Fishery management under uncertainty

Explanations of worldwide fishery collapse are numerous. There is general consensus that variability and uncertainty play important roles. The economics literature that has followed the work of Simon (1956) and Theil (1957) has indicated that under certain model structures one need not really worry about stochasticity. On the other hand, Clark and Kirkwood (1986) show that the optimal management of a fishery with stock uncertainty calls for non-monotonic and non-intuitive expected escapement. This state-of-the-art result is presented in an obscure fashion by the authors. The following analysis re-derives these results from first principles in a clear and transparent manner and also develops their analytical properties. It is shown that the probability of extinction increases in expected recruitment under certain conditions. Some of the results obtained depend on model specification; in particular, it matters whether the variance of recruitment is independent of its expectation. If uncertainty enters the model additively instead of multiplicatively, optimal expected escapement is constant in expected recruitment.; Roughgarden and Smith (1996) argue that in the presence of the following three sources of error—variability in fish dynamics, inaccurate stock size estimates, and inaccurate implementation of harvest quotas—adhering to the deterministic policy can quickly lead to extinction. However, they limit their analysis to a special class of solution and do not locate the optimum policy. The analysis below develops a bioeconomic model with these three sources of error, and solves for optimal harvest announcements bawd on measurements of fish stock in a discrete-time model. Among other results it is shown that: (1) when errors are large, the constant-escapement rule advocated by much of the existing literature is generally rejected, (2) inaccurate stock estimation affects policy in a fundamentally different way than the other error sources, and (3) when existence value is included, management is significantly more conservative, substantially increasing stock viability through time.