Modeling Dryland Landscapes

E. Meron

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 6, Issue: 1, page 163-187
  • ISSN: 0973-5348

Abstract

top
The discovery of nearly periodic vegetation patterns in arid and semi-arid regions motivated numerous model studies in the past decade. Most studies have focused on vegetation pattern formation, and on the response of vegetation patterns to gradients of the limiting water resource. The reciprocal question, what resource modifications are induced by vegetation pattern formation, which is essential to the understanding of dryland landscapes, has hardly been addressed. This paper is a synthetic review of model studies that address this question and the consequent implications for inter-specific plant interactions and species diversity. It focuses both on patch and landscape scales, highlighting bottom-up processes, where plant interactions at the patch scale give rise to spatial patterns at the landscape scale, and top-down processes, where pattern transitions at the landscape scale affect inter-specific interactions at the patch scale.

How to cite

top

Meron, E.. "Modeling Dryland Landscapes." Mathematical Modelling of Natural Phenomena 6.1 (2010): 163-187. <http://eudml.org/doc/197670>.

@article{Meron2010,
abstract = {The discovery of nearly periodic vegetation patterns in arid and semi-arid regions motivated numerous model studies in the past decade. Most studies have focused on vegetation pattern formation, and on the response of vegetation patterns to gradients of the limiting water resource. The reciprocal question, what resource modifications are induced by vegetation pattern formation, which is essential to the understanding of dryland landscapes, has hardly been addressed. This paper is a synthetic review of model studies that address this question and the consequent implications for inter-specific plant interactions and species diversity. It focuses both on patch and landscape scales, highlighting bottom-up processes, where plant interactions at the patch scale give rise to spatial patterns at the landscape scale, and top-down processes, where pattern transitions at the landscape scale affect inter-specific interactions at the patch scale. },
author = {Meron, E.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {vegetation patchiness; pattern formation; ecosystem engineer; woody-herbaceous systems; competition; facilitation; mathematical modeling},
language = {eng},
month = {6},
number = {1},
pages = {163-187},
publisher = {EDP Sciences},
title = {Modeling Dryland Landscapes},
url = {http://eudml.org/doc/197670},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Meron, E.
TI - Modeling Dryland Landscapes
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/6//
PB - EDP Sciences
VL - 6
IS - 1
SP - 163
EP - 187
AB - The discovery of nearly periodic vegetation patterns in arid and semi-arid regions motivated numerous model studies in the past decade. Most studies have focused on vegetation pattern formation, and on the response of vegetation patterns to gradients of the limiting water resource. The reciprocal question, what resource modifications are induced by vegetation pattern formation, which is essential to the understanding of dryland landscapes, has hardly been addressed. This paper is a synthetic review of model studies that address this question and the consequent implications for inter-specific plant interactions and species diversity. It focuses both on patch and landscape scales, highlighting bottom-up processes, where plant interactions at the patch scale give rise to spatial patterns at the landscape scale, and top-down processes, where pattern transitions at the landscape scale affect inter-specific interactions at the patch scale.
LA - eng
KW - vegetation patchiness; pattern formation; ecosystem engineer; woody-herbaceous systems; competition; facilitation; mathematical modeling
UR - http://eudml.org/doc/197670
ER -

References

top
  1. M. Shachak, B. Boeken, E. Groner, R. Kadmon, Y. Lubin, E. Meron, E.G. Neeman, A. Perevolotsky, Y. Shkedy, E. Ungar. Woody species as landscape modulators and their effect on biodiversity patterns. BioScience, 58 (2008), 209–221. 
  2. M. Scheffer, S. Carpenter, J.A. Foley, C. Folke, B. Walkerk. Catastrophic shifts in ecosystems. Nature, 413 (2001), 591–596. 
  3. J. von Hardenberg, E. Meron, M. Shachak, Y. Zarmi. Diversity of Vegetation Patterns and Desertification. Phys. Rev. Lett., 87 (2001), 198101. 
  4. M. Rietkerk, S.C. Dekker, P.C. de Ruiter, J. van de Koppel. Self-organized patchiness and catastrophic shifts in ecosystems. Science, 305 (2004), 1926–1029. 
  5. M. Loreau, S. Naeem, P. Inchausti, J. Bengtsson, J.P. Grime, A. Hector, D.U. Hooper, M.A. Huston, D. Raffaelli, B. Schmid, D. Tilman, D.A. Wardle. Biodiversity and Ecosystem Functioning: Current Knowledge and Future Challenges. Science, 294 (2001), 804–808. 
  6. Millennium Ecosystem Assessment. Ecosystems and Human Well-being: Desertification Synthesis. World Resources Institute, Washington, DC. 2005.  
  7. Millennium Ecosystem Assessment. Ecosystems and Human Well-being: Biodiversity Synthesis. World Resources Institute, Washington, DC. 2005.  
  8. N. Barbier, P. Coutron, J. Lejoly, V. Deblauwe, O. Lejeune. Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems. Journal of Ecology, 94 (2006), 537–547. 
  9. N. Barbier, P. Coutron, R. Lefever, V. Deblauwe, O. Lejune. Spatial decoupling of facilitation and competition at the origin of gapped vegetation patterns. Ecology, 89 (2008), 1521–1531. 
  10. I. Stavi, H. Lavee, E.D. Ungar, P. Sarah. Ecogeomorphic feedbacks in semiarid rangelands: A review. Pedosphere, 19 (2009) 217-229.  
  11. F. Borgogno, P. D’Odorico, F. Laio, L. Ridolfi. Mathematical models of vegetation pattern formation in ecohydrology. Reviews of Geophysics, 47 (2009), RG1005. 
  12. C. Valentin, J.M. d’Herbès, J. Poesen. Soil and water components of banded vegetation patterns. Catena, 37 (1999), 1–24. 
  13. V. Deblauwe, N. Barbier, P. Couteron, O. Lejeune, J. Bogaert. The global biogeography of semi-arid periodic vegetation patterns. Global Ecol. Biogeogr., 17 (2008), 715–723. 
  14. E. Gilad, J. von Hardenberg, A. Provenzale, M. Shachak, E. Meron. Ecosystem Engineers: From Pattern Formation to Habitat Creation. Phys. Rev. Lett., 93 (2004), 0981051. 
  15. E. Gilad, J. von Hardenberg, A. Provenzale, M. Shachak, E. Meron. A mathematical Model for Plants as Ecosystem Engineers. J. Theor. Biol., 244 (2007), 680–691. 
  16. E. Gilad, M. Shachak, E. Meron. Dynamics and spatial organization of plant communities in water limited systems. Theor. Pop. Biol., 72 (2007), 214–230. 
  17. A.Y. Kletter, J. von Hardenberg, E. Meron, A. Provenzale. Patterned vegetation and rainfall intermittency. J. Theor. Biol., 256 (2009), 574–583. 
  18. R. Matyssek, H. Schnyder, E.F. Elstner, J.C. Munch, H. Pretzsch, H. Sandermann. Growth and parasite defence in plants: the balance between resource sequestration and retention: in lieu of a guest editorial. Plant Biol., 4 (2002), 133-136. 
  19. P.M. Saco, G.R. Willgoose, G.R. Hancock. Eco-geomorphology of banded vegetation patterns in arid and semi-arid regions. Earth Syst. Sci.Hydrol., 11 (2007), 1717–1730. 
  20. S.E. Campbell, J.S. Seeler, S. Glolubic. Desert crust formation and soil stabilization. Arid Soil Res. and Rehab.3 (1989), 217–228. 
  21. N.E. West. Structure and function in microphytic soil crusts in wildland ecosystems of arid and semi-arid regions. Adv. Ecol. Res., 20 (1990), 179–223. 
  22. D.J. Eldridge, E. Zaady, M. Shachak. Infiltration through three contrasting biological soil crusts in patterned landscapes in the Negev, Israel. Catena, 40 (2000), 323–336. 
  23. S.C. Dekker, M. Rietkerk, M.F.P. Bierkens. Coupling microscale vegetation-soil water and macroscale vegetation-precipitation feedbacks in semiarid ecosystems. Global change biology, 34 (2007), 671–678. 
  24. S. Thompson, G. Katul, S. M. McMahon. Role of biomass spread in vegetation pattern formation within arid ecosystems. Water Resour. Res., 44 (2008), W10421. 
  25. R. Nathan, R. Casagrandi. A simple mechanistic model of seed dispersal, predation and plant establishment: Janzen-Connell and beyond. Journal of Ecology, 92 (2004), 733. 
  26. C.S. Holling. The functional response of invertebrate predators to prey density. Mem. Entomol. Soc. Canada, 48 (1966), 1–86. 
  27. M. Santillana, C. Dawson. A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations. Computational Geosciences, 14 (2010), 31–53. 
  28. J.L. Vázquez. The porous medium equation. Mathematical theory. Oxford University Press, Oxford, 2006.  
  29. E. Meron, E. Gilad, J. von Hardenberg, M. Shachak, Y. Zarmi. Vegetation Patterns Along a Rainfall Gradient. Chaos, Solitons and Fractals, 19 (2004), 367–376.  
  30. E. Meron, E. Gilad. Dynamics of plant communities in drylands: A pattern formation approach. In Complex Population Dynamics: Nonlinear Modeling in Ecology, Epidemiology and Genetics. Eds: B. Blasius, J. Kurths, and L. Stone, p. 49–76, World-Scientific, 2007.  
  31. M. Rietkerk, F. van den Bosch, J. van de Koppel. Site-specific properties and irreversible vegetation changes in semi-arid grazing systems. Oikos, 80 (1997), 241–252. 
  32. E. Meron, H. Yizhaq, E. Gilad. Localized structures in dryland vegetation: forms and functions. Chaos, 17 (2007), 037109. 
  33. M. Tlidi, R. Lefever, A. Vladimirov. Vegetation Clustering, Localized Bare Soil Spots and Fairy Circles. In Dissipative solitons: from optics to biology and medicine. Lecture Notes in Physics, vol. 751 Springer, 2008.  
  34. Y. Pomeau. Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D, 23 (1986), 3–11. 
  35. E. Knobloch. Spatially localized structures in dissipative systems: open problems. Nonlinearity, 21 (2008), T45-T60. 
  36. S. Kéfi, M. Rietkerk, C.L. Alados, Y. Pueyo, V.P. Papanastasis, A. ElAich, P.C. de Ruiter. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature, 449 (2007), 213–216. 
  37. T.M. Scanlon, K.C. Kelly, S.A. Levin, I. Rodriguez-Iturbe. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature, 449 (2007), 209–212. 
  38. J. von Hardenberg, A.Y. Kletter, H. Yizhaq, J. Nathan, E. Meron. Periodic vs. scale-free patterns in dryland vegetation. Proc. R. Soc. B, 277 (2010), 1771–1776. 
  39. H. Yizhaq, E. Gilad, E. Meron. Banded vegetation: Biological Productivity and Resilience. Physica A, 356 (2005), 139–144. 
  40. L.S. Tuckerman, D. Barkley. Bifurcation analysis of the Eckhaus instability. Physica D, 46 (1990), 57–86. 
  41. F.I. Pugnaire, M.T. Luque. Changes in plant interactions along a gradient of environmental stress. Oikos, 93 (2001), 42–49. 
  42. C. Holzapfel, K. Tielborger, H.A. Parag, J. Kigel, M. Sternberg. Annual plant-shrub interactions along an aridity gradient. Basic Appl. Ecol., 7 (2006), 268-279. 
  43. C.G. Jones, J.H Lawton, M. Shachak, Organisms as ecosystem engineers, Oikos, 69 (1994), 373–386. 
  44. C.G. Jones, J.H Lawton, M. Shachak. Positive and negative effects of organisms as ecosystem engineers. Ecology, 78 (1997), 1946–1957. 
  45. R.M. Callaway, L.R. Walker. Competition and facilitation: a synthetic approach to interactions in plant communities. Ecology, 78 (1997), 1958-1965. 
  46. F.T. Maestre, S. Bautista, J. Cortina. Positive, negative and net effects in grassŰshrub interactions in Mediterranean semiarid grasslands. Ecology, 84 (2003), 3186-3197. 
  47. C.M. Crain, M.D. Bertness M.D.. Ecosystem Engineering across Environmental Gradients: Implications for Conservation and Management. Bioscience, 56 (2006), 211–218. 
  48. See for example F. Ludwig, T.E. Dawson, H. Kroon, F. Berendse, H.H.T. Prins. Hydraulic lift in Acacia tortilis trees on an East African savanna. Oecologia, 134 (2003), 293-300. 
  49. E. Gilad. Mathematical models for vegetation patterns and biodiversity. Ph.D. thesis, Ben-Gurion University (2006).  
  50. E. Gilad, J. von-Hardenberg. A fast algorithm for convolution integrals with space and time variant kernels. Journal of Computational Physics, 216 (2006) 326–336.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.