Hearn and Polachek: Long-term growth rate changes in Thunnus maccoyli 



71 



Figure 5 



Comparison of the 1960s and 1980s best-fit estimates for the expected length of southern bluefin tuna as a 

 function of age, assuming that the expected length of an age-1 fish is 55 cm. 



age where the change in growth occurs is not well defined. 

 This, in turn, confounds the evaluation of the plausibility 

 of different specific possible biological hypotheses underly- 

 ing the change. Moreover, although the change in growth 

 patterns may be quite rapid, a large discontinuity in the 

 growth rates at a specific length seems unrealistic. The 

 continuous two-stage VBG model did not fit the 1960s and 

 1980s data as well as the discontinuous two-stage VBG 

 models. However, the two-phase VBG models fitted the 

 data better than the simple von Bertalanffy growth curve 

 (Table 1, A and B) and its generalization — the simple 

 Richards' ( 1959) curve (senior author, unpubl. results). 



From both the statistical estimation and biological per- 

 spective, we think there is scope for the development of 

 more appropriate complex growth models. In this context, 

 there is also need for the development of estimation proce- 

 dures for these complex models that can take into account 

 alternative error structures that allow for individual 

 variability in the growth rate parameters (e.g. Sainsbury, 

 1980: James, 1991; Wang et al., 1995 ). 



In the joint analysis of the 1960s and 1980s data, (7„, was 

 the only parameter found not to be significantly different 

 between the two data sets. However, caution is warranted 

 in any comparison and interpretation of growth curves 

 determining parameter values because of the well-known 

 negative correlation between k and L. of the VBG growth 



model and the bimodal nature of the likelihood surface, 

 as already noted. In particular, the differences in the esti- 

 mates of L^2 should not be taken as strong evidence that 

 the asymptotic growth of SBT decreased or that there was 

 a crossover in the growth rates. These complex growth 

 changes are difficult to explain from a biological perspec- 

 tive and, as noted above, the bootstrap results indicate 

 that the hypothesis that the L^g parameters are equal 

 cannot be rejected. Moreover, we would note that there is 

 a paucity of tag return data for larger fish. A total of only 

 seven tags were recovered from fish with lengths exceed- 

 ing 165 cm and only three for fish with lengths in excess of 

 170 cm. Fitting VBG models does not provide reliable es- 

 timates of growth when extrapolated beyond the range of 

 the data because of the large negative correlation between 

 k and L ^. We, therefore, do not think that the current data 

 are sufficient to determine whether, in fact, L^^ differed 

 between the 1960s and 1980s. 



One of the primary applications of the estimated SBT 

 growth curves is to provide estimates of the age distribu- 

 tion of commercial catch in stock assessments based on 

 catch-at-age analyses (e.g. Anonymous'*). The predicted 

 growth curves (assuming that an age-1 fish is 55 cm) 

 indicate that the estimated ages of 165-cm fish have di- 

 verged by about a year for the curve based on a common 

 L ,,, compared with those for which L„2 is allowed to differ 



