2n 



ddk 



and hence In 



f^dsk + ^f^ddk 

 ^^ddk 



ndsk ■•" 2A2ddfe 



= pexp(-Lffe) 

 = Inp — Ltfj 



= y. 



where Y^ is an estimate of the natural logarithm 

 of the proportion of tags retained up to time t/,. 

 Given n^idk , ^^s* > and t^ , then L and p can be esti- 

 mated using linear regression. We first estimated 

 these parameters using the usual least-squares 

 linear regression which assumes homoscedastic- 

 ity. We also believed that it would be appropriate 

 to consider that variability may increase as a func- 

 tion of time as the number of recoveries decreases. 

 To accomplish this, a weighting factor was intro- 

 duced and a weighted least-squares linear regres- 

 sion model was fitted to calculate values of Inp and 

 L, as was done by Bayliff and Mobrand (1972). The 

 weights for each time interval k (k = 1, 2, 3) were 

 equated to the ratio of the number of returns of 

 double-tagged fish during interval k to the total 

 number of returns of double-tagged fish during all 

 /j -periods. This can be simply expressed as: 



GJfe 



^ddk + l^dsk 

 3 



2 i^ddi + nasi) 



i=l 



While we consider this a reasonable first approxi- 

 mation of the correct weight, further investiga- 

 tions of the statistical properties of Yf^ to formally 



determine the correct weighting procedure are de- 

 sirable. Estimates of Inp and L were then made 

 using weighted linear regression. 



Results and Discussion 



The double-tag releases during 1971 through 

 1977 and returns in 1971 through 1978 are shown 

 by tag type (Table 1). A sufficient number of tag 

 returns existed to allow examination of three 

 separate recapture periods. Only a few returns 

 existed from beyond the third recapture period. 

 There were approximately equal numbers of each 

 tag type released each year. Table 1 constitutes 

 the basic data used throughout this study. Using 

 the basic data, we estimated values of immediate 

 (Type I) and instantaneous (Type II) shedding 

 rates for each tag type. Further, we tested several 

 hypotheses including: 1) equality of return rates 

 for same year recaptures; 2) equality of return 

 rates by estimated age; and 3) differences in re- 

 turns and nonreturns over 2 or 3 yr time periods 

 for various time intervals. 



Using the double-tagging release data for all 

 years combined (1971-77) the return rate for plas- 

 tic tags was 5.1% the first year, 8.6% the second 

 year, and 1.6% the third year. The return rate for 

 metal dart tags was 5.5% the first year, 9.1% the 

 second year, and 2.9% the third year. Therefore, 

 for both types of tags the return rates increased 

 the second year and decreased the third year. This 

 should be expected since tagging occurred at the 

 end of the purse seine season for several of the 

 release years studied. Chi-square tests (not cor- 



Table 1. — Tag releases and returns from northwestern Atlantic bluefin tuna double-tag study. For each of /z = 1, 2, or 3 recapture 

 periods the number of returns of double-tagged fish retaining both tags is n^^/^ and those retaining only one tags is n^^/^ . The average 

 number of days-at-large for each period is tf;. 



181 



