Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T13:04:46.085Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling Dryland Landscapes

Published online by Cambridge University Press:  09 June 2010

E. Meron
Get access

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.

Keywords

vegetation patchinesspattern formationecosystem engineerwoody-herbaceous systemscompetitionfacilitationmathematical modeling
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 1: Instability and patterns. Issue dedicated to the memory of A. Golovin , 2011 , pp. 163 - 187
Copyright
© EDP Sciences, 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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