FISHERY BULLETIN, VOL. 12. NO. 1 



frequencies from the 1971 Japanese longline 

 fishery are assumed to be the same as those of 

 the 1970 Japanese longline fishery; this as- 

 sumi)tion appears justifiable because year to 

 year changes in length frequencies from long- 

 line fisheries tend to be less than differences in 

 length frequencies between longline fisheries 

 and surface fisheries. 



Length-frequency data were available only 

 from the Jai)anese longline fishery, FIS surface 

 fisheries, and American large purse seine fishery. 

 Thus it was necessary to make several assump- 

 tions before estimating the length frequencies 

 of the total catch of yellowfin in the Atlantic. 

 Length frequencies for longline fisheries other 

 than Japan are assumed to be the same as 

 Japan's. Length frequencies for the bait boat 

 and small purse seine fisheries other than FIS 

 were assumed to be the same as the FIS fish- 

 ery. Length frequencies for the large purse 

 seine fisheries other than FIS and American 

 were assumed to be the same as those two 

 fisheries. 



Parameters 



The growth equation [L = 194.8 X (1 - 

 g-0.42 (< - o.62))j presented in LeGuen and 

 Sakagawa (1973) and length-weight relation- 

 ship {W = 0.0000214L2-9736) given by Lenarz 

 (19713)*^ were used, where L is fork length in 

 cm, t is age in years, and W is weight in kg. 



The annual instantaneous coefficient of nat- 

 ural mortality (M) is a difficult parameter to 

 estimate and due to a lack of data only pre- 

 liminary estimates have been made for the pa- 

 rameter in the Atlantic. We assume as most 

 authors have that M is constant over the ex- 

 ploited phase. Estimates of M = 2.61 and 1.50 

 for the Atlantic were made by Pianet and LeHir 

 (1971) based on data from bait boats and seiners, 

 respectively. These estimates seem unreason- 

 ably high perhaps because their data were only 

 from the Pointe Noire region which is a small 

 area compared to the total region in the Atlan- 

 tic where yellowfin tuna are found. Hennemuth 

 (1961) estimated that M is 0.8 in the Pacific 

 while Davidoff (1969) chose the upper bound 



of Hennemuth's estimate, 1.0. Hennemuth's 

 work was based on estimates of instantaneous 

 coefficient of total mortality (Z) made from age 

 compositions of catches by primarily bait boats 

 and an estimate of instantaneous coefficient of 

 fishing mortality (F) from Schaefer (1957). 

 Since bait boats appear to be selective for small 

 yellowfin, F and Z are not constant, and meth- 

 ods of ageing yellowfin have not been proven 

 correct, Hennemuth's estimate must be con- 

 sidered a first approximation. However, his 

 estimate seems reasonably consistent with what 

 is thought to be the life span of yellowfin. We 

 assumed for the purposes of our calculations 

 here that M is 0.8 as is conventional (based on 

 Hennemuth's work in the Pacific); we also used 

 values of 0.6 and 1.0 to encompass what we 

 believe is the range of reasonable values. 



Pianet and LeHir (1971) also estimated an 

 average F of 0.88 for the segment of the At- 

 lantic yellowfin tuna population that is exploit- 

 ed in the Pointe Noire region. As we have indi- 

 cated, their estimate is not representative for 

 the population as a whole. 



Our range of estimates of Z for 1967-71 is 

 0.91 to 1.82 (Lenarz and Sakagawa, 1972, see 

 footnote 5). If we assume that M = 0.8 for the 

 Atlantic population, then F is 0.11 to 1.02. We 

 believe that F is about 0.6 for recent years. 

 However, we used a range of F values in our 

 study. 



Computer Programs 



Most of the calculations were performed on 

 the Burroughs 6700-' computer at the Univer- 

 sity of California at San Diego. Programs used 

 in the analysis, except for FRG708 (Paulik 

 and Bayliff, 1967), were written by the authors; 

 they are as follows: 



1. Simplified Beverton and Holt yields per 

 recuit— YPER. 



2. Accuracy of knife-edged approximations 

 of age at entry and interactions between mini- 

 mum size and catch quota regulations — 

 GXPOPS. 



3. Yield-per-recruit isopleths under knife- 

 edged recruitment — FRG708. 



** Lenarz, W. 1971a. Length-weight relations for five 

 Atlantic scombrids. Southwest Fisheries Center, National 

 Marine Fisheries Service, La Jolla, Calif. Unpublished 

 manuscript. 



" Reference to trade names does not imply endorsement 

 by the National Marine Fisheries Service, NOAA. 



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