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Fishery Bulletin 103(4) 



that evidence from more than one source is required be- 

 fore conclusions can be drawn about differences between 

 models designed to describe nonlinear processes such as 

 growth. In the present study, bootstrapping techniques 

 proved to be informative as a way of visualizing the 

 behavior of the models used, and the distributions and 

 correlations of parameter estimates that could not be 

 determined readily from model likelihoods alone. They 

 also provided a basis for estimating nonparametrically 

 with randomization tests the differences, and CIs, of 

 growth estimators between populations. Hence we rec- 

 ommend bootstrapping, plots of parameter estimates, 

 and randomization tests to complement the "traditional" 

 statistical tests such as the LRTs. 



The standard VBGF has been criticized for the dif- 

 ficulty it causes in extracting biological meaning from 

 parameters (Knight, 1968; Roff, 1980; Francis, 1988b; 

 1992). The problem is particularly acute where only a 

 part of the size or age range (or both ranges) of animals 

 is available — a situation regularly faced in analyses of 

 fisheries data (Haddon, 2001). Data sets in our study 

 were limited, particularly by the lack of fish in the 

 lower age classes (cf. Ewing et al., 2003). Hence, any 

 attempt to interpret or compare l a or t as descrip- 

 tors of the growth of N. fucicola would be spurious. 

 Furthermore, because k and l x are highly correlated, 

 comparisons of k cannot be independent of the effects 

 of size or age selectivity on a data set. Because of the 

 limitations of such parameters, and as l a and k are 

 often inputs into population dynamics models and em- 

 pirical models estimating parameters such as natural 

 mortality (e.g., Pauly, 1979), extreme caution should be 

 exercised when extrapolating these values from limited 

 data. However, this instance exemplifies the utility of 

 the reparameterization, because even with limited data, 

 the useful parameters of mean lengths at age can be 

 estimated and compared. 



Variability in growth 



Models of growth can be used to estimate length-depen- 

 dent processes in fish populations, such as reproductive 

 output, increases in biomass due to individual growth, 

 selectivity of fishing gear, and the impact and appropri- 

 ateness of size limits as management tools. The results 

 of the present study demonstrate that growth varies 

 significantly across individuals, seasons, sexes, and 

 sites in N. fucicola. 



Although the significance of estimating the variabil- 

 ity in growth around the population mean (v) was not 

 explicitly tested during model parameterization, values 

 of v around 0.2 to 0.7 were estimated for all data sets 

 modeled. Values in this range have been estimated with 

 GROTAG from other species of bony fishes (Francis, 

 1988a; b; 1988c; 1992; Francis, et al., 1999) and car- 

 tilaginous fishes (Francis and Francis, 1992; Francis, 

 1997; Francis and Mulligan, 1998; Simpendorfer, 2000; 

 Simpendorfer, et al., 2000), indicating that considerable 

 individual variability in annual growth of size classes is 

 common. The extent of variability in individual growth 



is an important factor when quantifying growth be- 

 cause it may obscure other sources of growth variation, 

 particularly in situations where data are limited. This 

 effect may partially explain why age-based models failed 

 to detect any significant effect of sex on growth rates in 

 our study, whereas length-based modeling indicated that 

 among smaller size classes, females grew faster than 

 males at Lord's Bluff. On the basis of a large data set 

 (>1000 individuals), Ewing et al. (2003) demonstrated 

 that average length-at-age was significantly higher for 

 females than males in N. fucicola although the magni- 

 tude of this difference was small. No growth differences 

 between the sexes were evident at Point Bailey but 

 given slower growth rates, the absolute magnitude of 

 any expected growth differences related to sex would be 

 relatively small and difficult to detect statistically. 



Our study is the first to show that growth rates of N. 

 fucicola vary significantly across small spatial scales; 

 the two sites in our study were separated by less than 

 25 km. At Point Bailey, few individuals reach the mini- 

 mum legal size limit of 30 cm until 10 years of age, 

 whereas at Lord's Bluff they do so at least two years 

 earlier (Fig. 1). An equivalent conclusion is evident 

 from the GROTAG estimates, indicating that a 28-cm 

 fish at Point Bailey will take nearly 2 years on aver- 

 age to exceed 30 cm, whereas fish of the same size are 

 likely to reach legal size in just over a year at Lord's 

 Bluff. Hence relative yields and rates of replacement 

 of recruited size and age classes are likely to be lower 

 at Point Bailey than at Lord's Bluff. However, because 

 N. fucicola can be sexually mature at lengths of 12 cm 

 (Patterson, 2000), some individuals are likely to have 

 spawned for 6-8 years before recruitment to the fishery 

 at Lord's Bluff (Fig. 1). This size at maturity suggests 

 that the minimum legal size limit provides effective 

 protection of the reproductive output of the prerecruit 

 population of TV. fucicola at both sites. 



Using length-at-age estimated from whole otoliths, 

 Barrett (1999) found no growth differences between sev- 

 eral populations of N. fucicola in southeastern Tasmania 

 and used these findings to support the hypothesis that 

 populations are not resource limited. Our study did not 

 specifically address any hypothesis about resource limi- 

 tation but has clearly demonstrated that growth rates 

 can vary between populations at the scale of individual 

 reefs. Notolabrus fucicola are site-attached once they 

 settle out of the plankton, rarely having an ambit of 

 more than 500 m on contiguous reef, and rarely cross- 

 ing soft bottom habitat if they are resident on smaller 

 patch reef habitat (Barrett, 1995b). Intuitively, it fol- 

 lows that if productivity varies between reefs, then the 

 potential for growth of individual site-attached reef fish 

 may be limited. A variety of factors have been cited in 

 other temperate reef species where spatial variability in 

 length-at-age is evident, such as habitat type (Gilland- 

 ers, 1997; Barrett, 1999), conspecific competition and 

 variation in juvenile recruitment (Jones, 1980, 1984), 

 and impacts of exploitation (Buxton, 1993). Further 

 study is advocated to determine the factors that influ- 

 ence N. fucicola growth at this scale. 



