Fitting the exponential and logistic surplus yield models with mortality data: some explorations and new perspectives

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The paper explores the feasibility of different methods of fitting the logistic production model of Csirke and Caddy (1983) using data from two hake stocks: New England silver hake, and (separately for males and females) Peruvian hake. Using the natural mortality estimate generated by the logistic, the theory of production modelling with estimates of total mortality rate (Z) is extended to include the exponential model of Fox (1970). Linear and non-linear approaches were also used to fit the exponential model. The paper concludes that directly fitting the quadratic form of the logistic as advocated by Csirke and Caddy (1983) should be abandoned in favour of formulating an abundance index Y i (Z i − M) , and fitting it linearly against ( Z i − M). The bootstrap technique for fitting the models was very useful in estimating parameter variance, as well as in generating empirical distributions for population and management parameters such as r, M, Z msy , MSY, which showed clear maxima with this approach: those for M appear to be of the correct order of magnitude. Since these distributions are largely asymmetrical, the percentile approach to providing confidence intervals was followed. For bootstrapping with the examples chosen, this avoided problems with negative roots, a hazard of the direct fitting procedure. A simple approach to formulation of risk-averse management strategies was explored using the percentiles of a cumulative distribution of MSY estimates from bootstrapping against total mortality rate, which it is suggested, would allow fishery management advice to be generated based on annual mortality and yield vectors alone.