4, but the mechanisms underlying their origin and maintenance remain disputed. Particularly controversial are landscapes of overdispersed (evenly spaced) elements, such as North American Mima mounds, Brazilian murundus, South African heuweltjies, and, famously, Namibian fairy circles5,6,7,8,9,10,11,12,13. Two competing hypotheses are currently debated. On the one hand, models of scale-dependent feedbacks, whereby plants facilitate neighbours while competing with distant individuals, can reproduce various regular patterns identified in satellite imagery1,14,15. Owing to deep theoretical roots and apparent generality, scale-dependent feedbacks are widely viewed as a unifying and near-universal principle of regular-pattern formation1,16,17 despite scant empirical evidence18. On the other hand, many overdispersed vegetation patterns worldwide have been attributed to subterranean ecosystem engineers such as termites, ants, and rodents3,4,7,19,20,21,22. Although potentially consistent with territorial competition19,20,21,23,24, this interpretation has been challenged theoretically and empirically11,17,24,25,26 and (unlike scale-dependent feedbacks) lacks a unifying dynamical theory, fuelling scepticism about its plausibility and generality5,9,10,11,16,17,18,24,25,26. Here we provide a general theoretical foundation for self-organization of social-insect colonies, validated using data from four continents, which demonstrates that intraspecific competition between territorial animals can generate the large-scale hexagonal regularity of these patterns. However, this mechanism is not mutually exclusive with scale-dependent feedbacks. Using Namib Desert fairy circles as a case study, we present field data showing that these landscapes exhibit multi-scale patterning—previously undocumented in this system—that cannot be explained by either mechanism in isolation. These multi-scale patterns and other emergent properties, such as enhanced resistance to and recovery from drought, instead arise from dynamic interactions in our theoretical framework, which couples both mechanisms. The potentially global extent of animal-induced regularity in vegetation—which can modulate other patterning processes in functionally important ways—emphasizes the need to integrate multiple mechanisms of ecological self-organization27.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Social-insect nest distributions, in theory and in nature.
Figure 2: Simulation of FC emergence from termite engineering and vegetation feedbacks.
Figure 3: FC life cycle in the coupled termite-vegetation model.
Figure 4: Predicted and observed regular patterning of FC matrix vegetation.

References

  1. Rietkerk, M. & van de Koppel, J. Regular pattern formation in real ecosystems. Trends Ecol. Evol. 23, 169–175 (2008)

    PubMed  Article  Google Scholar 

  2. Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461, 53–59 (2009)

    ADS  CAS  PubMed  Google Scholar 

  3. Pringle, R. M., Doak, D. F., Brody, A. K., Jocqué, R. & Palmer, T. M. Spatial pattern enhances ecosystem functioning in an African savanna. PLoS Biol. 8, e1000377 (2010)

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  4. Bonachela, J. A. et al. Termite mounds can increase the robustness of dryland ecosystems to climatic change. Science 347, 651–655 (2015)

    ADS  CAS  PubMed  Article  Google Scholar 

  5. Cramer, M. D. & Barger, N. N. Are mima-like mounds the consequence of long-term stability of vegetation spatial patterning? Palaeogeogr. Palaeoclimatol. Palaeoecol. 409, 72–83 (2014)

    Article  Google Scholar 

  6. Tschinkel, W. R. The life cycle and life span of Namibian fairy circles. PLoS ONE 7, e38056 (2012)

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  7. Juergens, N. The biological underpinnings of Namib Desert fairy circles. Science 339, 1618–1621 (2013)

    ADS  CAS  PubMed  Article  Google Scholar 

  8. Vlieghe, K., Picker, M., Ross-Gillespie, V. & Erni, B. Herbivory by subterranean termite colonies and the development of fairy circles in SW Namibia. Ecol. Entomol. 40, 42–49 (2015)

    Article  Google Scholar 

  9. Zelnik, Y. R., Meron, E. & Bel, G. Gradual regime shifts in fairy circles. Proc. Natl Acad. Sci. USA 112, 12327–12331 (2015)

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  10. Getzin, S. et al. Adopting a spatially explicit perspective to study the mysterious fairy circles of Namibia. Ecography 38, 1–11 (2015)

    Article  Google Scholar 

  11. Getzin, S. et al. Discovery of fairy circles in Australia supports self-organization theory. Proc. Natl Acad. Sci. USA 113, 3551–3556 (2016)

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  12. Cramer, M. D. & Barger, N. N. Are Namibian “fairy circles” the consequence of self-organizing spatial vegetation patterning? PLoS ONE 8, e70876 (2013)

    ADS  CAS  PubMed  PubMed Central  Article  Google Scholar 

  13. Fernandez-Oto, C., Tlidi, M., Escaff, D. & Clerc, M. G. Strong interaction between plants induces circular barren patches: fairy circles. Phil. Trans. R. Soc. A 372, 20140009 (2014)

    ADS  PubMed  Article  Google Scholar 

  14. Meron, E. Modeling dryland landscapes. Math. Model. Nat. Phenom. 6, 163–187 (2011)

    MathSciNet  Article  Google Scholar 

  15. Gilad, E., von Hardenberg, J., Provenzale, A., Shachak, M. & Meron, E. A mathematical model of plants as ecosystem engineers. J. Theor. Biol. 244, 680–691 (2007)

    MathSciNet  CAS  PubMed  Article  Google Scholar 

  16. Deblauwe, V., Couteron, P., Lejeune, O., Bogaert, J. & Barbier, N. Environmental modulation of self-organized periodic vegetation patterns in Sudan. Ecography 34, 990–1001 (2011)

    Article  Google Scholar 

  17. Getzin, S. et al. Clarifying misunderstandings regarding vegetation self-organisation and spatial patterns of fairy circles in Namibia: a response to recent termite hypotheses. Ecol. Entomol. 40, 669–675 (2015)

    Article  Google Scholar 

  18. Tschinkel, W. R. Experiments testing the causes of Namibian fairy circles. PLoS ONE 10, e0140099 (2015)

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  19. Levings, S. C. & Traniello, J. Territoriality, nest dispersion, and community structure in ants. Psyche (Stuttg.) 88, 265–319 (1981)

    Article  Google Scholar 

  20. Korb, J. & Linsenmair, K. E. The causes of spatial patterning of mounds of a fungus-cultivating termite: results from nearest-neighbour analysis and ecological studies. Oecologia 127, 324–333 (2001)

    ADS  PubMed  Article  Google Scholar 

  21. Grohmann, C., Oldeland, J., Stoyan, D. & Linsenmair, K. E. Multi-scale pattern analysis of a mound-building termite species. Insectes Soc. 57, 477–486 (2010)

    Article  Google Scholar 

  22. Juergens, N. et al. Weaknesses in the plant competition hypothesis for fairy circle formation and evidence supporting the sand termite hypothesis. Ecol. Entomol. 40, 661–668 (2015)

    Article  Google Scholar 

  23. Laurie, H. Optimal transport in central place foraging, with an application to the overdispersion of heuweltjies. S. Afr. J. Sci. 98, 141–146 (2002)

    Google Scholar 

  24. Ryti, R. T. & Case, T. J. The role of neighborhood competition in the spacing and diversity of ant communities. Am. Nat. 139, 355–374 (1992)

    Article  Google Scholar 

  25. Schuurman, G. & Dangerfield, J. M. Dispersion and abundance of Macrotermes michaelseni colonies: a limited role for intraspecific competition. J. Trop. Ecol. 13, 39–49 (1997)

    Article  Google Scholar 

  26. Adams, E. S. & Tschinkel, W. R. Spatial dynamics of colony interactions in young populations of the fire ant Solenopsis invicta. Oecologia 102, 156–163 (1995)

    ADS  CAS  PubMed  Article  Google Scholar 

  27. Pringle, R. M. & Tarnita, C. E. Spatial self-organization of ecosystems: integrating multiple mechanisms of regular-pattern formation. Annu. Rev. Entomol. 62, 359–377 (2017)

    CAS  PubMed  Article  Google Scholar 

  28. Juergens, N. Exploring common ground for different hypotheses on Namib fairy circles. Ecography 38, 12–14 (2015)

    Article  Google Scholar 

  29. Thorne, B. L. & Haverty, M. I. A review of intracolony, intraspecific, and interspecific agonism in termites. Sociobiology 19, 115–145 (1991)

    Google Scholar 

  30. Liu, Q.-X. et al. Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems. Nature Commun. 5, 5234 (2014)

    ADS  CAS  Article  Google Scholar 

  31. Collins, N. M. Populations, age structure and survivorship of colonies of Macrotermes bellicosus (Isoptera: Macrotermitinae). J. Anim. Ecol. 50, 293–311 (1981)

    Article  Google Scholar 

  32. Holldobler, B. Territoriality in ants. Proc. Am. Phil. Soc. 123, 211–218 (1979)

    Google Scholar 

  33. Adams, E. S. Territory size and shape in fire ants: a model based on neighborhood interactions. Ecology 79, 1125–1134 (1998)

    Article  Google Scholar 

  34. Darlington, J. P. The underground passages and storage pits used in foraging by a nest of the termite Macrotermes michaelseni in Kajiado, Kenya. J. Zool. 198, 237–247 (1982)

    Article  Google Scholar 

  35. Palmer, T. M. Wars of attrition: colony size determines competitive outcomes in a guild of African acacia ants. Anim. Behav. 68, 993–1004 (2004)

    Article  Google Scholar 

  36. Abe, T., Bignell, D. E. & Higashi, M. Termites: Evolution, Sociality, Symbioses, Ecology (Springer, 2000)

  37. Keller, L. Queen lifespan and colony characteristics in ants and termites. Insectes Soc. 45, 235–246 (1998)

    Article  Google Scholar 

  38. Gilad, E. & von Hardenberg, J. A fast algorithm for convolution integrals with space and time variant kernels. J. Comput. Phys. 216, 326–336 (2006)

    ADS  MathSciNet  MATH  Article  Google Scholar 

  39. Guevara, A. & Giordano, C. V. Hydrotropism in lateral but not in pivotal roots of desert plant species under simulated natural conditions. Plant Soil 389, 257–272 (2015)

    CAS  Article  Google Scholar 

  40. Illian, J., Penttinen, A., Stoyan, H. & Stoyan, D. Statistical Analysis and Modelling of Spatial Point Patterns (John Wiley, 2008)

  41. Baddeley, A., Rubak, E. & Turner, R. Spatial Point Patterns: Methodology and Applications with R (Chapman and Hall/CRC, 2015)

  42. Mugglestone, M. A. & Renshaw, E. Detection of geological lineation on aerial photographs using two-dimensional spectral analysis. Comput. Geosci. 24, 771–784 (1998)

    ADS  Article  Google Scholar 

  43. Couteron, P. & Lejeune, O. Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model. J. Ecol. 89, 616–628 (2001)

    Article  Google Scholar 

  44. Tschinkel, W. R. The foraging tunnel system of the Namibian desert termite, Baucaliotermes hainesi. J. Insect Sci. 10, 65 (2010)

    PubMed  PubMed Central  Google Scholar 

  45. Baker, P. B. & Haverty, M. I. Foraging populations and distances of the desert subterranean termite, Heterotermes aureus (Isoptera: Rhinotermitidae), associated with structures in southern Arizona. J. Econ. Entomol. 100, 1381–1390 (2007)

    PubMed  Article  Google Scholar 

  46. Jones, S. C. Colony size of the desert subterranean termite Heterotermes aureus (Isoptera: Rhinotermitidae). Southwest. Nat. 35, 285–291 (1990)

    Article  Google Scholar 

  47. Haagsma, K. A. & Rust, M. K. Colony size estimates, foraging trends, and physiological characteristics of the western subterranean termite (Isoptera: Rhinotermitidae). Environ. Entomol. 24, 1520–1528 (1995)

    Article  Google Scholar 

  48. Grace, J. K., Abdallay, A. & Farr, K. R. Eastern subterranean termite (Isoptera: Rhinotermitidae) foraging territories and populations in Toronto. Can. Entomol. 121, 551–556 (1989)

    Article  Google Scholar 

  49. Husseneder, C., Powell, J. E., Grace, J. K., Vargo, E. L. & Matsuura, K. Worker size in the formosan subterranean termite in relation to colony breeding structure as inferred from molecular markers. Environ. Entomol. 37, 400–408 (2008)

    PubMed  Article  Google Scholar 

  50. Wood, T. G. & Sands, W. A. in Production Ecology of Ants and Termites (ed. Brian, M. V. ) 245–292 (Cambridge Univ. Press, 1978)

  51. Matsuura, K. Colony-level stabilization of soldier head width for head-plug defense in the termite Reticulitermes speratus (Isoptera: Rhinotermitidae). Behav. Ecol. Sociobiol. 51, 172–179 (2002)

    Article  Google Scholar 

  52. Darlington, J. P. E. C. Turnover in the populations within mature nests of the termite Macrotermes michaelseni in Kenya. Insectes Soc. 38, 251–262 (1991)

    Article  Google Scholar 

  53. Hadley, N. F. & Szarek, S. R. Productivity of desert ecosystems. Bioscience 31, 747–753 (1981)

    Article  Google Scholar 

  54. Thorne, B. L., Breisch, N. L. & Muscedere, M. L. Evolution of eusociality and the soldier caste in termites: influence of intraspecific competition and accelerated inheritance. Proc. Natl Acad. Sci. USA 100, 12808–12813 (2003)

    ADS  CAS  PubMed  Article  PubMed Central  Google Scholar 

  55. Golodets, C. et al. Climate change scenarios of herbaceous production along an aridity gradient: vulnerability increases with aridity. Oecologia 177, 971–979 (2015)

    ADS  PubMed  Article  Google Scholar 

  56. Cain, M. L. & Damman, H. Clonal growth and ramet performance in the woodland herb, Asarum canadense. J. Ecol. 85, 883–897 (1997)

    Article  Google Scholar 

  57. Milton, S. J. & Dean, W. Disturbance, drought and dynamics of desert dune grassland, South Africa. Plant Ecol. 150, 37–51 (2000)

    Article  Google Scholar 

  58. Evangelides, C., Arampatzis, G. & Tzimopoulos, C. Estimation of soil moisture profile and diffusivity using simple laboratory procedures. Soil Sci. 175, 118–127 (2010)

    ADS  CAS  Article  Google Scholar 

  59. Danin, A. Plants of Desert Dunes (Springer, 2012)

  60. Sheffer, E., Yizhaq, H., Shachak, M. & Meron, E. Mechanisms of vegetation-ring formation in water-limited systems. J. Theor. Biol. 273, 138–146 (2011)

    MathSciNet  PubMed  MATH  Article  Google Scholar 

Download references

Acknowledgements

This research is a product of US National Science Foundation grant DEB-1355122 to C.E.T. and R.M.P., with seed funding provided by the Princeton Environmental Institute’s Grand Challenges Program. J.A.B. was supported by the Marine Alliance for Science and Technology for Scotland (MASTS) pooling initiative, funded by the Scottish Funding Council (HR09011) and contributing institutions. WorldView-2 satellite imagery was obtained through a grant from the DigitalGlobe Foundation to R.A.L. We thank the Government of Namibia, N. Oldendaal and NamibRand Nature Reserve (www.namibrand.org) for permission to conduct research and for providing rainfall data; A. Lamb, D. Doak, E. Lombardi, G. Barrenechea, P. Davies, S. Levin, R. Martinez-Garcia, I. Rodriguez-Iturbe, A. Sabatino, and J. Ware for discussions and assistance; I. Arndt for Australian termite-mound images used in analyses and shown in Extended Data Fig. 3; and F. Lanting for connecting us to NamibRand Nature Reserve and for use of the image in Fig. 3d.

Author information

Authors and Affiliations

Authors

Contributions

C.E.T., J.A.B., and R.M.P. conceived the study and developed the models, with input from E.S. J.A.B. performed point-pattern analyses and all simulations. E.S. performed Voronoi and Fourier transform analyses. J.A.G., T.C.C., and R.A.L. contributed field data and remote-sensing analyses. C.E.T., J.A.B., and R.M.P. drafted the paper, and all authors provided comments.

Corresponding authors

Correspondence to Corina E. Tarnita or Juan A. Bonachela.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks A. Hastings, N. Juergens, and M. Rietkerk for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Probability functions associated with conflicts in the termite model.

a, Probability for colony A and colony B to engage in a war as a function of each colony’s population biomass. b, If colonies A and B engage in a war, probability functions for colony A (red curve) or B (blue curve) to win the war as a function of the ratio of colony population biomass. When the two colonies have roughly the same biomass, they coexist (green area).

Extended Data Figure 2 Results of the termite self-organization model with a fixed resource density level, Pcst.

a, b, Temporal behaviour of mature colonies in the termite model for Pcst = 50 g m−2. a, Average diameter of mature nests (blue shading, ±1 s.d.). b, Average distance between nearest neighbours, (where neighbours are nests that share territory borders). Both observables reach a clear stationary state after a transient period of ~200 years. cf, Emergent behaviour for the colonies at the stationary state as a function of the (annually) available level of resources. c, Average mound diameter, which reflects foraging-territory area, decreases as resource availability increases. d, Mean nearest-neighbour distance also decreases with increasing resource density. e, Termite population density (number of individuals per square metre) increases with available resources. f, Average colony biomass density (individuals/colony) increases with available resource density, and reaches a saturation value around Bmax(1−m/μ) (see Supplementary Information). g, Frequency distribution of neighbour numbers from Voronoi analysis for the model with different resource densities (inset: mean number of neighbours). Higher resource densities result in a higher number of colonies (numbers in parentheses in the legend) and therefore more powerful results. Results are obtained by averaging over 100 simulations for each resource level; error bars, ±1 s.d.

Extended Data Figure 3 Average number of neighbours in various field locations.

Upper left panel: average number of neighbours (±1 s.d.) from Voronoi analysis of model and field data; number of nests at each location is shown in parentheses. All other panels: satellite imagery and/or photographs used for data analysis. Mounds are highlighted for ease of observation. If a white rectangle is present then only the points within the rectangle were analysed; otherwise, the whole image was analysed. All scale bars, 100 m. Aerial photographs of Amitermes mounds in Australia courtesy of I. Arndt. Pleiades-1 satellite imagery of Kenya copyright 2013 CNES/Astrium (GeoTIFF file supplied by Apollo Mapping, Boulder, Colorado, USA). Multispectral WorldView-2 satellite imagery of Mozambique courtesy of the DigitalGlobe Foundation. Google Earth satellite imagery: images for Arizona copyright 2012 DigitalGlobe, for Brazil copyright 2016 CNES/Astrium, and for Namibia copyright 2016 DigitalGlobe.

Extended Data Figure 4 Spatial point-pattern analyses of various field locations.

Left: pair correlation function as a function of distances between nests. Right: Ripley’s L function for the same examples. Ninety-five per cent pointwise simulation envelopes (shaded areas) were calculated using the default function from the R package spatstat. These envelopes allow us to reject the null hypothesis (complete spatial randomness) at a confidence level of 95%; thus, if the focal function (red line) falls out of the envelope for a given distance r, the function differs from the expectation for a completely random point distribution. Both sets of panels show peaks (left panels) or valleys (right panels) of regularity that indicate the presence of overdispersion for each of these examples. Note the different number of nests present in the samples from each location (Extended Data Fig. 3), which leads to different levels of noise in the calculation of the two statistics.

Extended Data Figure 5 Rainfall data from NamibRand Nature Reserve.

Top: 10-year time-series of monthly rainfall totals 2004–2014, averaged across multiple sites within NamibRand Nature Reserve (data provided by V. Hartung). Bottom: mean monthly rainfall (that is, averaged for each month across all years) in NamibRand Nature Reserve from 2004 to 2014 (green line, ± 1 s.d. in red) and proposed rainfall function (blue). The noise term included in Rainfall(t) (equation (5) in Methods) ensures that the rainfall function variability is high during the rainy season and low in the dry season, consistent with the data.

Extended Data Figure 6 Vegetation dynamics with and without termite engineering.

a, b, Comparison of the stationary pattern obtained with the vegetation model alone using (a) the original symmetric implementation for the root kernel and (b) the modified root kernel that is allowed to grow asymmetrically. c, d, Stationary pattern obtained with the naive setup (that is, one single, static colony in the centre of the system; constant rainfall); c, the resulting pattern using the original, symmetric root kernel; d, the pattern obtained when the asymmetric root system growth is implemented. e, f, Simulation run measuring the recovery time after the death of a colony in the coupled model with variable rainfall and asymmetric roots; e, system a few months before reaching stationarity; a ring of taller and denser vegetation is formed around the gap, and matrix vegetation is reaching its stationary clumpy distribution; f, several decades after colony death, the gap closes fully, and the remaining large matrix clumps disappear shortly thereafter. Brown, soil; green, vegetation. Colour intensity indicates vegetation density. Parameters are as in Extended Data Tables 1 and 2.

Extended Data Figure 7 The effect of decreasing termite-induced plant mortality or increasing rainfall in the coupled system.

When on-nest enhanced plant mortality is low and/or rainfall is high, vegetation growth outpaces termite engineering and, consequently, vegetation is found also on nests, disrupting (and for high enough rainfall values completely removing) the bare discs. a, Low mortality enhancement (ν = 1.1); b, intermediate mortality enhancement (ν = 1.25); values in a and b are both lower than in Extended Data Table 1 but have the same average rainfall as Extended Data Fig. 5; c, intermediate mortality enhancement (ν = 1.25) and average rainfall increased by 10%. Brown, soil; green, vegetation. Colour intensity indicates vegetation density. df, Corresponding underlying termite territories and nests. Blue dots, established nests; red dots, incipient nests (including the initial diggings of an alate pair, leading to occasionally high local densities as shown in f). Snapshots taken for a peak in vegetation after the system has reached stationarity. Rest of the parameters as in Extended Data Tables 1 and 2.

Extended Data Figure 8 Distribution of FC lifetimes measured in the coupled model.

For n = 9 replicates of the merged model, we kept track for ~300 years (until the end of the simulation) of 100 randomly selected FCs that were born after the stationary state (reached after ~100 years). Fifty-three of these FCs disappeared before the end of the simulation, allowing lifespan estimates for that subset. The resulting lifespans range from <5 years to >165 years, within reported estimates for Namibian FCs. Note that the distribution is truncated on the right tail owing to the limit of available simulation times; however, the overall shape of the distribution should not be strongly affected since such long-lasting FCs are very infrequent.

Extended Data Table 1 List of parameters for the termite model and associated literature sources7,29,31,35,37,44,45,46,47,48,49,50,51,52,53,54 and estimation procedures
Extended Data Table 2 List of parameters for the vegetation parts of the merged model and associated literature sources9,10,15,55,56,57,58,59,60

Related audio

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data and additional references. (PDF 687 kb)

Dynamics of the termite model.

Pink dots represent the center of young (incipient) colonies; blue dots represent the center of mature (established) colonies. Pale blue = foraging territory; darker blue = territory boundary. (MOV 3111 kb)

Dynamics of the termite-vegetation model from initial state to stationarity.

Starting with a single colony and a homogeneous distribution of vegetation, the coupled system self-organizes to patterned vegetation and regularly-organized FCs. The birth and death of colonies marks the emergence and disappearance of FCs. The bottom panel shows the rainfall availability (orange = data-inferred function; red point = instantaneous value of the stochastic rainfall function; grey = historical rainfall within the year). The middle panel, shows the dynamics of termite territories, which influence (and are influenced by) the dynamics of vegetation (top panel). Note the gaps matching the location of the centers; they are surrounded by taller vegetation, which defines the FCs. (MOV 29840 kb)

Close-up view of the coupled dynamics of colonies and vegetation from initial state to stationarity, focused on the matrix vegetation.

Territories expand and coexist, giving rise to neighboring FCs. Shrinkage of territories due to competition gives the opportunity for young colonies to establish in the available space. Matrix vegetation self-organizes in response to scale-dependent feedbacks along the differences in soil moisture induced by the FCs. Panels are same as in Supplementary Video 2. (MOV 26784 kb)

Comparison of the response of coupled (left) and pure-SDF (right) 880 systems to 10 consecutive dry years (20% reduction of average rainfall) followed by return to baseline rainfall.

The same reduction in rainfall leads the SDF system to almost complete extinction of vegetation, which remains in densities that are much lower than in the FC case. After rainfall returns to baseline, vegetation in both systems recovers, but the FC ecosystem is fully restored to stationarity much faster than the SDF system. After the FC system reaches stationarity, the video focuses on only the pure-SDF system. For both systems, dry years are represented by blue lines in the rainfall function plot; baseline years are represented by grey lines. Snapshots taken the same month each year, represented by the red point on the rainfall (bottom) panel. (MOV 10940 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Tarnita, C., Bonachela, J., Sheffer, E. et al. A theoretical foundation for multi-scale regular vegetation patterns. Nature 541, 398–401 (2017). https://doi.org/10.1038/nature20801

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature20801

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing