Goodyear: Fish age from length: an evaluation of three methods 
45 
analysis, are presented in Figure 8 for ages up to 10. 
Again, the results were least favorable for the catch- 
at-age matrix developed from the growth model (Fig. 
8A), followed by the age-length key (Fig. 8B), and 
the probabilistic method (Fig. 80. The upward bias 
in estimated number at age from the probabilistic 
method in the absence of fishing mortality in Figure 
7D led to an underestimate of fishing mortality of 
Figure 8D. However, the bias was reduced by the fifth 
iteration and almost completely removed by the tenth 
iteration (Fig. 8, E-F). 
The relatively higher error in the catch at age for 
older ages estimated by using the growth model and 
age-length key (Fig. 6, A-B) led to relatively higher 
error in the estimates of numbers at age from their 
analysis. This resulted in poor estimation of fishing 
mortality for the oldest ages in the simulated catch 
which caused the correlation between true and esti- 
mated fishing mortalities to decline when fish older 
than 10 years were included in the analysis (Fig. 9, 
A-B). The results from the probabilistic approach 
also showed a similar trend but were much less sen- 
sitive than those for the other two methods (Fig. 9, 
D-F). 
Discussion 
These results indicate that for the situation evalu- 
ated here the probabilistic method is superior to age 
assignment from either a growth model or an age- 
length key. Factors leading to this conclusion include 
knowledge of the actual history of year-class 
strengths and perfect knowledge of growth, natural 
mortality, and the distribution of size at age. Imper- 
fect knowledge of any of these elements would de- 
grade the performance of the probabilistic method. 
If there are sufficient data to develop a growth curve 
then it should be possible to characterize the distri- 
bution of size at age, at least for the more abundant 
ages in the population. Poor knowledge of the growth 
curve itself would also adversely affect the estimates 
obtained directly from the growth curve. 
The results from the age-length key would be un- 
affected by poor knowledge of growth, past recruit- 
ment, and natural mortality. However, the compari- 
sons among methods in the current analysis assumed 
no error in age assignments for the age-length key. 
Experience suggests that there is uncertainty in age 
assignment from hard-part analysis, an uncertainty 
that increases with fish age (Beamish and Fournier, 
1981). Including such error would have added to the 
difference between the results of this method and 
those obtained with the probabilistic method. None- 
theless, the construction and application of age- 
A 
B 
^ • 
c 
D 
- 
E 
F 
- 
0 O- 1 ■ ■ ' ' 1 r- 1 , , , . T r- 
3 8 13 18 23 28 3 8 13 18 23 28 
Oldest age in analysis (yr) 
Figure 9 
Precision of fishing mortality estimates ( r 2 from correlations 
of true and estimated rates) 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). 
