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Fishery Bulletin 103(4) 



A Kolmogorov-Smirnov test was conducted to deter- 

 mine whether differences existed in the proportional 

 frequency distributions of lengths of fish at first capture 

 (Lj) between sites and between sexes within sites. 



Growth was modeled by using GROTAG (Eqs. 2 and 4 

 in Francis [1988a]), a reparameterization and extension 

 of the Fabens growth model for tag-recapture data that 

 incorporates seasonal growth: 



Table 2 



Parameters estimated in the five GROTAG models fitted 

 to each tag-recapture data set to evaluate optimal model 

 parameterization. 



GROTAG model 



Parameters estimated 



g a >gp v >P 



g a ,gp> v,p,u,w 

 g a .g lS ,v.p.s,m 



ga'gp v - u < "'• s ' '" 



g a ,gp, v,p, u. w,s,m 



ing no seasonal growth through to u=l indicating the 

 maximum seasonal growth effect, i.e., where growth 

 effectively ceases at some point each year). 



The model was fitted by minimizing negative log-like- 

 lihood (-A) function (Eq. 9 in Francis [1988a]). For each 

 data set, made up of i : = 1 to n growth increments: 



A = X,ln[(l-p)A,+p/i?], 



where A, =exp 



-^(AL,-^, -m) 2 /(CT, 2 + s 2 ) 

 [2^(cr, 2 + s 2 )J i 



(7) 



(8) 



The measured growth increment of the ;' th fish, AL ; , 

 has its corresponding expected mean growth increment, 

 H r as determined from Equation 5 above, where ,i( ; is 

 normally distributed with standard deviation o r In this 

 study, a, was assumed to be a function of the expected 

 growth increment j.i t (Eq. 5, Francis, 1988a): 



m- 



(9) 



AL- 



Pga-agp 

 S a -gp 



a-p ) 



AT-Ht 



sin\27r(T-w)] „ 



where 0, = u — - fori = 1,2. 



2/r 



(5) 



(6) 



The parameters g u and g. t are the estimated mean an- 

 nual growth (cm/yr) of fish of initial lengths a cm and 

 P cm, respectively, where a<p. The reference lengths a 

 and p were chosen such that the majority of values of L 1 

 in each data set fell between them (Francis, 1988a). For 

 site-specific estimates of growth, a and p were set at 20 

 and 30 cm, respectively, whereas p was set at 28 cm for 

 sex-specific models. Seasonal growth is parameterized 

 as w (the portion of the year in relation to 1 January 

 when growth is at its maximum) and u (u = indicat- 



where v is estimated as a scaling factor of individual 

 growth variability, assuming a monotonic increase in 

 variability around the mean growth increment as the 

 size of the increment increases. 



In its fully parameterized form, the likelihood func- 

 tion estimates the population measurement error in AL 

 as being normally distributed, and having a mean of m 

 and standard deviation of s. To estimate the proportion 

 of outliers, Francis (1988a) also included p, the prob- 

 ability that the growth increment for any individual 

 could exist erroneously in the data set as any value, 

 within the observed range of growth increments R. 

 This enables the proportion of outliers to be identified. 

 Francis (1988a) suggested that an estimate of p>0.05 

 indicates a high level of outliers and therefore some 

 caution would be required in interpreting the overall 

 model fit. 



The optimal model parameterization was determined 

 by fitting five different models, comprising different 



