FISHERY BULLETIN: VOL. 76, NO. 4 



random migration or dispersal and location of re- 

 cruitment of yellowfin tuna on estimates of mor- 

 tality and yield per recruit to each gear. We have 

 restricted our analysis to yellowfin tuna but be- 

 lieve that the concepts that we develop apply to the 

 other species as well. 



MATERIALS AND METHODS 



While stocks of yellowfin tuna are subjects of 

 important fisheries in all tropical oceans, infor- 

 mation on vital parameters is sketchy and 

 nonuniform. For example, tagging information 

 available in the Pacific is lacking for the Atlantic 

 stocks. On the other hand, regulation of the Pacific 

 fishery makes interpretation of the catch informa- 

 tion more difficult. Hence it is necessary to pick 

 and choose from the available information that 

 which is most relevant to the problems at hand. 

 Although the parameters are likely to differ for 

 fish from different oceans, if not fish from different 

 areas of the same ocean, few studies have conclu- 

 sively demonstrated that such differences exist. In 

 addition, several (e.g., Lenarz et al. 1974) have 

 found that conclusions from studies such as de- 

 scribed in this paper are often insensitive to the 

 likely range of values of parameters such as 

 natural mortality, fishing mortality, and growth. 

 In the first and second sections, we have used data 

 primarily from the eastern Atlantic because his- 

 torically catches have been more equally shared 

 by longline and surface fisheries than in the east- 

 ern Pacific; in the third section we have modelled 

 the eastern Pacific since information on migration 

 patterns is more extensive. In both instances, the 

 results are intended to be general rather than 

 specific. Data extracted from one area and used in 

 another is thought to be the best available and the 

 question of real differences is left for further inves- 

 tigation. 



With a noted exception, the growth equation L 

 = 194.8 X (1 - e-0 42u 0.67)) estimated by Le Guen 

 and Sakagawa ( 1973) and length-weight equation 

 W = 0.0000214L2^^36 estimated by Lenarz (1974) 



are used for yellowfin tuna where L is fork length 

 in centimeters, t is age in years, and W is weight in 

 kilograms. Unless otherwise stated, we assumed 

 that the annual instantaneous coefficient of 

 natural mortality (M) is 0.8 (Hennemuth 1961). 

 We estimated age-specific fecundity from two indi- 

 ces derived by Hayasi et al. ( 1972) (Table 1). Their 

 index I was obtained from longline data and their 

 index II was obtained from surface data. The 



Table 1. — Indices of fecundity of yellowfin tuna as interpolated 

 from Hayasi et al. ( 1972), for fish caught in the Pacific calculated 

 by multiplying average ova counts by percentage of mature 

 female fish for each age and then dividing each product by the 

 product calculated for age 3 fish. 



fecundity indices were calculated by Hayasi et al. 

 ( 1972) for fish caught in the Pacific by multiplying 

 mean ova counts by percentage of mature female 

 fish for each age and then dividing each product by 

 the product calculated for age 3 fish. For much of 

 our work, we used estimates of the 1967-71 aver- 

 age size (age) composition of the Atlantic yellowfin 

 tuna fishery made by Lenarz et al. (1974) (Table 2). 

 Use of length-age key assumes that length and age 

 are equivalent. Sex composition shown in Table 2 

 is based on data from the Pacific. 



Estimates of the size- (age-) specific instantane- 

 ous coefficient of fishing mortality (F,) on an an- 

 nual basis were made using the Gulland (1965) 

 and Murphy (1965) method. The computer pro- 

 gi-am COHORT, written by W. W. Fox, Jr., of the 

 Southwest Fisheries Center, was used to obtain 

 estimates of F, for each 5-cm size interval, begin- 

 ning at 32.5 cm. The estimation procedure was 

 initiated with a trial value of F, for the largest size 

 interval (Input F). 



Estimates of F, were obtained from the average 

 1967-71 catch composition data (Table 2) as was 

 done by Lenarz et al. (1974). When feasible it is 

 more desirable to estimate F, from individual 

 cohorts. This was not done because of the small 

 number of years in the data series and belief that 

 estimates from the average composition would 

 adequately reflect conditions of the fishery. In a 

 latter study, Fonteneau and Lenarz (1974) esti- 

 mated F; for individual cohorts from a longer time 



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