Glllanders et al,: Aging methods for Senola lalandt 



parameter model (a, b, Vj, andvo. case 1) were then 

 fitted to the data (Table 1). To determine whether 

 the addition of extra parameters resulted in a sig- 

 nificantly better fit, significance tests based on the 

 F-distribution were used (Schnute, 1981 ). Where the 

 same number of parameters were present in the 

 models (e.g. comparison of the two models with three 

 parameters ), the model with the lowest residual sums 

 of squares was selected as the best fit. 



Estimation of rates of growth from tagging data 



Senola lalandi tagged as part of the NSW Fisheries 

 Gamefish Tagging program (Pepperell, 1985, 1990) 

 were used to estimate growth. A major limitation of 

 these data were that measurement methods were not 

 standard and some measurements appeared spuri- 

 ous. Although most anglers measured total length, 

 some measured fork length only. Where this occurred 

 (17% offish), fork length (mm) was converted to to- 

 tal length with the equation TL (mm)=1.122 x FL + 

 9. This equation was calculated from fish obtained 

 for aging in which both fork and total lengths were 

 measured (n=570). All fish for which tagging data 

 were available (7?=816) were initially included in 

 analyses even if the data were highly improbable, as 

 with measurements indicating shrinkage between 

 100 and 350 mm (Fig. 3A). 



Growth estimates were obtained from the tagging 

 data by using the maximum-likelihood method and 

 the computer program GROTAG (Francis. 1988b). 

 The growth model fitted was Francis's ( 1995) mark- 

 recapture analog of Schnute's (1981) size-at-age 

 model (Table 1). This model provides estimates of^j 

 and ^2' the mean annual growth offish of lengths Vj 

 and ^2 respectively, where Vj and yg ^re chosen to 

 span the range of lengths at tagging. A simple three- 

 parameter model was initially fitted and then addi- 

 tional parameters (growth variability, seasonal 

 growth variation, measurement error, and curvature 

 in the model) were added in a stepwise manner by 

 selecting the parameter that gave the greatest in- 

 crease in log likelihood. At each step, likelihood ra- 

 tio tests were used to determine whether addition of 

 parameters resulted in significantly better fits 

 (Francis, 1988b). Better estimates of the growth pa- 

 rameters can be obtained if measurement error is 

 known (Francis, 1995). There was no way of estimat- 

 ing measurement error without using the current 

 data set; therefore, measurement error was not fixed 

 and this may have compromised estimates of growth. 

 After fitting of the growth model, plots of residuals 

 against length at tagging, time at liberty and ex- 

 pected growth increment were examined for any pos- 

 sible lack of fit of the model. 



300 



200 



100 - 



i» 



^^ffxTi-. i I .rdJJ-n-M-t-L 



" I ' 



J3 



E 



0.5 1 



200 r 



150 



100 



50 



1.5 2 2.5 3 3.5 4 4.5 

 Time at liberty (years) 



irn-i-i-t^-j 



200 400 600 800 1,000 1,200 



Total length at tagging (50 mm intervals) 



Figure 3 



Distribution of (A) differences in length between tagging 

 and recapture, (B) time at liberty and (C) length-at-tag- 

 ging for kingfish (?!=816). Fish recaptured within 30 days 

 are also indicated in A with shading (n=384). Time at lib- 

 erty (Bl includes a small number of fish recaptured the 

 same day that they were tagged (time at liberty=Ol. 



Estimation of rates of growth from length- 

 frequency data 



Length-frequency data were obtained from fish sold 

 at the Sydney Fish Markets between November 1985 

 and December 1989, prior to the introduction of a 

 size limit of 600 mm TL in February 1990. Data were 

 collected haphazardly amongst months and at locations 

 ranging from 30°S to 37°S. Fork length of fish was 

 measured to the nearest 10 mm and the sampling date 

 and fishing area were recorded. Measurements of ap- 

 proximately 16,000 fish were made, enabling stratifi- 

 cation of samples by month but not by year or area. 



The von Bertalanffy (VB) model was fitted to the 

 time series of 12 monthly length-frequency distribu- 

 tions by using MULTIFAN software (Fournier et al., 

 1990, 1991). Likelihood-based methods were used to 

 simultaneously analyze the length-frequency distri- 



