The ecological forecast horizon, and examples of its uses and determinants

Ecology Letters

Volumn 18, Issue 7, 2015, Pages 597-611

  Petchey, Owen L ^a,b   Pontarp, Mikael ^a,c   Massie, Thomas M ^a   Kéfi, Sonia ^d   Ozgul, Arpat ^a   Weilenmann, Maja ^a   Palamara, Gian Marco ^a   Altermatt, Florian ^a,b   Matthews, Blake ^b   Levine, Jonathan M ^e   Childs, Dylan Z ^f   Mcgill, Brian J ^g   Schaepman, Michael E ^a   Schmid, Bernhard ^a   Spaak, Piet ^b,e   Beckerman, Andrew P ^f   Pennekamp, Frank ^a   Pearse, Ian S ^h  

^a UNIVERSITY OF ZURICH   (Switzerland)

^b SWISS FEDERAL INSTITUTE OF AQUATIC SCIENCE AND TECHNOLOGY   (Switzerland)

^c UMEÅ UNIVERSITY   (Sweden)

^d UNIV MONTPELLIER   (France)

^e ETH ZURICH   (Switzerland)

^f UNIVERSITY OF SHEFFIELD   (United Kingdom)

^g UNIVERSITY OF MAINE   (United States)

^h UNIVERSITY OF ILLINOIS   (United States)

Author keywords

Dynamics; Ecosystems; Environmental change; Forecasting; Futures; Prediction; Scenarios

Indexed keywords

ABUNDANCE; BODY SIZE; COMMUNITY STRUCTURE; ENVIRONMENTAL CHANGE; FORECASTING METHOD; PHYLOGENETICS; POPULATION DISTRIBUTION; POPULATION STRUCTURE; PREDICTION; RESEARCH AND DEVELOPMENT; SPATIOTEMPORAL ANALYSIS; TEMPERATURE EFFECT; UNCERTAINTY ANALYSIS;

ECOLOGY; ECOSYSTEM; EVOLUTION; FORECASTING; PHYLOGENY; PROCEDURES; STATISTICAL MODEL;

BIOLOGICAL EVOLUTION; ECOLOGY; ECOSYSTEM; FORECASTING; MODELS, STATISTICAL; PHYLOGENY;

EID: 84931562756     PISSN: 1461023X     EISSN: 14610248     Source Type: Journal    
DOI: 10.1111/ele.12443     Document Type: Article

References (121)

1. Algar, A.C., Kharouba, H.M., Young, E.R. & Kerr, J.T. (2009). Predicting the future of species diversity: macroecological theory, climate change, and direct tests of alternative forecasting methods. Ecography, 32, 22-33.
2. Asner, G.P. (2009). Tropical forest carbon assessment: integrating satellite and airborne mapping approaches. Environ. Res. Lett., 4, 034009.
3. Aufderheide, H., Rudolf, L., Gross, T. & Lafferty, K.D. (2013). How to predict community responses to perturbations in the face of imperfect knowledge and network complexity. Proc. Biol. Sci., 280, 20132355.
4. Aurell, E., Boffetta, G., Crisanti, A., Paladin, G. & Vulpiani, A. (1997). Predictability in the large: an extension of the concept of Lyapunov exponent. J. Phys. A: Math. Gen., 30, 1-26.
5. Bahn, V. & McGill, B.J. (2007). Can niche-based distribution models outperform spatial interpolation? Glob. Ecol. Biogeogr., 16, 733-742.
6. Bahn, V. & McGill, B.J. (2013). Testing the predictive performance of distribution models. Oikos, 122, 321-331.
7. Bailey, B. (1996). Local lyapunov exponents: predictability depends on where you are. In: Nonlinear Dynamics and Economics: Proceedings of the Tenth International Symposium in Economic Theory and Econometrics. (eds Barnett, W.A., Kirman, A.P. & Salmon, M.). Cambridge University Press, Cambridge, pp. 345-360.
8. Beckage, B., Gross, L.J. & Kauffman, S. (2011). The limits to prediction in ecological systems. Ecosphere, 2, art125.
9. Becks, L., Ellner, S.P., Jones, L.E. & Hairston, N.G. (2010). Reduction of adaptive genetic diversity radically alters eco-evolutionary community dynamics. Ecol. Lett., 13, 989-997.
10. Begon, M., Harper, J.L. & Townsend, C.R. (1990). Ecology: Individuals, Populations and Communities. Blackwell Publishing, Oxford.
11. Benincà, E., Huisman, J., Heerkloss, R., Jöhnk, K.D., Branco, P., Van Nes, E.H. et al. (2008). Chaos in a long-term experiment with a plankton community. Nature, 451, 822-825.
12. Berlow, E.L., Dunne, J., Martinez, N.D., Stark, P.B., Williams, R.J. & Brose, U. (2009). Simple prediction of interaction strengths in complex food webs. Proc. Natl. Acad. Sci. USA, 106, 187-191.
13. Boffetta, G., Cencini, M., Falcioni, M. & Vulpiani, A. (2002). Predictability: a way to characterize complexity. Phys. Rep., 356, 367-474.
14. Brook, B.W., O'Grady, J.J., Chapman, P., Burgman, M., Akçakaya, H.R. & Frankham, R. (2000). Predictive accuracy of population viability analysis in conservation biology. Nature, 404, 385-387.
15. Cane, M.A., Eshel, G. & Buckland, R.W. (1994). Forecasting Zimbabwean maize yield using eastern equatorial Pacific sea surface temperature. Nature, 370, 204-205.
16. Cannell, M.G.R. & Smith, R.I. (1983). Thermal time, chill days and prediction of budburst in Picea Sitchensis. J. Appl. Ecol., 20, 951-963.
17. Carrara, F., Giometto, A., Seymour, M., Rinaldo, A. & Altermatt, F. (2015). Experimental evidence for strong stabilizing forces at high functional diversity of microbial communities. Ecology, doi: 10.1890/14-1324.1, in press.
18. Cavender-Bares, J., Keen, A. & Miles, B. (2006). Phylogenetic structure of floridian plant communities depends on taxonomic and spatial scale. Ecology, 87, S109-S122.
19. Chivers, C., Leung, B. & Yan, N.D. (2014). Validation and calibration of probabilistic predictions in ecology. Methods Ecol. Evol., 5, 1023-1032.
20. Clark, J.S., Carpenter, S.R., Barber, M., Collins, S., Dobson, A., Foley, J. et al. (2001). Ecological forecasts: an emerging imperative. Science, 293, 657-660.
21. Corbet, S.A., Saville, N.M., Fussell, M., Prŷs-Jones, O.E. & Unwin, D.M. (1995). The competition box: a graphical aid to forecasting pollinator performance. J. Appl. Ecol., 32, 707-719.
22. Coreau, A., Pinay, G., Thompson, J.D., Cheptou, P.-O. & Mermet, L. (2009). The rise of research on futures in ecology: rebalancing scenarios and predictions. Ecol. Lett., 12, 1277-1286.
23. Cork, S.J., Peterson, G.D., Bennett, E.M., Petschel-Held, G. & Zurek, M. (2006). Synthesis of the storylines. Ecol. Soc., 11, 11.
24. Corley, C.D., Pullum, L.L., Hartley, D.M., Benedum, C., Noonan, C., Rabinowitz, P.M. et al. (2014). Disease prediction models and operational readiness. PLoS ONE, 9, e91989.
25. Costello, M.J., Michener, W.K., Gahegan, M., Zhang, Z.-Q. & Bourne, P.E. (2013). Biodiversity data should be published, cited, and peer reviewed. Trends Ecol. Evol., 28, 454-461.
26. Courchamp, F., Dunne, J.A., Le Maho, Y., May, R.M., Thébaud, C. & Hochberg, M.E. (2015). Fundamental ecology is fundamental. Trends Ecol. Evol., 30, 9-16.
27. Dambacher, J., Li, H. & Rossignol, P. (2002). Relevance of community structure in assessing indeterminacy of ecological predictions. Ecology, 83, 1372-1385.
28. Dambacher, J., Li, H. & Rossignol, P. (2003). Qualitative predictions in model ecosystems. Ecol. Model., 161, 79-93.
29. Diez, J.M., Ibáñez, I., Miller-Rushing, A.J., Mazer, S.J., Crimmins, T.M., Crimmins, M. et al. (2012). Forecasting phenology: from species variability to community patterns. Ecol. Lett., 15, 545-553.
30. Dobrowski, S. & Thorne, J. (2011). Modeling plant ranges over 75 years of climate change in California, USA: temporal transferability and species traits. Ecol. Monogr., 81, 241-257.
31. Doebeli, M. & Ispolatov, I. (2014). Chaos and unpredictability in evolution. Evolution, 68, 1365-1373.
32. Ellner, S. & Turchin, P. (1995). Chaos in a noisy world: new methods and evidence from time-series analysis. Am. Nat., 145, 343-375.
33. Ellner, S.P. & Holmes, E.E. (2008). Commentary on Holmes et al. (2007): resolving the debate on when extinction risk is predictable. Ecol. Lett., 11, 1-5.
34. Ellner, S.P., Geber, M. & Hairston, N.G. (2011). Does rapid evolution matter? Measuring the rate of contemporary evolution and its impacts on ecological dynamics. Ecol. Lett., 14, 603-614.
35. Evans, M.R. (2012). Modelling ecological systems in a changing world. Philos. Trans. R. Soc. Lond. B Biol. Sci., 367, 181-190.
36. Evans, M.R., Norris, K.J. & Benton, T.G. (2012). Predictive ecology: systems approaches. Philos. Trans. R. Soc. Lond. B Biol. Sci., 367, 163-169.
37. Evans, M.R., Bithell, M., Cornell, S.J., Dall, S., Diaz, S., Emmott, S. et al. (2013). Predictive systems ecology. Proc. Biol. Sci., 280, 20131452.
38. Fischer, B.B., Kwiatkowski, M., Ackermann, M., Krismer, J., Roffler, S., Suter, M.J.F. et al. (2014). Phenotypic plasticity influences the eco-evolutionary dynamics of a predator-prey system. Ecology, 95, 3080-3092.
39. France, K.E. & Duffy, J.E. (2006). Diversity and dispersal interactively affect predictability of ecosystem function. Nature, 441, 1139-1143.
40. Fussmann, G., Ellner, S., Shertzer, K. & Hairston, J.N. (2000). Crossing the Hopf bifurcation in a live predator-prey system. Science, 290, 1358-1360.
41. Fussmann, K.E., Schwarzmüller, F., Brose, U., Jousset, A. & Rall, B.C. (2014). Ecological stability in response to warming. Nat. Clim. Chang., 4, 206-210.
42. Gao, C., Wand, H., Weng, E., Lakshmivarahan, S., Zhang, Y. & Luo, Y. (2011). Assimilation of multiple data sets with the ensemble Kalman filter to improve forecasts of forest carbon dynamics. Ecol. Appl., 21, 1461-1473.
43. Garland, J., James, R. & Bradley, E. (2014). Model-free quantification of time-series predictability. Phys. Rev. E, 90, 052910.
44. Gilbert, B., Tunney, T.D., McCann, K.S., DeLong, J.P., Vasseur, D., Savage, V. et al. (2014). A bioenergetic framework for the temperature dependence of trophic interactions. Ecol. Lett., 17, 902-914.
45. Godfray, H.C.J. & May, R.M. (2014). Open questions: are the dynamics of ecological communities predictable? BMC Biol., 12, 22.
46. Gotelli, N.J. & Ellison, A.M. (2006a). Forecasting extinction risk with nonstationary matrix models. Ecol. Appl., 16, 51-61.
47. Gotelli, N.J. & Ellison, A.M. (2006b). Food-web models predict species abundances in response to habitat change. PLoS Biol., 4, e324.
48. Gravel, D., Poisot, T., Albouy, C., Velez, L. & Mouillot, D. (2013). Inferring food web structure from predator-prey body size relationships. Methods Ecol. Evol., 4, 1083-1090.
49. Gregr, E.J. & Chan, K.M.A. (2014). Leaps of faith: how implicit assumptions compromise the utility of ecosystem models for decision-making. Bioscience, 65, 43-54.
50. Grimm, V. & Railsback, S.F. (2012). Pattern-oriented modelling: a "multi-scope" for predictive systems ecology. Philos. Trans. R. Soc. Lond. B Biol. Sci., 367, 298-310.
51. Guisan, A. & Thuiller, W. (2005). Predicting species distribution: offering more than simple habitat models. Ecol. Lett., 8, 993-1009.
52. Guisan, A., Tingley, R., Baumgartner, J.B., Naujokaitis-Lewis, I., Sutcliffe, P.R., Tulloch, A.I.T. et al. (2013). Predicting species distributions for conservation decisions. Ecol. Lett., 16, 1424-1435.
53. Hairston, N.G., Ellner, S.P., Geber, M., Yoshida, T. & Fox, J. (2005). Rapid evolution and the convergence of ecological and evolutionary time. Ecol. Lett., 8, 1114-1127.
54. Hare, J.A., Alexander, M.A., Fogarty, M.J., Williams, E.H. & Scott, J.D. (2010). Forecasting the dynamics of a coastal fishery species using a coupled climate - population model. Ecol. Appl., 20, 452-464.
55. Harfoot, M.B.J., Newbold, T., Tittensor, D.P., Emmott, S., Hutton, J., Lyutsarev, V. et al. (2014). Emergent global patterns of ecosystem structure and function from a mechanistic general ecosystem model. PLoS Biol., 12, e1001841.
56. Hartig, F. & Dormann, C.F. (2013). Does model-free forecasting really outperform the true model?. Proc. Natl. Acad. Sci. USA, 110, E3975.
57. Harwood, J. & Stokes, K. (2003). Coping with uncertainty in ecological advice: lessons from fisheries. Trends Ecol. Evol., 18, 617-622.
58. Homolová, L., Schaepman, M., Lamarque, P., Clevers, J.G.P.W., de Bello, F., Thuiller, W. et al. (2013). Comparison of remote sensing and plant trait-based modelling to predict ecosystem services in subalpine grasslands. Ecosphere, 5, 1-29.
59. Hudson, L. & Reuman, D. (2013). A cure for the plague of parameters: constraining models of complex population dynamics with allometries. Proc. Biol. Sci., 280, 20131901.
60. Hudson, L.N., Newbold, T., Contu, S., Hill, S.L., Lysenko, I., De Palma, A. et al. (2014). The PREDICTS database: a global database of how local terrestrial biodiversity responds to human impacts. Ecol. Evol., 4, 4701-4735.
61. Kattge, J., Díaz, S., Lavorel, S., Prentice, I.C., Leadley, P., Bönisch, G. et al. (2011). TRY - a global database of plant traits. Global Change Biol., 17, 2905-2935.
62. Komatsu, E., Fukushima, T. & Harasawa, H. (2007). A modeling approach to forecast the effect of long-term climate change on lake water quality. Ecol. Model., 209, 351-366.
63. Kooistra, L., Wamelink, W., Schaepman-Strub, G., Schaepman, M., van Dobben, H., Aduaka, U. et al. (2008). Assessing and predicting biodiversity in a floodplain ecosystem: assimilation of net primary production derived from imaging spectrometer data into a dynamic vegetation model. Remote Sens. Environ., 112, 2118-2130.
64. Levine, J.M. & Antonio, C.M.D. (2003). Forecasting biological invasions with international trade. Conserv. Biol., 17, 322-326.
65. Levins, R. (1966). The strategy of model building in population biology. Am. Sci., 54, 421-431.
66. Loarie, S.R., Duffy, P.B., Hamilton, H., Asner, G.P., Field, C.B. & Ackerly, D.D. (2009). The velocity of climate change. Nature, 462, 1052-1055.
67. Loreau, M., Mouquet, N. & Holt, R.D. (2003). Meta-ecosystems: a theoretical framework for a spatial ecosystem ecology. Ecol. Lett., 6, 673-679.
68. Lorenz, E. (1965). A study of the predictability of a 28-variable atmospheric model. Tellus, 17, 321-333.
69. Lou, Y., Keenan, T.F. & Smith, M.J. (2014). Predictability of the terrestrial carbon cycle. Global Change Biol., 21, 1737-1751.
70. Matthews, B., Narwani, A., Hausch, S., Nonaka, E., Peter, H., Yamamichi, M. et al. (2011). Toward an integration of evolutionary biology and ecosystem science. Ecol. Lett., 14, 690-701.
71. May, R.M. (2001). Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton.
72. McCann, K.S. (2000). The diversity-stability debate. Nature, 405, 228-233.
73. McGrady-Steed, J. & Harris, P. (1997). Biodiversity regulates ecosystem predictability. Nature, 390, 162-165.
74. Mouquet, N., Lagadeuc, Y. & Loreau, M. (2012). Ecologie prédictive and changement planétaire. Les Cah. Prospect. Rep., www.cnrs.fr/inee/outils/docs/prospectiveavignon2012.pdf, 9-44.
75. Nekola, J.C. & McGill, B.J. (2014). Scale dependency in the functional form of the distance decay relationship. Ecography, 37, 309-320.
76. Nekola, J. & White, P. (1999). The distance decay of similarity in biogeography and ecology. J. Biogeogr., 26, 867-878.
77. Novak, M., Wootton, J.T., Doak, D.F., Emmerson, M., Estes, J.A. & Tinker, M.T. (2011). Predicting community responses to perturbations in the face of imperfect knowledge and network complexity. Ecology, 92, 836-846.
78. Ollerenshaw, C.B. & Smith, L.P. (1969). Meteorological factors and forecasts of helminthic disease. Adv. Parasitol., 7, 283-323.
79. Palmer, P.I. & Smith, M.J. (2014). Model human adaptation to climate change. Nature, 512, 365-366.
80. Pearse, I.S. & Altermatt, F. (2013). Predicting novel trophic interactions in a non-native world. Ecol. Lett., 16, 1088-1094.
81. Pereira, H.M., Ferrier, S., Walters, M., Geller, G.N., Jongman, R.H.G., Scholes, R.J. et al. (2013). Essential biodiversity variables. Science, 339, 277-278.
82. Perretti, C.T., Munch, S.B. & Sugihara, G. (2013a). Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data. Proc. Natl. Acad. Sci. USA, 110, 5253-5257.
83. Perretti, C.T., Munch, S.B. & Sugihara, G. (2013b). Reply to Hartig and Dormann: the true model myth. Proc. Natl. Acad. Sci. USA, 110, 3976-3977.
84. Petchey, O., Brose, U. & Rall, B. (2010). Predicting the effects of temperature on food web connectance. Philos. Trans. R. Soc. Lond. B Biol. Sci., 365, 2081-2091.
85. Peterson, G.D., Carpenter, S.R. & Brock, W.A. (2003). Uncertainty and the management of multistate ecosystems: an apparently rational route to collapse. Ecology, 84, 1403-1411.
86. Pottier, J., Malenovský, Z., Psomas, A., Homolová, L., Schaepman, M.E., Choler, P. et al. (2014). Modelling plant species distribution in alpine grasslands using airborne imaging spectroscopy. Biol. Lett., 10, 20140347.
87. Purves, D. & Pacala, S. (2008). Predictive models of forest dynamics. Science, 320, 1452-1453.
88. Purves, D., Scharlemann, J., Harfoot, M., Newbold, T., Tittensor, D., Hutton, J. et al. (2013). Ecosystems: time to model all life on earth. Nature, 493, 295-297.
89. Raftery, A.E. (2014). Use and communication of probabilistic forecasts. arXiv: 1408.4812.
90. Regan, H., Colyvan, M. & Burgman, M. (2002). A taxonomy and treatment of uncertainty for ecology and conservation biology. Ecol. Appl., 12, 618-628.
91. Ripa, J., Storlind, L., Lundberg, P. & Brown, J. (2009). Niche coevolution in consumer-resource communities. Evol. Ecol. Res., 11, 305-323.
92. Salguero-Gómez, R., Jones, O.R., Archer, C.R., Buckley, Y.M., Che-Castaldo, J., Caswell, H. et al. (2015). The compadre Plant Matrix Database: an open online repository for plant demography. J. Ecol., 103, 202-218.
93. Salvino, L.W., Cawley, R., Grebogi, C. & Yorke, J.A. (1995). Predictability of time series. Phys. Lett. A, 209, 327-332.
94. Scheffer, M., Bascompte, J., Brock, W.A., Brovkin, V., Carpenter, S.R., Dakos, V. et al. (2009). Early-warning signals for critical transitions. Nature, 461, 53-59.
95. Schimel, D.S., Asner, G.P. & Moorcroft, P. (2013). Observing changing ecological diversity in the Anthropocene. Front. Ecol. Environ., 11, 129-137.
96. Schindler, D.E. & Hilborn, R. (2015). Prediction, precaution, and policy under global change. Science, 347, 953-954.
97. Seferian, R., Bopp, L., Gehlen, M., Swingedouw, D., Mignot, J., Guilyardi, E. et al. (2014). Multiyear predictability of tropical marine productivity. Proc. Natl. Acad. Sci. USA, 111, 11646-11651.
98. Shaman, J. & Karspeck, A. (2012). Forecasting seasonal outbreaks of influenza. Proc. Natl. Acad. Sci. USA, 109, 20425-20430.
99. Shuman, F. (1978). Numerical weather prediction. Bull. Am. Meteorol. Soc., 59, 5-17.
100. Simmons, A. & Hollingsworth, A. (2002). Some aspects of the improvement in skill of numerical weather prediction. Q. J. R. Meteorol. Soc., 128, 647-677.
101. Spiegelhalter, D., Pearson, M. & Short, I. (2011). Visualizing uncertainty about the future. Science, 333, 1393-1400.
102. Stevenson, T.C.E. (1864). New description of box for holding thermometers. J. Scottish Meteorol. Soc., 1, 122.
103. Stigall, A.L. (2012). Using ecological niche modelling to evaluate niche stability in deep time. J. Biogeogr., 39, 772-781.
104. Stillman, R.A., Railsback, S.F., Giske, J., Berger, U.T.A. & Grimm, V. (2015). Making predictions in a changing world: the Benefits of Individual-Based Ecology. Bioscience, 65, 140-150.
105. Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, M. et al. (2012). Detecting causality in complex ecosystems. Science, 338, 496-500.
106. Sutherland, W.J. (2006). Predicting the ecological consequences of environmental change: a review of the methods. J. Appl. Ecol., 43, 599-616.
107. Sutherland, W.J., Armstrong-Brown, S., Paul, R., Brereton, T.O.M., Brickland, J., Colin, D. et al. (2006). The identification of 100 ecological questions of high policy relevance in the UK. Journal of Applied Ecology, 43, 617-627.
108. Tallis, H.M. & Kareiva, P. (2006). Shaping global environmental decisions using socio-ecological models. Trends Ecol. Evol., 21, 562-568.
109. Travis, J., Coleman, F.C., Auster, P.J., Cury, P.M., Estes, J.A., Orensanz, J. et al. (2014). Correction for Travis et al., Integrating the invisible fabric of nature into fisheries management. Proc. Natl. Acad. Sci. USA, 111, 4644.
110. Turchin, P. (2003). Complex Population Dynamics: A Theoretical/Empirical Synthesis. Princeton University Press, Princeton.
111. Vandermeer, J. (1969). The competitive structure of communities: an experimental approach with protozoa. Ecology, 50, 362-371.
112. Vincenzi, S. (2014). Extinction risk and eco-evolutionary dynamics in a variable environment with increasing frequency of extreme events. J. R. Soc. Interface, 11, 20140441.
113. Ward, E.J., Holmes, E.E., Thorson, J.T. & Collen, B. (2014). Complexity is costly: a meta-analysis of parametric and non-parametric methods for short-term population forecasting. Oikos, 123, 652-661.
114. Wollrab, S., Diehl, S. & De Roos, A.M. (2012). Simple rules describe bottom-up and top-down control in food webs with alternative energy pathways. Ecol. Lett., 15, 935-946.
115. Wootton, J.T. (2002). Indirect effects in complex ecosystems: recent progress and future challenges. J. Sea Res., 48, 157-172.
116. Wootton, J.T. (2004). Markov chain models predict the consequences of experimental extinctions. Ecol. Lett., 7, 653-660.
117. Yachi, S. & Loreau, M. (1999). Biodiversity and ecosystem productivity in a fluctuating environment: the insurance hypothesis. Proc. Natl. Acad. Sci. USA, 96, 1463-1468.
118. Ye, H., Beamish, R.J., Glaser, S.M., Grant, S.C.H., Hsieh, C., Richards, L.J., Schnute, J.T. & Sugihara, G. (2015). Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling. Proceedings of the National Academy of Sciences, 201417063.
119. Yodzis, P. (1988). The indeterminacy of ecological interactions as perceived through perturbation experiments. Ecology, 69, 508-515.
120. Yoshida, T., Jones, L.E., Ellner, S.P., Fussmann, G.F. & Hairston, N.G. (2003). Rapid evolution drives ecological dynamics in a predator-prey system. Nature, 424, 303-306.
121. Ziehmann, C., Smith, L.A. & Kurths, J. (2000). Localized Lyapunov exponents and the prediction of predictability. Phys. Lett. A, 271, 237-251.