Incorporating Uncertainty into Fishery Models

Uncertainty, Risk, and Decision: The PVA Example

Daniel Goodman

doi: https://doi.org/10.47886/9781888569315.ch11

Uncertainty is pervasive in natural resource management; attainment of the management goals often depends both on present quantities that cannot be measured accurately and on future environmental disturbances that cannot be predicted accurately. When we make management decisions under such circumstances, we recognize that the outcome may be quite different from our intentions, and we perceive this possibility as risk. But, decisions must be made all the same, so we attempt to take the uncertainty, and hence the risk, into account in our decisions, through bet hedging and setting margins of safety. The point of this chapter will be to show that the decision process can still be, in its own way, an exact science, not withstanding the uncertainty.

Given that we cannot eradicate uncertainty, the sense in which decision making under uncertainty can be an exact science is a matter of coping with the uncertainty in a way that is recognizably optimal. That is, we have to learn to view natural resource management as a kind of gambling and consider how we might conduct that gambling as intelligently as possible. In this perspective, each management decision is equivalent to the placing of a bet, and the measure of success isn’t so much winning every bet, which is impossible, but rather, success lies in evaluating the odds well enough to place our bets so that in the long run our gains exceed our losses. To this end, we need a means to recognize what is a good bet, what is a bad bet, and what is a bet that would best be deferred until more information becomes available, even if there is some concrete cost to the delay or some cost to the additional information. The mathematical discipline of statistical decision theory is concerned with understanding this sort of decision making as a formal optimization problem (Berger 1985).

There are two key components to the evaluation of uncertain management decisions. These are the costs of each possible outcome and the probabilities of each outcome. Generally the costs (or benefits) are either measured in economic terms, such as yield, or in policy terms, having to do with the social value placed on such things as biodiversity. The probabilities are a more technical issue.

The present chapter will be devoted first to showing how the probabilities can be calculated in a rigorous, objective, and fairly preciseway, despite all the uncertainty; second, this chapter will show how the probabilities can be used for cost–benefit analysis, to optimize the decisions; and third, this chapter will show how the probabilities can be used for cost– benefit analysis to optimize the investment in more data. The exposition will be developed around an idealized application of these ideas to population viability analysis, for management of endangered populations.

Population viability analysis (PVA) is the enterprise of calculating the probability of population or species extinction. PVA attempts to take into account everything that is known and everything that is not known about the dynamics of the population in question. Factors that do not affect dynamics are irrelevant to the population viability analysis. Factors that do affect dynamics should be incorporated via their effects on dynamics. Where the effect on dynamics is uncertain, as with many genetic factors, the uncertainty in this effect should be quantified explicitly and carried through the analysis as an additional parameter that is represented by a distribution.

Everything that is known about the dynamics of a population should be captured in a statistical inference procedure that combines different kinds of information. Some information may be in the form of case specific data on the population in question; other relevant information may be in the form of comparative data on other “similar” populations. Bayes’ formula accomplishes the mathematical merging of case specific and comparative information.