342 
Fishery Bulletin 99(2) 
est fish (owing to lack of survey data for old fish). Total 
catch data from the fleet were also used in the VPA proce- 
dure. Converged VPA were, however, fairly independent of 
CPUE, and the limited dependence was not considered to 
have a large effect on the learning curve estimation. 
It seems reasonable, as seen from the plots in Figure 
1, to assume that epsf followed a learning curve pattern 
with time. The outliers around 1980 affected the regres- 
sion lines in Figure 1 (B and D) considerably. If these out- 
liers were caused by the fishermens’ response to the new 
regulations, they should perhaps be removed. Another so- 
lution is to develop learning curve models that account for 
such strong interventions. 
The sudden change in the relation between CPUE and 
VPA estimates in Figure 2 may have been caused by the 
introduction of fishery regulations, but there are other im- 
portant factors affecting the use of CPUE as an index 
of abundance. Some of these factors are similar to those 
mentioned above, under the discussion of the assumptions 
concerning the estimation of epsf. Another explanation for 
the sudden change of the ratio between CPUE and bio- 
mass estimates from VPA in Figure 2B and for the outliers 
in Figure 1 around 1980 is that CPUE and epsf (or equiva- 
lently the catchability) are functions of stock abundance. 
An increase in catchability at low stock size is suggested 
in Figure 2 by the relatively high catch rates (given the 
low biomass) in the early to mid 1980s. This increase may, 
however, be contradicted by the similar trend in biomass 
and adjusted CPUE in Figure 2B at the end of the time pe- 
riod, when stock abundance became relatively low again. 
If catchability is shown to be density dependent for Atlan- 
tic cod in the Barents Sea, it should be incorporated into 
the model when the learning curve is fitted. Both long- 
term changes (e.g. Gordoa and Hightower, 1991; Swain 
et ah, 1994) and density-dependent changes (Crecco and 
Overholtz, 1990; Rose and Kulka, 1999) in catchability of 
gadoids have been indicated when commercial CPUE is 
being used as an index of abundance. 
Conclusion 
Modeling of epsf using the learning curve seems be a prom- 
ising method for solving the old and well-known problem 
of learning when time series of commercial CPUEs are 
used as indices of abundance. Care needs to be taken when 
selecting data and observations for estimation of learning 
curves, especially in multispecies fisheries. 
Acknowledgments 
I am grateful to Michael Pennington for improving the 
manuscript and to Christopher Harmon for interdisci- 
plinary help. The work received financial support from the 
Research Council of Norway. The Norwegian Directorate 
of Fisheries is thanked for providing me with data. 
Literature cited 
Argot, L., and D. Epple. 
1990. Learning curves in manufacturing. Science (Wash., 
D.C.) 247:920-924. 
Casella, G., and R. L. Berger. 
1990. Statistical inference. Duxbury Press, Belmont, CA. 
650 p. 
Crecco, V., and W. J. Overholtz. 
1990. Causes of density-dependent catchability for Georges 
Bank haddock Melanogrammus aeglefinus. Can. J. Fish. 
Aquat. Sci. 47:385-394. 
Gavaris, S. 
1980. Use of a multiplicative model to estimate catch rate 
and effort from commercial data. Can. J. Fish. Aquat. Sci. 
37:2272-2275. 
Gordoa, A., and J. E. Hightower. 
1991. Changes in catchability in a bottom-trawl fishery for 
Cape hake (Merluccius capensis ). Can. J. Fish. Aquat. Sci. 
48:1887-1895. 
Gulland, J. A. 
1983. Fish stock assessment: a manual of basic methods. 
John Wiley and Sons, New York, NY, 223 p. 
Hilborn, R., and C. J. Walters. 
1992. Quantitative fisheries stock assessment. Chapman 
and Hall, New York, NY, 570 p. 
Ketchen, K. S. 
1964. Measures of abundance from fisheries for more than 
one species. Rapp. P-V. Reun. Cons. Int. Explor. Mer 155: 
113-116. 
Rose, G. A., and D. W. Kulka. 
1999. Hyperaggregation of fish and fisheries: how catch- per- 
unit-effort increased as the northern cod iGadus morhua) 
declined. Can. J. Fish. Aquat. Sci. 56(suppl. 11:118-127. 
Swain, D. P, G. A. Nielsen , A. F. Sinclair, and G. A. Chouinard. 
1994. Changes in catchability of Atlantic cod ( Gadus mor- 
hua) to an otter trawl fishery and research survey in the 
southern Gulf of St Lawrence. ICES J. Mar. Sci. 51:493- 
504. 
Ulltang, 0. 
1977. Sources of errors in and limitations of virtual pop- 
ulation analysis (cohort analysis). J. Cons. int. Explor. 
Mer 37:249-260. 
