McGarvey and Fowler: Seasonal growth of Sillagtnodes punctata 



547 



on tag recoveries over three decades (Fowler and March^) 

 indicated three largely self-sustaining subpopulations: 

 GulfSt. Vincent, Spencer Gulf and West Coast (Fig. 1). 



Young fish (two- and three-year-olds) were aged by 

 interpretation of the macrostructure of the whole sagit- 

 tae. For fish with more complex otoliths, the otolith was 

 snapped in two across the posterior-anterior axis through 

 the center, exposing the transverse face of both halves. 

 One of these halves was burnt in a bunsen flame and then 

 examined with a binocular dissecting microscope at 6-20x 

 magnification. The surface being examined was smeared 

 with immersion oil. The alternating opaque and trans- 

 lucent zones were counted. The periodicity of formation 

 of this macrostructure in sagittae of King George whit- 

 ing has been validated and the following algorithm was 

 developed for conversion of ring count to age (Fowler and 

 Short, 1998): 



a = 12N + w^ -I- m^„ 



where a = age in months; 



N = number of opaque zones; 

 nif^ = 8 = number of months from universal birth 

 date (i.e. 1 May) midway through spawning 

 season to the end of the year; and 

 m^ = number of months from the start of year to the 

 month of capture. 



Some samples offish were scaled in the commercial pro- 

 cessing plant prior to weighing and measuring for length. 

 Although this process did not affect their lengths, it did 

 result in an appreciable loss of weight. Consequently, for 

 estimation of weight-length relationships we corrected the 



 Fowler, A. J., and W. A. March. 2000. Adult movement pat- 

 terns. In Development of an integrated fisheries manage- 

 ment model for King George whiting (Sillaginodes punctata I in 

 South Australia fA. J. Fowler and R. McGarvey, eds.), p. 83-104. 

 FRDC Final Project Report 95/008. Fisheries Research and 

 Development Corporation, PO Box 222, Deakin West ACT 2600, 

 Australia. 



weights of scaled fish using a linear relationship that was 

 derived by weighing 155 fish before and after scaling. This 

 linear relationship was 



{corrected iveight) = 1.0176 x (scaled weight) + 

 3,5835 (r2=0.99, P<0.001, df=154). 



Growth: length-at-age 



In order to make explicit the absence of fish samples 

 smaller than LML, a truncated normal probability density 

 function of length was used to describe the probability of 

 capture of individual fish in each monthly age. This pdf 

 was employed as the likelihood of observation of each indi- 

 vidual, given its age. Truncation implies a zero predicted 

 probability of observing a commercially or recreationally 

 sampled fish less than LML. A few sublegal fish were mea- 

 sured and, being unrepresentative, were removed from the 

 six data sets. 



During the period of sampling, in September 1995, the 

 regulated size of LML for commercial and recreational 

 fishery samples was increased from 280 to 300 mm. The 

 likelihood truncation length was thus a function of date 

 of capture. This necessitated two forms of likelihood, for 

 LMLs of 280 and 300 mm. Smaller numbers of samples 

 obtained on scientific cruises were not subject to LML size 

 controls. Thus a third, regular untruncated, likelihood was 

 used to model research samples. 



A normal likelihood was fitted to model the distribution 

 of lengths at each age: 



1 



2jr oia, ) 



-exp 



J. u, 



2 



-/(g,) 

 aia,) 



(1) 



where /, = length offish sample ;'; and 



a, = age of fish sample i obtained from count of its 

 otolith annuli. 



