788 



Fishery Bulletin 98(4) 



The number of opaque zones in the whole and sectioned 

 otoliths of a subsample of 162 of the above 239 fish and the 

 number of annuli on the scales of a random subsample of 

 87 of those fish were also counted by a second reader to 

 determine the level of reproducibility of the counts made 

 of the growth zones on these hard structures by the senior 

 author. 



The birth date assigned to A. butcheri in each water body 

 corresponds to peak spawning activity, as estimated from 

 the trends exhibited by gonadosomatic indices, stages in 

 gonadal development and pattern of oocyte development 

 (SaiTe and Potter, 1999). Von Bertalanffy growth cur\'es 

 were fitted to the individual lengths of female and male fish 

 at their estimated ages at capture by a nonlinear technique 

 (Gallucci and Quinn, 1979) by using a nonlinear subroutine 

 in SPSS (SPSS Inc., 1988). The von Bertalanffy equation is 



LI- 



where L, = the total length at age n years); 



L , = the mean of the asymptote predicted by the 



equation; 

 k - the growth coefficient; and 

 <g = the hypothetical age at which fish would have 

 zero length, if growth followed that predicted 

 by the equation. 



The lengths at age of fish whose sex could not be deter- 

 mined under a dissecting microscope were selected at 

 random and placed alternately in the data sets for female 

 and male fish. 



Each of the gi-owth parameter estimates for female and 

 male fish in the same estuary and for each sex in the four 

 estuaries were compared by using a likelihood ratio test 

 (see Kimura, 1980). Comparisons were also made between 

 the growth parameters for the males of A. butcheri in Lake 

 Clifton, the sex which dominated the catches in that lake, 

 and those of the males of this species in the four estuaries. 



The likelihood ratio for the null hypothesis I Kimura. 

 1980) tests the null hypothesis against the alternative 

 hypothesis where 



H^^. states that the parameters L ,, k ,and ?„ satisfy some 

 set of r linear constraints; 



Hjj states that the parameters L . , k. and t^^ possibly 

 satisfy no linear constraints. 



The maximum likelihood estimates of the error vari- 

 ances ct^ andtr'r/r) are given by the sum of squares of 

 residuals from the iteratively reweighted least squares 

 procedure used to fit L . /?, and /,, subject to /• linear con- 

 straints. 



The likelihood ratio test statistic, as described by Cer- 

 rato ( 1990), for two data sets with sample sizes n , and n., 

 is given by 



-21og(A), 



/ . 

 where .\ = 





Under the null hypothesis -2 log(A) converges to a X"''"' 

 distribution with the degrees of freedom equal to the 

 number of equations required to specify the linear con- 

 straints applied to the model (Kimura, 1980). The null 

 hypothesis is rejected at the a level of significance when 

 -21og(A) > x^(r). 



The types of linear constraints applied to the von Ber- 

 talanffy growth equation, the null and alternative hypoth- 

 eses associated with each constraint and the degrees of 

 freedom of the test statistic are given in Table 1. 



Results 



Validation of annual deposition of opaque zones 

 in otoliths 



The mean monthly margmal increment on sectioned oto- 

 liths with one opaque zone declined sharply from 0.57 in 

 September and October 1993 to 0.11 in November 1993, 

 before gradually rising to a maximum of 0.93 in October 

 1994 (Fig. 2 1. As in 1993, the mean marginal increment 

 then declined markedly between October and November 

 1994 and subsequently rose over the ensuing months. The 

 trends exhibited by the mean monthly marginal incre- 

 ment on otoliths with two and three opaque zones were 

 the same as those just described for otoliths with one 

 opaque zone (Fig. 2). Because the number of fish with 

 otoliths displaying four or more opaque zones in the sam- 

 ples for some months was small, the marginal increments 

 for all such otoliths in each month were pooled. Although 

 the trends shown by the mean monthly marginal incre- 

 ments on these otoliths were not quite as "smooth" as 

 those shown by otoliths with one to three opaque zones, 

 they still clearly declined precipitously in November of 

 both 1993 and 1994 and subsequently rose progressively 

 during the ensuing months between early summer and 

 mid-autumn iFig. 2). 



The fact that, irrespective of the number of opaque zones 

 on otoliths, the mean monthly marginal increments on 

 otoliths underwent a pronounced decline and then a pro- 

 gressive rise only once during the year demonstrates that 

 a single opaque zone is formed in otoliths each year Thus, 

 the number of opaque zones in sectioned otoliths can be 

 used to determine the age of A. butcheri. 



