66 
Fishery Bulletin 106(1 ) 
Table 2 
Alternative annual model structures, with their parameters, for the three regional groups of collection sites. The number after 
each regional name denotes the number of free parameters fitted to the available data. For site locations see Figure 1 and Table 1. 
MaxAL is the hypothetical asymptotic maximum growth increment, L'g 0 is the initial length at which the midway point between 
the MaxAL and lowest growth increment is reached, and L'g 5 denotes the initial length at which 95% of the difference between 
the smallest and maximum increment is reached. Maxo L is the hypothetical asymptotic maximum standard deviation, L s 50 and 
L ‘ | 5 are the inverse-logistic parameters describing how the variability of residuals decreases with increasing L t , and Prod Kg is 
the relative productivity in kilograms derived from the respective transition matrix. See Equations 1 and 2. 
Model 
MaxAL, 
^”50 
J m 
U 95 
Maxa L 
L % 0 
^‘95 
Prod Kg 
Southwest 6 
20.393 
130.648 
164.824 
4.461 
163.736 
214.934 
473.5 
Southwest 5 
20.381 
130.669 
164.768 
4.396 
163.735 
210 
473.1 
Southwest 4 
20.364 
130.688 
164.551 
4.346 
T m 
U 95 
210 
472.1 
Actaeons 6 
23.922 
106.084 
144.431 
4.311 
138.679 
175.809 
308.4 
Actaeons 5 
23.889 
106.136 
144.243 
4.623 
142.934 
210 
308.6 
Actaeons 4 
23.873 
106.165 
144.152 
4.551 
T m 
U 95 
210 
308.1 
Bruny Island 6 
28.612 
119.736 
160.142 
4.267 
151.438 
160.876 
459.2 
Bruny Island 5 
28.386 
119.893 
159.105 
4.297 
173.763 
210 
453.3 
Bruny Island 4 
28.916 
119.421 
161.336 
4.603 
T m 
U 95 
210 
467.2 
Table 3 
For each model and parameter combination, the Bayesian information criterion (BIC), Akaike information criterion (AIC), nega- 
tive log-likelihood (-veLL), and total number of observations n are given. The italicized cells denote the minimum for each 
criterion and region. The columns labeled “Model 5” and “Model 4” denote the likelihood ratio test values compared to the models 
in the Model column. The comparisons in Model 5 column had one degree of freedom and for the 5-parameter model to be better 
than the 4-parameter, it had to be greater than x\ =3.84, and the comparisons in the Model 4 column had two degrees of free- 
dom and had to be greater than x% =5.99 for the models with more parameters to be significantly better than the 4-parameter 
model. 
Model 
BIC 
AIC 
-veLL 
n 
Model 5 
Model 4 
Southwest 6 
1395.1 
1373.9 
680.96 
252 
0.14 
0.18 
Southwest 5 
1389.7 
1372.1 
681.03 
252 
0.04 
Southwest 4 
1384.2 
1370.1 
681.05 
252 
Actaeons 6 
2716.3 
2690.9 
1339.5 
500 
3.6 
3.8 
Actaeons 5 
2713.7 
2692.7 
1341.3 
500 
0.2 
Actaeons 4 
2707.6 
2690.7 
1341.4 
500 
Bruny Island 6 
1747.6 
1725.5 
856.7 
295 
2.4 
4.8 
Bruny Island 5 
1744.2 
1725.8 
857.9 
295 
2.4 
Bruny Island 4 
1740.9 
1726.2 
859.1 
295 
eter model was optimal (Table 3). At the same time, 
the likelihood ratio test indicated in all cases that the 
4-parameter model was not significantly worse than any 
other model (Table 3; Fig. 3). 
The key differences that occur between the fitted 
models relate to how well they describe the trends in 
variation along the curves. The data for the southwest 
had the widest size range and the similarity of the 
fitted L| 0 parameter to the Z/§ 5 parameter was clear. 
At the same time, the L| 5 parameter was only slightly 
bigger than 210 mm (Table 2). Thus, the substitutions 
to create the 4-parameter model had little effect on the 
outcome if this model was used to predict the likely 
distribution of growth increments (Fig. 5). The main 
effect of reducing the number of parameters used was 
to slightly reduce the variation beyond about 170 mm 
initial shell length. 
The 6-parameter model has sufficient flexibility in 
that it can accurately describe both the mean growth 
trend and the pattern of variation around the expected 
mean growth increments. This was not necessarily an 
advantage when the high level of fishing mortality ap- 
plied to legal-size abalone means that the availability 
of larger size abalone in the tag return data can be 
