Fishery Bulletin 97(4), 1999 



butions sampled at different times to estimate the 

 number of cohorts in the population, the growth pa- 

 rameters (asymptotic length [L^J and growth coeffi- 

 cient [K] of the von Bertalanffy growth equation), 

 the age of the first cohort (assuming that the VB 

 curve passes through the origin) and the proportions 

 at age. The simplest model assumes that mean 

 lengths-at-age lie on the VB gi-owth curve and that 

 the standard deviations of length-at-age are identi- 

 caj for all cohorts. More complex models were also 

 tested that allowed 1) sampling bias for the first co- 

 hort, 2) age-dependent standard deviation in length- 

 at-age, and 3) seasonally oscillating growth to be 

 added as additional parameters in the model. The 

 more complex models incorporated all possible com- 

 binations of these parameters and used likelihood 

 ratio tests to identify the model of best fit. The sig- 

 nificance of improvement of fit within models by add- 

 ing year classes was tested for significance at the 

 0.10 level ( see Fournier et al., 1990 ), and significance 

 of improvement of fit between models by adding ex- 

 tra parameters was tested at the 0.05 level. 



The seasonal form of the von Bertalanffy equation 

 for the length-frequency data is 



1-p 



|(j-ll+l/„/12)+/'(/j] 



l^ja =w,+(;n,v-'"i> ^_ ,,v 1. 



where f(t„) = —^sin 

 " 2k 



12 



/j^^ = the mean length of fish of thej'" age 

 class in thea"^ length-frequency data 

 set; 



Wj = the mean length of the first age class; 



nij^. = the mean length of the last age class; 



p = the Brody growth coefficient; 



t^ = the number of months after the pre- 

 sumed birth month of the fish in the 

 a'*' length-frequency data set; 



A^ = thenumber of age classes present; and 



(pj and 02 describe the amplitude and phase 



of the seasonal component, respectively 



(Fournier et al., 1990, 1991; Francis and 



Francis, 1992). 



Comparisons of rates of growth from 

 calcified structures and from tagging 

 and length-frequency data 



Rates of gi-owth were estimated from aging struc- 

 tures and from length-frequency (both age-based) and 

 mark-recapture (length-based) data with methods 

 outlined in Francis (1995j. The aging error model of 



Richards et al. ( 1992) that showed the best fit to the 

 data matrix comprising two age readings from each 

 of the three aging structures was used to determine 

 a single age for each fish. Schnute's growth curve 

 (case 2) was then fitted to the age-size data and this 

 mean age-size relationship was used as a basis with 

 which to compare the estimates of growth from the dif- 

 ferent data sets. The annual growth for the age-size 

 data and length-frequency data was calculated as the 

 mean size at age .v minus the mean size-at-age (.v+1; 

 Francis, 1995 ). Annual growth at corresponding points 

 on the size-based line was then estimated at the size 

 the fish was at age x, as determined from the fit to the 

 mark-recapture data obtained by using GROTAG. 



Results 



Structures for aging Seriola lalandi were collected 

 from a total of 572 fish ranging in size from 323 to 

 1090 mm FL, although not all structures were col- 

 lected from all fish. Although S. lalandi is reported to 

 reach a total length of almost 2000 mm ( 1700 mm FL) 

 and a weight of 60 kg, fish of this size ai-e rare. In New 

 South Wales, few fish over 20 kg ( about 1200 mm FL ) 

 are caught by commercial fishermen and the largest 

 fish recorded in surveys of amateur fishermen has 

 been 1140 mm FL (Steffe et al.-). We were unable to 

 obtain fish larger than 1100 mm FL. 



All structures showed zones that could be inter- 

 preted as annuli (Fig. 1); however, zones were not 

 interpretable in all fish. Growth zones in whole 

 otoliths were more easily interpretable than those 

 in sectioned otoliths (Fig. 2); the latter showed nu- 

 merous striations that could rarely be interpreted. 

 Zones in sectioned otoliths were, however, clearer in 

 some larger fish (Fig. 2). A large number of scales 

 had to be collected because preliminary results 

 showed that two-thirds offish had at least some re- 

 generated scales. Vertebrae did not always stain well 

 and showed pronounced ridges which reduced read- 

 ability in many fish. 



Validation of aging methods 



Analysis of marginal increments showed different 

 patterns among stiaictures (Table 2). Otoliths and 

 scales revealed that one zone was laid down per year, 

 in August-September ( otoliths ) and between Decem- 



- Steffe, A.. J. Murphy, D. Chapman, B. E. TarHngton, G. N. G. 

 Gordon, and A. Grinberg. 1996. An assessment of the im- 

 pact of offshore recreational fishing in New South Wales on the 

 management of commercial fisheries. F'inal Report to 

 Fisherires Research Development Corporation, PO Box 222. 

 Deakin West ACT 2600, Australia. 



