May, R. M. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science 186, 645–647 (1974).
Google Scholar
Beddington, J. R., Free, C. A. & Lawton, J. H. Dynamic complexity in predator–prey models framed in difference equations. Nature 255, 58–60 (1975).
Google Scholar
Hastings, A., Hom, C. L., Ellner, S., Turchin, P. & Godfray, H. C. J. Chaos in ecology: is Mother Nature a strange attractor? Annu. Rev. Ecol. Syst. 24, 1–33 (1993).
Google Scholar
Cressie, N. & Wikle, C. K. Statistics for Spatio-Temporal Data (John Wiley & Sons, 2011).
The State of World Fisheries and Aquaculture 2020 (FAO, 2020).
Hastings, A. & Powell, T. Chaos in a three-species food chain. Ecology 72, 896–903 (1991).
Google Scholar
Huisman, J. & Weissing, F. J. Biodiversity of plankton by species oscillations and chaos. Nature 402, 407–410 (1999).
Google Scholar
Doebeli, M. & Ispolatov, I. Chaos and unpredictability in evolution. Evolution 68, 1365–1373 (2014).
Google Scholar
Pearce, M. T., Agarwala, A. & Fisher, D. S. Stabilization of extensive fine-scale diversity by ecologically driven spatiotemporal chaos. Proc. Natl Acad. Sci. USA 117, 14572–14583 (2020).
Google Scholar
Costantino, R. F., Desharnais, R. A., Cushing, J. M. & Dennis, B. Chaotic dynamics in an insect population. Science 275, 389–391 (1997).
Google Scholar
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).
Google Scholar
Benincá, E. et al. Chaos in a long-term experiment with a plankton community. Nature 451, 822–825 (2008).
Google Scholar
Tilman, D. & Wedin, D. Oscillations and chaos in the dynamics of a perennial grass. Nature 353, 653–655 (1991).
Google Scholar
Turchin, P. & Ellner, S. P. Living on the edge of chaos: population dynamics of fennoscandian voles. Ecology 81, 3099–3116 (2000).
Google Scholar
Ferrari, M. J. et al. The dynamics of measles in sub-Saharan Africa. Nature 451, 679–684 (2008).
Google Scholar
Benincà, E., Ballantine, B., Ellner, S. P. & Huisman, J. Species fluctuations sustained by a cyclic succession at the edge of chaos. Proc. Natl Acad. Sci. USA 112, 6389–6394 (2015).
Google Scholar
Hassell, M. P., Lawton, J. H. & May, R. M. Patterns of dynamical behaviour in single-species populations. J. Anim. Ecol. 45, 471–486 (1976).
Google Scholar
Sibly, R. M., Barker, D., Hone, J. & Pagel, M. On the stability of populations of mammals, birds, fish and insects. Ecol. Lett. 10, 970–976 (2007).
Google Scholar
Shelton, A. O. & Mangel, M. Fluctuations of fish populations and the magnifying effects of fishing. Proc. Natl Acad. Sci USA. 108, 7075–7080 (2011).
Google Scholar
Salvidio, S. Stability and annual return rates in amphibian populations. Amphib. Reptil. 32, 119–124 (2011).
Google Scholar
Snell, T. W. & Serra, M. Dynamics of natural rotifer populations. Hydrobiologia 368, 29–35 (1998).
Google Scholar
Gross, T., Ebenhöh, W. & Feudel, U. Long food chains are in general chaotic. Oikos 109, 135–144 (2005).
Google Scholar
Ispolatov, I., Madhok, V., Allende, S. & Doebeli, M. Chaos in high-dimensional dissipative dynamical systems. Sci. Rep. 5, 12506 (2015).
Google Scholar
Clark, T. J. & Luis, A. D. Nonlinear population dynamics are ubiquitous in animals. Nat. Ecol. Evol. 4, 75–81 (2020).
Google Scholar
Sivakumar, B., Berndtsson, R., Olsson, J. & Jinno, K. Evidence of chaos in the rainfall-runoff process. Hydrol. Sci. J. 46, 131–145 (2001).
Google Scholar
Hanski, I., Turchin, P., Korpimäki, E. & Henttonen, H. Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. Nature 364, 232–235 (1993).
Google Scholar
Turchin, P. & Taylor, A. D. Complex dynamics in ecological time series. Ecology 73, 289–305 (1992).
Google Scholar
Munch, S. B., Brias, A., Sugihara, G. & Rogers, T. L. Frequently asked questions about nonlinear dynamics and empirical dynamic modelling. ICES J. Mar. Sci. 77, 1463–1479 (2020).
Google Scholar
Sugihara, G. & May, R. M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990).
Google Scholar
Ellner, S. P. & Turchin, P. Chaos in a noisy world: new methods and evidence from time-series analysis. Am. Nat. 145, 343–375 (1995).
Google Scholar
Nychka, D., Ellner, S., Gallant, A. R. & McCaffrey, D. Finding chaos in noisy systems. J. R. Stat. Soc. B 54, 399–426 (1992).
Webber, C. L. & Zbilut, J. P. Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973 (1994).
Google Scholar
Bandt, C. & Pompe, B. Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88, 174102 (2002).
Google Scholar
Luque, B., Lacasa, L., Ballesteros, F. & Luque, J. Horizontal visibility graphs: exact results for random time series. Phys. Rev. E 80, 46103 (2009).
Google Scholar
Toker, D., Sommer, F. T. & D’Esposito, M. A simple method for detecting chaos in nature. Commun. Biol. 3, 11 (2020).
Google Scholar
Pikovsky, A. & Politi, A. Lyapunov Exponents: A Tool to Explore Complex Dynamics (Cambridge Univ. Press, 2016).
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).
Google Scholar
Dämmig, M. & Mitschke, F. Estimation of Lyapunov exponents from time series: the stochastic case. Phys. Lett. A 178, 385–394 (1993).
Google Scholar
Prendergast, J., Bazeley-White, E., Smith, O., Lawton, J. & Inchausti, P. The Global Population Dynamics Database (KNB, 2010); https://doi.org/10.5063/F1BZ63Z8
Thibaut, L. M. & Connolly, S. R. Hierarchical modeling strengthens evidence for density dependence in observational time series of population dynamics. Ecology 101, e02893 (2020).
Google Scholar
Knape, J. & de Valpine, P. Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance? Ecol. Lett. 15, 17–23 (2012).
Google Scholar
Takens, F. in Dynamical Systems and Turbulence (eds Rand, D. A. & Young, L. S.) 366–381 (Springer, 1981).
Sugihara, G. Nonlinear forecasting for the classification of natural time series. Philos. Trans. R. Soc. A 348, 477–495 (1994).
Loh, J. et al. The Living Planet Index: using species population time series to track trends in biodiversity. Philos. Trans. R. Soc. B 360, 289–295 (2005).
Google Scholar
Kendall, B. E. Cycles chaos, and noise in predator–prey dynamics. Chaos Solitons Fractals 12, 321–332 (2001).
Google Scholar
Anderson, C. N. K. et al. Why fishing magnifies fluctuations in fish abundance. Nature 452, 835–839 (2008).
Google Scholar
Anderson, D. M. & Gillooly, J. F. Allometric scaling of Lyapunov exponents in chaotic populations. Popul. Ecol. 62, 364–369 (2020).
Google Scholar
Graham, D. W. et al. Experimental demonstration of chaotic instability in biological nitrification. ISME J. 1, 385–393 (2007).
Google Scholar
Turchin, P. Nonlinear time-series modeling of vole population fluctuations. Res. Popul. Ecol. 38, 121–132 (1996).
Google Scholar
Becks, L. & Arndt, H. Different types of synchrony in chaotic and cyclic communities. Nat. Commun. 4, 1359 (2013).
Google Scholar
Becks, L. & Arndt, H. Transitions from stable equilibria to chaos, and back, in an experimental food web. Ecology 89, 3222–3226 (2008).
Google Scholar
Rezende, E. L., Albert, E. M., Fortuna, M. A. & Bascompte, J. Compartments in a marine food web associated with phylogeny, body mass, and habitat structure. Ecol. Lett. 12, 779–788 (2009).
Google Scholar
Krause, A. E., Frank, K. A., Mason, D. M., Ulanowicz, R. E. & Taylor, W. W. Compartments revealed in food-web structure. Nature 426, 282–285 (2003).
Google Scholar
The IUCN Red List of Threatened Species Version 2020-2 (IUCN, 2020); https://www.iucnredlist.org
Freckleton, R. P. & Watkinson, A. R. Are weed population dynamics chaotic? J. Appl. Ecol. 39, 699–707 (2002).
Google Scholar
May, R. M. Simple mathematical models with very complicated dynamics. Nature 261, 459–467 (1976).
Google Scholar
Mora, C., Tittensor, D. P., Adl, S., Simpson, A. G. B. & Worm, B. How many species are there on Earth and in the ocean? PLoS Biol. 9, e1001127 (2011).
Google Scholar
Munch, S. B., Giron-Nava, A. & Sugihara, G. Nonlinear dynamics and noise in fisheries recruitment: a global meta-analysis. Fish Fish. 19, 964–973 (2018).
Google Scholar
Boettiger, C., Harte, T., Chamberlain, S. & Ram, K. rgpdd: R Interface to the Global Population Dynamics Database. https://docs.ropensci.org/rgpdd, https://github.com/ropensci/rgpdd (2019).
Brook, B. W., Traill, L. W. & Bradshaw, C. J. A. Minimum viable population sizes and global extinction risk are unrelated. Ecol. Lett. 9, 375–382 (2006).
Google Scholar
Baars, J. W. M. Autecological investigations of marine diatoms, 2. Generation times of 50 species. Hydrobiol. Bull. 15, 137–151 (1981).
Google Scholar
Lavigne, A. S., Sunesen, I. & Sar, E. A. Morphological, taxonomic and nomenclatural analysis of species of Odontella, Trieres and Zygoceros (Triceratiaceae, Bacillariophyta) from Anegada Bay (Province of Buenos Aires, Argentina). Diatom Res. 30, 307–331 (2015).
Google Scholar
Anderson, D. M. & Gillooly, J. F. Physiological constraints on long-term population cycles: a broad-scale view. Evol. Ecol. Res. 18, 693–707 (2017).
Janes, M. J. Oviposition studies on the chinch bug, Blissus leucopterus (Say). Ann. Entomol. Soc. Am. 28, 109–120 (1935).
Google Scholar
Cook, L. M. Food-plant specialization in the moth Panaxia dominula L. Evolution 15, 478–485 (1961).
Google Scholar
Casey, T. M. Flight energetics of sphinx moths: power input during hovering flight. J. Exp. Biol. 64, 529–543 (1976).
Google Scholar
Kobayashi, A., Tanaka, Y. & Shimada, M. Genetic variation of sex allocation in the parasitoid wasp Heterospilus prosopidis. Evolution 57, 2659–2664 (2003).
Google Scholar
Hozumi, N. & Miyatake, T. Body-size dependent difference in death-feigning behavior of adult Callosobruchus chinensis. J. Insect Behav. 18, 557–566 (2005).
Google Scholar
Huntley, M. E. & Lopez, M. D. G. Temperature-dependent production of marine copepods: a global synthesis. Am. Nat. 140, 201–242 (1992).
Google Scholar
Cohen, R. E. & Lough, R. G. Length–weight relationships for several copepods dominant in the Georges Bank–Gulf of Maine area. J. Northwest Atl. Fish. Sci. 2, 47–52 (1981).
Google Scholar
World Register of Marine Species (WoRMS, accessed 1 November 2020); https://doi.org/10.14284/170
Nakamura, Y. Growth and grazing of a large heterotrophic dinoflagellate, Noctiluca scintillans, in laboratory cultures. J. Plankton Res. 20, 1711–1720 (1998).
Google Scholar
Boulding, E. G. & Platt, T. Variation in photosynthetic rates among individual cells of a marine dinoflagellate. Mar. Ecol. Prog. Ser. 29, 199–203 (1986).
Google Scholar
Rimet, F. et al. The Observatory on LAkes (OLA) database: sixty years of environmental data accessible to the public. J. Limnol. https://doi.org/10.4081/jlimnol.2020.1944 (2020).
Rudstam, L. Zooplankton Survey of Oneida Lake, New York, 1964 to Present (KNB, 2020); https://knb.ecoinformatics.org/view/kgordon.17.99https://knb.ecoinformatics.org/knb/metacat/kgordon.17.67/default
Dumont, H. J., Van de Velde, I. & Dumont, S. The dry weight estimate of biomass in a selection of Cladocera, Copepoda and Rotifera from the plankton, periphyton and benthos of continental waters. Oecologia 19, 75–97 (1975).
Google Scholar
Geller, W. & Müller, H. Seasonal variability in the relationship between body length and individual dry weight as related to food abundance and clutch size in two coexisting Daphnia species. J. Plankton Res. 7, 1–18 (1985).
Google Scholar
Branstrator, D. K. Contrasting life histories of the predatory cladocerans Leptodora kindtii and Bythotrephes longimanus. J. Plankton Res. 27, 569–585 (2005).
Google Scholar
Rosen, R. A. Length–dry weight relationships of some freshwater zooplankton. J. Freshw. Ecol. 1, 225–229 (1981).
Google Scholar
Peters, R. H. & Downing, J. A. Empirical analysis of zooplankton filtering and feeding rates. Limnol. Oceanogr. 29, 763–784 (1984).
Google Scholar
Eckmann, J. P., Kamphorst, S. O. & Ruelle, D. Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–977 (1987).
Google Scholar
Luque, B., Lacasa, L., Ballesteros, F. J. & Robledo, A. Analytical properties of horizontal visibility graphs in the Feigenbaum scenario. Chaos 22, 013109 (2012).
Google Scholar
McCaffrey, D. F., Ellner, S., Gallant, A. R. & Nychka, D. W. Estimating the Lyapunov exponent of a chaotic system with nonparametric regression. J. Am. Stat. Assoc. 87, 682–695 (1992).
Google Scholar
Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. Toward a metabolic theory of ecology. Ecology 85, 1771–1789 (2004).
Google Scholar
Ricker, W. E. Stock and recruitment. J. Fish. Board Can. 11, 559–623 (1954).
Google Scholar
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