44 
Fishery Bulletin 95( 1 ), 1997 
each of the scattergrams. Although the scattergrams 
involve transformations to reflect the error more ac- 
curately, the correlations themselves are based on 
the untransformed data. 
Results 
The estimates of catch at age from each of the meth- 
ods were highly correlated with the true values (Fig. 
6). But the error in catch at age was clearly highest 
for the ages assigned with the growth model (Fig. 
6A). Catch at age from the age-length key was con- 
siderably better than that from the growth model, 
particularly for the younger more abundant ages in 
the catch (Fig. 6B). The younger ages in these fig- 
ures tend to be to the right side of the scattergrams 
and the older, less abundant ages are on the left. 
The probabilistic method, given prior knowledge 
of fishing mortality and recruitment, provided the 
best result, with very little difference between true 
and estimated age compositions except at the oldest 
ages (Fig. 6C). The bias in the estimates obtained 
with this method with only natural mortality is evi- 
dent in Figure 6D, but even so, the estimates for the 
youngest ages are better than the estimates from the 
growth model. The bias was reduced by the fifth it- 
eration (Fig. 6E) and almost completely removed by 
the tenth iteration (Fig. 6F). 
The estimates of number at age derived from each 
set of catch at age by using an age-sequenced analy- 
sis are presented in Figure 7. Again the results were 
least favorable for the catch-at-age matrix developed 
from the growth model (Fig. 7 A), followed by the age- 
length key (Fig. 7B) and the probabilistic method 
(Fig. 7C). The bias in estimated number at age from 
the probabilistic method, where fishing mortality is 
not used, is even more pronounced than it was for 
the catch-at-age matrix (Figs. 5D and 6D). However, 
the bias was reduced by the fifth iteration by using 
the fishing mortality rates derived from prior itera- 
tions and almost completely removed by the tenth 
iteration (Fig. 7, E-F). The similarity of r 2 values for 
the correlations between observed and predicted val- 
ues for the age-length key and probabilistic methods 
in Figures 6 and 7 are somewhat misleading because 
of the very large dynamic range of the numbers and 
corresponding catches at age used in the analysis. 
In actuality, the precision of the estimates arising 
from applicaton of the age-length key was much lower 
than that for the probabilistic method for age classes 
that were infrequent in the catch. 
The estimates of fishing mortality at age, derived 
from each set of catch at age by using age-sequenced 
2 0- 
A 
B 
1 0- 
CD 
CD 
- - - - - - 
- - A~vr —v- • • - 
-1.0- 
-2.0- 
r 2 = 0.845 
r 2 = 0.994 
2.0- 
c 
■ 1) 
1.0- 
o.o- 
_ _^r. _ . 
' ~ “ 
-1.0- 
-2.0- 
r 2 = 0.997 
r 2 = 0.992 
2.0- 
E 
F 
1.0- 
00- 
- 
- 
-1.0- 
-2.0- 
r 2 = 0.996 
r 2 = 0.996 
2 3 4 5 6 
2 3 4 5 6 
Log (true catch at age) 
Figure 6 
Ratios of estimated to true catch at age from the growth 
model (A), age-length key (B), and from the probabilistic 
method with knowledge of prior survival (C), and probabi- 
listic iterations 1, 5 and 10 (D-F). 
Log (true number at age) 
Figure 7 
Ratios of estimated to true number at age from analysis 
of catch at age from the growth model (A), age-length key 
(B) , probabilistic method with knowledge of prior survival 
(C) , and probabilistic iterations 1, 5 and 10 (D-F). 
