Restrepo et al.: Monte Carlo simulation applied to Xiphias gladius and Gadus morhua 



745 



350 

 300 

 250- 



& 200 



u 



2 150- 



100 



50- 







r 



U 



p n n n 



13 17 21 25 29 

 Projected Yield (1000 MT) 



33 



cnia 



I 1990 



Figure 9 



Distribution of 1989 estimated swordfish Xiphias gladius 

 catches when fishing mortality is kept the same as in 1988 

 (open bars), and distribution of 1990 estimated catches when 

 fishing mortahty is equal to the midpoint between the 1988 

 fishing mortality and Fj ,, assuming 1989 fishing mortality 

 was the same as in 1988 (cross-hatched bars). 



certain than that for Fq.i as evidenced by the fact that 

 the distribution of multipliers is broader for F^ax than 

 for Foi- But, as an anonymous reviewer pointed out, 

 it is interesting to note that the mode of both distribu- 

 tions is about one-third of the status quo F. 



We also computed 1000 projected catches in weight 

 for 1989 with fishing mortality equal to that in 1988. 

 We then projected the catch for 1990 with fishing mor- 

 tality set at the midpoint between the fishing mortal- 

 ity in 1988 and F„.i (Fig. 9). This method gradually 

 reduces fishing mortality to minimize the short-term 

 impact of decreased landings on fishermen (see 

 Pelletier and Laurec 1990, for a discussion). Recruit- 

 ments for 1989 and 1990 were drawn randomly from 

 the empirical distribution of recruitments estimated 

 from 1978-87 on each iteration. If the fishing mortal- 

 ity does not change in 1989 from the level in 1988, 

 catches are likely to be somewhere around the 1988 

 yield of ~ 18,000 mt. The 1990 yields are likely to be 

 ~ll,000-13,000mt. 



Using the Monte Carlo results, it is equally simple 

 to obtain distributions of catches for fishing at other 

 exploitation levels or to obtain distributions of fishing 

 mortalities for fixed catch quotas. Similarly, the 

 distribution of other projected variables, such as the 

 spawning-potential ratio that results from various 

 catch and fishing mortality options, can be computed. 

 In doing so, it is important to have the values of the 

 inputs used in calibrating the SPAs (e.g., natural mor- 



tality) stored in each iteration, so that the projection 

 computations use the same values. 



Risks and costs: Application 

 to northern cod 



We studied the cod fishery in NAFO Divisions 2 J + 3KL 

 and based our simulations on the data and methods 

 described in Baird et al. (1990). Additional data, 

 described below, were obtained from the files at the 

 Northwest Atlantic Fisheries Centre, St. John's, New- 

 foundland. The simulations reflect our owti perceptions 

 and experience about the sources and nature of the 

 uncertainties in the assessment. As with the swordfish 

 example, the selection of management objectives for 

 simulation was made for illustrative purposes. 



This cod fishery is managed by quota. The assess- 

 ment uses trawl-survey data and commercial catch-rate 

 data to calibrate the SPA. 



Assessment and simulation procedures 



Only a brief description of the assessment procedure 

 is given here since the details are not important for 

 understanding the use of the simulation method. The 

 catch-at-age data for ages 3-13 for each year from 1978 

 to 1989 were taken from Table 7 of Baird et al. (1990). 

 Coefficients of variation of these catch estimates were 

 computed using the method of Gavaris and Gavaris 

 (1983); these coefficients were available in the files. The 

 coefficients of variation ranged from 2 to 17%. Age- 

 and year-specific catch rates from research-vessel 

 surveys for the period 1978-89 and associated coeffi- 

 cients of variation (Baird et al. 1990, table 23) were 

 used to tune the sequential population analysis. The 

 coefficients of variation were <30% in 87% of the 

 cases. Age- and year-specific catch rates from the off- 

 shore commercial trawl fishery for ages 5-8 for the 

 period 1983-89 were standardized by the method of 

 Gavaris (1980) for use as an index of abundance for 

 tuning the SPA (Baird et al. 1990, table 39). We 

 developed estimates of the coefficients of variation for 

 the commercial catch-rate indices. In all cases, these 

 were close to 10%. Natural mortality for this stock is 

 believed to be around 0.2/yr. 



In the simulations, the point estimates of the inputs 

 were replaced by random variables with the same ex- 

 pected values and coefficients of variation as specified 

 above. Catch at age values were generated as normal 

 random variables, while the research-vessel and the 

 commercial catch rates were generated as lognormal 

 random variables. The value of the natural mortality 

 rate was generated as a uniform random number be- 

 tween 0.15 and 0.25/yr. 



