882 



Fishery Bulletin 92|4|. 1994 



each annulus followed a body proportional hypothesis (Francis, 1990), using the equation L = L exp[g(ln(S )) 

 - g(ln(S))l, where L i is the estimated total length at the formation of the /th annulus, L is the total length at 

 capture, S. is the radius of the /th annulus, and S is otolith radius. 



Lengths at age and back-calculated lengths were used to construct growth curves using the traditional form 

 of the von Bertalanffy equation, L t = LJ\ - e\p[-k(t - 1 )]), where L, is the mean body length offish of age t, L^ 

 is the asymptotic mean length offish in the population, t is the theoretical age at which the length of fish is 

 zero, and k is the growth coefficient. Since the von Bertalanffy curves failed to describe adequately the full 

 range of data (see Discussion), the more flexible growth curve equation derived by Schnute (1981) was fitted 

 to the data. There are four possible forms of this equation, depending on the values of the parameters a and 6, 

 where y j andy 2 are the lengths of the fish at the specified ages T x and TV, (i.e. ages 1 and 4, which bounded the 

 majority of the data set in this application). 



Casel: a * 0,6*0 L, 



, h l-exp(-a«-T 1 ) 



V, +<y 2 -yi>- 



l-exp(-a(7 1 2 -T 1 )) 



Vfc 



Case 2: a* 0,6 = L, = y 1 exp 



log 



' y.,) l-exp(-a(t-T,)) 



Vi ) 



1- exp (-a (To-!;)) 



Case 3: a = 0,6*0 L, 



y, +(y 2 -y 1 ) T * 



i 2 1 j 



\h 



Case 4 : a = 0,6 = L t = y, exp 



I..- 



y 3 



t-T, 



T 9 -T, 



When a >0 and 6 = 1, the generalized growth curve 

 is equivalent to the traditional form of the von 

 Bertalanffy growth curve, with a = k. The resultant 

 form of the generalized growth equation was deter- 

 mined by the parameters a and 6 that resulted in 

 the minimum sum of squared deviations. Data were 

 fitted by using a nonlinear least squares method, 

 employing the nonlinear (NLIN) procedure of SAS 

 (Ihnen and Goodnight, 1987). All back calculations 

 and curve fittings were carried out separately for 

 each sex in both populations. Juveniles, for which 

 the sex could not be determined, were included in 

 calculating growth curves of both sexes from length- 

 at-age data. Calculations of all curves assumed a 

 birth date of 1 December in Wilson Inlet and 1 No- 

 vember in Swan Estuary (Laurenson et al., 1993a). 

 Each growth curve, fitted by using the traditional 

 form of the von Bertalanffy growth equation, was 

 compared with the corresponding generalized growth 

 curve by using a likelihood ratio test, an approach 

 adopted with several other fish species (Kimura, 

 1980; Kirkwood, 1983; Cerrato, 1990; Hampton, 

 1991; Buxton, 1993). The generalized growth curves 

 of both sexes in Wilson Inlet and Swan Estuary based 



on lengths at age and back calculated lengths, were 

 compared by using the same likelihood ratio test, 

 which involved determining the improvement of fit 

 obtained by using the two separate curves, rather 

 than a common curve. This involved 1) comparing 

 the curve for males with that for females in each sys- 

 tem, using first lengths at age and then back-calcu- 

 lated lengths; 2) comparing the curves for each sex 

 in Wilson Inlet with that for the corresponding sex 

 in Swan Estuary, using first lengths at age and then 

 back-calculated lengths; and 3) comparing the curves 

 calculated from lengths at age with those obtained 

 from back-calculated lengths, first for males in each 

 system and then for females in each system. 



Results 



Mean monthly percentages of otoliths from Wilson 

 Inlet with a peripheral translucent zone and one, two, 

 or three inner translucent zones followed similar 

 seasonal trends (Fig. 1). The percentage of such 

 otoliths rose sharply in early spring and fell to close 

 to zero in the late spring or early summer where they 



