Basically we’ve done some simple stuff and now would be a good time to think about tools for some heavy-lifting computational challenges standing in the way. Michael & Jim have been a great help on this, and Jake has also helped with theoretical underpinnings.
Statement of problem
We consider the impact of uncertainty in the harvesting of fisheries which involve alternative stable state dynamics.
Adding uncertainty in current state means optimal escapement isn’t the optimal solution (contrary to Reed model) (Sethi et. al. 2005)
We are considering uncertainty/variability entering at three levels: population dynamics (next yr’s stock, Reed case), stock assessment (this yr’s stock), and implementation of quotas, in the context of alternative stable states.
When the parameterization of these uncertainties is correctly known, the optimal solution surprisingly doesn’t face many more sudden crashes than the unharvested dynamics. (Casino “paradox” – income generated by a casino is highly predictable since the rules of uncertainty are well known).
Errors in the parameterization of the uncertainty or the biological parameters can have dramatic effects in the allee threshold model
Questions for further study
Is the optimal strategy risk adverse?
Can we add parameter uncertainty / Bayesian learning about parameters?
In particular, can we implement the case in which stock is not assessed directly but estimated from harvest and knowledge of harvest effort, under parameters we learn about?
Technical capacity and challenges
We’ve developed anR package for stochastic dynamic programming that allows a user to quickly experiment with different levels & types of uncertainty on different biological and economic models from a library of options and create visualizations of the solutions over an ensemble of realizations.
Curse of dimensionality is a major challenge to go beyond the 1D training problem into the 3D parrotfish model or the learning model. We investigated Heuristic Sampling Nicol & Chadès, 2011 as a possible solution but this far this seems to scale rather poorly with the size of the control space.
Sethi G, Costello C, Fisher A, Hanemann M and Karp L (2005). “Fishery Management Under Multiple Uncertainty.” Journal of Environmental Economics And Management, 50. ISSN 00950696, https://dx.doi.org/10.1016/j.jeem.2004.11.005.
Beyond Stochastic Dynamic Programming: A Heuristic Sampling Method For Optimizing Conservation Decisions in Very Large State Spaces, Sam Nicol, Iadine Chadès, (2011) Methods in Ecology And Evolution, 2 10.1111/j.2041-210X.2010.00069.x