Evaluating a dynamic approach to yield-mortality models

Production modelling using fishery yield but total mortality rate in place of fishing effort (yield-mortality models) does not Butler from undetected changes in catchability or fishing power From technological change, is easi er to apply to multi/gear fisheries for the same species, and produces biol ogically meaningful reference points. They can be calibrated against analyt ical models and may use the same data sets. Their disadvantage has been the equilibrium,assumption as per Csirke and Caddy (1983). Annual mortality ra tes array come from procedures such as catch curve analysis which make loca l equilibrium assumptions, but becomes dynamic if the mortality estimates a re annual. Theory and problems in fitting this model are described using th e same data sets as illustrated in the equilibrium yield-mortality (Y-Z) mo del in Caddy and Defeo (1996), but also for North Sea cod using data from t he working group report on the ICES website. A non-linear quasi-Newton fitt ing procedure was used in which all three parameters, (r, B-infinity, and M ) are constrained to positive values by a penalty function in the minimisat ion algorithm. For short time-series with high inter-annual variations in y ield, the model is very sensitive to initial values. We suggest using the e quilibrium model to generate seed values for dynamic fitting. Trials with t he North Sea cod data shove that with a long term and robust data set the d ynamic model explains a large proportion of the variance acid provides a go od fit to trends in the catch series. It recovered a value for natural mort ality rate similar to that used in other assessments. We also demonstrate t hat data sets for conventional VPA/cohort analysis can be successfully reus ed to deduce values of M, r, and B-infinity from Y-Z models. For all data s ets, the dynamic: model is snore sensitive to time series trends than the e quilibrium model although M values were generally lower, but fairly consist ent with published values. Guidelines for future work are suggested. (C) 20 01 International Council for the Exploration of the Sea.