McGaA/ey and Fowler: Seasonal growth of Sillaglnodes punctata 



553 



500 



400 - 



200 



females 



LML=280 mm 

 LML=300 mm 



researcher caught 

 fishermen caught 





 500 ^ 



400  



300 



200 



100 



males 



LML=280mm 

 Llv1L=300 mm 



13 



25 



37 49 



Age (months) 



73 



Figure 4 



Lengths at age for the South Australian West Coast, plotted as in Figure 2. 



a Bayesian context. Recently, Buckland et al. (1997) have 

 proposed averaging the estimates from the range of mod- 

 els examined, weighting each estimate by functions of the 

 Akaike or Hayes information criteria. This mitigates the 

 need to choose one specific model as we have done, and like 

 the Akaike or Bayes criteria, applies to nonhierarchically 

 related models. However, in situations where the growth 

 model will be incorporated into a larger stock assessment 

 estimation, a range of growth submodels would be chal- 

 lenging to implement. Moreover in cases where evidence 

 of overparameterization is given, a reduced-parameter 

 model can reduce both bias and the influence of sample 

 variation. 



Sinusoidal seasonality (Pauly and Gaschutz^) was 

 represented in a now standard way that preserves the 

 interpretation of ?q as the age at which length equals zero 

 (Somers, 1988; Hoenig and Hanumara, 1990). Pawlak and 

 Hanumara (1991) showed that this form of seasonality 

 model yielded statistical advantage. Hyndes et al. (1998) 



aged samples of King George whiting in southwestern 

 Australia that grew faster and reached larger maximum 

 lengths than those from South Australia. The analysis of 

 Hyndes et al. (1998) did not describe the distribution of 

 lengths-at-age or consider seasonality, which was less evi- 

 dent in their plotted data. 



The exponent, r, allowed nonlinear variation away from 

 the strict von Bertalanffy form. With the South Australian 

 King George whiting data sets, it improved the model de- 

 scription; fitted r's ranged from 1.25 to 4.59, outside the 

 range describable by the unmodified seasonal von Berta- 

 lanffy model where implicitly r = 1 fixed. 



We are not aware of previous attempts to use a truncat- 

 ed likelihood in an age-based description although Smith 

 and Botsford ( 1998) applied size truncation in fitting a von 

 Foerster equation to length samples. Truncation proved 

 effective in alleviating this potential large source of bias. 

 The extent of the bias is evident in the growth curve scat- 

 terplots (notably Figs. 2 and 4) where large numbers of 



