1 A management oriented approach to age-structured stock assessments Steven J.D. Martell, W.E. Pine III., and C.J. Walters Abstract: Age structured models are widely used in fisheries stock assessments and these models contain two very important parameters that determine the rate and amount of harvest that can be safely taken: the compensation rate in juvenile survival (δ) and the unfished biomass (B o ). These two parameters are normally estimated by fitting models to time series data on relative abundance, and such data must have sufficient contrast in order to resolve the confounding between Bo and δ. It is not uncommon for relative abundance indices to lack sufficient information in order to resolve B o and δ, and informative priors or fixing at least one of these parameters is necessary to develop management advice. Providing management advice proceeds by transforming estimates of Bo and δ into management reference points such as the maximum sustainable yield (C * ) and the fishing mortality rate that would achieve this yield (F * ). There is no analytical solution for the transformation of B o ,δ to C * ,F * for age-structured models with commonly used stock- recruitment functions and therefore must be done numerically. The opposite transition, however, does have an analytical solution for both the Beverton-Holt and Ricker recruitment models with partial selectivities for all age-classes. Use of these analytical solutions allows for age-structured assessment models to be directly parameterized in terms of the management quantities C * and F * . If relative abundance indices are uninformative, then the use and effects of informative priors on C * and F * on the results of the assessment model are completely transparent. Key words: stock assessment, management oriented approach, Bayesian statistics, prior distributions, fisheries management, Pacific hake. R´ esum´ e : Texte du resume Introduction The over-arching objectives of a stock assessment are 3- fold: (a) estimate key population parameters that determine the overall scale and productivity (e.g., unfished biomass B o and the Goodyear compensation ratio (Goodyear 1980) which we define as δ), (b) estimate the current state of the population rel- ative to a pre-defined reference point (usually B o ), and (c) pro- vide short-term projections of the population state subject to alternative harvest policies or the application of a pre-defined harvest rule (i.e., management advice). The assessment process has evolved to also characterize the uncertainty in the man- agement advice and primarily Bayesian approaches have been adopted. The process of proceeding through steps (a)-(c) and ultimately providing sound management advice is conditional on the information in the available data. In steps (a) and (b) population dynamics models are fitted to time series data on relative abundance and the ability to discern between a large- unproductive stock and a small-productive stock requires suffi- cient contrast in the abundance index (see Hilborn and Walters 1992). Step (c) involves a transformation of population param- eters (e.g., unfished stock size and the intrinsic rate of growth) into management parameters (e.g., target fishing rate and max- imum sustainable yield) and short-term projections of abun- dance based on estimated parameters in (a). Received . Revision received . Accepted . Revision accepted . S.J.D. Martell and C.J. Walters. Fisheries Centre, University of British Columbia, 2202 Main Mall, Vancouver, BC, V6T 1Z4 W.E. Pine III.. Department of Fisheries and Aquatic Sciences, University of Florida, 7922 NW 71st Street, Gainesville, FL 32653 Ricker (1975) first demonstrated that there was no analyti- cal solution to go from population parameters to management parameters for relative simple non-linear models (e.g., Ricker model). However, Schnute and Kronlund (1996) demonstrated that the opposite transition was possible and later Schnute and Richards (1998) extended this approach to age-structured mod- els that assume knife-edge recruitment and discrete mortality. They also demonstrated that this inverse approach improves the statistical properties of characterizing uncertainty and en- hances communication because the parameters in question are directly relevant to policy. Despite these statistical and com- municative advantages, to our knowledge there has been no application of this approach in North American stock assess- ments. A common situation throughout North American stock as- sessments is the lack of contrast in relative abundance indices that permit the joint estimation of productivity and population scale parameters. Many of the data sets consists of one-way trips (persistent decline or increase in relative abundance) or little to no variation in relative abundance indices. In such cir- cumstances a common practice is to use prior information on productivity parameters or derive independent estimates for the proportionality constant that relates relative- to absolute- abundance, or both. The reality of such practice is that the pol- icy parameter(s), such as the maximum sustainable yield (C ∗ ) and the fishing mortality rate (F ∗ ) that achieves C ∗ , are de- fined prior to fitting the models to time series data. Consider a simple example using the Schaefer production model dB dt = rB  1 - B K  - hB and relating this model to a relative abundance observation (I ) Can. J. Fish. Aquat. Sci. XX: 1–11 (2007) DOI: 10.1139/ c  2007 NRC Canada