FISHERY BULLETIN; VOL. 72, NO. 4 



Table 3.— Chi-square tests of equality of return probabilities between sport and commercial gear releases of tagged 

 bluefin tuna in the northwestern Atlantic Ocean. Each test has 1 degree of freedom. 



the 5 yr. The data cannot be pooled over years to 

 increase the numbers in individual cells in the 

 chi-square tables since the recovery percentages 

 and numbers tagged vary so greatly from year- 

 to-year. 



However, the Mantel-Haenszel test can be used 

 to examine the data in toto (Snedecor and Coch- 

 ran, 1967:255-256). The calculations resulted in 

 a value of 8.89, which is highly significant. As is 

 discussed in a later section, we think that most of 

 the difference between return rates of sport and 

 commercial tagged fish is caused by immediate 

 tagging mortality. Immediate tagging mortality 

 does not affect estimates of instantaneous total 

 mortality. Therefore, we decided to use as much of 

 the available data as possible and combined the 

 data for estimates of mortality rates. Immediate 

 tagging mortality does affect estimates of rates of 

 exploitation and the components of mortality. Ad- 

 justments were made in an attempt to remove the 

 effects of immediate tagging mortality and tag 

 shedding. 



Total Mortality Estimates - 

 Chapman and Robson Method 



Following the notation of Bayliff and Mobrand 

 ( 1972), the number of tags remaining on bluefin at 

 time t (years) is given by 



p = portion of tags which are retained 

 after Type-I shedding takes place 



Z = instantaneous total losses on an 

 annual basis. 



Z ^F + X 



where F = instantaneous fishing mortality 

 on an annual basis 

 X = instantaneous other losses on 

 an annual basis. 



X=M+G+L+E 



where M = instantaneous natural mortality 



on an annual basis 

 G = instantaneous Type-II tagging 



mortality on an annual basis 

 L = instantaneous Type-II tag 



shedding on an annual basis 

 E = instantaneous emigration from 



fishing grounds on an 



annual basis. 



The number of tags returned during a year is 

 given by 



n, = 



FcN, 



a-e'^) 



(2) 



A^, =A^, TTpe-^' 



(1) 



where Nf = Number of tags remaining on 

 bluefin at time t 

 number of released tags 

 portion of bluefin which remain 

 alive after Type-I, immediate, 

 tagging mortality takes place 



Nn = 



77 - 



where rii = 



c = 



number of tags returned 

 between t and t + 1 



portion of recovered tags 

 that are returned. 



Many assumptions are implicit in the above 

 model. An exponential model is assumed to be 



906 



