results obtained through 1972, for 580 double- 

 tagged bluefin tuna released during 1971 off the 

 east coast of the United States, were reported by 

 Lenarz et al. ( 1973). Their results were partially 

 based on tags supplied by the FRBC, some of which 

 had longer streamers than the tags supplied by 

 WHOI. For our present analysis, we used only 

 data from the WHOI tags. 



In this paper we present the overall findings 

 obtained through 1978 for 3,121 double-tagged 

 bluefin tuna. These fish were released primarily 

 from U.S. purse seine vessels fishing off the east 

 coast of the United States from Virginia to Mas- 

 sachusetts from 1971 through 1977. 



Methods 



The U.S. double-tagging program for Atlantic 

 bluefin tuna was conducted jointly by the NMFS 

 and WHOI. Tags and tagging procedures were 

 those described by the Food and Agriculture Or- 

 ganization (1972). All fish were tagged and re- 

 leased from U.S. purse seine vessels (98% of all 

 releases) and from a few sport fishing vessels. 

 Tagging occurred throughout the purse seine 

 fishing season during 1971, 1973, and 1974, and at 

 the end of the season during 1972, 1975, 1976, and 

 1977. The double-tagging operation was con- 

 ducted entirely by John Mason during each year 

 except 1974, when two assistants aided in the dou- 

 ble tagging. Precise release dates were available 

 for all of the fish. In a few instances only the month 

 and year were known for the recapture data. In 

 these cases, the 15th of the month was arbitrarily 

 selected to represent the recapture date. The vast 

 majority of returns fall into an annual cycle dur- 

 ing which the recapture periods are approxi- 

 mately 2-3 summer months. The interval mid- 

 points of the time intervals can be considered to be 

 on a yearly cycle. Therefore, we grouped returns 

 into "first year returns," "second year returns," 

 etc., and calculated average days out from the 

 individual days out for each return. Tag shedding 

 rates were estimated using the notation and 

 methodology of Bayliff and Mobrand (1972) for 

 yellowfin tuna, which Lenarz et al. (1973) used for 

 bluefin tuna and Laurs et al. (1976) used for North 

 Pacific albacore. Chapman et al. (1965) developed 

 the original model with the assumption of only one 

 type of shedding which occurs at a constant in- 

 stantaneous rate. Bayliff and Mobrand (1972) as- 

 sumed that there are two types. Type I which oc- 

 curs immediately after the fish are released and 



180 



Type II, the type described by Chapman et al. 

 (1965). 



Bayliff and Mobrand's modifications^ of the 

 Chapman et al. (1965) approximate equations for 

 tag returns of double-tagged fish are: 



nddk^FrNj)Trp^e^p-iF + X + 2L)tk (1) 



n^sk = 2FtNd 7rp(l - pexp{-Ltk)) 



expi-{F + X + L)tk) (2) 



where n^^ = number of returns of double-tagged 

 fish retaining both tags caught dur- 

 ing the recapture period tk, 



n^gi^ = number of returns of double-tagged 

 fish retaining only one tag caught 

 during the period ^^ , 



F = instantaneous rate of fishing mortal- 

 ity, 



A^^ = number of double-tagged fish re- 

 leased, 



77 = proportion of tagged fish which re- 

 main alive after the Type-I mortality 

 (immediate) has taken place, 



p = proportion of the tags which are re- 

 tained after Type-I shedding (im- 

 mediate) has taken place, 



X = instantaneous rate of mortality due 

 to natural causes, Type-II tagging 

 mortality (long term), and emigra- 

 tion from the fishing grounds, 



L = instantaneous rate of tag shedding 

 (Type II), and 



tf^ = time at the middle of the /sth recap- 

 ture period of length T(k = 1, 2, 3). 



From Equations (1) and (2) it follows that 

 ^dsk 2(1 - pexp(-L^fe ))exp(L^fe ) 



n 



ddk 



and therefore 



ridsk expiLtk)-p exp(L^fe) 2nddk 



^^ddk 



^^ddk 



Rearranging terms yields 



^As pointed out by Laurs et al. ( 1976), there was typographical 



error in both Bayliffand Mobrand (1972) and Lenarz etal (1973) 

 in Equation (2). 



