Advertisement

Integrating Short- and Long-Range Processes into Models: The Emergence of Pattern

  • Kelly K. Caylor
  • Greg S. Okin
  • Laura Turnbull
  • John Wainwright
  • Thorsten Wiegand
  • Trenton E. Franz
  • Anthony J. Parsons
Chapter

Abstract

The production of pattern requires feedbacks operating on different spatial and/or temporal scales and thus the integration of short- and long-range processes. More flexible models – ones able to represent the dynamics of change over more than just spatiotemporal snapshots – must be able to reconfigure their state and process representations. Scale and process are critically linked when considering the state and function of dryland ecosystems: different processes dominate at different scales. There are four scales at which land degradation in drylands is typically considered: plant-interspace, patch, landscape and region. However, cross-scale process interactions are a critical element of modelling dryland degradation. There are intimate relationships between scale, process and pattern in drylands and many of these relationships involve cross-scale interactions. One possible consequence of these cross-scale interactions is the manifestation of bistability, which may also be present at different scales. A key issue for modelling is the mismatch between temporal scales of processes, which are typically short term, and degradation scales, which are typically long term, and the feedbacks that exist between these two sets of scales. To add to this complexity, ecological, biogeochemical and geomorphological fluxes redistribute energy and materials either vertically, or horizontally, or both. Interactions between these lateral and vertical fluxes are intrinsic to ecosystem dynamics and pattern formation in drylands. In all modelling, the important challenge remains of how to strike the balance between the technical details of a particular system and the strategic simplifications necessary to maintain generality, and to employ appropriate strategies that will permit generalization from specific case studies.

Keywords

Land Degradation Wind Erosion Vegetation Pattern Vertical Flux Specific Case Study 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This chapter is a contribution to the book Patterns of Land Degradation in Drylands: Understanding Self-Organised Ecogeomorphic Systems, which is the outcome of an ESF-funded Exploratory Workshop – “Self-organized ecogeomorphic systems: confronting models with data for land degradation in drylands” – which was held in Potsdam, Germany, 7–10 June 2010.

References

  1. Allen TFH, Starr TB (1982) Hierarchy: perspectives for ecological complexity. University of Chicago Press, ChicagoGoogle Scholar
  2. Barbier N, Couteron P, Lefever R, Deblauwe V, Lejeune O (2008) Spatial decoupling of facilitation and competition at the origin of gapped vegetation patterns. Ecology 89(6):1521–1531CrossRefGoogle Scholar
  3. Barrow JR, Lucero ME, Reyes-Vera I, Havstad KM (2008) Do symbiotic microbes have a role in plant evolution, performance and response to stress? Commun Integr Biol 1(1):69–73CrossRefGoogle Scholar
  4. Bastos LS, O’Hagan A (2009) Diagnostics for Gaussian process emulators. Technometrics 51:425–438CrossRefGoogle Scholar
  5. Belyea LR, Baird AJ (2006) Beyond “The limits to peat bog growth”: cross-scale feedback in peatland development. Ecol Monogr 76:299–322CrossRefGoogle Scholar
  6. Bestelmeyer BT, Kalil NI, Peters DPC (2007) Does shrub invasion indirectly limit grass establishment via seedling herbivory? A test at grassland-shrubland ecotones. J Veg Sci 18(3):363–370CrossRefGoogle Scholar
  7. Bochet E, Poesen J, Rubio JL (2000) Mound development as an interaction of individual plants with soil, water erosion and sedimentation processes on slopes. Earth Surf Proc Land 25(8):847–867CrossRefGoogle Scholar
  8. Borgogno F, D’Odorico P, Laio F, Ridolfi L (2009) Mathematical models of vegetation pattern formation in ecohydrology. Rev Geophys 47, RG1005. doi: 10.1029/2007RG000256 CrossRefGoogle Scholar
  9. Bugmann H (2001) A review of forest gap models. Clim Chang 51:259–305CrossRefGoogle Scholar
  10. Calabrese JM, Vazquez F, López C, Miguel MS, Grimm V (2010) The independent and interactive effects of tree-tree establishment competition and fire on savanna structure and dynamics. Am Nat 175:E44–E65CrossRefGoogle Scholar
  11. Caylor KK, Scanlon TM, Rodriguez-Iturbe I (2009) Ecohydrological optimization of pattern and processes in water-limited ecosystems: a trade-offbased hypothesis. Water Resour Res 45, W08407. doi:10.1029/2008WR007230Google Scholar
  12. Charley JL, West NE (1975) Plant-induced soil chemical patterns in some shrub-dominated semi-desert ecosystems of Utah. J Ecol 63:945–963CrossRefGoogle Scholar
  13. Charney JG (1975) Dynamics of deserts and drought in Sahel. Q J R Meteorol Soc 101(428):193–202CrossRefGoogle Scholar
  14. Charney J, Stone PH, Quirk WJ (1975) Drought in Sahara – biogeophysical feedback mechanism. Science 187(4175):434–435CrossRefGoogle Scholar
  15. Clark DB, Xue YK, Harding RJ, Valdes PJ (2001) Modeling the impact of land surface degradation on the climate of tropical north Africa. J Climate 14(8):1809–1822CrossRefGoogle Scholar
  16. Coffin DP, Lauenroth WK (1990) A gap dynamics simulation model of succession in the shortgrass steppe. Ecol Model 49:229–266CrossRefGoogle Scholar
  17. D’Antonio CM (2000) Fire, plant invasions, and global change. In: Mooney HA, Hobbs RJ (eds) Invasive species in a changing world. Island Press, Washington, DCGoogle Scholar
  18. D’Odorico P, Laio F, Ridolfi L (2006a) A probabilistic analysis of fire-induced tree-grass coexistence in savannas. Am Nat 167(3):E79–E87CrossRefGoogle Scholar
  19. D’Odorico P, Laio F, Ridolfi L (2006b) Patterns as indicators of productivity enhancement by facilitation and competition in dryland vegetation. J Geophys Res 111, G03010CrossRefGoogle Scholar
  20. D’Odorico P, Laio F, Porporato A, Ridolfi L, Barbier N (2007) Noise-induced vegetation patterns in fire-prone savannas. J Geophys Res-Biogeosci 112, G02021. doi:10.1029/2006JG000261Google Scholar
  21. De Boer DH (1992) Hierarchies and spatial scale in process geomorphoiogy: a review. Geomorphology 4:303–318CrossRefGoogle Scholar
  22. deMenocal P, Ortiz J, Guilderson T, Adkins J, Sarnthein M, Baker L, Yarusinsky M (2000) Abrupt onset and termination of the African Humid Period: rapid climate responses to gradual insolation forcing. Quaternary Sci Rev 19(1–5):347–361CrossRefGoogle Scholar
  23. Diggle PJ (1981) Binary mosaics and the spatial pattern of heather. Biometrics 37:531–539CrossRefGoogle Scholar
  24. Dunkerley DL (1999) Banded chenopod shrublands of arid Australia: modelling responses to interannual rainfall variability with cellular automata. Ecol Modell 121:127–138CrossRefGoogle Scholar
  25. Duran KL, Lowrey TK, Parmenter RR, Lewis PO (2005) Genetic diversity in Chihuahuan Desert populations of creosotebush (Zygophyllaceae: Larrea tridentata). Am J Bot 92:722–729CrossRefGoogle Scholar
  26. Franz TE, Caylor KK, Nordbotten JM, Rodriguez-Iturbe RI, Celia MA (2010) An ecohydrological approach to predicting regional woody species distribution patterns in dryland ecosystems. Adv Water Resour 33(2):215–230CrossRefGoogle Scholar
  27. Franz TE, King EG, Caylor KK, Robinson DA (2011) Coupling vegetation patterns to soil resource heterogeneity in a Central Kenyan dryland using geophysical imagery. Water Resour Res 47(7), W07531. doi:10.1029/2010WR010127Google Scholar
  28. Franz TE, Caylor KK, King EG, Nordbotten JM, Rodriguez-Iturbe RI, Celia MA (2012) An ecohydrological approach to predicting hillslope scale vegetation patterns in dryland ecosystems. Water Resour Res 48(1), W01515. doi:10.1029/2011WR010524Google Scholar
  29. Gillette DA, Herrick JE, Herbert GA (2006) Wind characteristics of mesquite streets in the northern Chihuahuan Desert, New Mexico, USA. Environ Fluid Mech 6:241–275CrossRefGoogle Scholar
  30. Grimm V, Railsback SF (2005) Individual-based modeling and ecology. Princeton University Press, Princeton, 480 ppGoogle Scholar
  31. Grimm V, Revilla E, Berger U, Jeltsch F, Mooij W, Railsback SF, Thulke H, Weiner J, Wiegand T, DeAngelis DL (2005) Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991CrossRefGoogle Scholar
  32. Grimm V, Berger U, Bastiansen F, Eliassen S, Ginot V, Giske J, Goss-Custard J, Grand T, Heinz SK, Huseg G, Huth A, Jepsen JU, Jørgensen C, Mooij WM, Muller B, Pe’er G, Piou C, Railsback SF, Robbins AM, Robbins MM, Rossmanith E, Ruger N, Strand E, Souissi S, Stillman RA, Vabøg R, Visser U, DeAngelis DL (2006) A standard protocol for describing individual-based and agent-based models. Ecol Model 198(1–2):115–126CrossRefGoogle Scholar
  33. Grimm V, Berger U, DeAngelis DL, Polhill JG, Giskee J, Railsback SF (2010) The ODD protocol: a review and first update. Ecol Model 221:2760–2768CrossRefGoogle Scholar
  34. HilleRisLambers R, Rietkerk M, van den Bosch F, Prins HHT, de Croon H (2001) Vegetation pattern formation in semi-arid grazing systems. Ecology 82:50–61CrossRefGoogle Scholar
  35. Holling CS (1966) The strategy of building models of complex ecological systems. In: Watt KEF (ed) Systems analysis in ecology. Academic, New YorkGoogle Scholar
  36. Janssen RHH, Meinders MBJ, van Nes EH, Scheffer M (2008) Microscale vegetation-soil feedback boosts hysteresis in a regional vegetation-climate system. Glob Change Biol 14(5):1104–1112CrossRefGoogle Scholar
  37. Jeltsch F, Milton SJ, Moloney K (1999) Detecting process from snap-shot pattern – lessons from tree spacing in the southern Kalahari. Oikos 85:451–467CrossRefGoogle Scholar
  38. Jenerette GD, Barron-Gafford GA, Guswa AJ, McDonnell JJ, Villegas JC (2011) Organization of complexity in water limited ecohydrology. Ecohydrology. doi: 10.1002/eco.217 Google Scholar
  39. Kefi S, Rietkerk M, Alados CL, Pueyo Y, Papanastasis VP, ElAich A, de Ruite PC (2007) Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449(7159):213–U215CrossRefGoogle Scholar
  40. King E, Franz T, Caylor K (2010) Proliferation of a native succulent in Kenyan drylands: ecohydrology and resilience. Ecol Soc Am Annu MeetGoogle Scholar
  41. Klausmeier CA (1999) Regular and irregular patterns in semiarid vegetation. Science 284:1826–1828CrossRefGoogle Scholar
  42. Laio F, Porporato A, Ridolfi L, Rodriguez-Iturbe I (2001) Plants in watercontrolled ecosystems: active role in hydrologic processes and response to water stress – ii. probabilistic soil moisture dynamics. Adv Water Resour 24(7):707–723CrossRefGoogle Scholar
  43. Li J, Okin GS, Alvarez L, Epstein H (2007) Quantitative effects of vegetation cover on wind erosion and soil nutrient loss in a desert grassland of southern New Mexico, USA. Biogeochemistry 85:317–332CrossRefGoogle Scholar
  44. Ludwig JA, Eager RW, Bastin GN, Chewings VH, Liedloff AC (2002) A leakiness index for assessing landscape function using remote sensing. Landscape Ecol 17(2):157–171CrossRefGoogle Scholar
  45. Ludwig JA, Bastin GN, Chewings VH, Eager RW, Liedloff AC (2007) Leakiness: a new index for monitoring the health of arid and semiarid landscapes using remotely sensed vegetation cover and elevation data. Ecol Indic 7(2):442–454CrossRefGoogle Scholar
  46. Manor A, Shnerb NM (2008) Facilitation, competition, and vegetation patchiness: from scale free distribution to patterns. J Theor Biol 253(4):838–842CrossRefGoogle Scholar
  47. May RM (1973) Stability and complexity in model ecosystems. Princeton University Press, PrincetonGoogle Scholar
  48. Moreno-de las Heras M, Saco PM, Willgoose GR, Tongway DJ (2011) Assessing landscape structure and health of semiarid ecosystems with patchy vegetation using patch-size distributions. Ecol Appl 21:2793–2805Google Scholar
  49. Mueller EN, Wainwright J, Parsons AJ (2008) Spatial variability and nutrient characteristics of semi-arid grasslands and shrubalnds, Jornada Basin, New Mexico. Ecohydrology 1:3–12Google Scholar
  50. Mulligan M, Wainwright J (2013) Modelling and model building. In: Wainwright J, Mulligan M (eds) Environmental modelling: finding simplicity in complexity, 2nd edn. Wiley-Blackwell, Chichester, pp 7–26CrossRefGoogle Scholar
  51. Newman BD, Wilcox BP, Archer SR, Breshears DD, Dahm CN, Duffy CJ, McDowell NG, Phillips FM, Scanlon BR, Vivoni ER (2006) Ecohydrology of water-limited environments: a scientific vision. Water Resour Res 42, Article Number W06302, doi: 10.1029/2005WR004141
  52. Noy-Meir I (1975) Stability of grazing systems: an application of predator prey graphs. J Ecol 63:459481Google Scholar
  53. O’Neill RV, DeAngelis DL, Waide JB, Allen TFH (1986) A hierarchical concept of ecosystems. Princeton University Press, PrincetonGoogle Scholar
  54. O’Sullivan D, Haklay M (2000) Agent-based models and individualism: is the world agent-based? Environ Plan A 32:1409–1425CrossRefGoogle Scholar
  55. O’Sullivan D, Millington JMA, Perry GLW, Wainwright J (2012) Agent-based models – because they’re worth it? In: Heppenstall AJ, Crooks AT, See LM, Batty M (eds) Spatial agent-based models: principles, concepts and applications. Springer, Berlin, pp 109–123Google Scholar
  56. Okin GS (2008) A new model of wind erosion in the presence of vegetation. J Geophys Res-Earth Surf 113. Article number F02S10. doi: 10.1029/2007JF000758
  57. Okin GS, D’Odorico P, Archer SR (2009) Impacts of feedbacks on Chihuahuan Desert grasslands: transience and metastability driven by grass recruitment. J Geophys Res 114, G01004CrossRefGoogle Scholar
  58. Parker DC, Brown DG, Polhill JG, Deadman PJ, Manson SM (2008) Ilustrating a new “conceptual design pattern” for agent-based models of land use via five case studies – the MR POTATOHEAD framework. In: Lopez Paredes A, Hernandez I (eds) Agent-based modelling in natural resource management. INSISOC, Valladolid, pp 23–51Google Scholar
  59. Parsons AJ, Stone PM (2006) Effects of intra-storm variations in rainfall intensity on interill runoff and erosion. Catena 67:68–78CrossRefGoogle Scholar
  60. Parsons AJ, Abrahams AD, Wainwright J (1994) Rainsplash and erosion rates in an interrill area on semiarid grassland, Southern Arizona. Catena 22:215–226CrossRefGoogle Scholar
  61. Parton WJ, Hartman M, Ojima D, Schimel D (1998) DAYCENT and its land surface submodel: description and testing. Glob Planet Change 19:35–48CrossRefGoogle Scholar
  62. Paruelo JM, Pütz S, Weber G, Bertiller M, Golluscio RA, Aguiar MR, Wiegand T (2008) Assessing the long-term dynamics of a semiarid grass steppe under stochastic climate and different grazing regimes. J Arid Environ 72:2211–2231CrossRefGoogle Scholar
  63. Peters DPC (2002) Plant species dominance at a grassland-shrubland ecotone: an individual- based gap dynamics model of herbaceous and woody species. Ecol Model 152:5–32CrossRefGoogle Scholar
  64. Peters DPC, Bestelmeyer BT, Herrick JE, Fredrickson EDL, Monger HC, Havstad KM (2006) Disentangling complex landscapes: new insights to forecasting arid and semiarid system dynamics. Bioscience 56:491–501CrossRefGoogle Scholar
  65. Poole GC (2002) Fluvial landscape ecology: addressing uniqueness within the river discontinuum. Freshw Biol 47:641–660CrossRefGoogle Scholar
  66. Railsback SF, Grimm V (2012) Agent-based and individual-based modeling: a practical introduction. Princeton University Press, Princeton, 352 ppGoogle Scholar
  67. Robinson DA, Campbell CS, Hopmans JW, Hornbuckle BK, Jones SB, Knight R, Ogden F, Selker J, Wendroth O (2008) Soil moisture measurement for ecological and hydrological watershed-scale observatories: a review. Vadose Zone J 7:358–389CrossRefGoogle Scholar
  68. Robinson DA, Lebron I, Kocar B, Phan K, Sampson M, Crook N, Fendorf S (2009) Time-lapse geophysical imaging of soil moisture dynamics in tropical deltaic soils: an aid to interpreting hydrological and geochemical processes. Water Resour Res 45, W00D32. doi: 10.1029/2008WR006984 CrossRefGoogle Scholar
  69. Rodriguez-Iturbe I, Porporato A (2004) Ecohydrology of water-controlled ecosystems. Cambridge University Press, CambridgeGoogle Scholar
  70. Saco PM, Willgoose GR, Hancock GR (2007) Eco-geomorphology of banded vegetation patterns in arid and semi-arid regions. Hydrol Earth Syst Sci 11:1717–1730CrossRefGoogle Scholar
  71. Scanlon TM, Caylor KK, Rodriguez-Iturbe I, Levin SA (2007) Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature 449:209–212CrossRefGoogle Scholar
  72. Schlesinger WH, Reynolds JF, Cunningham GL, Huenneke LF, Jarrell WM, Virginia RA, Whitford WG (1990) Biological feedbacks in global desertification. Science 247:1043–1048CrossRefGoogle Scholar
  73. Shugart HH (1998) Terrestrial ecosystems in changing environments. Cambridge University Press, CambridgeGoogle Scholar
  74. Stewart J, Parsons AJ, Wainwright J, Okin GS, Bestelmeyer BT, Fredrickson EL, Schlesinger WH (in press) Modelling emergent patterns of dynamic desert ecosystems. Ecol MonogrGoogle Scholar
  75. Taylor CM, Lambin EF, Stephenne N, Harding RJ, Essery RLH (2002) The influence of land use change on climate in the Sahel. J Climate 15(24):3615–3629CrossRefGoogle Scholar
  76. Tongway DJ, Ludwig JA (2001) Theories on the origins, maintenance, dynamics and functioning of banded landscapes. Banded vegetation patterning in arid and semiarid environments: ecological processes and consequences for managment. Springer, HeidelbergCrossRefGoogle Scholar
  77. Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond B Bio Sci 237:37–72CrossRefGoogle Scholar
  78. Turnbull L, Wainwright J, Brazier RE (2010a) Changes in hydrology and erosion over a transition from grassland to shrubland. Hydrol Process 24:393–414. doi: 10.1002/hyp.7491 Google Scholar
  79. Turnbull L, Wainwright J, Brazier RE, Bol R (2010b) Changes in biotic and abiotic components of ecosystem structure over a transition from semi-arid grassland to shrubland in South-Western USA. Ecosystems 13:1239–1255. doi: 10.1007/s10021-010-9384-8 CrossRefGoogle Scholar
  80. Van Auken OW (2000) Shrub invasions of North American semiarid grasslands. Annu Rev Ecol Syst 31:197–215CrossRefGoogle Scholar
  81. von Hardenberg J, Kletter AY, Yizhaq H, Nathan J, Meron E (2010) Periodic versus scale-free patterns in dryland vegetation. Proc Roy Soc B-Biol Sci 277(1688):1771–1776CrossRefGoogle Scholar
  82. Wainwright J, Parsons AJ (2002) The effect of temporal variations in rainfall on scale dependency in runoff coefficients. Water Resour Res. Article number 1271. doi: 10.1029/2000WR000188
  83. Wainwright J, Parsons AJ, Müller EN, Brazier RE, Powell DM, Fenti B (2008) A transport-distance approach to scaling erosion rates: 1. background and model development. Earth Surf Proc Land 33:813–826. doi: 10.1002/esp.1624 CrossRefGoogle Scholar
  84. Wu J, David JL (2002) A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications. Ecol Model 153:7–26CrossRefGoogle Scholar
  85. Xue YK, Shukla J (1993) The influence of land-surface properties on Sahel climate.1. desertification. J Climate 6(12):2232–2245CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Kelly K. Caylor
    • 1
  • Greg S. Okin
    • 2
  • Laura Turnbull
    • 3
  • John Wainwright
    • 4
  • Thorsten Wiegand
    • 5
  • Trenton E. Franz
    • 6
  • Anthony J. Parsons
    • 7
  1. 1.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Department of GeographyUniversity of CaliforniaLos AngelesUSA
  3. 3.Institute of Hazards, Risk and Resilience, Department of GeographyDurham UniversityDurhamUK
  4. 4.Department of GeographyUniversity of DurhamDurhamUK
  5. 5.Department of Ecological ModellingHelmholtz Centre for Environmental Research UFZLeipzigGermany
  6. 6.Department of Hydrology and Water ResourcesUniversity of ArizonaTucsonUSA
  7. 7.Sheffield Centre for International Drylands ResearchUniversity of SheffieldSheffieldUK

Personalised recommendations