Punt: Managing West Coast groundfish resources through simulations 



863 



0.2 — i.e. just below the level that defines an overfished 

 stock). Sensitivity to alternative values for the ratio of the 

 spawning output at the start of year 41 to Bq is explored 

 (Table 1). 



Generating future data 



The data available for assessment purposes are survey 

 indices of relative abundance, age-composition data from 

 surveys, catch-rate-based indices of relative abundance, 

 and age-composition data from the commercial catches. 

 Table 2 lists the baseline specifications regarding the fre- 

 quency at which the various data sources are collected and 

 the parameters that determine the sampling variability 

 associated with each data source. 



The survey and catch-rate indices are generated by using 

 the equations 



B':">" = B'/'-"'''''\ 



/= By' -'"■'■ '\ 



ef ~/v(0;(CT'r); (3a) 

 f;:~/v(0;(cr')-); (3b) 



where £*■"''''' = the survey index for year j; 



B^ = the survey selected-biomass during yeary: 



fi: = £H-„5;,/V„,„.-''""; 



(4a) 



w^ = the mass of an animal of age a; 

 Sj, = the selectivity of the survey gear on animals of age 

 a (assumed to be governed by a logistic function 

 and to be independent of time); 

 ^\a ~ ^^^ number of animals of age a at the start of year 



.v; 

 Z,,^ = the total mortality on animals of age a during year 



y\ 



cTj = the standard deviation of the random fluctuations 

 in survey catchability; 

 "max - ^^^^ oldest age considered in the operating model; 

 /^, = the catch-rate index for year y; 

 B^ = is the exploitable biomass during yeary; 



fi:=X»'.%^^..,(" -<-"'■■'); 



(4b) 



CT'' = the standard deviation of the random fluctuations in 

 fishery catchability. 



Note that Equations 3a and 3b assume that the survey and 

 fishery catchability coefficients are unity. This assumption 

 can be made without loss of generality because the stock 

 assessment method is not provided with this information 

 and instead estimates these catchability coefficients. Note 

 also that the key difference between the survey index 

 and the catch-rate index is that selectivity for the latter 

 changes over time (see Eq. 1), whereas selectivity for the 

 former is time-invariant. 



The age-composition data are generated by selecting 

 a sample multinomially from the age-composition of the 

 survey catch and of the fishery catch (see Eqs. 5a and 5b 

 for the relative survey and fishery catches-at-age): 



Sln^. 



•7^«v.a(l-^ )• 



(5a) 



(5b) 



F^ = the fully selected fishing mortality during year y; 

 and 



The PFMC management procedure 



The "PFMC management procedure" (see Fig. 2 for an 

 overview) involves first conducting a stock assessment 

 by fitting an age-structured population dynamics model 

 to the available data by maximizing a likelihood func- 

 tion. This approach mimics the common use of the stock 

 synthesis framework (Methot, 2000) when conducting 

 assessments of West Coast groundfish resources. The 

 likelihood function is determined by assuming that the 

 age-composition data are multinomially distributed (in 

 the simulations with effective sample sizes given by the 

 actual effective sample sizes) and by assuming that the 

 survey and catch-rate series are log-normally distributed 

 about the appropriate model quantities. The estimable 

 parameters of the model are the annual recruitments, 

 the annual fishing mortalities, the catchability coef- 

 ficients, and the parameters that determine selectivity 

 (the survey and fishery selectivity are [correctly] assumed 

 to be governed by logistic and double-logistic equations). 

 The values for the remaining parameters (weight-at-age, 

 fecundity-at-age, and natural mortality) are assumed to 

 be known without error. The key outputs from the assess- 

 ment are time-series of recruitments and spawning out- 



