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Fishery Bulletin 104(3) 



ability (a) are shown in Figure 1. In general, the 

 prior probability of h increased rapidly at low h 

 values, and then remained at constant values at 

 high h values. As expected, when recruitment vari- 

 ability (a) increased, h values were higher to com- 

 pensate for higher recruitment variability (Fig. 1). 

 Table 1 shows parameter values of logistic curves 

 fitted to derived /; prior distributions as natural 

 mortality (M) ranged from 0.05 to 0.7 and recruit- 

 ment variability (o) ranged from 0.2 to 1.6. These 

 fitted curves would be convenient to use in stock 

 assessment models for given natural mortality and 

 recruitment variability, and values can be interpo- 

 lated for intermediate cases. Derived h prior curves 

 for four A^^ values were plotted (Fig. 2). The figure 

 shows patterns similar to those for recruitment 

 variability, namely that as A^, values increase, /; 

 values are higher to increase recruitment potential 

 for the population. Derived /( prior curves for four 

 natural mortality (M) values (M=0.1, 0.15, 0.3, and 

 0.5, respectively) are shown in Figure 3. As M values 

 increase, h values also increase. 



where 



hv 



h-0.2 

 0.8 



(11) 



and 0], ft,, and ftg are parameters for a logistic equa- 

 tion. 



Note that the derived /? priors produced above are 

 relative probabilities, but that is what is needed for the 

 assessment models and Bayesian priors. 



Results 



Derived h prior curves for M = 0.15, A^^ = O.IA'^,,, and T = 

 500 years at four different values of recruitment vari- 



Discusslon 



This article presents a simple modeling approach 

 that allows one to use life history criteria to derive 

 steepness priors for a fish stock where no sufficient 

 historical data could be used to establish reason- 

 able stock recruitment relationships. The model 

 used in this article requires a few assumptions, 

 most of which could be inferred from the life history 

 of the species. However, there is a shortcoming in 

 our approach: a simple population model is used to 

 derive h priors and then applied to the stock assess- 

 ment model that is an age-structured population 

 model. To derive h priors by using age-structured 

 models would require some age-specific parameters, 

 such as fecundity, growth, and possibly age-specific 

 natural mortality rates. That is, "prior" information 

 on these parameters for age-structured models is 

 needed but in many cases they are not readily avail- 

 able (if they were, the entire stock assessment would 

 be much easier). The parameters for age-structured 

 models could be borrowed from stock assessment 

 models, but applying priors back to stock assess- 

 ment models could be deemed to be "double" uses of 

 data (Minte-Vera et al., 2005). Our simple population 

 model approach has been widely used in many other 

 applications, such as in computing extinction risk in 

 conservation biology (Hakoyama et al., 2000) and in 

 simple production models in fisheries assessments (Mac- 

 Call, 2002). In these applications, simple (non-age- 

 structured) models were used for populations that are 

 known to have age- or size-structures. 



Although there are only a few parameters needed for 

 the model, there are uncertainties in choosing ranges 

 of values for each parameter. One of the important pa- 

 rameters in determining the priors is N , the parameter 



