Evaluating a dynamic approach to yield-mortality models

Abstract

Production modelling using fishery yield but total mortality rate in place of fishing effort (yield-mortality models) does not suffer from undetected changes in catchability or fishing power from technological change, is easier to apply to multi/gear fisheries for the same species, and produces biologically meaningful reference points. They can be calibrated against analytical models and may use the same data sets. Their disadvantage has been the equilibrium assumption as per Csirke and Caddy (1983). Annual mortality rates may come from procedures such as catch curve analysis which make local equilibrium assumptions, but becomes dynamic if the mortality estimates are annual. Theory and problems in fitting this model are described using the same data sets as illustrated in the equilibrium yield-mortality (Y-Z) model in Caddy and Defeo (1996), but also for North Sea cod using data from the working group report on the ICES website. A non-linear quasi-Newton fitting procedure was used in which all three parameters, (r, B ∞ , and M) are constrained to positive values by a penalty function in the minimisation algorithm. For short time-series with high inter-annual variations in yield, the model is very sensitive to initial values. We suggest using the equilibrium model to generate seed values for dynamic fitting. Trials with the North Sea cod data show that with a long term and robust data set the dynamic model explains a large proportion of the variance and provides a good fit to trends in the catch series. It recovered a value for natural mortality rate similar to that used in other assessments. We also demonstrate that data sets for conventional VPA/cohort analysis can be successfully reused to deduce values of M, r, and B ∞ from Y-Z models. For all data sets, the dynamic model is more sensitive to time series trends than the equilibrium model although M values were generally lower, but fairly consistent with published values. Guidelines for future work are suggested.