586 



Fishery Bulletin 89(4). 1991 



The results of the simulations in which Loo; and K ; 

 were assumed to be correlated are given in Table 

 5. These results are essentially identical to those in 

 Table 4; therefore, the assumption of independence 

 does not affect parameter estimation in this instance. 



Testing the assumption of normally-distributed l 2 i 



Tests of normality of l 2 i were performed for 30 com- 

 binations of 1 and t. For each of the combinations, the 

 statistic G Or distributed with 49 degrees of freedom) 

 and the probability, P, of wrongful rejection of the null 

 hypothesis of normally-distributed l 2 j were calculated 

 (Table 6). In each case, P is greater than 0.10, and 

 usually substantially so; therefore the null hypothesis 

 is not rejected for any of the combinations of 1 and t. 



Discussion 



The estimation of von Bertalanffy growth parameters 

 is one of the more frequently applied analyses in fish- 

 eries research. Despite this, the interpretation of the 



parameter estimates is often ill-founded. This is par- 

 ticularly so with L m , which is frequently given the in- 

 terpretation of maximum possible length. This would 

 be the case only if every fish grew exactly according 

 to the derived model, i.e., there was no model error or 

 individual variation in growth. In reality, the growth 

 of all individual fish will not follow a single von Ber- 

 talanffy growth curve exactly; there will be variations 

 among individuals resulting from exogenous (environ- 

 mental) and endogenous (genetic) effects (Francis 

 1988). The correct interpretation of L^ estimated in 

 the standard way is that it is the average maximum 

 length that would be attained in the population repre- 

 sented by the data being analysed. Models have been 

 proposed in this paper that take explicit account of 

 model error and individual variation in growth, thereby 

 eliminating the need for such interpretations. 



Previous estimates of southern bluefin growth 

 parameters have differed substantially (Table 7). The 

 previous estimates of L^ obtained from tag-return 

 data are somewhat smaller than the estimate derived 

 using model 1 in this paper. This is possibly because 



