Transient Dynamics

by

Christopher Heggerud, Karen Abbott, Alan Hastings

• LAST MODIFIED: 12 January 2023
• DOI: 10.1093/obo/9780199830060-0241

Introduction

While much of theoretical ecology has focused on the study of long-term asymptotic dynamics of populations, a growing realization is that the study of dynamics on more ecologically relevant timescales is of equal or greater importance. Often, dynamics that occur on shorter, ecologically relevant, timescales are referred to as transient dynamics, and include examples such as disease outbreaks and regime shifts. While any perturbation or environmental change that moves a system away from equilibrium will trigger a transient, this article focuses specifically on those “long transients” whose impact persists over a meaningful timescale (very roughly, dozens of generations or longer). Transient dynamics often lead to significant qualitative changes in an ecological system’s state that can occur with little to no warning at all. In the context of management, transients can cloud the manager’s judgment of the stability of a system. It would be easy to assume the system is in a stable state when it may be near a regime shift (long transients), which may result in inaccurate predictions of long-term dynamics based solely on short-term data. Consequently, the study of transient dynamics involves several avenues, including mathematical theory, management implications, and empirical understanding. New literature in these areas has begun to emerge. The notion of transient dynamics was discussed as early as the mid-1900s, where the idea that steady states are the most ecologically relevant quantities was challenged and the exploration of more complex ecological dynamics was sought. In more recent literature, transient dynamics, the underlying theory, empirical evidence, management implications, and ecological implications have all been more explicitly discussed. One major challenge when dealing with transient dynamics is the infancy of the mathematical theory that underpins much of the necessary analysis. Additionally, the implications transient dynamics have on management and ecological applications are still being developed. However, the significance of transients is now appreciated and research in such areas is attracting much attention. Several important avenues for future research have been made apparent in ecology, and new insights continue to be developed.

Foundational Work Related to Transient Dynamics

Although the study of explicit transient dynamics is relatively new, a fair amount of historical work has led us to the current state of knowledge, and the concept of transient dynamics has long been alluded to in the ecological literature. In particular, early ideas of transient dynamics sought to uncover much more complex ecological dynamics that were divergent from the study of steady states. For example, Watt 1947 conjectured that the observed cyclic succession of plants implied a more complex dynamic not related to steady states. Additionally, Hutchinson 1961 coined the paradox of the plankton and postulated that the observed diversity of phytoplankton in a given water body was due to the fact that the system was in a transient state, and that the mathematical equilibrium that the competitive exclusion principle implies had not or will not be achieved due to changing environmental conditions. Although these ideas challenged the notion of steady-state dynamics as a focal point, other seminal papers focused on the existence of multiple steady states. The existence of multiple steady states has transient implications in the sense that perturbations and slowly changing environmental characteristics can cause qualitative changes in ecological systems. Scheffer, et al. 1993 discusses the bistability of a clear water and turbid water state in a shallow lake and how this bistability can give strong insight toward restoration of the lake. Van Langevelde, et al. 2003 studies the frequently observed changes between a tree and grass coexistence state and a tree only state in a savanna ecosystem, while Norstrom, et al. 2009 looks into the management implications the existence of alternative stable states have on a coral reef system. These transitions hint at a transient dynamic stemming from ecological feedbacks. Although these examples are distinct in their ecology, the underlying issue of transitions among states link heavily to a focus on transient dynamics and have, in part, motivated a much deeper exploration of such dynamics.

• Hutchinson, G. E. 1961. The paradox of the plankton. American Naturalist 95.882: 137–145.

  DOI: 10.1086/282171

  Seminal work on the diversity of phytoplankton species. Coined the paradox of the plankton, in which the observed diversity of phytoplankton is contrary to the analytical expectation of competitive exclusion. Hutchinson conjectures that the asymptotic states may not have been reached due to environmental fluctuations indicating the existence of transient dynamics.

• Norstrom, A. V., M. Nystrom, J. Lokrantz, and C. Folke. 2009. Alternative states on coral reefs: Beyond coral-macroalgal phase shifts. Marine Ecology Progress Series 376:295–306.

  DOI: 10.3354/meps07815

  Coral reefs are shown to have phase shifts where macroalgae becomes dominant and are difficult to reverse. However, it has also been shown that other benthic life can dominate, suggesting alternative stable states. Shifts among these states occur for a variety of reasons, including top-down and bottom-up effects. Such shifts are spurred on by perturbations and perpetuated by feedback mechanisms throughout the ecosystem. Predicting and understanding such shifts is directly related to the study of transients.

• Scheffer, M., S. H. Hosper, M. L. Meijer, B. Moss, and E. Jeppesen. 1993. Alternative equilibria in shallow lakes. Trends in Ecology and Evolution 8.8: 275–279.

  DOI: 10.1016/0169-5347(93)90254

  Historical example of hysteresis in shallow eutrophic lakes. Two alternative stable states—a clear water state and a turbid water state—exist, complicating the permanent recovery of a lake through hysteresis by nutrient reduction alone. However, it is discussed that other management, such as food-web manipulation, can help return the lake to a clear state. Such transitions between stable states get at the very essence of transient dynamics and the existence of ghost, or weak attractors.

• van Langevelde, F., C. van de Vijver, L. Kumar, et al. 2003. Effects of fire and herbivory on the stability of savanna ecosystems. Ecology 84.2: 337–350.

  DOI: 10.1890/0012-9658(2003)084[0337:EOFAHO]2.0.CO;2

  Herbivory, fire, and state of a savanna ecosystem are shown to be intertwined with multiple states. A positive feedback between grass biomass and subsequent fire intensity is illustrated. Furthermore, fire intensity increases tree destruction, which in turn promotes the growth of grass, potentially leading to more intense fires under limited grazing. Such feedbacks lead to multiple steady states and, in this instance, continually changing dynamics. Furthermore, this example illustrates that such systems readily generate transient dynamics.

• Watt, A. S. 1947. Pattern and process in the plant community. Journal of Ecology 35.1: 1–22.

  DOI: 10.2307/2256497

  Seminal work on plant communities and their succession. Suggests that the succession of plant communities did not fit within the structure of terminal dynamics, but rather a reoccurring pattern suggesting, what we now call transient dynamics.