Eluding catastrophic shifts

Proceedings of the National Academy of Sciences of the United States of America

Volumn 112, Issue 15, 2015, Pages E1828-E1836

  Villa Martín, Paula ^a   Bonachela, Juan A ^b,d   Levin, Simon A ^b   Muñoz, Miguel A ^c  

^a UNIVERSITY OF GRANADA   (Spain)

^b PRINCETON UNIVERSITY   (United States)

^c UNIVERSITY OF GRANADA   (Spain)

^d UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Catastrophic shifts; Critical transitions; Demographic stochasticity; Nonequilibrium phase transitions; Renormalization group

Indexed keywords

ARTICLE; BIODIVERSITY; CATASTROPHIC SHIFT; COMPUTER SIMULATION; ECOSYSTEM; ENVIRONMENTAL CHANGE; GENETIC HETEROGENEITY; LIMITED MOBILITY; NEUROSCIENCE; PHASE TRANSITION; PHENOMENOLOGY; POPULATION GENETICS; POPULATION GROWTH; POSITIVE FEEDBACK; PRIORITY JOURNAL; SOCIOECONOMICS; SOCIOLOGY; STEADY STATE; STOCHASTIC MODEL; SYSTEMS BIOLOGY; ALGORITHM; DISASTER; DISASTER PLANNING; ENVIRONMENTAL PROTECTION; HUMAN; PREVENTION AND CONTROL; PROCEDURES; THEORETICAL MODEL;

ANTHOZOA;

ALGORITHMS; COMPUTER SIMULATION; CONSERVATION OF NATURAL RESOURCES; DISASTER PLANNING; DISASTERS; ECOSYSTEM; HUMANS; MODELS, THEORETICAL;

EID: 84928154835     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1414708112     Document Type: Article

References (83)

1. Scheffer M (2009) Critical Transitions in Nature and Society, Princeton Studies in Complexity (Princeton University Press, Princeton).
2. Scheffer M, et al. (2012) Anticipating critical transitions. Science 338(6105):344-348.
3. May RM, Levin SA, Sugihara G (2008) Complex systems: Ecology for bankers. Nature 451(7181):893-895.
4. Lade SJ, Tavoni A, Levin SA, Schlüter M (2013) Regime shifts in a social-ecological system. Theor Ecol 6(3):359-372.
5. Scheffer M (1998) The Ecology of Shallow Lake (Chapman and Hall, London).
6. Staver AC, Archibald S, Levin SA (2011) The global extent and determinants of savanna and forest as alternative biome states. Science 334(6053):230-232.
7. Hirota M, Holmgren M, Van Nes EH, Scheffer M (2011) Global resilience of tropical forest and savanna to critical transitions. Science 334(6053):232-235.
8. Frank KT, Petrie B, Fisher JA, Leggett WC (2011) Transient dynamics of an altered large marine ecosystem. Nature 477(7362):86-89.
9. Carpenter SR, et al. (2011) Early warnings of regime shifts: A whole-ecosystem experiment. Science 332(6033):1079-1082.
10. Kéfi S, Rietkerk M, van Baalen M, Loreau M (2007) Local facilitation, bistability and transitions in arid ecosystems. Theor Popul Biol 71(3):367-379.
11. Verwijmeren M, Rietkerk M, Wassen MJ, Smit C (2013) Interspecific facilitation and critical transitions in arid ecosystems. Oikos 122(3):341-347.
12. von Hardenberg J, Meron E, Shachak M, Zarmi Y (2001) Diversity of vegetation patterns and desertification. Phys Rev Lett 87(19):198101.
13. Scheffer M, Carpenter S, Foley JA, Folke C, Walker B (2001) Catastrophic shifts in ecosystems. Nature 413(6856):591-596.
14. Scheffer M, Carpenter SR (2003) Catastrophic regime shifts in ecosystems: Linking theory to observation. Trends Ecol Evol 18(12):648-656.
15. Kéfi S, et al. (2007) Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449(7159):213-217.
16. Scanlon TM, Caylor KK, Levin SA, Rodriguez-Iturbe I (2007) Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature 449(7159):209-212.
17. Solé R (2007) Ecology: Scaling laws in the drier. Nature 449(7159):151-153.
18. Staver AC, Levin SA (2012) Integrating theoretical climate and fire effects on savanna and forest systems. Am Nat 180(2):211-224.
19. Taylor CM, Hastings A (2005) Allee effects in biological invasions. Ecol Lett 8(8): 895-908.
20. Zucker RS, Regehr WG (2002) Short-term synaptic plasticity. Annu Rev Physiol 64: 355-405.
21. Pal M, Pal AK, Ghosh S, Bose I (2013) Early signatures of regime shifts in gene expression dynamics. Phys Biol 10(3):036010.
22. Solé RV (2011) Phase Transitions (Princeton University Press, Princeton).
23. Solé RV, Bascompte J (2006) Self-Organization in Complex Ecosystems (Princeton University Press, Princeton).
24. Murray JD (2002) Mathematical Biology: I. An Introduction (Springer-Verlag, New York).
25. Ott E (2002) Chaos in Dynamical Systems (Cambridge University Press, Cambridge).
26. Henkel M, Hinrichsen H, Lübeck S (2008) Non-Equilibrium Phase Transitions (Springer, Berlin), Vol 1.
27. Hinrichsen H (2000) Non-equilibrium critical phenomena and phase transitions into absorbing states. Adv Phys 49(7):815-958.
28. Ódor G (2008) Universality in Nonequilibrium Lattice Systems: Theoretical Foundations (World Scientific, Singapore), pp 276-572.
29. Scheffer M, et al. (2009) Early-warning signals for critical transitions. Nature 461(7260):53-59.
30. Dai L, Vorselen D, Korolev KS, Gore J (2012) Generic indicators for loss of resilience before a tipping point leading to population collapse. Science 336(6085):1175-1177.
31. Dai L, Korolev KS, Gore J (2013) Slower recovery in space before collapse of connected populations. Nature 496(7445):355-358.
32. Lade SJ, Gross T (2012) Early warning signals for critical transitions: A generalized modeling approach. PLOS Comput Biol 8(2):e1002360.
33. Boettiger C, Hastings A (2012) Early warning signals and the prosecutor's fallacy. Proc Biol Sci 279(1748):4734-4739.
34. Boettiger C, Hastings A (2012) Quantifying limits to detection of early warning for critical transitions. J R Soc Interface 9(75):2527-2539.
35. Levin S, Pacala S (1997) Theories of Simplification and Scaling of Spatially Distributed Processes, eds Tilman D, Kareiva P (Princeton University Press, Princeton), pp 271-296.
36. Dakos V, Kéfi S, Rietkerk M, van Nes EH, Scheffer M (2011) Slowing down in spatially patterned ecosystems at the brink of collapse. Am Nat 177(6):E153-E166.
37. Dakos V, van Nes E, Donangelo R, Fort H, Scheffer M (2010) Spatial correlation as leading indicator of catastrophic shifts. J Theor Ecol 3(3):163-174.
38. Carpenter SR, Brock WA (2010) Early warnings of regime shifts in spatial dynamics using the discrete fourier transform. Ecosphere 1(5):10.
39. Bel G, Hagberg A, Meron E (2012) Gradual regime shifts in spatially extended ecosystems. J Theor Ecol 5(4):591-604.
40. Nes EHV, Scheffer M (2005) Implications of spatial heterogeneity for catastrophic regime shifts in ecosystems. Ecology 86(7):1797-1807.
41. Fort H, Mazzeo N, Scheffer M, Nes EV (2010) Catastrophic shifts in ecosystems: Spatial early warnings and management procedures. J Phys 246(1):012035.
42. Drake JM, Griffen BD (2010) Early warning signals of extinction in deteriorating environments. Nature 467(7314):456-459.
43. Fernández A, Fort H (2009) Catastrophic phase transitions and early warnings in a spatial ecological model. J Stat Mech 2009(9):P09014.
44. Guttal V, Jayaprakash C (2009) Spatial variance and spatial skewness: Leading indicators of regime shifts in spatial ecological systems. J Theor Ecol 2(1):3-12.
45. Rietkerk M, Dekker SC, de Ruiter PC, van de Koppel J (2004) Self-organized patchiness and catastrophic shifts in ecosystems. Science 305(5692):1926-1929.
46. Manor A, Shnerb NM (2008) Facilitation, competition, and vegetation patchiness: From scale free distribution to patterns. J Theor Biol 253(4):838-842.
47. Manor A, Shnerb NM (2008) Origin of Pareto-like spatial distributions in ecosystems. Phys Rev Lett 101(26):268104.
48. Weissmann H, Shnerb NM (2014) Stochastic desertification. Europhys Lett 106(2): 28004.
49. García-Ojalvo J, Sancho JM (1999) Noise in Spatially Extended Systems (Springer, New York).
50. Hidalgo J, Seoane LF, Cortés JM, Muñoz MA (2012) Stochastic amplification of fluctuations in cortical up-states. PLoS ONE 7(8):e40710.
51. Binney JJ, Dowrick NJ, Fisher AJ, Newman MEJ (1992) The Theory of Critical Phenomena (Clarendon Press, Oxford).
52. Scanlon T, Caylor K, Manfreda S, Levin S, Rodriguez-Iturbe I (2005) Dynamic response of grass cover to rainfall variability: Implications for the function and persistence of savanna ecosystems. Adv Water Resour 28(3):291-302.
53. Vazquez F, López C, Calabrese JM, Muñoz MA (2010) Dynamical phase coexistence: A simple solution to the "savanna problem". J Theor Biol 264(2):360-366.
54. Hohenberg PC, Halperin BI (1977) Theory of dynamic critical phenomena. Rev Mod Phys 49(3):435-479.
55. Gardiner C (2009) Stochastic Methods: A Handbook for the Natural and Social Sciences, Springer Series in Synergetics (Springer, Berlin).
56. Binder K (1987) Theory of first-order phase transitions. Rep Prog Phys 50(7):783-859.
57. Carpenter S (2001) Alternate States of Ecosystems: Evidence and Some Implications, ed Levin S (Blackwell Science, Oxford), pp 357-383.
58. Thom R (1969) Topological models in biology. Topology 8(3):313-335.
59. Crauel H, Flandoli F (1994) Attractors for random dynamical systems. Probab Theory Relat Fields 100(3):365-393.
60. Chow PL (1982) Stability of nonlinear stochastic-evolution equations. J Math Anal Appl 89(2):400-419.
61. Bates PW, Lisei H, Lu K (2006) Attractors for stochastic lattice dynamical systems. Stoch Dyn 6(1):1-21.
62. Cerrai S (2003) Stochastic reaction-diffusion systems with multiplicative noise and non-Lipschitz reaction term. Probab Theory Relat Fields 125(2):271-304.
63. Caraballo T, Lu K (2008) Attractors for stochastic lattice dynamical systems with a multiplicative noise. Front Math China 3(3):317-335.
64. Caraballo T, Langa JA, Robinson JC (2001) A stochastic pitchfork bifurcation in a reaction-diffusion equation. Proc R Soc London Ser A 457(2013):2041-2061.
65. Cerrai S, et al. (2004) Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipshitz reaction term. Ann Probab 32(18):1100-1139.
66. Meerson B, Sasorov PV (2011) Extinction rates of established spatial populations. Phys Rev E Stat Nonlin Soft Matter Phys 83(1 Pt 1):011129.
67. Elgart V, Kamenev A (2004) Rare event statistics in reaction-diffusion systems. Phys Rev E Stat Nonlin Soft Matter Phys 70(4 Pt 1):041106.
68. Dornic I, Chaté H, Muñoz MA (2005) Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions. Phys Rev Lett 94(10):100601.
69. Bonachela JA, Muñoz MA, Levin SA (2012) Patchiness and demographic noise in three ecological examples. J Stat Phys 148(4):723-739.
70. Dickman R, Tomé T (2004) First-order phase transition in a one-dimensional nonequilibrium model. Phys Rev A 44(8):4833-4838.
71. Villa Martín P, Bonachela JA, Muñoz MA (2014) Quenched disorder forbids discontinuous transitions in nonequilibrium low-dimensional systems. Phys Rev E Stat Nonlin Soft Matter Phys 89(1):012145.
72. Muñoz MA, Dickman R, Vespignani A, Zapperi S (1999) Avalanche and spreading exponents in systems with absorbing states. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 59(5 Pt B):6175-6179.
73. McPeek MA, Holt RD (1992) The evolution of dispersal in spatially and temporally varying environments. Am Nat 140(6):1010-1027.
74. Imry Y, Ma SK (1975) Random-field instability of the ordered state of continuous symmetry. Phys Rev Lett 35(21):1399-1401.
75. Aizenman M, Wehr J (1989) Rounding of first-order phase transitions in systems with quenched disorder. Phys Rev Lett 62(21):2503-2506.
76. Berker AN (1993) Critical behavior induced by quenched disorder. Physica A 194(1-4): 72-76.
77. Vojta T (2006) Rare region effects at classical, quantum and nonequilibrium phase transitions. J Phys A 39(22):R143-R205.
78. Wilson KG (1974) Confinement of quarks. Phys Rev D Part Fields 10(8):2445-2459.
79. Ludwig D, Jones DD, Holling CS (1978) Qualitative analysis of insect outbreak systems: The spruce budworm and the forest. J Anim Ecol 47(1):315-332.
80. Vazquez F, Bonachela JA, López C, Muñoz MA (2011) Temporal Griffiths phases. Phys Rev Lett 106(23):235702.
81. Janssen HK (1981) On the nonequilibrium phase transition in reaction-diffusion systems with an absorbing stationary state. Z Phys B Condens Matter 42(2):151-154.
82. Grassberger P (1982) On phase transitions in Schlögls second model. Z Phys B Condens Matter 47(4):365-374.
83. Ohtsuki T, Keyes T (1987) Nonequilibrium critical phenomena in one-component reaction-diffusion systems. Phys Rev A 35(6):2697-2703.