FISHERY BULLETIN: VOL. 76, NO. 4 



60 70 80 90 100 110 120 130 140 150 160 170 

 LENGTH (cm) 



Figure 6. — Length distribution by sex of longline-caught yel- 

 lowfin tuna in the central Pacific Ocean (Murphy and Shomura 

 1972). 



relationship of LeGuen and Sakagawa (1973), we 

 estimated that beyond 140 cm 



]nR = 6.74 - 1.96^ (4) 



where R = ratio of females to males 

 t = age in years. 



One interpretation of the above result (assum- 

 ing that males have a coefficient of instantaneous 

 natural mortality of 0.8 on an annual basis as do 

 all fish <145 cm) is that female yellowfin tuna 

 >140 cm have a coefficient of apparent natural 

 mortality of 2.76. Assuming that the results of 

 Murphy and Shomura apply to the Atlantic and 

 that all yellowfin tuna are equally available to 

 both gears, we separated the catch of yellowfin 

 tuna into males and females using Equation (4) 

 and Table 2, and estimated F for the males using 

 Input F values of 0.2 and 0.8 for fish >177.5 cm 

 (Lenarz et al. 1974). An alternative method would 

 be to use the same Input F for the three hypotheses 

 at the smallest size interval. This was attempted 

 and resulted in either estimates of F, which, based 

 on the results of other studies, appeared to be too 

 low under the 1:1 hypothesis or too high under 

 the other hypotheses. The estimates of size- 

 specific F are similar except for very large yel- 

 lowfin tuna (Figure 7). Since the deviations in sex 

 ratio from 1:1 occurs only at large sizes, we used 

 both sets of estimates of F. 



o 



35 55 



75 95 115 

 SIZE (cm) 



T — r 

 135 155 175 



HIGH M 

 Female 



BEH Female 

 1 — f~— I — r 



SIZE (cm) 



Figure 7. — Estimates of size and sex specific coefficient of in- 

 stEintEineous fishing mortahty on annual basis (F) for Atlantic 

 yellowfin tuna for 1:1, BEH and HIGH M hypotheses (see text): 

 (a) low Input F, B) high Input F. 



For females, three hypotheses were examined 

 for estimating F: 1 ) the observed differences in sex 

 ratios are artifacts, and consequently females 

 have the same values of F and M as males (de- 

 noted 1:1); 2) females >140 cm have a higher 

 natural mortality rate than males but are 

 exploited at the same rate as males for all sizes 

 (denoted as HIGH M); and 3) females have the 

 same natural mortality rate as males but become 

 less subject to fishing mortality beyond 140 cm 

 (denoted as BEH for behavior changes). Under the 

 BEH hypothesis, F, for females >140 cm is equal 

 to the ratio of the catch of females to the catch of 

 males times F, estimated for males. The alterna- 

 tive hypotheses considerably affected the esti- 

 mates of size-specific F (Figure 7). 



In the following analyses, we found that the 

 BEH and HIGH M hypotheses produce similar 

 results. To save space, we refer to only the one 

 hypothesis that produced results which showed 

 the greatest difference from the 1:1 hypothesis. 

 Also, when not specifically indicated, size of re- 

 cruitment and effort are assumed to be those at the 

 time of the study, i.e., 1967-71 where the multi- 

 plier of effort is equal to unity. 



Estimates of yield per recruit as a function of 

 fishing effort are shown in Figure 8. The choice of 

 Input F has little effect on the relative values of 



814 



