## Risk analysis as a framework in fishery systems

Risk analysis (Anand 2002) is the appropriate decision tool when the science is ambiguous (almost always true in environmental problem solving) and this is especially true for fisheries (Rosenberg and Restrepo 1994, Tyutyunov et al. 2002). To illustrate the idea as simply as possible, imagine a stock for which we know that r = 0.12 yr_1 but that carrying capacity is uncertain, known to be either 1000 mt, with probability p or 2000 mt, with probability 1 -p In the former case, the MSY harvest is 30 mt/yr and in the latter case, the MSY harvest is 60 mt/yr. Now the average value of carrying capacity is K = 1000p + 2000(1 - p) = 1000(2 - p and the average of the MSY harvest is 30p + 60(1 -p = 30(2 -¿>). However, it is pretty clear, because of the simplicity of this problem, that if we had to choose a value of the harvest rate, it would be nonsensical to choose the average of the MSY harvests. If the true carrying capacity is 1000 mt, then choosing the average of the MSY harvests will overfish the stock as long as p > 0. On the other hand, if the true carrying capacity is 2000 mt, applying the average of the MSY harvest will cause the loss of sustainable yield as long as p < 1. Whether it is better to overfish the stock or lose sustainable yield is a question that cannot be answered by quantitative methods alone (and may not even be within the purview of quantitative methods (Ludwig et a/. 2001)), but it is clear that averaging uncertain values as a means of attaining a ''consensus'' value for action is arbitrary (Mangel et a/. 1993).

The procedures of risk analysis recognize that one must be explicit about the potential states of nature, the actions one takes, and the consequences of those actions. In the simplest case we have two states of nature S1, S2; two possible actions, A1, A2; and values Vy = V(S;-, Ay) that accrue when the state of nature is S;- and the action is Ay. These are best summarized in a table; ifp is the probability that the state of nature is S1, then the table looks like this.

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