Transient Phenomena in Ecology
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RESEARCH ◥ a systematic study of transient dynamics in REVIEW SUMMARY ecological systems. As illustrated in the figure, a relatively small number of ideas from dynam- ical systems are used to categorize the differ- ECOLOGY ent ways that transients can arise. Translating these abstract results from dynamical systems Transient phenomena in ecology into observations about both ecological models ◥ and ecological system dy- ON OUR WEBSITE namics, it is possible to un- Alan Hastings*, Karen C. Abbott, Kim Cuddington, Tessa Francis, Gabriel Gellner, Read the full article derstand when transients Ying-Cheng Lai, Andrew Morozov, Sergei Petrovskii, at http://dx.doi. arelikelytooccurandthe Katherine Scranton, Mary Lou Zeeman org/10.1126/ various properties of these science.aat6412 transients, with implica- .................................................. BACKGROUND: Much of ecological theory transient is a persistent dynamical regime— tions for ecosystem man- and the understanding of ecological systems including near-constant dynamics, cyclic dy- agement and basic ecological theory. Transients has been based on the idea that the observed namics, or even apparently chaotic dynamics— can provide an explanation for observed re- states and dynamics of ecological systems can that persists for more than a few and as many gime shifts that does not depend on under- be represented by stable asymptotic behavior as tens of generations, but which is not the sta- lying environmental changes. Systems that of models describing these systems. Beginning ble long-term dynamic that would eventually continually change rapidly between different with early work by Lotka and Volterra through occur. These examples have demonstrated the long-lasting dynamics, such as insect outbreaks, Downloaded from the seminal work of May in the 1970s, this view potential importance of transients but have may most usefully be viewed using the frame- has dominated much of ecological thinking, often appeared to be a set of idiosyncratic work of long transients. although concepts such as the idea of tipping cases. What is needed is an organized approach An initial focus on conceptual systems, such points in ecological systems have played an that describes when a transient behavior is as two-species systems, establishes the ubiq- increasingly important role. In contrast to the likely to appear, predicts what factors enhance uity of transients and an understanding of implied long time scales of asymptotic behavior long transients, and describes the character- what ecological aspects can lead to transients, http://science.sciencemag.org/ in mathematical models, both observations of istics of this transient behavior. A theory of long includingthepresenceofmultipletimescales ecological systems and questions related to the ecological transients is a counterpart to the and particular nonlinear interactions. The in- management of ecological systems are typically related question of tipping points, where pre- fluences of stochasticity and more realistic focused on relatively short time scales. vious work based on an analysis of simple bi- higher-dimensional dynamics are shown to A number of models and observations demon- furcations has provided broad insights. increase the likelihood, and possibly the tem- strate possible transient behavior that may poral extent, of transient dynamics. persist over very long time periods, followed ADVANCES: Just as ideas based on the saddle- by rapid changes in dynamics. In these ex- node bifurcation provide a basis for under- OUTLOOK: The development of such a frame- amples, focusing solely on the long-term be- standing tipping points, a suite of ideas from work for organizing the study of transients in havior of systems would be misleading. A long dynamical systems provides a way to organize ecological systems opens up a number of on September 11, 2018 avenues for future research and application. The approach we describe also raises impor- AB tant questions for further development in dy- Long transient before continuing cycle namical systems. We have not, for example, emphasized nonautonomous systems, which Slow change mayberequiredtounderstandtheimplica- during a saddle tions of a changing environment for transients. Species 2 crawl-by “landscape” Systems with explicit time dependence as well as stochastic nonlinear systems still present Population dynamic great mathematical challenges. Slow change in Implications for management and basic Species 1 system state near ecological understanding depend on both the ghost attractor results we describe and future developments. A recognition of the difficulty of prediction caused by long transients, and of the corre- Long transient sponding need to match dynamics to transient before reaching behaviors of models, shows that basing either stable state (well) Multiple High management or interpretation of ecological Stochasticity time scales dimension observations only on long-term dynamics can be seriously flawed.▪ Two ways that long transients arise in ecology, illustrated as a ball rolling downhill. (A)Slow transition away from a ghost attractor: a state that is not an equilibrium, but would be under slightly different conditions. (B) Lingering near a saddle: a state that is attracting from The list of author affiliations is available in the full article online. *Corresponding author. Email: [email protected] some directions but repelling from others. Additional factors such as stochasticity, multiple time Cite this article as A. Hastings et al., Science 361, eaat6412 scales, and high system dimension can extend transients. (2018). DOI: 10.1126/science.aat6412 Hastings et al., Science 361, 990 (2018) 7 September 2018 1of1 RESEARCH ◥ point.” In turn, the directional change in pa- REVIEW rameter values is often assumed to result from an exogenous process such as, for instance, global climate change. Intense study of one kind of ECOLOGY exogenously triggered regime shift (those caused by saddle-node bifurcations) has provided im- portant insights (3, 5, 6) across a range of eco- Transient phenomena in ecology logical systems. There is, however, a growing body of evidence that we review here, from both Alan Hastings1*, Karen C. Abbott2, Kim Cuddington3, Tessa Francis4, Gabriel Gellner5, empirical and modeling studies, suggesting alter- Ying-Cheng Lai6, Andrew Morozov7,8, Sergei Petrovskii7, native underlying mechanisms for some regime Katherine Scranton9, Mary Lou Zeeman10 shifts. The approach for understanding regime shifts The importance of transient dynamics in ecological systems and in the models that describe can be extended to a much broader range of them has become increasingly recognized. However, previous work has typically treated phenomena and systems by focusing on transients each instance of these dynamics separately. We review both empirical examples and model in ecological systems, where once again ideas from systems, and outline a classification of transient dynamics based on ideas and concepts dynamical systems can organize what may at first from dynamical systems theory. This classification provides ways to understand the likelihood appear to be a disparate set of observations and of transients for particular systems, and to guide investigations to determine the timing explanations. In the cases we focus on here, the ecological dynamics are essentially transient of sudden switches in dynamics and other characteristics of transients. Implications for both Downloaded from 7–12 management and underlying ecological theories emerge. ( ) and shifts occur in the absence of any clear trend in the environmental properties. Ecological transients can arise for a number of nderstanding ecological dynamics over cilitate understanding of transient dynamics, reasons, including responses to environmental relevant time scales underpins almost all each example appears novel and idiosyncratic. fluctuation as well as a variety of human inter- major questions in ecology, such as ex- Concepts from dynamical systems (Table 1) can ventions. Some transients are short; others can U planations for observed distributions and provide tools for a more systematic approach last for a very long time. An ecosystem exhibit- http://science.sciencemag.org/ abundances of species, population changes to the incorporation of transient dynamics in ing long transient behavior would typically show through time, and management of ecological ecological models and theories, as well as guide an apparently stable dynamic (e.g., periodic os- systems. There is a growing recognition that applications to natural and managed systems. cillations,asinFig.1,A,D,andE)overtimethat dynamics on ecological time scales, called tran- Tools will emerge for understanding which eco- may span dozens or even hundreds of genera- sients, may be different from asymptotic dynamics. logical factors produce long transients, and for tions before experiencing a sudden transition to The inherent impermanence of transients means identifying appropriate responses to the possi- another state (e.g., extinction) or another regime that an ecological system in a transient state can bility of sudden system changes in management (e.g., oscillations with a very different mean change abruptly, even without any underlying and in experimental and observational studies. value). Therefore, long transients may provide change in environmental conditions (parameters). A major ecological question is how to relate Conversely, the possibility of long transients im- observations of