Mathematical models predict that species interactions such as competition and predation can generate chaos1,2,3,4,5,6,7,8. However, experimental demonstrations of chaos in ecology are scarce, and have been limited to simple laboratory systems with a short duration and artificial species combinations9,10,11,12. Here, we present the first experimental demonstration of chaos in a long-term experiment with a complex food web. Our food web was isolated from the Baltic Sea, and consisted of bacteria, several phytoplankton species, herbivorous and predatory zooplankton species, and detritivores. The food web was cultured in a laboratory mesocosm, and sampled twice a week for more than 2,300 days. Despite constant external conditions, the species abundances showed striking fluctuations over several orders of magnitude. These fluctuations displayed a variety of different periodicities, which could be attributed to different species interactions in the food web. The population dynamics were characterized by positive Lyapunov exponents of similar magnitude for each species. Predictability was limited to a time horizon of 15–30 days, only slightly longer than the local weather forecast. Hence, our results demonstrate that species interactions in food webs can generate chaos. This implies that stability is not required for the persistence of complex food webs, and that the long-term prediction of species abundances can be fundamentally impossible.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
May, R. M. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645–647 (1974)
May, R. M. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976)
Gilpin, M. E. Spiral chaos in a predator–prey model. Am. Nat. 113, 306–308 (1979)
Hastings, A. & Powell, T. Chaos in a three-species food chain. Ecology 72, 896–903 (1991)
Vandermeer, J. Loose coupling of predator–prey cycles: entrainment, chaos, and intermittency in the classic MacArthur consumer–resource equations. Am. Nat. 141, 687–716 (1993)
Huisman, J. & Weissing, F. J. Biodiversity of plankton by species oscillations and chaos. Nature 402, 407–410 (1999)
Van Nes, E. H. & Scheffer, M. Large species shifts triggered by small forces. Am. Nat. 164, 255–266 (2004)
Huisman, J., Pham Thi, N. N., Karl, D. M. & Sommeijer, B. Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature 439, 322–325 (2006)
Ellner, S. P. & Turchin, P. Chaos in a noisy world: new methods and evidence from time-series analysis. Am. Nat. 145, 343–375 (1995)
Costantino, R. F., Desharnais, R. A., Cushing, J. M. & Dennis, B. Chaotic dynamics in an insect population. Science 275, 389–391 (1997)
Becks, L., Hilker, F. M., Malchow, H., Jürgens, K. & Arndt, H. Experimental demonstration of chaos in a microbial food web. Nature 435, 1226–1229 (2005)
Graham, D. W. et al. Experimental demonstration of chaotic instability in biological nitrification. ISME J. 1, 385–393 (2007)
Zimmer, C. Life after chaos. Science 284, 83–86 (1999)
McCann, K., Hastings, A. & Huxel, G. R. Weak trophic interactions and the balance of nature. Nature 395, 794–798 (1998)
Neutel, A. M., Heesterbeek, J. A. P. & de Ruiter, P. C. Stability in real food webs: weak links in long loops. Science 296, 1120–1123 (2002)
Heerkloss, R. & Klinkenberg, G. A long-term series of a planktonic foodweb: a case of chaotic dynamics. Verh. Int. Verein. Theor. Angew. Limnol. 26, 1952–1956 (1998)
Scheffer, M. & Rinaldi, S. Minimal models of top-down control of phytoplankton. Freshwat. Biol. 45, 265–283 (2000)
Fussmann, G. F., Ellner, S. P., Shertzer, K. W. & Hairston, N. G. Crossing the Hopf bifurcation in a live predator–prey system. Science 290, 1358–1360 (2000)
Sugihara, G. & May, R. M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990)
Nychka, D., Ellner, S., Gallant, A. R. & McCaffrey, D. Finding chaos in noisy systems. J. R. Stat. Soc. B 54, 399–426 (1992)
Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Perseus, Cambridge, Massachusetts, 1994)
Takens, F. in Dynamical Systems and Turbulence, Warwick 1980 (Lecture Notes in Mathematics vol. 898) (ed. Rand, D. A. & Young, L.S.) 366–381 (Springer, Berlin, 1981)
Kantz, H. & Schreiber, T. Nonlinear Time Series Analysis (Cambridge Univ. Press, Cambridge, UK, 1997)
Rosenstein, M. T., Collins, J. J. & De Luca, C. J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134 (1993)
Lorenz, E. N. Atmospheric predictability experiments with a large numerical model. Tellus 34, 505–513 (1982)
Gaedeke, A. & Sommer, U. The influence of the frequency of periodic disturbances on the maintenance of phytoplankton diversity. Oecologia 71, 25–28 (1986)
Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. B 57, 289–300 (1995)
Redfield, A. C. The biological control of chemical factors in the environment. Am. Sci. 46, 205–221 (1958)
Kendall, B. E. Cycles, chaos, and noise in predator–prey dynamics. Chaos Solitons Fract. 12, 321–332 (2001)
Theiler, J. Spurious dimension from correlation algorithms applied to limited time-series data. Phys. Rev. A 34, 2427–2432 (1986)
We thank W. Ebenhöh for suggestions on the experimental design, H. Albrecht, G. Hinrich, J. Rodhe, S. Stolle and B. Walter for help during the experiment, T. Huebener, I. Telesh, R. Schumann, M. Feike and G. Arlt for advice in taxonomic identification, and B. M. Bolker and V. Dakos for comments on the manuscript. The research of E.B., K.D.J. and J.H. was supported by the Earth and Life Sciences Foundation (ALW), which is subsidized by the Netherlands Organisation for Scientific Research (NWO). S.P.E.’s research was supported by a grant from the Andrew W. Mellon Foundation.
Author Contributions R.H. ran the experiment, counted the species and measured the nutrient concentrations. E.B., J.H., K.D.J., P.B. and S.P.E. performed the time series analysis. E.B., J.H., M.S. and S.P.E. wrote the manuscript. All authors discussed the results and commented on the manuscript.
The Supplementary Information presents detailed information on the following aspects of the long-term experiment and subsequent time series analysis:1) Materials and methods of the mesocosm experiment; 2) Earlier analysis of the same time series; 3) Transformation of the time series (including Figures S1-S2); 4) Spectral analysis (Figures S3-S4); 5) Predictability (Table S1, Figure S5); Methods for estimating Lyapunov exponents (Figures S6-S7); 7) Temperature fluctuations (Table S2, Figure S8). (PDF 1204 kb)
About this article
Cite this article
Benincà, E., Huisman, J., Heerkloss, R. et al. Chaos in a long-term experiment with a plankton community. Nature 451, 822–825 (2008). https://doi.org/10.1038/nature06512
Communications Biology (2021)
Scientific Reports (2021)
Annals of Operations Research (2021)
Mathematical analysis of laboratory microbial experiments demonstrating deterministic chaotic dynamics
Biologia Futura (2021)