Hampton Natural mortality and movement rates of Thunnus maccoyn 



593 



season) used for those returns where an exact recap- 

 ture time was not available. The numbers of such 

 returns were relatively few (experiment 1: 27, experi- 

 ment 2: 114, experiment 3: 47, experiment 4: 35. 



Methods of analysis 



General assumptions of tagging experiments 



Before describing the analytical methods used in this 

 study, some discussion of general assumptions required 

 for the estimation of mortality rates from tag-return 

 data is warranted. These assumptions relate mostly to 

 accounting for all forms of tag loss. In particular, tag 

 losses due to tag shedding, tagging-induced mortality 

 (e.g., through infection, or increasing the probability 

 of predation or capture), and non-reporting of recov- 

 ered tags must be absent or accounted for. This is fre- 

 quently achieved by carrying out separate experiments 

 to estimate parameters of models that describe these 

 processes, e.g., double- tagging experiments to estimate 

 tag-shedding rates, holding-tank experiments to test 

 for tagging-induced mortality, and tag-seeding experi- 

 ments to estimate the proportion of recovered tags that 

 are returned to the tagging authority. The approach 

 taken in this paper was to account for tag shedding 

 using estimates derived by Hampton and Kirkwood 

 (1990), assume tagging-induced mortality to be absent 

 on the basis of various field observations, and repeat 

 the parameter estimations over a range of plausible 

 tag-reporting rates. 



In addition to assumptions regarding tag loss, for 

 analyses that include parameters or data relating to 

 the recapture fishery, it is necessary to assume that 

 the tagged and untagged populations are equally vul- 

 nerable to capture from the moment of release. Com- 

 pliance with these and other assumptions for the pres- 

 ent application are discussed in a later section. 



ly known, M is constant, the experiment is completed 

 (i.e., no tagged fish remain alive at the time of the last 

 tag recapture), and all tagged fish remain vulnerable 

 to the fishery through a possibly variable but ultimately 

 non-zero level of fishing mortality. Cessation of fishing 

 would violate the assumption of completion, while perm- 

 anent emigration of tagged fish away from the fishery 

 would violate the assumption of complete vulnerability. 

 Let N fish be released and n recaptures recorded 

 at times ti<t 2 <  .  t n after release. If the above as- 

 sumptions are satisfied, the natural mortality rate esti- 

 mator, M, is obtained by solving the equation, derived 

 by Hearn et al. (1987), 



N f 



i=l 



Mt; 



= o, 



(1) 



using a numerical method such as the Newton-Raphson 

 (Courant 1937). 



Tag shedding is accounted for by introducing for each 

 return a correction factor, w i? which is the probabil- 

 ity of a tagged fish retaining at least one tag at time 

 tj. For double-tagging experiments, 



Wi = Q(tj) [2 - Q(t,)], 



(2) 



where Q(t ; ) is the probability of a tag being retained 

 at time tj after release. Tag-shedding models have 

 been fit to double-tagging data for each of the experi- 

 ments (Hampton and Kirkwood 1990), the results of 

 which are given in Table 2. 



The tag-shedding correction is incorporated into 

 Equation (1) as follows: 



_ n _ e Mt; 



No - I — = 0. 



(3) 



The HSH model 



In addition to the assumptions regarding tag loss, it 

 is assumed here that all recapture times are accurate- 



Similarly, the non-reporting of recaptured tagged 

 fish can be allowed for if the fraction, R, of recaptured 

 tagged fish actually reported to the tagging authority 

 is known or assumed. Equation (3) then becomes 



