Confounding of Gear Selectivity and the Natural Mortality Rate in Cases where the Former is a Nonmonotone Function of Age

Abstract

An "exponential–logistic" selectivity function is presented in which a single parameter (γ) determines whether gear selectivity is asymptotic (γ = 0) or reaches a maximum at finite age (γ > 0). The function is used to develop a model in which both γ and the natural mortality rate M are formally indeterminate and in which the coming year's catch limit can be viewed as a response function of either estimated γ or estimated M. Decision theory is then used to derive the optimal catch. The optimal catch is shown to increase with the degree of uncertainty surrounding M, although this conclusion may depend on the short managerial time frame assumed. Three "suboptimal" strategies are also considered: (1) setting catch at the level corresponding to the expected value of M, (2) setting catch at the minimum of the response function, and (3) setting catch at the level corresponding to γ = 0. The first suboptimal strategy never results in a catch greater than the optimum and always results in a lower expected loss than the second. The performance of the third strategy (relative to the others) depends on parameter values.