LENARZ and ZWEIFEL: INTERACTION BETWEEN LONGLINE AND SURFACE FISHERIES 



strata with low expected values. The probability 

 under Equation ( 1) of a returned tag being from a 

 surface-caught fish (P,ik) is 



P.u = N.u/Nik 



(2) 



The exact probability of all returns during the 

 1963-66 period being from surface-caught fish, 

 given the distribution of returns among year and 

 size categories, is 



p.i. = n n (Pnk)"'" 

 1=1 * = 1 



(3) 



Our estimate of P j is 0.00152, which is very low 

 and indicates that Equation (1) does not hold. 

 Thus we may conclude that 1) tag returns are not 

 independent (e.g., fish that were captured from a 

 school and tagged may remain in the same school 

 until recaptured), and/or 2) longline recoveries are 

 reported at lower rates than surface recoveries, 

 and/or 3) the fish were not equally available to 

 both gears. Since all fish were at liberty for more 

 than 10 mo before being recovered, the assump- 

 tion of tag returns being independent seems likely 

 to be valid. The independence of tag returns would 

 seem to be a desirable subject for further research 

 since the assumption is so often made in analyses 

 of tag returns. A considerable number of southern 

 bluefin tuna have been recovered and returned by 

 longliners (Shingu 1970), indicating longline 

 fishermen do cooperate in tagging programs. Dur- 

 ing the period of the study, the surface fishery was 

 only beginning to move offshore (Calkins and 

 Chatwin 1971), while the longline fishery was dis- 

 tributed throughout the area (Kume and Joseph 

 1969). Also, the fish that were released were 

 caught by surface gear, tagged, and released in 

 nearshore areas. Thus, tagged fish were probably 

 more representative of fish exploited by the sur- 

 face fishery than those that were exploited by the 

 longline fishery, if two groups offish existed. Thus 

 it seems plausible that the tagged fish were not 

 equally available to longline and surface gears. 



This is further evidence of unequal availability 

 of yellowfin tuna to the two gears in the Pacific. 

 Previously, Hisada (1973) showed that yellowfin 

 tuna caught near the surface using handlines 

 were of the same size as those caught by longliners 

 at the same time and in the same area of the 

 western Pacific. However, the surface-caught fish 

 tended to be more sexually mature except in areas 

 in which the 26°C isotherm occurred at depths 



fished by longliners. He attributed this phenome- 

 non to a preference for warmer waters by sexually 

 mature fish and noted that larvae of yellowfin 

 tuna tend to be found at water temperatures ex- 

 ceeding 26°C. Thus, some yellowfin tuna evidently 

 behave in a fashion that makes them available to 

 surface fishing but not to longline fishing. Further 

 evidence along these lines is provided by Shingu 

 and Tomlinson (Patrick K. Tomlinson, Inter- 

 American Tropical Tuna Commission, La Jolla, 

 Calif. Pers. commun., 1974) who found that the 

 length-weight relationship estimated by Lenarz 

 (1974) for surface-caught yellowfin tuna in the 

 Atlantic was more representative of the longline 

 catch in the eastern Pacific than was the relation- 

 ship estimated by Chatwin (1959) for surface- 

 caught yellowfin tuna in the eastern Pacific. 



With the above in mind, we considered three 

 hypothetical stock structures for the Atlantic yel- 

 lowfin tuna fishery: 1) the same stock(s) are 

 equally available to both gears, 2) half of the catch 

 of the longline fishery comes from stock(s) not 

 available to the surface fishery, and 3) the entire 

 catch of the longline fishery comes from stock(s) 

 not available to the surface fishery. The effects of 

 the three hypotheses on estimates of fishing mor- 

 tality and yield per recruit to the gear were 

 examined. 



Using the data in Table 2, we estimated the 

 vector F of size-specific instantaneous mortality 

 rates F, under the three hypotheses which are 

 identified by the proportion </) of the longline catch 

 which comes from the stocks exploited by the sur- 

 face fishery as = 1.0, 0.5, and 0.0 respectively. 

 For 4) = 1.0, all of the data in Table 2 was used to 

 estimate the F vector. For </> = 0.5, the surface 

 catch plus 50% of the longline catch was used and 

 for (t> - 0.0 only the surface catch was used for 

 estimating F. When (/> - 0, an additional F vector 

 was estimated for a longline fishery operating 

 without the presence of a surface fishery by using 

 only the longline catch. The F vectors were then 

 used to calculate yield per recruit to the two gears. 

 Estimation of a vector of size-specific F requires an 

 estimate of natural mortality and size-specific F 

 for one size category. In all instances, we chose to 

 use an estimate of size-specific F for the fish 

 > 177.5 cm. This estimate will be referred to as 

 Input F. The final value of size-specific F was set at 

 0.2 following Lenarz et al. (1974). The estimates 

 (Figure 1) indicate that values of F for large fish 

 are directly related to the portion of the longline 

 catch that comes from the stock(s) exploited by the 



811 



