Modeling Dryland Landscapes

E. Meron^1, 2

¹ Institute for Dryland Environmental Research, BIDR, Ben-Gurion University, Sede Boqer Campus, 84990, Israel
² Department of Physics, Ben-Gurion University, Beer-Sheva, 84105, Israel

Mathematical modelling of natural phenomena, Tome 6 (2011) no. 1, pp. 163-187

Résumé

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.

Détail

DOI : 10.1051/mmnp/20116109

Bibliographie

[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 2008 209 221

[2] M. Scheffer, S. Carpenter, J.A. Foley, C. Folke, B. Walkerk Catastrophic shifts in ecosystems Nature 2001 591 596

[3] J. Von Hardenberg, E. Meron, M. Shachak, Y. Zarmi Diversity of Vegetation Patterns and Desertification Phys. Rev. Lett. 2001

[4] M. Rietkerk, S.C. Dekker, P.C. De Ruiter, J. Van De Koppel Self-organized patchiness and catastrophic shifts in ecosystems Science 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 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 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 2008 1521 1531

[10] I. Stavi, H. Lavee, E.D. Ungar, P. Sarah Ecogeomorphic feedbacks in semiarid rangelands: A review Pedosphere 2009 217 229

[11] F. Borgogno, P. D’Odorico, F. Laio, L. Ridolfi Mathematical models of vegetation pattern formation in ecohydrology Reviews of Geophysics 2009

[12] C. Valentin, J.M. D’Herbès, J. Poesen Soil and water components of banded vegetation patterns Catena 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. 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. 2004

[15] E. Gilad, J. Von Hardenberg, A. Provenzale, M. Shachak, E. Meron A mathematical Model for Plants as Ecosystem Engineers J. Theor. Biol. 2007 680 691

[16] E. Gilad, M. Shachak, E. Meron Dynamics and spatial organization of plant communities in water limited systems Theor. Pop. Biol. 2007 214 230

[17] A.Y. Kletter, J. Von Hardenberg, E. Meron, A. Provenzale Patterned vegetation and rainfall intermittency J. Theor. Biol. 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. 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. 2007 1717 1730

[20] S.E. Campbell, J.S. Seeler, S. Glolubic Desert crust formation and soil stabilization Arid Soil Res. and Rehab. 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. 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 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 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. 2008

[25] R. Nathan, R. Casagrandi A simple mechanistic model of seed dispersal, predation and plant establishment: Janzen-Connell and beyond Journal of Ecology 2004

[26] C.S. Holling The functional response of invertebrate predators to prey density Mem. Entomol. Soc. Canada 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 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 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 1997 241 252

[32] E. Meron, H. Yizhaq, E. Gilad Localized structures in dryland vegetation: forms and functions Chaos 2007

[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 1986 3 11

[35] E. Knobloch Spatially localized structures in dissipative systems: open problems Nonlinearity 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 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 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 2010 1771 1776

[39] H. Yizhaq, E. Gilad, E. Meron Banded vegetation: Biological Productivity and Resilience Physica A 2005 139 144

[40] L.S. Tuckerman, D. Barkley Bifurcation analysis of the Eckhaus instability Physica D 1990 57 86

[41] F.I. Pugnaire, M.T. Luque Changes in plant interactions along a gradient of environmental stress Oikos 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. 2006 268 279

[43] C.G. Jones, J.H Lawton, M. Shachak Organisms as ecosystem engineers Oikos 1994 373 386

[44] C.G. Jones, J.H Lawton, M. Shachak Positive and negative effects of organisms as ecosystem engineers Ecology 1997 1946 1957

[45] R.M. Callaway, L.R. Walker Competition and facilitation: a synthetic approach to interactions in plant communities Ecology 1997 1958 1965

[46] F.T. Maestre, S. Bautista, J. Cortina Positive, negative and net effects in grassŰshrub interactions in Mediterranean semiarid grasslands Ecology 2003 3186 3197

[47] C.M. Crain, M.D. Bertness, M.D. Ecosystem Engineering across Environmental Gradients: Implications for Conservation and Management Bioscience 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 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 2006 326 336