Welsford and Lyle: Estimates of growth of Notolabrus fuacola from length- and age-based models 



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combinations of parameters (Table 2), with unfitted 

 parameters held at zero. A LRT was used to deter- 

 mine the improvement in model fit with the different 

 parameterizations (Francis, 1988a). For models with 

 an equal number of parameters, the model producing 

 the lowest negative log likelihood (-A) was considered 

 the best fit. 



As with the otolith models, LRTs were conducted 

 on the GROTAG models to compare between sites and 

 sexes, and models were also bootstrapped 5000 times. 

 First-order corrected 959c CIs were calculated for pa- 

 rameter estimates (Haddon, 2001), and pairwise com- 

 parisons of growth parameters, by using CIs and ran- 

 domization tests, as described above for otolith-based 

 models. 



Results 



Otolith interpretation 



Kolmogorov-Smirnov tests showed no significant dif- 

 ference in age-frequency distributions generated by 

 repeat readings of 55 otoliths by the primary reader 

 (Z) 005 =0.259, D max =0.072, not significant) or between 

 readers (D 05 =0.259, Z) max =0.109, not significant). The 

 IAPE score for all three readings was calculated as 6.9%, 

 and no systematic under- or over-estimation of ages was 

 apparent in age bias plots within or between readers. 

 Therefore age estimates derived from the first readings 

 by the primary author were used for modeling. 



Age-based growth modeling 



Site comparisons No significant differences in length 

 frequencies were detected in a Kolmogorov-Smirnov test 

 between sites (D 005 =0.169, -D max =0.097, not significant). 



Length-at-age estimates showed high variability 

 among individuals, as evidenced by the spread of data 

 points around the fitted models (Fig. 1), and estimates 

 of a ranged from 1.16 to 2.17 cm across all models 

 (Table 3). However, mean lengths-at-age were adequate- 

 ly described by the VBGF across the ages represented 

 by the samples from the two sites. The plots of the 

 site-specific VBGFs indicated that mean length-at-age 

 at Lord's Bluff was higher than at Point Bailey. 



Because of the absence of young (0+ and 1+) fish in 

 the samples from both sites, and fish >14+ at Lord's 

 Bluff, the standard VBGF parameters were difficult 

 to interpret biologically. Confidence intervals for the 

 three standard VBGF parameters largely overlapped 

 in comparisons between sites (Table 3). Plots of the 

 bootstrap parameter estimates showed strong nonlinear 

 correlations, particularly between l a and k, revealing 

 minimal overlap between sites, most easily visualized 

 with logarithmic axes (Fig. 2A). Nonlinear correla- 

 tion between parameter estimates and minimal over- 

 lap between sites were also true to a lesser extent in 

 estimates of l x versus t (Fig. 2B). LRTs showed that 

 differences between sites were highly significant overall 



but could not be attributed to significant differences in 

 individual parameters (Table 4). 



Confidence intervals for the Francis (1988b) repa- 

 rameterized version of the VBGF clearly indicated sig- 

 nificant differences in growth rates between sites in all 

 three parameters, and no overlap between sites in the 

 CIs of the estimates of mean length at 4, 7, or 10 years 

 old (Table 3). These differences were also evident in plots 

 of bootstrap parameter estimates, the two sites being 

 clearly separated in the parameter space, and showed 

 none of the high nonlinear correlations evident in the 

 standard VGBF estimates (Fig. 3B). Randomization tests 

 produced CIs of the difference between sites of 1.16-2.67, 

 2.48-3.50, and 2.82-4.44 cm for Z 4 , / 7 , and l 10 , respec- 

 tively. Highly significant differences in all individual 

 parameters growth parameters in the reparameterized 

 model were also shown in LRTs between sites, but no 

 significant difference in o was detected (Table 4). 



Sex comparisons Confidence intervals for the standard 

 and reparameterized von Bertalanffy parameters sig- 

 nificantly overlapped in all comparisons between sexes 

 (Table 3). Likelihood ratio tests showed no significant 

 differences between models of sexes within sites — a 

 conclusion supported by considerable overlap in plots of 

 bootstrap estimates (not shown). 



Length-based growth modeling 



Model parameterization Site-specific data sets were 

 optimally parameterized under the most complex model, 



