545 



Abstract-Samples of 11.000 King 

 George whiting iSillagi nodes punctata ) 

 from the South Austrahan commercial 

 and recreational catch, supplemented 

 hy research samples, were aged from 

 otoliths. Samples were analyzed from 

 three coastal regions and by sex. Most 

 sampling was undertaken at fish pro- 

 cessing plants, from which only fish 

 longer than the legal minimum length 

 were obtained. A left-truncated normal 

 distribution of lengths at monthly 

 age was therefore employed as model 

 likelihood. Mean length-at-monthly-age 

 was described by a generalized von 

 Bertalanffy formula with sinusoidal 

 seasonality. Likelihood standard devia- 

 tion was modeled to vary allometrically 

 with mean length. A range of related 

 formulas (with 6 to 8 parameters) for 

 seasonal mean length at age were com- 

 pared. In addition to likelihood ratio 

 tests of relative fit, model selection cri- 

 teria were a minimum occurrence of 

 high uncertainties (>20'7t SE), of high 

 correlations O0.9, >0.95, and >0.99) and 

 of parameter estimates at their biologi- 

 cal limits, and we sought a model with a 

 minimum number of parameters. A gen- 

 eralized von Bertalanffy formula with ^^ 

 fixed at was chosen. The truncated 

 likelihood alleviated the overestimation 

 bias of mean length at age that would 

 otherwise accrue from catch samples 

 being restricted to legal sizes. 



Seasonal growth of King George whiting 

 (Sillaginodes punctata) estimated from 

 length-at-age samples of the legal-size harvest 



Richard McGarvey 



Anthony J. Fowler 



SARDI Aquatic Sciences 



2 Hamra Avenue 



West Beach 



South Australia 5024, Australia 



E-mail address (for R, McGarvey) mcgarvey.richard@saugov.sa.gov.au 



Manuscript accepted 15 February 2002. 

 Fish. Bull. 100:545-558 (2002). 



In this stu(iy, we estimate(i growth curves 

 from six data sets of fish sampled from 

 the commercial and recreational catch 

 of an important fish species in South 

 Australia (Fig. 1), King George whit- 

 ing (Sillaginodes punctata). Like many 

 temperate fish populations, recruitment 

 and growth can be assumed to follow a 

 yearly cycle. A variety of methods have 

 been used to measure seasonal variation 

 in fish growth including mark-recapture 

 (Francis, 1988; Coggan, 1997) and oto- 

 lith annulus-diameter increments in 

 combination with tetracycline marking 

 (Panfili et al., 1994; Fabre and St. Paul, 

 1998; Francis et al, 1999). The method 

 used in our study is the most widely 

 employed, of fitting to lengths-at-age, 

 where the age of each sampled fish is 

 read as a count of yearly otolith annuli 

 from samples of the harvest. 



The model-fitting algorithm had 

 three key objectives, each to represent 

 a specific feature of the growth of South 

 Australian King George whiting, or of 

 the data set. These were expressed 

 mathematically as deviations from a 

 standard 3-parameter von Bertalanffy 

 model fitted with a normal likelihood. 



The first two objectives were elabo- 

 rations on the standard von Berta- 

 lanffy growth curve (understood as a 

 deterministic function of mean length 

 versus age). The first objective was to 

 make seasonality explicit in the growth 

 curve (Pitcher and MacDonald, 1973; 

 Somers, 1988; Hoenig and Hanumara, 

 1990; Pauly and GaschiitzM and the 

 second objective was to allow a wider 

 range of curvatures by using the r-ex- 

 ponent (Schnute, 1981). 



For application of this growth descrip- 

 tion in length- and age-based stock as- 

 sessment modeling, we also estimated 

 the shape of the length-at-age probabil- 

 ity density function (pdH, which quanti- 

 fies the distribution of fish of different 

 lengths at each age. 



The principal regulation of both rec- 

 reational and commercial King George 

 whiting harvest is by legal minimum 

 length (LML); fish smaller than the 

 LML cannot be landed and must be 

 returned to the sea. Therefore fish 

 obtained from the catch are a biased 

 sample. The third objective was to ex- 

 plicitly account for the absence of fish 

 below the LML, for which a truncated 

 pdf was used. This truncated normal 

 density, the pdf of observed lengths-at- 

 age, was also used as the likelihood for 

 each individual sample. 



A range of models were examined 

 that met these three objectives. These 

 included a seasonal version of the 

 Richards (1959) model proposed by 

 Akamine (1993), which makes differ- 

 ent use of the /-exponent. Therefore a 

 fourth objective was to apply standard 

 statistical model selection techniques. 

 Methods to choose the most appropri- 

 ate model for a given growth data set 

 were reviewed by Quinn and Deriso 

 (1999). Hierarchical model fits are sta- 

 tistically comparable using their likeli- 



 Pauly, D., and G. Gaschutz. 1979. A 

 simple method for fitting oscillating length 

 growth data, with a program for pocket 

 calculators. Demersal Fish Committee, 

 ICES council meeting 1979/G:24. ICES, 

 PaliEgade 2-4 DK-1261 Copenhagen K, 

 Denmark. 



