Experimental demonstration of chaos in a microbialfood webLutz Becks1*, Frank M. Hilker2, Horst Malchow2, Klaus Ju¨rgens3,4& Hartmut Arndt1*Discovering why natural population densities change over timeand vary with location is a central goal of ecological and evolu-tional disciplines. The recognition that even simple ecologicalsystems can undergo chaotic behaviour has made chaos a topic ofconsiderable interest among theoretical ecologists1–4. However,there is still a lack of experimental evidence that chaotic behaviouroccurs in the real world of coexisting populations in multi-speciessystems. Here we study the dynamics of a defined predator–preysystem consisting of a bacterivorous ciliate and two bacterial preyspecies. The bacterial species preferred by the ciliate was thesuperior competitor. Experimental conditions were kept constantwith continuous cultivation in a one-stage chemostat. We showthat the dynamic behaviour of such a two-prey, one-predatorsystem includes chaotic behaviour, as well as stable limit cyclesand coexistence at equilibrium. Changes in the populationdynamics were triggered by changes in the dilution rates of thechemostat. The observed dynamics were verified by estimating thecorresponding Lyapunov exponents. Such a defined microbialfood web offers a new possibility for the experimental study ofdeterministic chaos in real biological systems.Apart from the intuitive understanding that external (extrinsic)stimuli influence the variability of abundances, mathematical modelshave made it apparent that the internal (intrinsic) qualities of apopulation give rise to population dynamics with large and (atcertain parameter ranges) even chaotic fluctuations of abundances,even under wholly constant and predictable conditions5. Predator–prey interactions have been considered as a possible driving force ofpopulation dynamics since the beginning of ecological studies6,7.Inhis analysis of mathematical models, May1found that even simpleprocesses of population growth can show (for a certain range ofparameters) an unpredictable behaviour driven by intrinsic mecha-nisms. May’s studies marked the beginning of an intensive debate onthe question of whether or not natural systems are characterized bychaotic behaviour. In this context, the term ‘deterministic chaos’can be defined as bounded aperiodic fluctuations with sensitivedependence on initial conditions4. Under chaotic conditions, popu-lation abundances never show a precisely repeated pattern over time;such patterns are only observable in populations at equilibrium or atstable limit cycles. Theoreticians can clearly define parameter rangesof mathematical models that create chaotic behaviour in idealizedbiological systems3,8–10. However, only a ver y few experimentsindicating that bifurcations of dynamic behaviour might occur inthe real world have been conducted (for example, ciliate–bacteriainteractions11, flour beetle (Tribolium castaneum) dynamics12,13and rotifer–algae interactions14). Indications of chaotic dynamicsunder controlled conditions have so far been reported for one-speciessystems only13. A robust tool to verify obser ved dynamics isestimations of Lyapunov exponents from time series, which test forthe exponential divergence of nearby trajectories. Mathematically,stable (convergent) systems show negative Lyapunov exponents,whereas chao tic (divergent) systems have at least o ne positiveLyapunov exponent4.The aim of the present study was to verify the biological relevanceof chaotic behaviour in a real multi-species system. The longgeneration durations of most organisms and the complexity ofnatural environments have generally made the explanation of under-lying ecological mechanisms difficult15. However, experiments usingmicrobial populations propagated in controlled environmentsreduce ecosystem complexity to the point at which understandingsimple processes in isolation becomes possible. The rapid reproduc-tion of bacteria and protists is one of the main advantages of workingwith microorganisms as model organisms7,16,17. In addition, thecommunity structure can be exactly defined; for example, singlestrains of bacteria and protists can be selected. Microorganisms canalso be cultured under chemostat conditions. This has the greatadvantage that extrinsic factors are negligible and changes in popu-lation dynamics can be attributed to intrinsic factors. In terms ofpredation and interspecific competition, one of the simplest systemsimaginable is a three-species system with two prey organisms and onepredator. Several theoretical studies have been made of such modelsystems8–10,18. Generally, different patterns of population dynamicsare predicted by models; for example, the extinction of one or twospecies and the coexistence of all three species. Assuming that the twoprey populations compete with each other and assuming that thebetter competitor is the preferred prey, three patterns may occur:coexistence at equilibrium, coexistence at stable limit cycles, andcoexistence at chaos8–10,18.Our study was aimed at identifying these different patterns ofcoexistence in controlled experiments in a chemostat. We used thedilution rate as the bifurcation parameter in t he experiments,because the dynamical behaviour of chemostat models can changewith dilution rate9,10,14. We constructed one-stage chemostat systemsconsisting of axenic cultures of three species: a predator (the ciliateTetrahymena pyriformis) and two coexisting prey bacteria, the rod-shaped Pedobacter and the coccus Brevundimonas . The effectiveconsumption of these bacteria by the ciliate and its food preferencewas analysed by immunofluorescence techniques. The ciliate canestablish stable populations when feeding on either bacterium, but itdies off in the highly diluted organic medium when bacteria areabsent. The growth conditions for the bacteria and the mortality ofthe ciliate are determined by the dilution rates (controlled byperistaltic pumps). Brevundimonas was always outcompeted inchemostat experiments containing both bacterial strains without apredator. Thus, Pedobacter was considered to have a better fitness. InLETTERS1Department of General Ecology and Limnology, Zoological Institute, University of Cologne, D-50923 Ko¨ln, Germany.2Department of Mathematics and Computer Science,Institute of Environmental Systems Research, University of Osnabru¨ck, D-49069 Osnabru¨ck, Germany.3Max Planck Institute for Limnology, PO Box 165, D-24302