136 



Fishery Bulletin 92(1). 1994 



Monte Carlo simulation 



The age-structure method produced catches specific 

 to the observed time-series of recruitment and age- 

 specific catchability coefficients during 1980- 88. 

 Additional information can be gained by estimating 

 what the trend in catches would be if the recruit- 

 ment and catchability trends were different. In or- 

 der to explore the range of resulting catches which 

 might have occurred under various conditions, a 

 Monte Carlo simulation was used. Paired simula- 

 tions were performed for both the observed mixed- 

 mode fishery and a fishery in which all effort was 

 directed toward non-dolphin-associated tuna. Fre- 

 quency distributions of differences between catches 

 from the two simulated fisheries provide a more 

 comprehensive estimate of future expectations. 



The simulations used quarterly time steps and 

 1,000 replicates. At each quarter of each year in each 

 replicate, a year between 1980 and 1988 was ran- 

 domly selected with replacement (i.e., each year 

 could be selected more than once). Pairs of quarterly 

 catchability coefficients (one from the observed mix- 

 ture of fishing modes and one for the non-dolphin 

 sets only) estimated for the corresponding year, were 

 used in the calculations during the time steps. Quar- 

 terly coefficients were calculated with the same 

 equation as that for the monthly coefficients with 

 months replaced by quarters. Quarterly fishing ef- 

 forts were set to the 1980-88 averages. The same 

 average total effort was applied to both the observed 

 and non-dolphin fishing-mode models. 



Recruitment was simulated to occur in the second 

 and fourth quarter. For each year in each simula- 

 tion, a randomly selected year was chosen. Recruit- 

 ment pairs (X and Y) from the randomly selected 

 year were used for both fishery models. Initial popu- 

 lation sizes and age structures were also set to the 

 1980-88 averages. 



One thousand differences between the simulated 

 catches for the mixed- mode and non-dolphin only 

 scenarios were generated for a time series of nine 

 years. The 95% confidence intervals corresponded to 

 the 50th and 950th highest differences from the 

 1,000 simulations. Because yellowfin usually live for 

 less than 5 years (Fig. 3), results for the last (9th) 

 year were unaffected by the initial age structure. 



Results 



Deterministic approach 



If trends in total effort, recruitment, and non-dol- 

 phin-set catchability coefficients had been the same 

 as during 1980-88, with all effort directed at non- 

 dolphin sets, yellowfin catches (Table 1, column 



Table 1 



Estimated annual tuna (Scombridae) catches by 

 purse seiners in the eastern Pacific ocean, in 

 thousands of metric tons. 



OYF 

 NYF 



yellowfin tuna iThunnus albacares) - observed mixture 

 of set types. 



yellowfin tuna - all effort directed at non-dolphin 

 ( Delphimdae) sets, using the observed monthly 

 catchability coefficients for non-dolphin sets. 



QYF = yellowfin tuna - all effort directed at non-dolphin sets, 

 using the average, observed, quarterly catchability co- 

 efficients for non-dolphin sets. 



OSJ = skipjack tuna {Katsuwonus pelamis) - observed mixture 

 of set types. 



skipjack tuna - all effort directed at non-dolphin sets, 

 yellowfin plus skipjack tuna - observed mixture of set 

 types. 



yellowfin plus skipjack tuna - effort directed at non-dol- 

 phin sets, using quarterly average catchability coeffi- 

 cients. 



yellowfin plus skipjack tuna - all effort directed at non- 

 dolphin sets, using monthly catchability coefficients. 



NSJ = 

 OT = 



QT = 



NT 



NYF) were estimated to have averaged 77% of the 

 observed catch (Table 1, column OYF). The range 

 was from 58% in 1985 when dolphin-associated tuna 

 fishing was good to 93% in 1983 when dolphin-as- 

 sociated tuna fishing was poor. The reasons why the 

 ratio of estimated catch without dolphin sets to the 

 observed catch varied annually can be seen in Fig- 

 ures 3-7. For example, the high estimated bio- 

 masses of 1.5-year-old yellowfin in 1988 (Fig. 4), 

 coupled with their high non-dolphin-set catchability 

 coefficients (Fig. 5), produced an estimated catch of 

 266,000 t for all effort directed at non-dolphin sets, 

 which was almost as high as the 303,000 t catch 

 estimated from the catchability coefficients for the 

 observed mixture of set types (Fig. 6). Catchabilities 

 could have increased in 1988 for a variety of reasons, 

 including the use of deeper nets, the use of "bird 

 radar" (relatively new radar used for detecting birds 

 which commonly have tuna beneath them) or envi- 

 ronmental factors, such as a shoaling of the ther- 

 mocline (Green, 1967). For a given level of effort, 

 catches depended on the age-specific abundances 

 (Figs. 3 and 4) and catchability coefficients (Figs. 5 

 and 6). Consequently, the estimated catches if all 

 effort were directed at non-dolphin sets approached 



