Oceanography The Official Magazine of
The Oceanography Society
Volume 26 Issue 03

View Issue TOC
Volume 26, No. 3
Pages 220 - 231

OpenAccess

Nonlinear Dynamics and Alternative Stable States in Shallow Coastal Systems

By Karen J. McGlathery , Matthew A. Reidenbach, Paolo D’Odorico , Sergio Fagherazzi, Michael L. Pace, and John H. Porter  
Jump to
Article Abstract Citation References Copyright & Usage
Article Abstract

The dynamics of shallow-water coastal environments are controlled by external drivers—sea level rise, storms, and sediment and nutrient supplies—and by internal feedbacks. Interactions of biotic processes (vegetation growth, trophic dynamics) and abiotic drivers can lead to nonlinear responses to changing conditions and to the emergence of thresholds, hysteresis, and alternative stable states. We develop a conceptual framework for studying interactions between the dynamics of marshes and habitats in shallow coastal bays with unconsolidated sediments (seagrass, oyster reefs). Using examples primarily from the Virginia Coast Reserve Long Term Ecological Research site, we show that in the subtidal part of the landscape, two alternative stable states can exist—one dominated by seagrass up to a certain depth that represents a tipping point to the second, unvegetated stable state. The depth limit of the seagrass stable state is influenced by (1) the positive feedback of vegetation on reducing sediment suspension and improving the light environment for growth, (2) climate (e.g., temperature), and (3) water quality. Two stable states are also present in intertidal areas, with salt marshes lying above mean sea level and tidal flats below mean sea level. State transitions are driven by sediment availability, sea level rise, the relative strength of wind waves with respect to tidal currents, and the biotic feedback of vegetation on sediment stabilization and accretion. State-change dynamics in one system may propagate to adjacent systems, and this coupling may influence the landscape-scale response to environmental change. Seagrass meadows and oyster reefs affect adjacent marshes both positively (wave attenuation) and negatively (reduced sediment supply), and marsh-edge erosion could negatively influence the light environment for seagrass growth. Forecasting the resilience of coastal ecosystems and the landscape-scale response to environmental change in the next century requires an understanding of nonlinear dynamics, including the possibility of multiple stable states, the coupled evolution of adjacent systems, and potential early warning signs of thresholds of change.

Citation

McGlathery, K.J., M.A. Reidenbach, P. D’Odorico, S. Fagherazzi, M.L. Pace, and J.H. Porter. 2013. Nonlinear dynamics and alternative stable states in shallow coastal systems. Oceanography 26(3):220–231, https://doi.org/10.5670/oceanog.2013.66.

References
    Angelini, C., and B.R. Silliman. 2012. Patch size-dependent community recovery after massive disturbance. Ecology 93:101–110, https://doi.org/10.1890/11-0557.1.
  1. Bartol, I.K., and R. Mann. 1997. Small-scale settlement patterns of the oyster Crassostrea virginica on a constructed intertidal reef. Bulletin of Marine Science 61:881–897.
  2. Bestelmeyer, B.T., A.M. Ellison, W.R. Fraser, K.B. Gorman, S.J. Holbrook, C.M. Laney, M.D. Ohman, D.P.C. Peters, F.C. Pillsbury, A. Rassweiler, and others. 2011. Analysis of abrupt transitions in ecological systems. Ecosphere 2(12):129, https://doi.org/10.1890/ES11-00216.1.
  3. Biggs, R., S.R. Carpenter, and W.A. Brock. 2009. Turning back from the brink: Detecting an impending regime shift in time to avert it. Proceedings of the National Academy of Sciences of the United States of America 106:826–831, https://doi.org/10.1073/pnas.0811729106.
  4. Briceño, H.O., and J.N. Boyer. 2010. Climatic controls on phytoplankton in a subtropical estuary, Florida Bay, USA. Estuaries and Coasts 33:541–553, https://doi.org/10.1007/s12237-009-9189-1.
  5. Carpenter, S.R. 2002. Ecological futures: Building an ecology of the long now. Ecology 83:2,069–2,083, https://doi.org/​10.1890/0012-9658(2002)083[2069:EFBAEO]2.0.CO;2.
  6. Carpenter, S.R. 2003. Regime Shifts in Lake Ecosystems: Pattern and Variation. Ecology Institute, Oldendorf/Luhe, Germany, 199 pp.
  7. Carpenter, S.R., J.J. Cole, M.L. Pace, R. Batt, W.A. Brock, T. Cline, J. Coloso, J.R. Hodgson, J.F. Kitchell, D.A. Seekell, and others. 2011. Early warnings of regime shifts: A whole-ecosystem experiment. Science 332:1,079–1,082, https://doi.org/10.1126/science.1203672
  8. Carr, J.A., P. D’Odorico, K.J. McGlathery, and P.L. Wiberg. 2010. Stability and bistability of seagrass ecosystems in shallow coastal lagoons: Role of feedbacks with sediment suspension and light availability. Journal of Geophysical Research 115, G03011, https://doi.org/​10.1029/2009JG001103.
  9. Carr, J.A., P. D’Odorico, K.J. McGlathery, and P.L. Wiberg. 2012a. Stability and resilience of seagrass meadows to seasonal and interannual dynamics and environmental stress. Journal of Geophysical Research 117, G01007, https://doi.org/10.1029/2011JG001744.
  10. Carr, J.A., P. D’Odorico, K.J. McGlathery, and P.L. Wiberg. 2012b. Modeling the effects of climate change on eelgrass stability and resilience: Future scenarios and leading indicators of collapse. Marine Ecology Progress Series 448:289–301, https://doi.org/10.3354/meps09556.
  11. Cerco, C.F., and M.R. Noel. 2007. Can oyster restoration reverse cultural eutrophication in Chesapeake Bay? Estuaries and Coasts 30:331–343, https://doi.org/10.1007/BF02700175.
  12. Clark, J.S., R. Carpenter, M. Barber, S. Collins, A. Dobson, J. Foley, D. Lodge, M. Pascual, R. Pielke Jr., W. Pizer, and others. 2001. Ecological forecasting: An emerging imperative. Science 293:657–660, https://doi.org/10.1126/science.293.5530.657.
  13. Coen, L.D., and M.W. Luckenbach. 2000. Developing success criteria and goals for evaluating oyster reef restoration: Ecological function or resource exploitation? Ecological Engineering 15:323–343, https://doi.org/​10.1016/S0925-8574(00)00084-7.
  14. Contamin, R., and A.M. Ellison. 2009. Indicators of regime shifts in ecological systems: What do we need to know and when do we need to know it. Ecological Applications 19:799–816, https://doi.org/10.1890/08-0109.1.
  15. Dai, L., D. Vorselen, K.S. Korolev, and J. Gore. 2012. Generic indicators for loss of resilience before a tipping point leading to a population collapse. Science 336:1,175–1,177, https://doi.org/10.1126/science.1219805.
  16. Dakos, V., E. Benincà, E.H. van Nes, C.J.M. Philippart, M. Scheffer, and J. Huisman. 2009. Interannual variability in species composition explained as seasonally entrained chaos. Proceedings of the Royal Society B 276:2,871–2,880, https://doi.org/​10.1098/rspb.2009.0584.
  17. Dame, R.F., R.G. Zingmark, and E. Haskin. 1984. Oyster reefs as processors of estuarine materials. Journal of Experimental Marine Biology and Ecology 83:239–247, https://doi.org/10.1016/S0022-0981(84)80003-9.
  18. Day, J.W. Jr., F. Scarton, A. Rismondo, and D. Are. 1998. Rapid deterioration of a salt marsh in Venice Lagoon, Italy. Journal of Coastal Research 14:583–590.
  19. Deegan, L.A., D.S. Johnson, R.S. Warren, B.J. Peterson, J.W. Fleeger, S. Fagherazzi, and W.M. Wolheim. 2012. Coastal eutrophication as a driver of salt marsh loss. Nature 490:389–392, https://doi.org/10.1038/nature11533
  20. Di Lorenzo, E., and M.D. Ohman. 2013. A double-integration hypothesis to explain ocean ecosystem response to climate forcing. Proceedings of the National Academy of Sciences of the United States of America 110: 2,496–2,499, https://doi.org/10.1073/pnas.1218022110.
  21. Drake, J.M., and B.D. Griffin. 2010. Early warning signals of extinction in deteriorating environments. Nature 467:456–459, https://doi.org/​10.1038/nature09389.
  22. Duarte, C.M., D.J. Conley, J. Carstensen, and M. Sanchez-Camacho. 2009. Return to Neverland: Shifting baselines affect eutrophication restoration targets. Estuaries and Coasts 32:29–36, https://doi.org/10.1007/s12237-008-9111-2.
  23. Fagherazzi, S., L. Carniello, L. D’Alpaos, and A. Defina. 2006. Critical bifurcation of shallow microtidal landforms in tidal flats and salt marshes. Proceedings of the National Academy of Sciences of the United States of America 103:8,337–8,341, https://doi.org/​10.1073/pnas.0508379103.
  24. Fagherazzi, S., D.M. Fitzgerald, R.W. Fulweiler, P.L. Wiberg, K.J. McGlathery, J.T. Morris, T.J. Tolhurst, L.A. Deegan, and D.S. Johnson. 2012a. Ecogeomorphology of salt marshes. Pp. 182–200 in Treatise on Geomorphology, vol. 12, Ecogeomorphology. D. Butler and C. Hupp, eds, J. Shroder, exec. ed., Elsevier, https://doi.org/10.1016/B978-0-12-374739-
    6.00329-8
    .
  25. Fagherazzi, S., D.M. Fitzgerald, R.W. Fulweiler, P.L. Wiberg, K.J. McGlathery, J.T. Morris, T.J. Tolhurst, L.A. Deegan, and D.S. Johnson. 2012b. Ecogeomorphology of tidal flats. Pp. 201–220 in Treatise on Geomorphology, vol. 12, Ecogeomorphology. D. Butler and C. Hupp, eds, J. Shroder, exec. ed., Elsevier, https://doi.org/10.1016/B978-0-12-374739-
    6.00403-6
    .
  26. Fagherazzi, S., C. Palermo, M.C. Rulli, L. Carniello, and A. Defina. 2007. Wind waves in shallow microtidal basins and the dynamic equilibrium of tidal flats. Journal of Geophysical Research 112, F02024, https://doi.org/​10.1029/2006JF000572.
  27. Fagherazzi, S., and P.L. Wiberg. 2009. Importance of wind conditions, fetch, and water levels on wave-generated shear stresses in shallow intertidal basins. Journal of Geophysical Research 114, F03022, https://doi.org/​10.1029/2008JF001139.
  28. Feagin, R.A., S.M. Lozada-Bernard, T.M. Ravens, I. Moller, K.M. Yeager, and A.H. Baird. 2009. Does vegetation prevent wave erosion of salt marsh edges? Proceedings of the National Academy of Sciences of the United States of America 106:10,109–10,113, https://doi.org/​10.1073/pnas.0901297106.
  29. Folkard, A.M. 2005. Hydrodynamics of model Posidonia oceanica patches in shallow water. Limnology and Oceanography 50:1,592–1,600.
  30. Folkard, A.M. 2011. Flow regimes in gaps within stands of flexible vegetation: Laboratory flume simulations. Environmental Fluid Mechanics 11:289–306, https://doi.org/​10.1007/s10652-010-9197-5.
  31. Fredriksson, D.W., C.N. Steppe, L. Wallendorf, S. Sweeney, and D. Kriebel. 2010. Biological and hydrodynamic design considerations for vertically oriented oyster grow out structures. Aquaculture Engineering 42:57–69, https://doi.org/10.1016/j.aquaeng.2009.11.002.
  32. Fuchs, H.L., M.G. Neubert, and L.S. Mullineaux. 2007. Effects of turbulence-mediated larval behavior on larval supply and settlement in tidal currents. Limnology and Oceanography 52:1,156–1,165, https://doi.org/10.4319/lo.2007.52.3.1156.
  33. Groffman, P.M., J.S. Baron, T. Blett, A.J. Gold, I. Goodman, L.H. Gunderson, B.M. Levinson, M.A. Palmer, H.W. Paerl, G.D. Peterson, and others. 2006. Ecological thresholds: The key to successful environmental management or an important concept with no practical application. Ecosystems 9:1–13, https://doi.org/10.1007/s10021-003-0142-z.
  34. Gruber, R.K., and W.M. Kemp. 2010. Feedback effects in a coastal canopy forming submersed plant bed. Limnology and Oceanography 55: 2,285–2,298, https://doi.org/10.4319/lo.2010.55.6.2285.
  35. Hansen, J.C.R., and M.A Reidenbach. 2012. Wave and tidally driven flows within Zostera marina seagrass beds and their impact on sediment suspension. Marine Ecology Progress Series 448:271–287, https://doi.org/10.3354/meps09225.
  36. Hansen, J.C.R., and M.A. Reidenbach. 2013. Seasonal growth and senescence of a Zostera marina seagrass meadow alters wave-dominated flow and sediment suspension within a coastal bay. Estuaries and Coasts, https://doi.org/10.1007/s12237-013-9620-5.
  37. Harrold, C., and D.C. Reed. 1985. Food availability, sea-urchin grazing, and kelp forest community structure. Ecology 66:1,160–1,169, https://doi.org/10.2307/1939168.
  38. Hutchings, J.A. 1996. Spatial and temporal variation in the density of northern cod and a review of hypotheses for the stock’s collapse. Canadian Journal of Fisheries and Aquatic Science 53:943–962.
  39. Kemp, W.M., W.R. Boynton, J.E. Adolf, D.F. Boesch, W.C. Boicourt, G. Brush, J.C. Cornwell, T.R. Fisher, P.M. Glibert, J.D. Hagy, and others. 2005. Eutrophication of Chesapeake Bay: Historical trends and ecological interactions. Marine Ecology Progress Series 303:1–29, https://doi.org/10.3354/meps303001.
  40. Kirwan, M.L., G.R. Guntenspergen, A. D’Alpaos, J.T. Morris, S.M. Mudd, and S. Temmerman. 2010. Limits on the adaptability of coastal marshes to rising sea level. Geophysical Research Letters 37, L2340, https://doi.org/​10.1029/2010GL045489.
  41. Kirwan, M.L., and A.B. Murray. 2007. A coupled geomorphic and ecological model of tidal marsh evolution. Proceedings of the National Academy of Sciences of the United States of America 104:6,118–6,122, https://doi.org/10.1073/pnas.0700958104
  42. Koch, E.M., J.D. Ackerman, J. Verduin, and M. van Keulen. 2006. Fluid dynamics in seagrass ecology: From molecules to ecosystems. Pp. 193–225 in Seagrass Biology, Ecology and Conservation. A.W.D. Larkum, R.J. Orth, and C. Duarte, eds, Springer.
  43. Koehl, M.A.R., and M.G. Hadfield. 2010. Hydrodynamics of larval settlement from a larva’s point of view. Integrative and Comparative Biology 50(4):539–551, https://doi.org/10.1093/icb/icq101.
  44. Lenihan, H.S. 1999. Physical-biological coupling on oyster reefs: How habitat structure influences individual performance. Ecological Monographs 69:251–275, https://doi.org/​10.1890/0012-9615(1999)069[0251:PBCOOR]2.0.CO;2.
  45. Levin, L.A. 2006. Recent progress in understanding larval dispersal: New directions and digressions. Integrated and Comparative Biology 46:282–297, https://doi.org/10.1093/icb/icj024.
  46. Lindegren, M, V. Dakos, J.P. Gröger, A. Gårdmark, G. Kornilova, S.A. Otto, and C. Möllmann. 2012. Early detection of ecosystem regime shifts: A multiple method evaluation for management application. PLoS One 7:e3841, https://doi.org/​10.1371/journal.pone.0038410.
  47. Mackenzie, C. 1983. To increase oyster production in the northeastern United States. Marine Fisheries Review 45:1–22.
  48. Marani, M., A. D’Alpaos, S. Lanzoni, L. Carniello, and A. Rinaldo. 2007. Biologically controlled multiple equilibria of tidal landforms and the fate of the Venice lagoon. Geophysical Research Letters 34, L11402, https://doi.org/​10.1029/2007GL030178.
  49. Marani, M., A. D’Alpaos, S. Lanzoni, L. Carniello, and A. Rinaldo. 2010. The importance of being coupled: Stable states and catastrophic shifts in tidal biomorphodynamics. Journal of Geophysical Research 115, F04004, https://doi.org/10.1029/2009JF001600
  50. Marani, M., C. Da Lio, and A. D’Alpaos. 2013. Vegetation engineers marsh morphology through multiple competing stable states. Proceedings of the National Academy of Sciences of the United States of America, https://doi.org/10.1073/pnas.1218327110.
  51. Mariotti, G., and S. Fagherazzi. 2012. Modeling the effect of tides and waves on benthic biofilms. Journal of Geophysical Research 117, G04010, https://doi.org/10.1029/2012JG002064.
  52. Mariotti, G., and S. Fagherazzi. 2013. A two-point dynamic model for the coupled evolution of channels and tidal flats. Journal of Geophysical Research Earth Surface, https://doi.org/​10.1002/jgrf.20070
  53. Mariotti, G., S. Fagherazzi, P.L. Wiberg, K.J. McGlathery, L. Carniello, and A. Defina. 2010. Influence of storm surges and sea level on shallow tidal basin erosive processes. Journal of Geophysical Research 115, C11012, https://doi.org/10.1029/2009JC005892.
  54. May, R.M. 1977. Thresholds and breakpoint in ecosystems with multiplicity of stable states. Nature 269:471–477, https://doi.org/​10.1038/269471a0.
  55. McCormick-Ray, M. 1998. Oyster reefs in 1878 seascape pattern: Winslow revisited. Estuaries and Coasts 21:784–800, https://doi.org/​10.2307/1353281.
  56. McCormick-Ray, J. 2005. Historical oyster reef connections to Chesapeake Bay: A framework for consideration. Estuarine, Coastal and Shelf Science 64:119–134, https://doi.org/10.1016/​j.ecss.2005.02.011.
  57. McGlathery, K.J., L.K. Reynolds, L.W. Cole, R.J. Orth, and A. Schwarzschild A. 2012. Recovery trajectories during state change from bare sediment to eelgrass dominance. Marine Ecology Progress Series 448:209–221, https://doi.org/10.3354/meps09574.
  58. McGlathery, K.J., K. Sundback, and I.C. Anderson. 2007. Eutrophication in shallow coastal bays and lagoons: The role of plants in the coastal filter. Marine Ecology Progress Series 348:1–18, https://doi.org/10.3354/meps07132
  59. Millennium Assessment. 2005. Ecosystems and Human Well-Being: A Manual for Assessment Practitioners. Island Press, Washington, DC, 288 pp.
  60. Morris, J.T., P.V. Sundareshwar, C.T. Nietch, B. Kjerfve, and D.R. Cahoon. 2002. Responses of coastal wetlands to rising sea level. Ecology 83:2,869–2,877, https://doi.org/​10.1890/0012-9658(2002)083[2869:ROCWTR]​2.0.CO;2.
  61. Nelson, K.A., L.A. Leonard, M.H. Posey, T.D. Alphin, and M.A. Mallin. 2004. Using transplanted oyster (Crassostrea virginica) beds to improve water quality in small tidal creeks: A pilot study. Journal of Experimental and Marine Biological Ecology 298:347–368, https://doi.org/10.1016/S0022-0981(03)00367-8.
  62. Nestlerode, J.A., M.L. Luckenbach, and F.X. O’beirn. 2007. Settlement and survival of the oyster Crassostrea virginica on created oyster reef habitats in Chesapeake Bay. Restoration Ecology 15:273–283, https://doi.org/10.1111/j.1526-100X.2007.00210.x.
  63. Newell, R.I.E. 1988. Ecological changes in Chesapeake Bay: Are they the result of over harvesting the american oyster, Crassostrea virginica? Understanding the Estuary: Advances in Chesapeake Bay Research 129:536–546.
  64. Ogburn, M.B., and M. Alber. 2006. An investigation of salt marsh dieback in Georgia using field transplants. Estuaries and Coasts 29:54–62, https://doi.org/10.1007/BF02784698
  65. Pace, M.L., S.R. Carpenter, R.A. Johnson, and J.T. Kurtzweil. 2013. Zooplankton provide early warnings of a regime shift in a whole lake manipulation. Limnology and Oceanography 58:525–532, https://doi.org/​10.4319/lo.2013.58.2.0525
  66. Papanicolaou, A.N., P. Diplas, C.L. Dancey, and M. Balakrishnan. 2001. Surface roughness effects in near-bed turbulence: Implications to sediment entrainment. Journal of Engineering Mechanics 127:211–218, https://doi.org/​10.1061/(ASCE)0733-9399(2001)127:3(211).
  67. Paterson, D.M. 1989. Short-term changes in the erodability of intertidal cohesive sediments related to the migratory behavior of epipelic diatoms. Limnology and Oceanography 34(1):223–234.
  68. Peterson, C.H. 1984. Does a rigorous criterion for environmental identity preclude the existence of multiple stable points? American Naturalist 124:127–133.
  69. Petraitis, P.S., E.T. Methratta, E.C. Rhile, N.A. Vidarga, and S.R. Dudgeon. 2009. Experimental confirmation of multiple community states in a marine ecosystem. Oecologia 161:139–148, https://doi.org/​10.1007/s00442-009-1350-9.
  70. Phillips, J.D. 1986. Coastal submergence and marsh fringe erosion. Journal of Coastal Research 2:427–436.
  71. Porter, J.H. 2007. Landscape change data layer for the Virginia Coast Reserve, 1973–2001. Long Term Ecological Research Network, https://doi.org/10.6073/pasta/9b8531de67842c4f82e84ab343e6634c.
  72. Rassweiler, A., R.J. Schmitt, and S.J. Holbrook. 2010. Triggers and maintenance of multiple shifts in the state of a natural community. Oecologia 164:489–498, https://doi.org/​10.1007/s00442-010-1666-5.
  73. Reynolds, L.K., M. Waycott, K.J. McGlathery, R.J. Orth, and J.C. Zieman. 2012. Eelgrass restoration by seed maintains genetic diversity: Case study from a coastal bay system. Marine Ecology Progress Series 448:223–233, https://doi.org/​10.3354/meps09386.
  74. Rotschild, B.J., J.S. Ault, P. Goulletquer, and M. Heral. 1994. Decline of the Chesapeake Bay oyster population: A century of habitat destruction and overfishing. Marine Ecology Progress Series 111:29–39.
  75. Scheffer, M. 2009. Critical Transitions in Nature and Society. Princeton University Press, Princeton, NJ, 384 pp.
  76. Scheffer, M., J. Bascompte, W.A. Brock, V. Brovkin, S.R. Carpenter, V. Dakos, H. Held, E.H. van Nes, M. Rietkerk, and G. Sugihara. 2009. Early warning signals for critical transitions. Nature 461:53–59, https://doi.org/​10.1038/nature08227.
  77. Scheffer, M., S.R. Carpenter, J.A. Foley, C. Folke, and B. Walker. 2001. Catastrophic shifts in ecosystems. Nature 413:591–596, https://doi.org/​10.1038/35098000.
  78. Schulte, D.M., R.P. Burke, and R.N. Lipcius. 2009. Unprecedented restoration of a native oyster metapopulation. Science 325:1,124–1,128, https://doi.org/10.1126/science.1176516.
  79. Schröder, A., L. Persson, A.M. De Roos. 2005. Direct experimental evidence for alternative stable states: A review. Oikos 110:3–19, https://doi.org/10.1111/j.0030-1299.2005.13962.x.
  80. Schwimmer, R.A. 2001. Rates and processes of marsh shoreline erosion in Rehoboth Bay, Delaware, USA. Journal of Coastal Research 17:672–683.
  81. Scyphers, S.B., S.P. Powers, K.L. Heck Jr., and D. Byron. 2011. Oyster reefs as natural breakwaters mitigate shoreline loss and facilitate fisheries. PLoS ONE 6(8):e22396, https://doi.org/10.1371/journal.pone.0022396.
  82. Seekell, D.A., S.R. Carpenter, T.J. Cline, and M.L. Pace. 2012. Conditional heteroskedasticity forecasts regime shift in a whole-ecosystem experiment. Ecosystems 15:751–757, https://doi.org/10.1007/s10021-012-9542-2.
  83. Soniat, T.M., C.M. Finelli, and J.T. Ruiz. 2004. Vertical structure and predator refuge mediate oyster reef development and community dynamics. Journal of Experimental Marine Biology and Ecology 310:163–182, https://doi.org/10.1016/j.jembe.2004.04.007.
  84. Steneck, R.S., M.H. Graham, B.J. Bourque, D. Corbet, J.M. Erlandson, J.A. Estes, M.J. Tegner. 2002. Kelp forest ecosystems: Biodiversity, stability, resilience, and future. Environmental Conservation 29:436–459, https://doi.org/10.1017/S0376892902000322.
  85. Tonelli, M., S. Fagherazzi, and M. Petti. 2010. Modeling wave impact on salt marsh boundaries. Journal of Geophysical Research Oceans 115, C09028, https://doi.org/​10.1029/2009JC006026.
  86. van der Heide, T., T.J. Bouma, H. Egbert, J. van Nes, J. van de Koppel, M. Scheffer, J.G.M. Roelofs, M.M. van Katwijk, and A.J.P. Smolders. 2010. Spatial self-organized patterning in seagrasses along a depth gradient of an intertidal ecosystem. Ecology 91:362–369, https://doi.org/​10.1890/08-1567.1.
  87. van der Wal, D., and K. Pye. 2004. Patterns, rates and possible causes of saltmarsh erosion in the Greater Thames area (UK). Geomorphology 61:373–391, https://doi.org/10.1016/j.geomorph.2004.02.005.
  88. Van Katwijk, M.M., A.R. Bos, V.N. de Jonge, L. Hanssen, D.C.R. Hermus, and D.J. de Jong. 2009. Guidelines for seagrass restoration: Importance of habitat selection and donor population, spreading of risks, and ecosystem engineering effects. Marine Pollution Bulletin 58:179–188, https://doi.org/10.1016/​j.marpolbul.2008.09.028.
  89. Van Nes, E.H., and M. Scheffer. 2007. Slow recovery from perturbations as a generic indicator of nearby catastrophic shift. American Naturalist 170:660.
  90. Veraart, A.J., E.J. Faassen, V. Dakos, E.H. van Nes, M. Lurling, and M. Scheffer. 2012. Recovery rates reflect distance to a tipping point in a living system. Nature 481:357–359, https://doi.org/10.1038/nature10723.
  91. Verhagen, J.H.G., and P.H. Nienhuis. 1983. A simulation-model of production, seasonal-changes in biomass and distribution of eelgrass (Zostera marina) in lake Grevelingen. Marine Ecology Progress Series 10:187–195.
  92. Wachnicka, A., L.S. Collins, and E.E. Gaiser. 2013. Response of diatom assemblages to 130 years of environmental change in Florida Bay (USA). Journal of Paleolimnology 49:83–101, https://doi.org/10.1007/s10933-011-9556-3.
  93. Walker, B., and J.A. Meyers. 2004. Thresholds in ecological and social-ecological systems: A developing database. Ecology and Society 9(2):3, http://www.ecologyandsociety.org/vol9/iss2/art3
  94. Walker, B.H., and D. Salt. 2006. Resilience Thinking: Sustaining Ecosystems and People in a Changing World. Island Press, Washington, DC, 174 pp.
  95. Weerman, E.J., J.J. van Belzen, M. Rietkirk, S. Temmerman, S. Kefi, P.M.J. Herman, and J. van de Koppel. 2012. Changes in diatom patch-size distribution and degradation in a spatially self-organized intertidal mudflat ecosystem. Ecology 93:608–618, https://doi.org/​10.1890/11-0625.1.
  96. Whitman, E.R., and M.A. Reidenbach. 2012. Benthic flow environments affect recruitment of Crassostrea virginica larvae to an intertidal oyster reef. Marine Ecology Progress Series 463:177–191, https://doi.org/10.3354/meps09882.
  97. Wilson, C.A., and M.A. Allison. 2008. An equilibrium profile model for retreating marsh shorelines in southeast Louisiana. Estuarine, Coastal and Shelf Science 80:483–494, https://doi.org/​10.1016/j.ecss.2008.09.004
  98. Zharova, N., A. Sfriso, A. Voinov, and B. Pavoni. 2001. A simulation model for the annual fluctuation of Zostera marina biomass in the Venice lagoon. Aquatic Botany 70:135–150, https://doi.org/10.1016/S0304-3770(01)00151-6.
  99. Zhou, Y., H. Yang, T. Zhang, S. Liu, S. Zhang, Q. Liu, J. Xiang, and F. Zhang. 2006. Influence of filtering and biodeposition by the cultured scallop Chlamys farreri on benthic-pelagic coupling in a eutrophic bay in China. Marine Ecology Progress Series 317:127–141, https://doi.org/10.3354/meps317127.
Copyright & Usage

This is an open access article made available under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution, and reproduction in any medium or format as long as users cite the materials appropriately, provide a link to the Creative Commons license, and indicate the changes that were made to the original content. Images, animations, videos, or other third-party material used in articles are included in the Creative Commons license unless indicated otherwise in a credit line to the material. If the material is not included in the article’s Creative Commons license, users will need to obtain permission directly from the license holder to reproduce the material.