Appropriate complexity landscape modeling

Earth-Science Reviews

Volumn 160, Issue , 2016, Pages 111-130

  Larsen, Laurel G ^a   Eppinga, Maarten B ^b   Passalacqua, Paola ^c   Getz, Wayne M ^d,e   Rose, Kenneth A ^f   Liang, Man ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UTRECHT UNIVERSITY   (Netherlands)

^c The University of Texas at Austin   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e UNIVERSITY OF KWAZULU NATAL   (South Africa)

^f LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Complex systems; Emergent properties; Forecasting; Landscapes; Modeling

Indexed keywords

CLIMATE CHANGE; CLIMATE EFFECT; ENVIRONMENTAL MANAGEMENT; ENVIRONMENTAL RESTORATION; FORECASTING METHOD; INFILTRATION; LANDSCAPE; MODELING;

EID: 84978252830     PISSN: 00128252     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.earscirev.2016.06.016     Document Type: Review

References (142)

1. Abdul Razak, F., Jensen, H.J., Quantifying “causality” in complex systems: understanding transfer entropy. PLoS One, 9, 2014, e99462.
2. Arditi, R., Ginzburg, L.R., Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139 (1989), 311–326.
3. Augusiak, J., Van den Brink, P.J., Grimm, V., Merging validation and evaluation of ecological models to “evaludation”: a review of terminology and a practical approach. Ecol. Model. 280 (2014), 117–128.
4. Austin, M., Species distribution models and ecological theory: a critical assessment and some possible new approaches. Ecol. Model. 200 (2007), 1–19.
5. Avgar, T., Deardon, R., Fryxell, J.M., An empirically parameterized individual based model of animal movement, perception, and memory. Ecol. Model. 251 (2013), 158–172.
6. Barraquand, F., Benhamou, S., Animal movements in heterogeneous landscapes: identifying profitable places and homogeneous movement bouts. Ecology 89 (2008), 3336–3348.
7. Bascompte, J., Solé, R.V., Rethinking complexity: modelling spatiotemporal dynamics in ecology. Trends Ecol. Evol. 10 (1995), 361–366.
8. Belyea, L.R., Baird, A.J., Beyond “the limits to peat bog growth”: cross-scale feedback in peatland development. Ecol. Monogr. 76 (2006), 299–322.
9. Bowler, D.E., Benton, T.G., Causes and consequences of animal dispersal strategies: relating individual behaviour to spatial dynamics. Biol. Rev. 80 (2005), 205–225.
10. Chapin, F.S. III, Walker, B.H., Hobbs, R.J., Hooper, D.U., Lawton, J.H., Sala, O.E., Tilman, D., Biotic control over the functioning of ecosystems. Science 277 (1997), 500–504.
11. Clark, A.T., Ye, H., Isbell, F., Deyle, E.R., Cowles, J., Tilman, G.D., Sugihara, G., Spatial convergent cross mapping to detect causal relationships from short time series. Ecology 96 (2015), 1174–1181.
12. Cloern, J.E., Knowles, N., Brown, L.R., Cayan, D., Dettinger, M.D., Morgan, T.L., Schoellhamer, D.H., Stacey, M.T., van der Wegen, M., Wagner, R.W., Jassby, A.D., Projected evolution of California's San Francisco Bay-Delta-River system in a century of climate change. PLoS One, 6, 2011, e24465.
13. Coco, G., Zhou, Z., van Maanen, B., Olabarrieta, M., Tinoco, R., Townend, I., Morphodynamics of tidal networks: advances and challenges. Mar. Geol. 346 (2013), 1–16.
14. Collie, J.S., Botsford, L.W., Hastings, A., Kaplan, I.C., Largier, J.L., Livingston, P.A., Plagányi, É., Rose, K.A., Wells, B.K., Werner, F.E., Ecosystem models for fisheries management: finding the sweet spot. Fish Fish., 2014.
15. Corenblit, D., Tabacchi, E., Steiger, J., Gurnell, A.M., Reciprocal interactions and adjustments between fluvial landforms and vegetation dynamics in river corridors: a review of complementary approaches. Earth Sci. Rev. 84 (2007), 56–86.
16. Coulthard, T.J., Van De Wiel, M.J., A cellular model of river meandering. Earth Surf. Process. Landf. 31 (2006), 123–132.
17. Courant, R., Friedrichs, K., Lewy, H., On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11 (1967), 215–234.
18. D'Alpaos, A., Lanzoni, S., Marani, M., Rinaldo, A., Landscape evolution in tidal embayments: modeling the interplay of erosion, sedimentation, and vegetation dynamics. J. Geophys. Res., 112, 2007, F01008.
19. de Roos, A.M., Persson, L., Population and Community Ecology of Ontogenetic Development. 2013, Princeton University Press.
20. de Valpine, P., Scranton, K., Knape, J., Ram, K., Mills, N.J., The importance of individual developmental variation in stage-structured population models. Ecol. Lett. 17 (2014), 1026–1038.
21. DeAngelis, D.L., Mooij, W.M., Individual-based modeling of ecological and evolutionary processes. Annu. Rev. Ecol. Evol. Syst., 2005, 147–168.
22. DeAngelis, D.L., Rose, K.A., Crowder, L.B., Marschall, E.A., Lika, D., Fish cohort dynamics: application of complementary modeling approaches. Am. Nat. 142 (1993), 604–622.
23. Doeschl-Wilson, A.B., Ashmore, P.E., Assessing a numerical cellular braided-stream model with a physical model. Earth Surf. Process. Landf. 30 (2005), 519–540.
24. Edmonds, D.A., Paola, C., Hoyal, D.C.J.D., Sheets, B.A., Quantitative metrics that describe river deltas and their channel networks. J. Geophys. Res. Earth Surf., 116, 2011, F04022.
25. Eppinga, M.B., de Ruiter, P.C., Wassen, M.J., Rietkerk, M., Nutrients and hydrology indicate the driving mechanisms of peatland surface patterning. Am. Nat. 173 (2009), 803–818.
26. Eppinga, M.B., Rietkerk, M., Belyea, L.R., Nilsson, M.B., Ruiter, P.C.D., Wassen, M.J., Resource contrast in patterned peatlands increases along a climatic gradient. Ecology 91 (2010), 2344–2355.
27. Eppinga, M.B., Rietkerk, M., Borren, W., Lapshina, E.D., Bleuten, W., Wassen, M.J., Regular surface patterning of peatlands: confronting theory with field data. Ecosystems 11 (2008), 520–536.
28. Eppstein, M.J., Molofsky, J., Invasiveness in plant communities with feedbacks. Ecol. Lett. 10 (2007), 253–263.
29. Evans, M.R., Grimm, V., Johst, K., Knuuttila, T., de Langhe, R., Lessells, C.M., Merz, M., O'Malley, M.A., Orzack, S.H., Weisberg, M., et al. Do simple models lead to generality in ecology?. Trends Ecol. Evol. 28 (2013), 578–583.
30. Fagherazzi, S., Kirwan, M.L., Mudd, S.M., Guntenspergen, G.R., Temmerman, S., D'Alpaos, A., Koppel, J., Rybczyk, J.M., Reyes, E., Craft, C., Clough, J., Numerical models of salt marsh evolution: ecological, geomorphic, and climatic factors. Rev. Geophys., 50, 2012.
31. Falcini, F., Jerolmack, D.J., A potential vorticity theory for the formation of elongate channels in river deltas and lakes. J. Geophys. Res. Earth Surf., 115, 2010, F04038.
32. Getz, W.M., An introspection on the art of modeling in population ecology. Bioscience 48 (1998), 540–552.
33. Getz, W.M., Computational population biology: linking the inner and outer worlds of organisms. Israel J. Ecol. Evol. 59 (2013), 2–16.
34. Glaser, S.M., Ye, H., Sugihara, G., A nonlinear, low data requirement model for producing spatially explicit fishery forecasts. Fish. Oceanogr. 23 (2014), 45–53.
35. Goodwin, R.A., Nestler, J.M., Anderson, J.J., Weber, L.J., Loucks, D.P., Forecasting 3-D fish movement behavior using a Eulerian–Lagrangian–agent method (ELAM). Ecol. Model. 192 (2006), 197–223.
36. Granger, C.W., Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 1969, 424–438.
37. Grassberger, P., Procaccia, I., Characterization of strange attractors. Phys. Rev. Lett. 50 (1983), 346–349.
38. Grassberger, P., Procaccia, I., Measuring the strangeness of strange attractors. Phys. D 9 (1983), 189–208.
39. Grimm, V., Railsback, S.F., Pattern-oriented modelling: a “multi-scope”for predictive systems ecology. Philos. Trans. R. Soc. B 367 (2012), 298–310.
40. Grimm, V., Railsback, S.F., Individual-based Modeling and Ecology. 2013, Princeton University Press.
41. Groves, D.G., Sharon, C., Knopman, D., Planning Tool to Support Louisiana's Decisionmaking on Coastal Protection and Restoration., 2012 (Product Page) http://www.rand.org/pubs/technical_reports/TR1266.html.
42. Hajek, E.A., Wolinsky, M.A., Simplified process modeling of river avulsion and alluvial architecture: connecting models and field data. Sediment. Geol. 257 (2012), 1–30.
43. Harsch, M.A., Zhou, Y., HilleRisLambers, J., Kot, M., Keeping pace with climate change: stage-structured moving-habitat models. Am. Nat. 184 (2014), 25–37.
44. Hartig, F., Calabrese, J.M., Reineking, B., Wiegand, T., Huth, A., Statistical inference for stochastic simulation models – theory and application. Ecol. Lett. 14 (2011), 816–827.
45. Hastings, A., Transient dynamics and persistence of ecological systems. Ecol. Lett. 4 (2001), 215–220.
46. Hastings, A., Transients: the key to long-term ecological understanding?. Trends Ecol. Evol. 19 (2004), 39–45.
47. Heffernan, J.B., Wetlands as an alternative stable state in desert streams. Ecology 89 (2008), 1261–1271.
48. Hoffman, J.D., Frankel, S., Numerical Methods for Engineers and Scientists. 2001, CRC Press, Second Edition.
49. Holling, C.S., The components of predation as revealed by a study of small-mammal predation of the European pine sawfly. Can. Entomol. 91 (1959), 293–320.
50. Hossain, F., Sivakumar, B., Spatial pattern of arsenic contamination in shallow wells of Bangladesh: regional geology and nonlinear dynamics. Stoch. Env. Res. Risk A. 20 (2005), 66–76.
51. Jackisch, C., Zehe, E., Samaniego, L., Singh, A.K., An experiment to gauge an ungauged catchment: rapid data assessment and eco-hydrological modelling in a data-scarce rural catchment. Hydrol. Sci. J. 59 (2014), 2103–2125.
52. Jones, C.G., Lawton, J.H., Shachak, M., Organisms as ecosystem engineers. Oikos 69 (1994), 373–386.
53. Kendall, B.E., Fox, G.A., Fujiwara, M., Nogeire, T.M., Demographic heterogeneity, cohort selection, and population growth. Ecology 92 (2011), 1985–1993.
54. Kennedy, A.D., Dong, X., Xi, B., Xie, S., Zhang, Y., Chen, J., A comparison of MERRA and NARR Reanalyses with the DOE ARM SGP data. J. Clim. 24 (2011), 4541–4557.
55. Khosronejad, A., Kozarek, J.L., Sotiropoulos, F., Simulation-based approach for stream restoration structure design: model development and validation. J. Hydraul. Eng., 140, 2014, 04014042.
56. Kim, W., Mohrig, D., Twilley, R., Paola, C., Parker, G., Is it feasible to build new land in the Mississippi River Delta?. EOS Trans. Am. Geophys. Union 90 (2009), 373–374.
57. Kirwan, M.L., Murray, A.B., A coupled geomorphic and ecological model of tidal marsh evolution. Proc. Natl. Acad. Sci. 104 (2007), 6118–6122.
58. Konings, A.G., Dekker, S.C., Rietkerk, M., Katul, G.G., Drought sensitivity of patterned vegetation determined by rainfall-land surface feedbacks. J. Geophys. Res. Biogeosci.(2005–2012), 2011, 116.
59. Larsen, L.G., Harvey, J.W., How vegetation and sediment transport feedbacks drive landscape change in the Everglades and wetlands worldwide. Am. Nat. 176 (2010), E66–E79.
60. Larsen, L.G., Harvey, J.W., Modeling of hydroecological feedbacks predicts distinct classes of landscape pattern, process, and restoration potential in shallow aquatic ecosystems. Geomorphology 126 (2011), 279–296.
61. Larsen, L.G., Choi, J., Nungesser, M.K., Harvey, J.W., Directional connectivity in hydrology and ecology. Ecol. Appl. 22 (2012), 2204–2220.
62. Larsen, L.G., Harvey, J.W., Crimaldi, J.P., A delicate balance: ecohydrological feedbacks governing landscape morphology in a lotic peatland. Ecol. Monogr. 77 (2007), 591–614.
63. Larsen, L., Thomas, C., Eppinga, M., Coulthard, T., Exploratory modeling: extracting causality from complexity. EOS Trans. Am. Geophys. Union 95 (2014), 285–286.
64. Levin, S.A., The problem of pattern and scale in ecology: the Robert H. MacArthur award lecture. Ecology 73 (1992), 1943–1967.
65. Levins, R., The strategy of model building in population biology. Am. Sci., 1966, 421–431.
66. Li, W., Qin, B., Zhu, G., Forecasting short-term cyanobacterial blooms in Lake Taihu, China, using a coupled hydrodynamic–algal biomass model. Ecohydrology 7 (2014), 794–802.
67. Liang, M., Geleynse, N., Edmonds, D.A., Passalacqua, P., A reduced-complexity model for river delta formation — part 2: assessment of the flow routing scheme. Earth Surf. Dyn. 3 (2015), 87–104.
68. Liang, M., Van Dyk, C., Passalacqua, P., Quantifying the patterns and dynamics of river deltas under conditions of steady forcing and relative sea level rise. J. Geophys. Res. Earth Surf., 2016.
69. Liang, M., Voller, V.R., Paola, C., A reduced-complexity model for river delta formation — part 1: modeling deltas with channel dynamics. Earth Surf. Dyn. 3 (2015), 67–86.
70. Liu, Q.-X., Doelman, A., Rottschäfer, V., de Jager, M., Herman, P.M.J., Rietkerk, M., van de Koppel, J., Phase separation explains a new class of self-organized spatial patterns in ecological systems. Proc. Natl. Acad. Sci. 110 (2013), 11905–11910.
71. Liu, H., Fogarty, M.J., Glaser, S.M., Altman, I., Hsieh, C., Kaufman, L., Rosenberg, A.A., Sugihara, G., Nonlinear dynamic features and co-predictability of the Georges Bank fish community. Mar. Ecol. Prog. Ser. 464 (2012), 195–207.
72. Lorenzo-Seva, U., Ten Berge, J.M., Tucker's congruence coefficient as a meaningful index of factor similarity. Methodology 2 (2006), 57–64.
73. MacArthur, R., Levins, R., The limiting similarity, convergence, and divergence of coexisting species. Am. Nat., 1967, 377–385.
74. Massie, T.M., Ryabov, A., Blasius, B., Weithoff, G., Gaedke, U., Complex transient dynamics of stage-structured populations in response to environmental changes. Am. Nat. 182 (2013), 103–119.
75. May, R.M., Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186 (1974), 645–647.
76. McGarigal, K., Landscape Pattern Metrics. 2006, John Wiley & Sons, Ltd., Encyclopedia of Environmetrics.
77. Meinhardt, H., Morphogenesis of lines and nets. Differentiation 6 (1976), 117–123.
78. Milly, P.C.D., Betancourt, J., Falkenmark, M., Hirsch, R.M., Kundzewicz, Z.W., Lettenmaier, D.P., Stouffer, R.J., Stationarity is dead: Whither water management?. Science 319 (2008), 573–574.
79. Moeckel, R., Murray, B., Measuring the distance between time series. Phys. D 102 (1997), 187–194.
80. Monod, J., The growth of bacterial cultures. Annu. Rev. Microbiol. 3 (1949), 371–394.
81. Mooij, W.M., DeAngelis, D.L., Uncertainty in spatially explicit animal dispersal models. Ecol. Appl. 13 (2003), 794–805.
82. Morales, Y., Weber, L.J., Mynett, A.E., Newton, T.J., Effects of substrate and hydrodynamic conditions on the formation of mussel beds in a large river. J. N. Am. Benthol. Soc. 25 (2006), 664–676.
83. Murray, A.B., Contrasting the goals, strategies, and predictions associated with simplified numerical models and detailed simulations. Geophys. Monogr. 135 (2003), 151–168.
84. Murray, A.B., Reducing model complexity for explanation and prediction. Geomorphology 90 (2007), 178–191.
85. Murray, A.B., Paola, C., A cellular model of braided rivers. Nature 371 (1994), 54–57.
86. Murray, A.B., Paola, C., Properties of a cellular braided-stream model. Earth Surf. Process. Landf. 22 (1997), 1001–1025.
87. Murray, A.B., Paola, C., Modelling the effect of vegetation on channel pattern in bedload rivers. Earth Surf. Process. Landf. 28 (2003), 131–143.
88. Murray, A.B., Knaapen, M.a.F., Tal, M., Kirwan, M.L., Biomorphodynamics: physical-biological feedbacks that shape landscapes. Water Resour. Res., 44, 2008, W11301.
89. Nicholas, A.P., Modelling the continuum of river channel patterns. Earth Surf. Process. Landf. 38 (2013), 1187–1196.
90. Nicholas, A.P., Quine, T.A., Crossing the divide: representation of channels and processes in reduced-complexity river models at reach and landscape scales. Geomorphology 90 (2007), 318–339.
91. Nicholas, A.P., Sandbach, S.D., Ashworth, P.J., Amsler, M.L., Best, J.L., Hardy, R.J., Lane, S.N., Orfeo, O., Parsons, D.R., Reesink, A.J., Modelling hydrodynamics in the Rio Paraná, Argentina: an evaluation and inter-comparison of reduced-complexity and physics based models applied to a large sand-bed river. Geomorphology 169 (2012), 192–211.
92. Odenbaugh, J., The strategy of “the strategy of model building in population biology.”. Biol. Philos. 21 (2006), 607–621.
93. Oreskes, N., Shrader-Frechette, K., Belitz, K., Verification, validation, and confirmation of numerical models in the earth sciences. Science 263 (1994), 641–646.
94. Palmer, M.A., Bernhardt, E.S., Allan, J.D., Lake, P.S., Alexander, G., Brooks, S., Carr, J., Clayton, S., Dahm, C.N., Follstad Shah, J., Standards for ecologically successful river restoration. J. Appl. Ecol. 42 (2005), 208–217.
95. Passalacqua, P., Lanzoni, S., Paola, C., Rinaldo, A., Geomorphic signatures of deltaic processes and vegetation: the Ganges-Brahmaputra-Jamuna case study. J. Geophys. Res. Earth Surf. 118 (2013), 1838–1849.
96. Patil, D.J., Hunt, B.R., Kalnay, E., Yorke, J.A., Ott, E., Local low dimensionality of atmospheric dynamics. Phys. Rev. Lett., 86, 2001, 5878.
97. Realpe-Gomez, J., Baudena, M., Galla, T., McKane, A.J., Rietkerk, M., Demographic noise and resilience in a semi-arid ecosystem model. Ecol. Complex. 15 (2013), 97–108.
98. Ricker, W.E., Numerical relations between abundance of predators and survival of prey. Can. Fish. Cult. 13 (1952), 5–9.
99. Rietkerk, M., Van de Koppel, J., Regular pattern formation in real ecosystems. Trends Ecol. Evol. 23 (2008), 169–175.
100. Rose, K.A., Sable, S., DeAngelis, D.L., Yurek, S., Trexler, J.C., Graf, W., Reed, D.J., Proposed best modeling practices for assessing the effects of ecosystem restoration on fish. Ecol. Model. 300 (2015), 12–29.
101. Ruddell, B.L., Kumar, P., Ecohydrologic process networks: 1. Identification. Water Resour. Res., 45, 2009.
102. Ruddell, B.L., Brunsell, N.A., Stoy, P., Applying information theory in the geosciences to quantify process uncertainty, feedback, scale. EOS Trans. Am. Geophys. Union, 94, 2013, 56.
103. Rykiel, E.J. Jr., Testing ecological models: the meaning of validation. Ecol. Model. 90 (1996), 229–244.
104. Saco, P.M., Moreno-de las Heras, M., Ecogeomorphic coevolution of semiarid hillslopes: emergence of banded and striped vegetation patterns through interaction of biotic and abiotic processes. Water Resour. Res. 49 (2013), 115–126.
105. Saco, P.M., Rodríguez, J.F., 2.14 Modeling Ecogeomorphic Systems A2 - Shroder, John F. Pages 201–220 Treatise on Geomorphology. 2013, Academic Press, San Diego.
106. Salah, A.M., Nelson, E.J., Williams, G.P., Tools and algorithms to link horizontal hydrologic and vertical hydrodynamic models and provide a stochastic modeling framework. J. Adv. Model. Earth Syst., 2, 2010.
107. Sapozhnikov, V.B., Murray, A.B., Paola, C., Foufoula-Georgiou, E., Validation of braided-stream models: spatial state-space plots, self-affine scaling, and island shapes. Water Resour. Res. 34 (1998), 2353–2364.
108. Scheffer, M., Szabó, S., Gragnani, A., van Nes, E.H., Rinaldi, S., Kautsky, N., Norberg, J., Roijackers, R.M.M., Franken, R.J.M., Floating plant dominance as a stable state. Proc. Natl. Acad. Sci. U. S. A. 100 (2003), 4040–4045.
109. Schmeeckle, M.W., Numerical simulation of turbulence and sediment transport of medium sand. J. Geophys. Res. Earth Surf. 119 (2014), 1240–1262.
110. Schmolke, A., Thorbek, P., DeAngelis, D.L., Grimm, V., Ecological models supporting environmental decision making: a strategy for the future. Trends Ecol. Evol. 25 (2010), 479–486.
111. Schreiber, T., Measuring information transfer. Phys. Rev. Lett., 85, 2000, 461.
112. Seybold, H., Andrade, J.S., Herrmann, H.J., Modeling river delta formation. Proc. Natl. Acad. Sci. 104 (2007), 16804–16809.
113. SFWMD (South Florida Water Management District), Documentation of the South Florida Water Management Model Version 5.5. Page 305. 2005, South Florida Water Management District, West Palm Beach, FL.
114. Siteur, K., Mao, J., Nierop, K.G.J., Rietkerk, M., Dekker, S.C., Eppinga, M.B., Soil water repellency: a potential driver of vegetation dynamics in coastal dunes. Ecosystems, 2016 (in press).
115. Sivakumar, B., Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward. Stoch. Env. Res. Risk A. 23 (2009), 1027–1036.
116. Smirnov, N., Table for estimating the goodness of fit of empirical distributions. Ann. Math. Stat., 1948, 279–281.
117. Stark, C.P., Passalacqua, P., A dynamical system model of eco-geomorphic response to landslide disturbance. Water Resour. Res. 50 (2014), 8216–8226.
118. Suding, K.N., Gross, K.L., The dynamic nature of ecological systems: multiple states and restoration trajectories. Foundations of Restoration Ecology, 2006, 190–209.
119. Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, M., Munch, S., Detecting causality in complex ecosystems. Science 338 (2012), 496–500.
120. Takens, F., Dynamical Systems and Turbulence (Detecting Strange Attractors in Fluid Turbulence). 1981.
121. Thiery, J.M., D'Herbes, J.-M., Valentin, C., A model simulating the genesis of banded vegetation patterns in Niger. J. Ecol. 83 (1995), 497–507.
122. Thomas, R., Nicholas, A.P., Simulation of braided river flow using a new cellular routing scheme. Geomorphology 43 (2002), 179–195.
123. Tilman, D., Resource Competition and Community Structure. (Mpb-17). 1982, Princeton University Press.
124. Topping, C.J., Hansen, T.S., Jensen, T.S., Jepsen, J.U., Nikolajsen, F., Odderskær, P., ALMaSS, an agent-based model for animals in temperate European landscapes. Ecol. Model. 167 (2003), 65–82.
125. Tucker, G.E., Hancock, G.R., Modelling landscape evolution. Earth Surf. Process. Landf. 35 (2010), 28–50.
126. Tuljapurkar, S., Caswell, H., Structured-population Models in Marine, Terrestrial, and Freshwater Systems. 2012, Springer Science & Business Media.
127. Turing, A.M., The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. Ser. B Biol. Sci. 237 (1952), 37–72.
128. USEPA (U.S. Environmental Protection Agency), Chesapeake Bay Phase 5.3 Community Watershed Model. EPA 903S10002 - CBP/TRS-303-10. 2010, U.S. Environmental Protection Agency, Chesapeake Bay Program Office, Annapolis, MD.
129. van de Koppel, J., Crain, C.M., Scale-dependent inhibition drives regular tussock spacing in a freshwater marsh. Am. Nat. 168 (2006), E136–E147.
130. Volterra, V., Variations and fluctuations of the number of individuals in animal species living together. J. Cons. Int. Explor. Mer 3 (1928), 3–51.
131. Voroney, R.P., Van Veen, J.A., Paul, E.A., Organic C dynamics in grassland soils. 2. Model validation and simulation of the long-term effects of cultivation and rainfall erosion. Can. J. Soil Sci., 2011.
132. Watts, D.L., Cohen, M.J., Heffernan, J.B., Osborne, T.Z., Hydrologic modification and the loss of self-organized patterning in the ridge–slough mosaic of the Everglades. Ecosystems 13 (2010), 813–827.
133. Weerman, E.J., Van de Koppel, J., Eppinga, M.B., Montserrat, F., Liu, Q.-X., Herman, P.M., Spatial self-organization on intertidal mudflats through biophysical stress divergence. Am. Nat. 176 (2010), E15–E32.
134. Werner, B.T., Eolian dunes: computer simulations and attractor interpretation. Geology 23 (1995), 1107–1110.
135. Werner, B.T., Modeling landforms as self-organized, hierarchical dynamical systems. Prediction in Geomorphology, 2003, 133–150.
136. Willgoose, G., Mathematical modeling of whole landscape evolution. Annu. Rev. Earth Planet. Sci. 33 (2005), 443–459.
137. Willgoose, G., Bras, R.L., Rodriguez-Iturbe, I., A coupled channel network growth and hillslope evolution model: 2. Nondimensionalization and applications. Water Resour. Res. 27 (1991), 1685–1696.
138. Wilson, J.A., Acheson, J.M., Metcalfe, M., Kleban, P., Chaos, complexity and community management of fisheries. Mar. Policy 18 (1994), 291–305.
139. Ye, H., Beamish, R.J., Glaser, S.M., Grant, S.C.H., Hsieh, C., Richards, L.J., Schnute, J.T., Sugihara, G., Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling. Proc. Natl. Acad. Sci. 112 (2015), E1569–E1576.
140. Yoo, K., Amundson, R., Heimsath, A.M., Dietrich, W.E., Process-based model linking pocket gopher (Thomomys bottae) activity to sediment transport and soil thickness. Geology 33 (2005), 917–920.
141. Zhang, D., Narteau, C., Rozier, O., Morphodynamics of barchan and transverse dunes using a cellular automaton model. J. Geophys. Res. Earth Surf.(2003 − 2012), 2010, 115.
142. Zhang, D., Narteau, C., Rozier, O., Courrech du Pont, S., Morphology and dynamics of star dunes from numerical modelling. Nat. Geosci. 5 (2012), 463–467.