552 



Fishery Bulletin 100(3) 



600 



500 



400 - 



300 



200 



females 



LML=300 mm 

 LML=280 mm 



researcher caught 

 fishermen caught 



males 



Figure 3 



Lengths versus age of King George whiting sampled from Spencer Gulf, 

 plotted as in Figure 2. 



ratio tests showed that /3 did not differ significantly from 

 3.2 (Table 4). With /} = 3.2 fi.xed. values of a among the six 

 data sets differed little (Table 5, Fig. 7). 



Discussion 



In this study we estimated parameters of length at age 

 for six data sets, comparing the fits of different models by 

 using four standard diagnostic tools, notably likelihood 

 ratios, correlations, standard errors, and parameter esti- 

 mates among data sets either varying widely or varying 

 little, to evaluate the estimators being compared. Simi- 

 larly, for weight versus length in the same population, we 

 assessed six data sets, and used likelihood ratio to com- 

 pare model fits. For both length at age and weight versus 

 length, the diagnostic analysis suggested the initial full 

 models were overparameterized and indicated which 

 parameters should be fixed and what values. 



Likelihood ratio tests allow comparisons only between 

 hierarchical models, that is in comparing full and reduced 

 models, the latter a subcase of the full model obtained 

 by fixing one or more parameters in the full model. In 

 the case of generalized von Bertalanffy and Akamine- 

 Richards, setting r = 1 yielded the same model, namely 

 seasonal von Bertalanffy. The other two reduced models 

 analyzed (gVB with /q=0 and with both fg=0 and Sj=0.3) 

 were reduced models only of generalized von Bertalanffy. 

 Although other comparison tests are possible for hier- 

 archical models (Quinn and Deriso, 1999), the Neyman 

 Pearson lemma assures that in the situation where it ap- 

 plies, the likelihood-ratio test is optimal in that it yields 

 the most powerful test for any given choice of significance 

 level, a (Rice, 1995). 



Fits of nonhierarchical models can be compared by us- 

 ing the Akaike or Bayes information criteria (Quinn and 

 Deriso, 1999). Fournieret al. (1998) applied the Aitkin pos- 

 terior Bayes factors for hypothesis model comparisons in 



