172 



Fishery Bulletin 103(1) 



where L xl , k v t 01 



VBGF parameters applied to the 

 first growth phase; 

 L l2 , k 2 , t 02 = VBGF parameters applied to the 

 second growth phase; 

 L s = length of transference from one 



growth phase to the next; and 

 t s = age of transference from one growth 

 phase to the next; calculated as. 



* =v 



In 



A 



L, 



(5) 



Having fitted Equation 4, we smoothed the discon- 

 tinuity from the first growth stanza to the second, as- 

 suming normal distribution around the age at transfer- 

 ence by integrating a normal probability cumulative 

 distribution function (PDF) where the mean is equal 

 to the age of transference (4.4 years) and where the 

 standard deviation is arbitrarily set at 1.0. This model 

 is referred to as the two-phase von Bertalanffy growth 

 function (VBGF TP ) and is now represented as 



♦''' i 



-■<-(„, f )\ 



,1, Os/2k 



(L_ 1 (l-e-*'"-'» , )+ £ )+ 



, (6) 



(*•. 



" 1 



', o-n/2/t 



(L 6 +(L, 2 -L')a-e- k '"'"') + e) 



where t max = maximum age present in the sample; 

 and 

 a 2 = standard deviation of cumulative density 

 function with mean t 6 . 



The model that best represented the data was judged 

 on a combination of parsimony as determined by the 

 Akaike information criterion (AIC) (Akaike, 1974), qual- 

 ity of fit by minimization of the negative log-likelihood 

 value derived from each model, visual inspection of the 

 residuals, and as an index of fit, the percent deviation 

 of L x for each model from the maximum observed length 



The hypothesis of sexual dimorphism in growth was 

 tested by using likelihood ratio tests (Kimura, 1980) 

 for both the VBGF S and VBGF TP models fitted to the 

 length-at-age data of all individuals whose sex had been 

 determined. 



Mortality estimation 



Mortality estimates were calculated by using the param- 

 eters of both the VBGF S and VBGF TP functions. An esti- 

 mate of instantaneous rate of total mortality (Z) for the 

 offshore hook fishery was calculated for 1998 by applying 

 a length converted catch curve analysis (LCCCA sensu 

 Pauly, 1983) to the length-frequency data. 



Estimates of instantaneous rate of natural mortality 

 (M) were calculated by using two empirical equations. 

 The first equation, derived by Pauly (1980), is described 



log 10 M = -0.0066 - 0.279 log^L^y 

 + 0.6543 log 10 k y + 0.4634 log 10 T, 



(7) 



where L„ and ky = parameters derived from the VBGF S 

 or from the second growth phase of 

 the VBGF TP ; and 

 T = average annual sea surface tempera- 

 ture (°C) at the area of capture. 



The mean annual sea surface temperature on the east 

 coast of Tasmania in 1998 was estimated as 14°C 

 (NOAA-CIRES 3 ). The second equation used was the 

 regression equation of Hoenig (1983): 



In Z = 1.46 - 1.01 In t max ; M~Z assuming F~0, (8) 



where t max = the maximum age for the species in years. 



Estimates of fishing mortality (F) were calculated by 

 subtracting natural mortality from total mortality. 



Results 



Males ranged in length from 203 mm to 815 mm (n = 504) 

 and females ranged from 269 mm to 950 mm (n = 565). 

 Length-frequency distributions did not differ signifi- 

 cantly between sexes (Kolmogorov-Smirnov; Z = 0.91 

 P=0.38). 



Pooling the length-frequency data of all individuals 

 produced a bimodal frequency distribution. However, 

 when grouped by depth (Fig. 1), the data revealed a 

 significant depth-based stratification between the shal- 

 low (<50 m stratum) and the deeper strata (Kolmogorov- 

 Smirnov; Z=13.8 P<0.001), occurring at around 450 mm 

 in length. 



Analysis of residual sums of squares indicated no 

 significant difference between the sex-specific length- 

 weight relationships (F=0.02 df=2 P=0.10); consequently 

 a power regression was applied to the length-weight 

 data of all individuals combined (Table 2). 



The sex ratio of males to females (1.0:1.3) from the 

 inshore net fishery showed a low level of significant 

 difference from 1:1 (x" = 3.88 P=0.049 n=232), whereas, 

 the ratio of males to females (1.0:1.1) caught from the 

 offshore hook fishery did not show significant difference 

 from 1:1 (x~ = 0.933 P=0.334 n = 840). 



Age estimates 



Age was successfully estimated for 776 (89%) individu- 

 als. Transverse otolith sections showed typical distinct 

 alternate light and dark zone formations within the 



