746 



Fishery Bulletin 90(4), 1992 



The specific formulation of the ADAPT model was 

 as follows. The research-vessel indices were obtained 

 in the fall and were assumed to represent population 

 size at the end of November. The commercial catch- 

 rate indices were assumed to represent population size 

 at the beginning of the year. The fishing mortality F 

 for the oldest age-group (13) was calculated as 50% of 

 the mean F for ages 7-9 weighted by population 

 number at age. The objective function to be minimized 

 differed from equation (4) in that lognormal errors were 

 assumed and the weights, Aj, were fixed to be 1.0. 



Projections for 1990 and 1991 were made using the 

 same procedures used in the most recent annual assess- 

 ment (Baird et al. 1990). Population and fishing mor- 

 tality projections for 1990 were made by randomly 

 selecting a value for recruitment from the historical 

 set of estimated recruitments and assuming that (1) 

 the total catch in 1990 is 225,000 mt (the fixed Cana- 

 dian quota in place when the assessment was done in 

 1990, plus an additional 25,000 mt in expected foreign 

 catch), and (2) the partial recruitment (selectivity) 

 vector for 1990 is equal to that estimated for 1989 in 

 each simulated SPA. 



Catch projections for 1991 were made in two ways. 

 In one, we set the fishing mortality for 1991 equal to 

 that for 1990 and solved for the catch. In the other, 

 we set the fishing mortality for 1991 equal to 



min{(Fo.i+Fi99o)/2, 2 Fd}. 



This is the 50% rule formulated by the Canadian 

 Atlantic Fisheries Scientific Advisory Committee 

 (Canada Department of Fisheries and Oceans 1991) for 

 a gradual movement towards Fq.i . We also computed 

 the fate of yield foregone and the distribution of popula- 

 tion changes for various choices of the total catch. 



Results of cod simulations 



We generated risk curves for two fishing mortality 

 objectives for 1991 (Figs. 2a, b). These curves can 

 be put in perspective by noting that the Canadian total 

 allowable catch for 1990 was 199,262 mt while the 

 total catch (Canadian plus international) may have been 

 as high as 235,000 mt. To have a 50% risk of increas- 

 ing the fishing mortality in 1991 over the 1990 level, 

 one would set the total catch at 225,500 mt; to have 

 a 50% chance of exceeding the fishing mortality asso- 

 ciated with the 50% rule would entail setting the total 

 catch at 1 63,000 mt. It appears that a cut in the TAC 

 would be necessary to have a reasonable chance of 

 preventing the fishing mortality from exceeding the 

 1990 value. Substantial cuts in the harvest would be 

 required to ensure a high probability of meeting the 

 50% rule. 



For values of the TAC for which the risk is less than 

 25%, the expected value of the yield foregone is ap- 

 proximately a linear function of the TAC (Figs. 2a, b). 

 That is, for every change in the TAC of 1000 mt, the 

 expected yield foregone changes by ~1000mt. The fate 

 of biomass left in the water is to increase by ~13% in 

 a year (mean of 1000 simulations = median = 12.9%; 

 95% confidence band based on 2.5th and 97.5th percen- 

 tiles is 7.2% andl8.4%). The relative change in biomass 

 of fish aged 3 and above is also a linear function of the 

 TAC (Fig. 3). Note, however, that the relative change 

 in biomass cannot be determined very precisely as 

 evidenced by the wide confidence bands. 



We presented results of catch projections for two 

 scenarios. Often, one might like to examine a larger 

 number of options. For example, if current fishing mor- 

 tality exceeds F^^, then one could explore various 

 ways to reduce fishing mortality in gradual steps as 

 well as exploring the consequences of various types of 

 "status quo" options. The simulation approach is ver- 

 satile enough to handle fixed catch, fishing mortality, 

 and biomass objectives, as well as objectives involving 

 relative change. Thus, one could have any of the follow- 

 ing objectives for fishing mortality: achieve F = 0.40/ 

 yr, achieve F = Fo.i, reduce F by 40%, or adjust F so 

 that biomass changes a given fixed or relative amount. 



In some fisheries, catch and population projections 

 may be highly dependent on the assumptions made 

 about recruitment. When this is the case, it may be 

 helpful to quantify the uncertainty separately for 

 various segments of the population. For example, we 

 computed the distribution of relative change in age 3 -t- 

 biomass of cod (from 1989 to 1991) for various choices 

 of the TAC. The wide confidence bands (Fig. 3) reflect 

 the large uncertainty in future recruitment. We could 

 have quantified the relative change in the biomass of 

 age 5 -I- fish. From the ADAPT run based on 1989 data, 

 we already have an estimate of age-3 biomass in 1989. 

 This biomass can be projected forward to age 5 in 1991; 

 hence, we do not need to generate a random value for 

 recruitment. The uncertainty in the biomass of age 5 -t- 

 fish should thus be smaller than the uncertainty in age 

 3 + biomass. Unfortunately, the latter quantity may be 

 of greater interest. 



Conclusions 



Monte Carlo simulation has long been regarded as a 

 very useful quantitative tool, especially for sensitivity 

 analysis (e.g., Pope and Gray 1983, Rivard 1983). It 

 is also quite useful for studying the properties of 

 specific assessment procedures (e.g., Mohn 1983, 

 Kimura 1989). Here, we follow Francis (1991) and use 

 it to quantify the risks of not meeting the objectives 



