Submitted my abstract for ESA 2012, in Portland. Getting a title and abstract pinned down about seven months in advance is itself an exercise in decision making under uncertainty. I’ve added some further background below.
Unknown unknowns: management strategies under uncertainty & alternate stable states
The effective management of natural resource populations such as fisheries or forests and the ecosystems in which they are embedded is a central goal of much work in both theoretical and applied ecological research. Management decisions must be made in an uncertain world, coping with errors in data, uncertainty in model parameters and even the choice of models being used. Advances in areas such risk management, optimization under uncertainty, and adaptive management methods have offered a way forward in spite of such uncertainty. We have only to admit what we don’t know, and make the best decision based on the information at hand.
The realization that such complex systems can contain tipping points – thresholds at which the system can transition into a less desirable state rapidly and with little warning – poses a fundamental challenge to these approaches. Such approaches require that we know what we don’t know: we don’t use the best guess of a parameter, instead, we have a distribution of possible values it may take. As recent events of the economy have illustrated, estimating the distribution isn’t easy; and for complex systems with alternate stable states, a little bit more uncertainty can make a big difference. How then, do we make the best decision based on the information available without exposing the system to these sudden crashes? How do we handle that uncertainty we just cannot parameterize – the unknown unknowns?
We combine methods from optimal control and stochastic dynamic programming with methods from ecological resilience and early warning signals to study both simulated and empirical examples of these systems.
We begin with two examples that illustrate these challenges. The first highlights the danger of handling only the risks we know how to handle. The second illustrates the difficulty of implementing resilience-based concepts in the place of risk-based management. We then present our mathematical framework for bridging these approaches on these systems & discuss the successes and obstacles to this united approach.
The literature has done a better job enunciating this question than tackling it. ((Knight’s 1921 text on Risk, Uncertainty & Profit would be a more erudite citation than Rumsfeld’s memorable phrase.)) The TREE review, (Polasky et. al. 2011), provides a nice introduction to the problem, identifying decision-theoretic and thresholds/resilience approaches, though gets little farther than the opinion piece suggesting the need for this work (Fischer et. al. 2009) two years prior.
A nice if intuitive result (Peterson et al 2003) ((Peterson, G., & Carpenter, S. (2003). Uncertainty and the management of multi-state ecosystems: an apparently rational route to collapse. Ecology, 84(6), 1403-1411. https://www.jstor.org/stable/3107958)) shows optimization that misses the alternate stable state description performing rather poorly, similar to my examples. A more illuminating result is (Brozović & Schlenker, 2011), which provides an explicit example where the outcome of optimization in a system with alternate stable states depends entirely on small differences in noise regime. A more general understanding of when stochastic optimization will give results that are sensitive to assumptions of the noise would be useful. Any takers for integrating over the uncertainty in the uncertainty?
A more immediate problem is the computational limitations of decision-theoretic approaches in handling full system complexity. The curse of dimensionality is exacerbated by the need for higher dimensions to model parameter uncertainty as well as dynamic state variables, where adaptive management can learn actively or passively to update this uncertainty.
Polasky S, Carpenter S, Folke C and Keeler B (2011). “Decision-Making Under Great Uncertainty: Environmental Management in an Era of Global Change.” Trends in Ecology & Evolution, 26. ISSN 01695347, https://dx.doi.org/10.1016/j.tree.2011.04.007.
Fischer J, Peterson G, Gardner T, Gordon L, Fazey I, Elmqvist T, Felton A, Folke C and Dovers S (2009). “Integrating Resilience Thinking And Optimisation For Conservation.” Trends in Ecology & Evolution, 24. ISSN 01695347, https://dx.doi.org/10.1016/j.tree.2009.03.020.
Brozović N and Schlenker W (2011). “Optimal Management of an Ecosystem With an Unknown Threshold.” Ecological Economics, 70. ISSN 09218009, https://dx.doi.org/10.1016/j.ecolecon.2010.10.001.