1932

Abstract

Chaos was proposed in the 1970s as an alternative explanation for apparently noisy fluctuations in population size. Although readily demonstrated in models, the search for chaos in nature proved challenging and led many to conclude that chaos is either rare or nigh impossible to detect. However, in the intervening half-century, it has become clear that ecosystems are replete with the enabling conditions for chaos. Chaos has been repeatedly demonstrated under laboratory conditions and has been found in field data using updated detection methods. Together, these developments indicate that the apparent rarity of chaos was an artifact of data limitations and overreliance on low-dimensional population models. We invite readers to reevaluate the relevance of chaos in ecology, and we suggest that chaos is not as rare or undetectable as previously believed.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-ecolsys-111320-052920
2022-11-02
2024-10-04
Loading full text...

Full text loading...

/deliver/fulltext/ecolsys/53/1/annurev-ecolsys-111320-052920.html?itemId=/content/journals/10.1146/annurev-ecolsys-111320-052920&mimeType=html&fmt=ahah

Literature Cited

  1. Abarbanel HDI. 2013. Predicting the Future: Completing Models of Observed Complex Systems New York: Springer
    [Google Scholar]
  2. Abarbanel HDI, Brown R, Kennel MB. 1992. Local Lyapunov exponents computed from observed data. J. Nonlinear Sci. 2:3343–65
    [Google Scholar]
  3. Allen JC. 1990. Factors contributing to chaos in population feedback systems. Ecol. Model. 51:3281–98
    [Google Scholar]
  4. Allen JC, Schaffer WM, Rosko D. 1993. Chaos reduces species extinction by amplifying local population noise. Nature 364:6434229–32
    [Google Scholar]
  5. Allesina S, Tang S. 2015. The stability–complexity relationship at age 40: a random matrix perspective. Popul. Ecol. 57:163–75
    [Google Scholar]
  6. Anderson DM, Gillooly JF. 2020. Allometric scaling of Lyapunov exponents in chaotic populations. Popul. Ecol. 62:3364–69
    [Google Scholar]
  7. Bailey BA, Ellner S, Nychka DW 1997. Chaos with confidence: asymptotics and applications of local Lyapunov exponents. Nonlinear Dynamics and Time Series: Building a Bridge Between the Natural and Statistical Sciences C Cutler, DT Kaplan 115–34 Providence, RI: Am. Math. Soc.
    [Google Scholar]
  8. Bandt C, Pompe B. 2002. Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88:17174102
    [Google Scholar]
  9. Banerjee M, Volpert V. 2017. Spatio-temporal pattern formation in Rosenzweig–MacArthur model: effect of nonlocal interactions. Ecol. Complex. 30:2–10
    [Google Scholar]
  10. Baron JW, Galla T. 2020. Dispersal-induced instability in complex ecosystems. Nat. Commun. 11:16032
    [Google Scholar]
  11. Becks L, Arndt H. 2008. Transitions from stable equilibria to chaos, and back, in an experimental food web. Ecology 89:113222–26
    [Google Scholar]
  12. Becks L, Arndt H. 2013. Different types of synchrony in chaotic and cyclic communities. Nat. Commun. 4:1359
    [Google Scholar]
  13. Beddington JR, Free CA, Lawton JH. 1975. Dynamic complexity in predator-prey models framed in difference equations. Nature 255:550358–60
    [Google Scholar]
  14. Benincà E, Ballantine B, Ellner SP, Huisman J. 2015. Species fluctuations sustained by a cyclic succession at the edge of chaos. PNAS 112:206389–94
    [Google Scholar]
  15. Benincà E, Huisman J, Heerkloss R, Jöhnk KD, Branco P et al. 2008. Chaos in a long-term experiment with a plankton community. Nature 451:7180822–25
    [Google Scholar]
  16. Berryman AA, Millstein JA. 1989. Are ecological systems chaotic—and if not, why not?. Trends Ecol. Evol. 4:126–28
    [Google Scholar]
  17. Bjørnstad ON, Grenfell BT. 2001. Noisy clockwork: time series analysis of population fluctuations in animals. Science 293:5530638–43
    [Google Scholar]
  18. Bolker B, Grenfell B. 1995. Space, persistence and dynamics of measles epidemics. Philos. Trans. R. Soc. B 348:1325309–20
    [Google Scholar]
  19. Bolnick DI, Svanbäck R, Fordyce JA, Yang LH, Davis JM et al. 2003. The ecology of individuals: incidence and implications of individual specialization. Am. Nat. 161:11–28
    [Google Scholar]
  20. Brias A, Munch SB. 2021. Ecosystem based multi-species management using Empirical Dynamic Programming. Ecol. Model. 441:109423
    [Google Scholar]
  21. Cencini M, Falcioni M, Olbrich E, Kantz H, Vulpiani A. 2000. Chaos or noise: difficulties of a distinction. Phys. Rev. E. 62:1427–37
    [Google Scholar]
  22. Clark TJ, Luis AD. 2020. Nonlinear population dynamics are ubiquitous in animals. Nat. Ecol. Evol. 4:175–81
    [Google Scholar]
  23. Cressie N, Wikle CK. 2011. Statistics for Spatio-Temporal Data Hoboken, NJ: John Wiley & Sons
    [Google Scholar]
  24. Dakos V, Benincà E, Van Nes EH, Philippart CJM, Scheffer M, Huisman J. 2009. Interannual variability in species composition explained as seasonally entrained chaos. Proc. R. Soc. B 276:16692871–80
    [Google Scholar]
  25. Deissler RJ, Kaneko K. 1987. Velocity-dependent Lyapunov exponents as a measure of chaos for open-flow systems. Phys. Lett. A. 119:8397–402
    [Google Scholar]
  26. Dennis B, Desharnais RA, Cushing JM, Costantino RF. 1997. Transitions in population dynamics: equilibria to periodic cycles to aperiodic cycles. J. Anim. Ecol. 66:5704–29
    [Google Scholar]
  27. Dennis B, Desharnais RA, Cushing JM, Henson SM, Costantino RF. 2003. Can noise induce chaos?. Oikos 102:2329–39
    [Google Scholar]
  28. Dercole F, Ferriere R, Rinaldi S. 2010. Chaotic Red Queen coevolution in three-species food chains. Proc. R. Soc. B 277:16922321–30
    [Google Scholar]
  29. Desharnais RA, Costantino RF, Cushing JM, Henson SM, Dennis B. 2001. Chaos and population control of insect outbreaks. Ecol. Lett. 4:3229–35
    [Google Scholar]
  30. Dietze MC. 2017. Prediction in ecology: a first-principles framework. Ecol. Appl. 27:72048–60
    [Google Scholar]
  31. Doebeli M. 1996. Quantitative genetics and population dynamics. Evolution 50:2532–46
    [Google Scholar]
  32. Doebeli M, Ispolatov I. 2014. Chaos and unpredictability in evolution. Evolution 68:51365–73
    [Google Scholar]
  33. Doebeli M, Koella JC. 1994. Sex and population dynamics. Proc. R. Soc. B 257:134817–23
    [Google Scholar]
  34. Doebeli M, Koella JC. 1995. Evolution of simple population dynamics. Proc. R. Soc. B 260:1358119–25
    [Google Scholar]
  35. Earn DJD, Levin SA, Rohani P. 2000. Coherence and conservation. Science 290:1360–64
    [Google Scholar]
  36. Ebenman B, Johansson A, Jonsson T, Wennergren U. 1996. Evolution of stable population dynamics through natural selection. Proc. R. Soc. B 263:13741145–51
    [Google Scholar]
  37. Eide RM, Krause AL, Fadai NT, Van Gorder RA. 2018. Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. J. Theor. Biol. 451:19–34
    [Google Scholar]
  38. Ellner SP, Becks L. 2011. Rapid prey evolution and the dynamics of two-predator food webs. Theor. Ecol. 4:2133–52
    [Google Scholar]
  39. Ellner SP, Seifu Y, Smith RH. 2002. Fitting population dynamic models to time-series data by gradient matching. Ecology 83:82256–70
    [Google Scholar]
  40. Ellner SP, Turchin P. 1995. Chaos in a noisy world: new methods and evidence from time-series analysis. Am. Nat. 145:3343–75
    [Google Scholar]
  41. Ellner SP, Turchin P. 2005. When can noise induce chaos and why does it matter: a critique. Oikos 111:3620–31
    [Google Scholar]
  42. Estay SA, Lima M, Labra FA, Harrington R. 2012. Increased outbreak frequency associated with changes in the dynamic behaviour of populations of two aphid species. Oikos 121:4614–22
    [Google Scholar]
  43. Fryxell JM, Falls JB, Falls EA, Brooks RJ. 1998. Long-term dynamics of small-mammal populations in Ontario. Ecology 79:1213–25
    [Google Scholar]
  44. Gamarra JGP, Solé RV. 2000. Bifurcations and chaos in ecology: lynx returns revisited. Ecol. Lett. 3:2114–21
    [Google Scholar]
  45. Gao JB, Hu J, Tung WW, Cao YH. 2006. Distinguishing chaos from noise by scale-dependent Lyapunov exponent. Phys. Rev. E 74:666204
    [Google Scholar]
  46. Gilpin ME. 1979. Spiral chaos in a predator-prey model. Am. Nat. 113:2306–8
    [Google Scholar]
  47. Gilpin W, Feldman MW. 2017. A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape. PLOS Comput. Biol. 13:7e1005644
    [Google Scholar]
  48. Ginzburg LR, Taneyhill DE. 1994. Population cycles of forest Lepidoptera: a maternal effect hypothesis. J. Anim. Ecol. 63:179–92
    [Google Scholar]
  49. Giron-Nava A, Ezcurra E, Brias A, Velarde E, Deyle E et al. 2021. Environmental variability and fishing effects on the Pacific sardine fisheries in the Gulf of California. Can. J. Fish. Aquat. Sci. 78:5623–30
    [Google Scholar]
  50. Gomes AA, Manica E, Varriale MC. 2008. Applications of chaos control techniques to a three-species food chain. Chaos Solitons Fractals 35:3432–41
    [Google Scholar]
  51. Gottwald GA, Melbourne I. 2004. A new test for chaos in deterministic systems. Proc. R. Soc. A 4602042:603–11
    [Google Scholar]
  52. Graham DW, Knapp CW, Van Vleck ES, Bloor K, Lane TB, Graham CE. 2007. Experimental demonstration of chaotic instability in biological nitrification. ISME J 1:5385–93
    [Google Scholar]
  53. Grassberger P, Badii R, Politi A. 1988. Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors. J. Stat. Phys. 51:1135–78
    [Google Scholar]
  54. Gravel D, Massol F, Leibold MA. 2016. Stability and complexity in model meta-ecosystems. Nat. Commun. 7:12457
    [Google Scholar]
  55. Gross T, Ebenhöh W, Feudel U. 2005. Long food chains are in general chaotic. Oikos 109:1135–44
    [Google Scholar]
  56. Grover JP, McKee D, Young S, Godfray HCJ, Turchin P. 2000. Periodic dynamics in Daphnia populations: biological interactions and external forcing. Ecology 81:102781–98
    [Google Scholar]
  57. Gyllenberg M, Söderbacka G, Ericsson S. 1993. Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model. Math. Biosci. 118:125–49
    [Google Scholar]
  58. Hassell MP, Comins HN, May RM. 1994. Species coexistence and self-organizing spatial dynamics. Nature 370:6487290–92
    [Google Scholar]
  59. Hassell MP, Lawton JH, May RM. 1976. Patterns of dynamical behaviour in single-species populations. J. Anim. Ecol. 45:2471–86
    [Google Scholar]
  60. Hastings A. 1993. Complex interactions between dispersal and dynamics: lessons from coupled logistic equations. Ecology 74:51362–72
    [Google Scholar]
  61. Hastings A, Abbott KC, Cuddington K, Francis T, Gellner G et al. 2018. Transient phenomena in ecology. Science 361:6406eaat6412
    [Google Scholar]
  62. Hastings A, Hom CL, Ellner S, Turchin P, Godfray HCJ. 1993. Chaos in ecology: Is Mother Nature a strange attractor?. Annu. Rev. Ecol. Syst. 24:1–33
    [Google Scholar]
  63. Heilmann IT, Starke J, Andersen KH, Thygesen UH, Sørensen MP. 2016. Dynamics of a physiologically structured population in a time-varying environment. Ecol. Complex. 28:54–61
    [Google Scholar]
  64. Henson SM, Costantino RF, Cushing JM, Desharnais RA, Dennis B, King AA. 2001. Lattice effects observed in chaotic dynamics of experimental populations. Science 294:5542602–5
    [Google Scholar]
  65. Herrel A, Joly D, Danchin E. 2020. Epigenetics in ecology and evolution. Funct. Ecol. 34:2381–84
    [Google Scholar]
  66. Higgins K, Hastings A, Botsford LW. 1997. Density dependence and age structure: nonlinear dynamics and population behavior. Am. Nat. 149:2247–69
    [Google Scholar]
  67. Huisman J, Weissing FJ. 1999. Biodiversity of plankton by species oscillations and chaos. Nature 402:407–10
    [Google Scholar]
  68. Huisman J, Weissing FJ. 2001. Fundamental unpredictability in multispecies competition. Am. Nat. 157:5488–94
    [Google Scholar]
  69. Ispolatov I, Madhok V, Allende S, Doebeli M. 2015. Chaos in high-dimensional dissipative dynamical systems. Sci. Rep. 5:112506
    [Google Scholar]
  70. Jafari S, Sprott JC, Nazarimehr F. 2015. Recent new examples of hidden attractors. Eur. Phys. J. Spec. Top. 224:81469–76
    [Google Scholar]
  71. Jaggi S, Joshi A. 2001. Incorporating spatial variation in density enhances the stability of simple population dynamics models. J. Theor. Biol. 209:2249–55
    [Google Scholar]
  72. Jankovic M, Petrovskii S, Banerjee M. 2016. Delay driven spatiotemporal chaos in single species population dynamics models. Theor. . Popul. Biol. 110:51–62
    [Google Scholar]
  73. Jaynes ET. 1989. Clearing up mysteries—the original goal. Maximum Entropy and Bayesian Methods J Skilling 1–27 Dordrecht, Neth.: Springer Netherlands
    [Google Scholar]
  74. Johst K, Doebeli M, Brandl R. 1999. Evolution of complex dynamics in spatially structured populations. Proc. R. Soc. B 266:1147–54
    [Google Scholar]
  75. Kendall BE. 2001. Cycles, chaos, and noise in predator–prey dynamics. Chaos Solitons Fractals 12:2321–32
    [Google Scholar]
  76. Kenitz K, Williams RG, Sharples J, Selsil Ö, Biktashev VN. 2013. The paradox of the plankton: species competition and nutrient feedback sustain phytoplankton diversity. Mar. Ecol. Prog. Ser. 490:107–19
    [Google Scholar]
  77. Klein E, Glaser S, Jordaan A, Kaufman L, Rosenberg AA. 2016. A complex past: Historical and contemporary fisheries demonstrate nonlinear dynamics and a loss of determinism. Mar. Ecol. Prog. Ser. 557:237–46
    [Google Scholar]
  78. Knape J, de Valpine P. 2012. Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?. Ecol. Lett. 15:117–23
    [Google Scholar]
  79. Kot M, Schaffer WM. 1984. The effects of seasonality on discrete models of population growth. Theor. . Popul. Biol. 26:340–60
    [Google Scholar]
  80. Krkošek M, Drake JM. 2014. On signals of phase transitions in salmon population dynamics. Proc. R. Soc. B 281:178420133221
    [Google Scholar]
  81. Lacasa L, Luque B, Ballesteros F, Luque J, Nuño JC. 2008. From time series to complex networks: the visibility graph. PNAS 105:134972–75
    [Google Scholar]
  82. Lacitignola D, Petrosillo I, Zurlini G. 2010. Time-dependent regimes of a tourism-based social-ecological system: period-doubling route to chaos. Ecol. Complex. 7:144–54
    [Google Scholar]
  83. Lande R, Engen S, Saether B-E. 2003. Stochastic Population Dynamics in Ecology and Conservation Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  84. Lindström J, Kokko H. 1998. Sexual reproduction and population dynamics: the role of polygyny and demographic sex differences. Proc. R. Soc. B 265:1395483–88
    [Google Scholar]
  85. Ma H, Leng S, Aihara K, Lin W, Chen L 2018. Randomly distributed embedding making short-term high-dimensional data predictable. PNAS 115:43E9994–10002
    [Google Scholar]
  86. Maquet J, Letellier C, Aguirre LA. 2007. Global models from the Canadian lynx cycles as a direct evidence for chaos in real ecosystems. J. Math. Biol. 55:121–39
    [Google Scholar]
  87. Marwan N. 2011. How to avoid potential pitfalls in recurrence plot based data analysis. Int. J. Bifurc. Chaos 21:041003–17
    [Google Scholar]
  88. Massoud EC, Huisman J, Benincà E, Dietze MC, Bouten W, Vrugt JA. 2018. Probing the limits of predictability: data assimilation of chaotic dynamics in complex food webs. Ecol. Lett. 21:193–103
    [Google Scholar]
  89. May RM. 1972. Will a large complex system be stable?. Nature 238:5364413–14
    [Google Scholar]
  90. May RM. 1974. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186:4164645–47
    [Google Scholar]
  91. May RM, Conway GR, Hassell MP, Southwood TRE. 1974. Time delays, density-dependence and single-species oscillations. J. Anim. Ecol. 43:3747–70
    [Google Scholar]
  92. Medvinsky AB, Adamovich BV, Chakraborty A, Lukyanova EV, Mikheyeva TM et al. 2015. Chaos far away from the edge of chaos: a recurrence quantification analysis of plankton time series. Ecol. Complex. 23:61–67
    [Google Scholar]
  93. Miner BG, Sultan SE, Morgan SG, Padilla DK, Relyea RA. 2005. Ecological consequences of phenotypic plasticity. Trends Ecol. Evol. 20:12685–92
    [Google Scholar]
  94. Mitchell L, Gottwald GA. 2012. On finite-size Lyapunov exponents in multiscale systems. Chaos 22:223115
    [Google Scholar]
  95. Morozov AY, Banerjee M, Petrovskii SV. 2016. Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect. J. Theor. Biol. 396:116–24
    [Google Scholar]
  96. Mueller LD, Joshi A, Borash DJ. 2000. Does population stability evolve?. Ecology 81:51273–85
    [Google Scholar]
  97. Munch SB, Brias A, Sugihara G, Rogers TL. 2020. Frequently asked questions about nonlinear dynamics and empirical dynamic modelling. ICES J. Mar. Sci. 77:41463–79
    [Google Scholar]
  98. Munch SB, Poynor V, Arriaza JL. 2017. Circumventing structural uncertainty: a Bayesian perspective on nonlinear forecasting for ecology. Ecol. Complex. 32:134–43
    [Google Scholar]
  99. Nowak MA, Sigmund K 2004. Evolutionary dynamics of biological games. Science 303:5659793–99
    [Google Scholar]
  100. Nychka D, Ellner S, Gallant AR, McCaffrey D. 1992. Finding chaos in noisy systems. J. R. Stat. Soc. Ser. B 54:2399–426
    [Google Scholar]
  101. Ott E, Grebogi C, Yorke JA. 1990. Controlling chaos. Phys. Rev. Lett. 64:111196–99
    [Google Scholar]
  102. Pal S, Hossain M, Panday P, Pati NC, Pal N, Chattopadhyay J. 2020. Cooperation delay induced chaos in an ecological system. Chaos 30:883124
    [Google Scholar]
  103. Pearce MT, Agarwala A, Fisher DS. 2020. Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos. PNAS 117:2514572–83
    [Google Scholar]
  104. Pecora LM, Carroll TL. 1990. Synchronization in chaotic systems. Phys. Rev. Lett. 64:8821–24
    [Google Scholar]
  105. Pennekamp F, Iles AC, Garland J, Brennan G, Brose U et al. 2019. The intrinsic predictability of ecological time series and its potential to guide forecasting. Ecol. Monogr. 89:2e01359
    [Google Scholar]
  106. Perretti CT, Sugihara G, Munch SB. 2013. Nonparametric forecasting outperforms parametric methods for a simulated multispecies system. Ecology 94:4794–800
    [Google Scholar]
  107. Petrovskii SV, Malchow H. 2001. Spatio-temporal chaos in an ecological community as a response to unfavourable environmental changes. Adv. Complex Syst. 4:2–3227–49
    [Google Scholar]
  108. Prendergast J, Bazeley-White E, Smith O, Lawton J, Inchausti P. 2010. The Global Population Dynamics Database. Knowledge network for biocomplexity. https://doi.org/10.5063/F1BZ63Z8
    [Crossref]
  109. Priklopil T. 2012. Chaotic dynamics of allele frequencies in condition-dependent mating systems. Theor. Popul. Biol. 82:2109–16
    [Google Scholar]
  110. Reynolds A, Santini G, Chelazzi G, Focardi S. 2017. The Weierstrassian movement patterns of snails. R. Soc. Open Sci. 4:6160941
    [Google Scholar]
  111. Roelke D, Augustine S, Buyukates Y 2003. Fundamental predictability in multispecies competition: the influence of large disturbance. Am. Nat. 162:5615–23
    [Google Scholar]
  112. Rogers TL, Johnson BJ, Munch SB. 2022. Chaos is not rare in natural ecosystems. Nat. Ecol. Evol. 6:110511
    [Google Scholar]
  113. Rosenstein MT, Collins JJ, De Luca CJ. 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D Nonlinear Phenom. 65:117–34
    [Google Scholar]
  114. Roy F, Barbier M, Biroli G, Bunin G. 2020. Complex interactions can create persistent fluctuations in high-diversity ecosystems. PLOS Comput. Biol. 16:5e1007827
    [Google Scholar]
  115. Roy S, Chattopadhyay J. 2007. Towards a resolution of ‘the paradox of the plankton’: a brief overview of the proposed mechanisms. Ecol. Complex. 4:126–33
    [Google Scholar]
  116. Salvidio S. 2011. Stability and annual return rates in amphibian populations. Amphib. Reptil. 32:1119–24
    [Google Scholar]
  117. Sauve AMC, Taylor RA, Barraquand F. 2020. The effect of seasonal strength and abruptness on predator–prey dynamics. J. Theor. Biol. 491:110175
    [Google Scholar]
  118. Schaffer WM. 1985. Order and chaos in ecological systems. Ecology 66:193–106
    [Google Scholar]
  119. Schaffer WM, Kot M. 1986. Chaos in ecological systems: the coals that Newcastle forgot. Trends Ecol. Evol. 1:358–63
    [Google Scholar]
  120. Scheffer M, Rinaldi S, Huisman J, Weissing FJ. 2003. Why plankton communities have no equilibrium: solutions to the paradox. Hydrobiologia 491:9–18
    [Google Scholar]
  121. Schreiber SJ, Bürger R, Bolnick DI. 2011. The community effects of phenotypic and genetic variation within a predator population. Ecology 92:81582–93
    [Google Scholar]
  122. Seity Y, Brousseau P, Malardel S, Hello G, Bénard P et al. 2011. The AROME-France convective-scale operational model. Mon. Weather Rev. 139:3976–91
    [Google Scholar]
  123. Shelton AO, Mangel M. 2011. Fluctuations of fish populations and the magnifying effects of fishing. PNAS 108:177075–80
    [Google Scholar]
  124. Shintani M, Linton O. 2003. Is there chaos in the world economy? A nonparametric test using consistent standard errors. Int. Econ. Rev. 44:1331–57
    [Google Scholar]
  125. Sibly RM, Barker D, Hone J, Pagel M. 2007. On the stability of populations of mammals, birds, fish and insects. Ecol. Lett. 10:10970–76
    [Google Scholar]
  126. Silva JAL, De Castro ML, Justo DAR. 2001. Stability in a metapopulation model with density-dependent dispersal. Bull. Math. Biol. 63:3485–505
    [Google Scholar]
  127. Snell TW, Serra M. 1998. Dynamics of natural rotifer populations. Hydrobiologia 368:1–329–35
    [Google Scholar]
  128. Solé RV, Gamarra JGP, Ginovart M, López D. 1999. Controlling chaos in ecology: from deterministic to individual-based models. Bull. Math. Biol. 61:61187–207
    [Google Scholar]
  129. Stark J. 1999. Delay embeddings for forced systems. I. Deterministic forcing. J. Nonlinear Sci. 9:3255–332
    [Google Scholar]
  130. Stark J, Broomhead DS, Davies ME, Huke J. 2003. Delay embeddings for forced systems. II. Stochastic forcing. J. Nonlinear Sci. 13:6519–77
    [Google Scholar]
  131. Stemler T, Judd K 2009. A guide to using shadowing filters for forecasting and state estimation. Phys. D Nonlinear Phenom. 238:141260–73
    [Google Scholar]
  132. Sugihara G. 1994. Nonlinear forecasting for the classification of natural time series. Philos. Trans. R. Soc. A 348:1688477–95
    [Google Scholar]
  133. Sugihara G, Casdagli M, Habjan E, Hess D, Dixon P, Holland G. 1999. Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts. PNAS 96:2514210–15
    [Google Scholar]
  134. Sugihara G, May RM. 1990. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344:April734–41
    [Google Scholar]
  135. Takens F 1981. Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, eds. DA Rand, LS Young 366–81 New York: Springer
    [Google Scholar]
  136. Toker D, Sommer FT, D'Esposito M 2020. A simple method for detecting chaos in nature. Commun. Biol. 3:111
    [Google Scholar]
  137. Toledo S, Shohami D, Schiffner I, Lourie E, Orchan Y et al. 2020. Cognitive map-based navigation in wild bats revealed by a new high-throughput tracking system. Science 369:6500188–93
    [Google Scholar]
  138. Tuda M, Shimada M. 2005. Complexity, evolution, and persistence in host-parasitoid experimental systems with Callosobruchus beetles as the host. Adv. Ecol. Res. 37:37–75
    [Google Scholar]
  139. Tuljapurkar S. 1989. An uncertain life: demography in random environments. Theor. Popul. Biol. 35:3227–94
    [Google Scholar]
  140. Turchin P, Ellner SP. 2000. Living on the edge of chaos: population dynamics of Fennoscandian voles. Ecology 81:113099–116
    [Google Scholar]
  141. Turchin P, Taylor AD. 1992. Complex dynamics in ecological time series. Ecology 73:1289–305
    [Google Scholar]
  142. Upadhyay RK, Iyengar SRK, Rai V. 1998. Chaos: an ecological reality?. Int. J. Bifurc. Chaos 8:61325–33
    [Google Scholar]
  143. Ushio M, Hsieh CH, Masuda R, Deyle ER, Ye H et al. 2018. Fluctuating interaction network and time-varying stability of a natural fish community. Nature 554:7692360–63
    [Google Scholar]
  144. van der Meer J, Beukema JJ, Dekker R. 2000. Population dynamics of two marine polychaetes: the relative role of density dependence, predation, and winter conditions. ICES J. Mar. Sci. 57:51488–94
    [Google Scholar]
  145. Vance RR. 1978. Predation and resource partitioning in one predator–two prey model communities. Am. Nat. 112:987797–813
    [Google Scholar]
  146. Vandermeer J. 1993. Loose coupling of predator-prey cycles: entrainment, chaos, and intermittency in the classic Macarthur consumer-resource equations. Am. Nat. 141:5687–716
    [Google Scholar]
  147. Webber CL Jr., Zbilut JP. 1994. Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76:2965–73
    [Google Scholar]
  148. Werner CM, Stuble KL, Groves AM, Young TP. 2020. Year effects: interannual variation as a driver of community assembly dynamics. Ecology 101:9e03104
    [Google Scholar]
  149. Wolf A, Swift JB, Swinney HL, Vastano JA. 1985. Determining Lyapunov exponents from a time series. Phys. D Nonlinear Phenom. 16:3285–317
    [Google Scholar]
  150. Wood SN. 2010. Statistical inference for noisy nonlinear ecological dynamic systems. Nature 466:73101102–4
    [Google Scholar]
  151. Yao Q, Tong H. 1994. On prediction and chaos in stochastic systems. Philos. Trans. R. Soc. A 348:1688357–69
    [Google Scholar]
  152. Ye H, Sugihara G. 2016. Information leverage in interconnected ecosystems: overcoming the curse of dimensionality. Science 353:6302922–25
    [Google Scholar]
  153. Ylioja T, Roininen H, Ayres MP, Rousi M, Price PW. 1999. Host-driven population dynamics in an herbivorous insect. PNAS 96:1910735–40
    [Google Scholar]
  154. Ziebarth NL, Abbott KC, Ives AR. 2010. Weak population regulation in ecological time series. Ecol. Lett. 13:121–31
    [Google Scholar]
  155. Zimmer C. 1999. Life after chaos. Science 284:541183–86
    [Google Scholar]
  156. Zurlini G, Marwan N, Semeraro T, Jones KB, Aretano R et al. 2018. Investigating landscape phase transitions in Mediterranean rangelands by recurrence analysis. Landsc. Ecol. 33:91617–31
    [Google Scholar]
/content/journals/10.1146/annurev-ecolsys-111320-052920
Loading
/content/journals/10.1146/annurev-ecolsys-111320-052920
Loading

Data & Media loading...

Supplementary Data

  • 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