Ecological management of stochastic systems with long transients


Long transients may be common in ecological dynamics, but the implications such dynamics have for ecological management have not been fully explored. Long transient periods can easily be mistaken for stable state dynamics, but may require dramatically different management policies. Here, I explore the optimal management of stochastic ecological systems that may contain either a tipping point or a ghost attractor: an important mechanism which can give rise to long transients. I consider three approaches of increasing sophistication: (1) dynamic management under a fixed model, (2) management that accounts for uncertainty over possible models, and (3) adaptive management that actively learns the correct model over the management process. This analysis confirms the prediction that long transients can create considerable uncertainty and give rise to very different optimal management policies, and also illustrates that dynamic management that can either plan for this uncertainty or actively learn to decrease the uncertainty can promote successful management of long transients.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. Boettiger C (2018) From noise to knowledge: how randomness generates novel phenomena and reveals information. Ecology Letters.

  2. Boettiger C, Ross N, Hastings A (2013) Early warning signals: the charted and uncharted territories. Theoretical Ecology.

  3. Boettiger C, Memarzadeh M (2018) Mdplearning: Bayesian Learning Algorithms for Markov Decision Processes. (version 0.1.0). Zenodo.

  4. Clark CW (1990) Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 2nd Edn. Wiley-Interscience

  5. Deco G, Jirsa VK (2012) Ongoing cortical activity at rest: criticality, multistability, and ghost attractors. The J. Neurosci.: The Official Journal of the Society for Neuroscience 32(10):3366–75.

    Article  CAS  Google Scholar 

  6. Fischer J, Peterson GD, Gardner TA, Gordon LJ, Fazey I, Elmqvist T, Felton A, Folke C, Dovers S (2009) Integrating resilience thinking and optimisation for conservation. Trends in Ecology & Evolution 24(10):549–54.

    Article  Google Scholar 

  7. Folke C, Carpenter S, Walker B, Scheffer M, Elmqvist T, Gunderson L, Holling CS (2004) Regime shifts, resilience, and biodiversity in ecosystem management. Annu Rev Ecol Evol Syst 35(1):557–81.

    Article  Google Scholar 

  8. François-Lavet V, Henderson P, Islam R, Bellemare MG, Pineau J (2018) An introduction to deep reinforcement learning. Foundations and Trends® in Machine Learning 11(3-4):219–354.

    Article  Google Scholar 

  9. Grossberg S (1980) Biological competition: decision rules, pattern formation, and oscillations. Proc Natl Acad Sci USA 77(4):2338–42.

    Article  PubMed  CAS  Google Scholar 

  10. Harvey BJ, Donato DC, Turner MG (2014) Recent mountain pine beetle outbreaks, wildfire severity, and postfire tree regeneration in the US Northern Rockies 111 (42).

  11. Hastings A, Abbott KC, Cuddington K, Francis T, Gellner G, Lai Ying C, Morozov A, Petrovskii S, Scranton K, Zeeman ML (2018) Transient phenomena in ecology. Science, 361(6406).

  12. Hastings A, Higgins K (1994) Persistence of transients in spatially structured ecological models. Science 263(5150):1133–6.

    Article  PubMed  CAS  Google Scholar 

  13. Levins R (1966) The strategy of model building in population biology. American Scientist 54(4):421–31

    Google Scholar 

  14. Mangel M (1985) Decision and control in uncertain resource systems, 255.

  15. Marescot L, Chapron G, Chadès I, Fackler PL, Duchamp C, Marboutin E, Gimenez O (2013) Complex decisions made simple: a primer on stochastic dynamic programming. Methods in Ecology and Evolution 4(9):872–84.

    Article  Google Scholar 

  16. May RM (1977) Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269(5628):471–77.

    Article  Google Scholar 

  17. Memarzadeh M, Boettiger C (2019) Resolving the measurement uncertainty paradox in ecological management. The American Naturalist 193(5):645–60.

    Article  PubMed  Google Scholar 

  18. Memarzadeh M, Britten GL, Worm B, Boettiger C (2019) Rebuilding global fisheries under uncertainty. Proc Nat Acad Sci 116(32):15985–90.

    Article  PubMed  CAS  Google Scholar 

  19. Polasky S, Carpenter SR, Folke C, Keeler B (2011) Decision-Making Under great uncertainty: environmental management in an era of global change. Trends in ecology & evolution, May 1–7.

  20. Raffa KF, Aukema BH, Bentz BJ, Carroll AL, Hicke JA, Turner MG, Romme WH (2008) Cross-scale drivers of natural disturbances prone to anthropogenic amplification: the dynamics of bark beetle eruptions. BioScience 58(6):501–17.

    Article  Google Scholar 

  21. Ratajczak Z, Carpenter SR, Ives AR, Kucharik CJ, Ramiadantsoa T, Allison Stegner M, Williams JW, Zhang J, Turner MG (2018) Abrupt change in ecological systems: inference and diagnosis. Trends Ecol Evol 33(7):513–26.

    Article  PubMed  Google Scholar 

  22. R Core Team (2019) R: A Language and Environment for Statistical Computing (version 3.6.2). R Foundation for Statistical Computing, Vienna.

    Google Scholar 

  23. Scheffer M, Carpenter SR, Foley JA, Folke C, Walker BH (2001) Catastrophic shifts in ecosystems. Nature 413(6856):591–6.

    Article  PubMed  CAS  Google Scholar 

  24. Smallwood RD, Sondik EJ (1973) The optimal control of partially observable markov processes over a finite horizon. Operations Res 21(5):1071–88.

    Article  Google Scholar 

  25. Sondik EJ (1978) The optimal control of partially observable markov processes over the infinite horizon : discounted costs. Operations Res 26(2):282–304

    Article  Google Scholar 

  26. Walters CJ (1986) Adaptive Management of Renewable Resources. Biological Resource Management, Macmillan.

    Google Scholar 

  27. Walters CJ, Hilborn R (1978) Ecological optimization and adaptive management. Annu Rev Ecol Syst 9(1):157–88.

    Article  Google Scholar 

Download references


This work was inspired and influenced many discussions at the 2019 NIMBioS workshop on transient dynamics in ecology, and the 2019 organized oral session on ecological transients.


CB received computational resources from NSF’s XSEDE Jetstream (DEB160003) and Chameleon cloud platforms, as well as the support from UC Berkeley and the USDA Hatch project CA-B-INS-0162-H.

Author information



Corresponding author

Correspondence to Carl Boettiger.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Boettiger, C. Ecological management of stochastic systems with long transients. Theor Ecol (2020).

Download citation


  • Transients
  • Optimal control
  • Adaptive management
  • Stochasticity
  • Uncertainty
  • Ecological management