1932

Abstract

Spatial patterns are ubiquitous in animate matter. Besides their intricate structure and beauty they generally play functional roles. The capacity of living systems to remain functional in changing environments is a question of utmost importance, but its intimate relationship to pattern formation is largely unexplored. Here, we address this relationship using dryland vegetation as a case study. Following a brief introduction to pattern-formation theory, we describe a mathematical model that captures several mechanisms of vegetation pattern formation and discuss ecological contexts that showcase different mechanisms. Using this model, we unravel the different vegetation patterns that keep dryland ecosystems viable along the rainfall gradient, identify multistability ranges where fronts separating domains of alternative stable states exist, and highlight the roles of front dynamics in mitigating or reversing desertification. The utility of satellite images in testing model predictions is discussed. An outlook on outstanding open problems concludes this paper.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-033117-053959
2018-03-10
2024-04-25
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/9/1/annurev-conmatphys-033117-053959.html?itemId=/content/journals/10.1146/annurev-conmatphys-033117-053959&mimeType=html&fmt=ahah

Literature Cited

  1. Blagodatski A, Sergeev A, Kryuchkov M, Lopatina Y, Katanaev VL. 1.  2015. PNAS 112:10750–55
  2. Ball P. 2.  2001. The Self-Made Tapestry: Pattern Formation in Nature Oxford, UK: Oxford Univ. Press
  3. Cross M, Hohenberg P. 3.  1993. Rev. Mod. Phys. 65:851
  4. Meron E. 4.  2015. Nonlinear Physics of Ecosystems Boca Raton, FL: CRC Press, Taylor & Francis Group
  5. Bodenschatz E, Pesch W, Ahlers G. 5.  2000. Annu. Rev. Fluid Mech. 32:709–78
  6. Winfree AT. 6.  1972. Science 175:634–36
  7. Vanag VK, Epstein IR. 7.  2001. Phys. Rev. Lett. 87:228301
  8. Saffman PG. 8.  1986. J. Fluid Mech. 173:73–94
  9. Trivedi R, Somboonsuk K. 9.  1985. Acta Metall 33:1061–68
  10. Firth W. 10.  1990. J. Mod. Opt. 37:151–53
  11. Umbanhowar P, Melo F, Swinney HL. 11.  1996. Nature 382:793–96
  12. Moloney JV, Newell AC. 12.  2003. Nonlinear Optics Boulder, CO: Westview
  13. Manneville P. 13.  2004. Instabilities, Chaos and Turbulence: An Introduction to Nonlinear Dynamics and Complex Systems London: Imp. Coll. Press
  14. Hoyle RB. 14.  2006. Pattern Formation: An Introduction to Methods Cambridge, UK: Cambridge Univ. Press
  15. Pismen L. 15.  2006. Patterns and Interfaces in Dissipative Dynamics. Springer Series in Synergetics Berlin/Heidelberg/New York: Springer
  16. Cross M, Greenside H. 16.  2009. Pattern Formation and Dynamics in Nonequilibrium Systems Cambridge, UK: Cambridge Univ. Press
  17. Karma A. 17.  2013. Annu. Rev. Condensed Matter Phys. 4:313–37
  18. Alonso S, Bär M, Echebarria B. 18.  2016. Rep. Prog. Phys. 79:096601
  19. Ben-Jacob E. 19.  1997. Contemp. Phys. 38:205–41
  20. Matsushita M, Wakita J, Itoh H, Ràfols I, Matsuyama T. 20.  et al. 1998. Phys. A: Stat. Mech. Appl. 249:517–24
  21. Tyson JJ, Murray JD. 21.  1989. Development 106:421–26
  22. Kicheva A, Cohen M, Briscoe J. 22.  2012. Science 338:210–12
  23. Oates AC, Morelli LG, Ares S. 23.  2012. Development 139:625–39
  24. Tayar AM, Karzbrun E, Noireaux V, Bar-Ziv RH. 24.  2015. Nat. Phys. 11:1037–41
  25. Cerda E, Mahadevan L. 25.  2003. Phys. Rev. Lett. 90:074302
  26. Klein Y, Efrati E, Sharon E. 26.  2007. Science 315:1116–20
  27. Stoop N, Lagrange R, Terwagne D, Reis PM, Dunkel J. 27.  2014. Nat. Mater. 14:337–42
  28. Rietkerk M, van de Koppel J. 28.  2008. Trends Ecol. Evol. 23:169–75
  29. Deblauwe V, Barbier N, Couteron P, Lejeune O, Bogaert J. 29.  2008. Glob. Ecol. Biogeogr. 17:715–23
  30. Getzin S, Yizhaq H, Bell B, Erickson TE, Postle AC. 30.  et al. 2016. PNAS 113:3551–56
  31. Levine H, Ben-Jacob E. 31.  2004. Phys. Biol. 1:P14
  32. Kuzdzal-Fick JJ, Queller DC, Strassmann JE. 32.  2010. Biol. Lett. 6:800–2
  33. Kastberger G, Schmelzer E, Kranner I. 33.  2008. PLOS ONE 3:1–16
  34. Silliman BR, McCoy MW, Angelini C, Holt RD, Griffin JN, van de Koppel J. 34.  2013. Annu. Rev. Ecol. Evol. Syst. 44:503–38
  35. Jones C, Lawton J, Shachak M. 35.  1994. Oikos 69:373–86
  36. Jones C, Lawton J, Shachak M. 36.  1997. Ecology 78:1946–57
  37. Shachak M, Boeken B, Groner E, Kadmon R, Lubin Y. 37.  et al. 2008. BioScience 58:209–21
  38. Tilman D, Isbell F, Cowles JM. 38.  2014. Annu. Rev. Ecol. Evol. Syst. 45:471–93
  39. Adeel Z, Safriel U, Niemeijer D, White R. 39.  2005. Ecosystems and Human Well-Being: Desertification Synthesis. A Report of the Millennium Ecosystem Assessment. Washington, DC: World Resour. Inst.
  40. Duraiappah AK, Naeem S. 40.  2005. Ecosystems and Human Well-Being: Biodiversity Synthesis. A Report of the Millennium Ecosystem Assessment Washington, DC: World Resour. Inst.,
  41. Valentine C, d'Herbes J, Poesen J. 41.  1999. Catena 37:1–24
  42. Kéfi S, Rietkerk M, Alados CL, Pueyo Y, Papanastasis VP. 42.  et al. 2007. Nature 449:213–16
  43. Scanlon TM, Kelly KC, Levin SA, Rodriguez-Iturbe I. 43.  2007. Nature 449:209–12
  44. Meron E, Yizhaq H, Gilad E. 44.  2007. Chaos 17:3037109
  45. Getzin S, Wiegand K, Wiegand T, Yizhaq H, von Hardenberg J, Meron E. 45.  2015. Ecography 38:1–11
  46. Meloni F, Granzotti C, Bautista F, Martinez AS. 46.  2017. Ecosphere 8:e01690
  47. Borgogno F, D'Odorico P, Laio F, Ridolfi L. 47.  2009. Rev. Geophys. 47:RG1005
  48. Meron E. 48.  2016. Math. Biosci. 271:1–18
  49. Reid WV, Mooney HA, Cropper A, Capistrano D, Carpenter SR. 49.  et al. 2005. Ecosystems and Human Well-Being: Synthesis. A Report of the Millennium Ecosystem Assessment. Washington, DC: World Resour. Inst. and Island
  50. Castets V, Dulos E, Boissonade J, De Kepper P. 50.  1990. Phys. Rev. Lett. 64:2953–56
  51. Murray J. 51.  2001. Mathematical Biology: I. An Introduction: Pt. 1., Vol. 17 Interdisciplinary Applied Mathmatics SS Antman, JE Marsden, L Sirovich, S Wiggins Berlin/Heidelberg: Springer. , 3rd ed..
  52. Sick S, Reinker S, Timmer J, Schlake T. 52.  2006. Science 314:1447–50
  53. Lejeune O, Couteron P, Lefever R. 53.  1999. Acta Oecol 20:171–83
  54. Kletter AY, von Hardenberg J, Meron E. 54.  2012. Commun. Pure Appl. Anal. 11:261–73
  55. Rudovics B, Barillot E, Davies PW, Dulos E, Boissonade J, De Kepper P. 55.  1999. J. Phys. Chem. A 103:1790–800
  56. Knobloch E. 56.  2015. Annu. Rev. Condens, Matter Phys. 6:325–59
  57. Pomeau Y. 57.  1986. Physica D 23:3
  58. Bel G, Hagberg A, Meron E. 58.  2012. Theor. Ecol. 5:591–604
  59. Lloyd DJB, Sandstede B, Avitabile D, Champneys AR. 59.  2008. SIAM J. Appl. Dyn. Syst. 7:1049–100
  60. Walden RW, Kolodner P, Passner A, Surko CM. 60.  1985. Phys. Rev. Lett. 45:496–99
  61. Knobloch E. 61.  1986. Phys. Rev. A 34:1538–49
  62. Rovinsky A, Menzinger M. 62.  1992. Phys. Rev. A 46:106315–22
  63. Deblauwe V, Couteron P, Lejeune O, Bogaert J, Barbier N. 63.  2010. Ecography 33:1–13
  64. Lee KJ, McCormick WD, Ouyang Q, Swinney HL. 64.  1993. Science 261:192–94
  65. Elphick C, Hagberg A, Meron E. 65.  1999. Phys. Rev. E 59:5285–91
  66. Yochelis A, Hagberg A, Meron E, Lin A, Swinney H. 66.  2002. SIAM J. Appl. Dyn. Syst. 1:236–47
  67. Langer JS. 67.  1980. Rev. Mod. Phys. 52:1–28
  68. Ben-Jacob E, Goldenfeld N, Langer JS, Schön G. 68.  1983. Phys. Rev. Lett. 51:1930–32
  69. Ben-Jacob E, Garik P. 69.  1990. Nature 343:523–30
  70. Bensimon D, Kadanoff LP, Liang S, Shraiman BI, Tang C. 70.  1986. Rev. Mod. Phys. 58:977–99
  71. Bischofberger I, Ramachandran R, Nagel SR. 71.  2014. Nat. Commun. 5:5265
  72. Mullins WW, Sekerka FF. 72.  1963. J. Appl. Phys. 34:323–29
  73. van Saarloos W. 73.  1998. Phys. Rep. 301:9–43
  74. Müller J, van Saarloos W. 74.  2002. Phys. Rev. E 65:061111
  75. Giverso C, Verani M, Ciarletta P. 75.  2015. J. R. Soc. Interface 12:20141290
  76. Ikeda H, Mimura M, Nishiura Y. 76.  1989. Nonlinear Anal.: Theory, Methods Appl. 13:507–26
  77. Coullet P, Lega J, Houchmanzadeh B, Lajzerowicz J. 77.  1990. Phys. Rev. Lett. 65:1352
  78. Hagberg A, Meron E. 78.  1993. Phys. Rev. E 48:705–8
  79. Hagberg A, Meron E. 79.  1994.a Nonlinearity 7:805–35
  80. Gilli JM, Morabito M, Frisch T. 80.  1994. J. Phys. II, EDP Sci. 4:319–31
  81. Marts B, Hagberg A, Meron E, Lin A. 81.  2004. Phys. Rev. Lett. 93:1–4
  82. Esteban-Martín A, Taranenko VB, García J, de Valcárcel GJ, Roldán E. 82.  2005. Phys. Rev. Lett. 94:223903
  83. Frisch T. 83.  1995. Physica D 84:601–614
  84. Hagberg A, Meron E. 84.  1994.b Phys. Rev. Lett. 72:2494–97
  85. Hagberg A, Meron E. 85.  1994.c Chaos 4:477–84
  86. Hagberg A, Meron E. 86.  1997. Phys. Rev. Lett. 78:1166–69
  87. Hagberg A, Meron E. 87.  1998. Physica D 123:460–73
  88. Grimm V, Railsback SF. 88.  2005. Individual-Based Modeling and Ecology Princeton, NJ: Princeton Univ. Press
  89. DeAngelis DL, Yurek S. 89.  2017. Ecosystems 20:284–300
  90. Frey E. 90.  2010. Phys. A: Stat. Mech. Appl. 389:4265–98
  91. Kletter A, Von Hardenberg J Meron E, Provenzale A. 91.  2009. J. Theor. Biol. 256:574–83
  92. Zelnik YR, Meron E, Bel G. 92.  2016. Ecol. Complex. 25:26–34
  93. Lefever R, Lejeune O. 93.  1997. Bull. Math. Biol. 59:263–94
  94. Klausmeier C. 94.  1999. Science 284:1826–28
  95. von Hardenberg J, Meron E, Shachak M, Zarmi Y. 95.  2001. Phys. Rev. Lett. 89:198101
  96. Shnerb N, Sarah P, Lavee H, Solomon S. 96.  2003. Phys. Rev. Lett. 90:0381011
  97. HilleRisLambers R, Rietkerk M, Van den Bosch F, Prins H, de Kroon H. 97.  2001. Ecology 82:50–61
  98. Gilad E, von Hardenberg J, Provenzale A, Shachak M, Meron E. 98.  2004. Phys. Rev. Lett. 93:098105
  99. Gilad E, von Hardenberg J, Provenzale A, Shachak M, Meron E. 99.  2007. J. Theor. Biol. 244:680
  100. Meinhardt H. 100.  1992. Rep. Prog. Phys. 55:797
  101. Ursino N. 101.  2005. Adv. Water Resour. 28:956–63
  102. Borthagaray AI, Fuentes MA, Marquet PA. 102.  2010. J. Theor. Biol. 265:18–26
  103. Verrecchia E, Yair A, Kidron GJ, Verrecchia K. 103.  1995. J. Arid Environ. 29:427–37
  104. Eldridge DJ, Zaady EMS. 104.  2012. J. Stat. Phys. 148:723–39
  105. Walker B, Ludwig D, Holling C, Peterman R. 105.  1981. J. Ecol. 69:473–98
  106. Nathan J, Osem Y, Shachak M, Meron E. 106.  2016. J. Ecol. 104:419–29
  107. Richards LA. 107.  1931. Physics 1:318–33
  108. Santillana M, Dawson C. 108.  2010. Comput. Geosci. 14:31–53
  109. Saco PM, Willgoose GR, Hancock GR. 109.  2007. Hydrol. Earth Syst. Sci. 11:1717–30
  110. Dekker SC, Rietkerk M, Bierkens MFP. 110.  2007. Glob. Change Biol. 34:671–78
  111. Juergens N. 111.  2013. Science 339:1618–21
  112. Tschinkel WR. 112.  2015. PLOS ONE 10:1–22
  113. Cramer MD, Barger NN, Tschinkel WR. 113.  2016. Ecography 40:101210–20
  114. Cramer MD, Barger NN. 114.  2013. PLOS ONE 8:e70876
  115. Ravi S, Wang L, Kaseke KF, Buynevich IV, Marais E. 115.  2017.b J. Geophys. Res.: Biogeosci. 122:2405–14
  116. Yizhaq H, Gilad E, Meron E. 116.  2005. Physica A 356:139
  117. Zelnik YR, Kinast S, Yizhaq H, Bel G, Meron E. 117.  2013. Philos. Trans. R. Soc. A 371:20120358
  118. Siteur K, Siero E, Eppinga MB, Rademacher JD, Doelman A, Rietkerk M. 118.  2014. Ecol. Complex. 20:81–96
  119. Gowda K, Riecke H, Silber M. 119.  2014. Phys. Rev. E 89:022701
  120. Rietkerk M, Boerlijst M, van Langevelde F, HilleRisLambers R, van de Koppel J. 120.  et al. 2002. Am. Nat. 160:524–30
  121. Lejeune OMT, Lefever R. 121.  2004. Int. J. Q. Chem. 98:261–71
  122. Kinast S, Zelnik YR, Bel G, Meron E. 122.  2014. Phys. Rev. Lett. 112:078701
  123. Gilad E, Shachak M, Meron E. 123.  2007. Theor. Popul. Biol. 72:214–30
  124. Brooker RW, Maestre FT, Callaway RM, Lortie CL, Cavieres LA. 124.  et al. 2008. J. Ecol. 96:18–34
  125. Malkinson D, Tielbörger K. 125.  2010. Oikos 119:1546–52
  126. Sherratt JA. 125a.  2005. J. Math. Biol. 51:183–97
  127. Rovinsky AB, Menzinger M. 126.  1992.b Phys. Rev. Lett. 69:1193–96
  128. Barbier N, Couteron P, LeJoly J, DeBlauwe V, LeJeune O. 127.  2006. J. Ecol. 94:537–47
  129. Deblauwe V, Couteron P, Bogaert J, Barbier N. 128.  2012. Ecol. Monogr. 82:3–21
  130. Tlidi M, Lefever R, Vladimirov A. 129.  2008. Dissipative Solutions: From Optics to Biology and Medicine, Vol. 751 Lecture Notes in Physics N Akhmediev, A Ankiewica 381–402 Berlin/Heidelberg: Springer-Verlag
  131. Fernandez-Oto C, Tlidi M, Escaff D, Clerc MG. 130.  2014. Philos. Trans. A Math. Phys. Eng. Sci. 372:20140009
  132. Zelnik YR, Meron E, Bel G. 131.  2015. PNAS 112:12327–31
  133. Tarnita C, Bonachela JA, Sheffer E, Guyton JA, Coverdale TC. 132.  et al. 2017. Nature 541:398–401
  134. Pringle RM, Tarnita C. 133.  2017. Annu. Rev. Entomol. 62:359–77
  135. Field CB, Barros V, Stocker TF, Qin D, Dokken DJ. 134.  et al. 2013. Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation Cambridge, UK: Cambridge Univ. Press
  136. Scheffer M, Carpenter SR. 135.  2003. Trends Ecol. Evol. 18:648–56
  137. Carpenter SR, Brock WA. 136.  2006. Ecol. Lett. 9:308–15
  138. Dakos V, Scheffer M, van Nes EH, Brovkin V, Petoukhov V, Held H. 137.  2008. PNAS 105:14308–12
  139. Guttal V, Jayaprakash C. 138.  2008. Ecol. Lett. 11:450–60
  140. Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR. 139.  et al. 2009. Nature 461:387–93
  141. van Heijster P, Doelman A, Kaper TJ, Promislow K. 140.  2010. SIAM J. Appl. Dyn. Syst. 9:292–332
  142. Knobloch E. 141.  2008. Nonlinearity 21:T45
  143. Tschinkel W. 142.  2012. PLOS ONE 7:e38056
  144. Sinclair ARE. 143.  1977. The African Buffalo: A Study of Resource Limitation of Populations Chicago: Chicago Univ. Press
  145. Gueron S, Levin SA. 144.  1993. J. Theor. Biol. 165:541–52
  146. Mimura M, Tohma M. 145.  2015. Ecol. Complex. 21:215–32
  147. Zelnik YR, Meron E. 146.  2018. Ecol. Indic. Accepted. https://doi.org/10.1016/j.ecolind.2017.10.068 [Crossref]
  148. Hagberg A, Yochelis A, Yizhaq H, Elphick C, Pismen L, Meron E. 147.  2006. Phys. D: Nonlinear Phenom. 217:186–92
  149. Sultan SE. 148.  2005. Trends Plant Sci 5:537–42
  150. Daszkowska-Golec A, Szarejko I. 149.  2013. Front. Plant Sci. 4:138
  151. D'Odorico P, He Y, Collins S, De Wekker SFJ, Engel V, Fuentes JD. 150.  2013. Glob. Ecol. Biogeogr. 22:364–79
/content/journals/10.1146/annurev-conmatphys-033117-053959
Loading
/content/journals/10.1146/annurev-conmatphys-033117-053959
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error