Salthaug: Adjustment of commercial effort for Gadus morhua 
339 
\n(epsf) = ln(a) - b • ln(f). (3) 
By fitting a regression line to In (epsf) versus In (t), esti- 
mates of the parameters ln(al and b in the learning curve 
are obtained. An unbiased estimator for a is exp(ln(a)+ 
MSE/2) (Casella and Berger, 1990), where ln(a) is the 
intercept of the regression line and MSE is the mean 
squared error from the regression. A learning curve can 
be estimated at the fleet level by using average epsf of 
the vessels, and at the vessel level by using an individual 
vessel’s epsf. These two approaches are somewhat differ- 
ent because the efficiency of a fleet is increased both by 
improvement of existing vessels and by addition of new 
and better vessels. 
The effort units in a time series of CPUE can be adjust- 
ed to the level of one of the elements (index time) in the 
time series as follows: 
e P s f \ (4 ) 
epsf, ) 
where ef = the adjusted effort at time z; 
and 
epsf index = the effort per stock fraction modelled 
and epsf t with the estimated learning curve at the index 
time and time i, respectively. 
Note that the learning curve model is a continous 
function and CPUE is normally given as a discrete time 
series. Time i should, therefore, correspond to the mid- 
point of the time interval over which the corresponding 
CPUE observation is calculated. 
The catch and effort data were taken from a logbook 
database collected by the Norwegian Directorate of Fish- 
eries. Logbooks from the Norwegian bottom trawler fleet 
have been recorded since 1971 and each individual record 
includes vessel, species, date, and summarized duration 
(in hours) and summarized catch (in kilograms) of the 
trawl hauls each day. Estimates of trawlable biomass (Bf 
of Atlantic cod in the Barents Sea were taken from VPA 
(virtual population analysis) estimates of stock biomass 
at the beginning of each year (ICES 1 ). Only 20% of the 
3-year-old cod and 50% of the 4-year-old cod were consid- 
ered to belong in the trawlable part of the biomass because 
of mesh selection in the trawls. This selection of young cod 
corresponded broadly to the retention probabilities in the 
beginning of the year based on a trawl selection curve. The 
effort ( e ) is hours of trawling. Because the VPA estimates 
of stock size are given for the start of the year, the sum- 
mation of catch and effort for a given year (t ) are over the 
period from July in year t — 1 to June in year t. In this 
way the stock estimates from VPA are given for the mid- 
dle of the time period. Only records with more than 20%> 
1 ICES (International Council for the Exploration of the Sea). 
2000. Report of the Arctic Fisheries Working Group, Copenha- 
gen, 23. August-1. September 1999. ICES CM 2000/Assess:3, 
311 p. ICES, Palaegade 2-4 DK-1261 Copenhagen K, Denmark. 
(in weight) cod for a recorded day were used to increase 
the probability that cod was the target species. Varying 
the minimum accepted proportion of a species in catches 
lias been shown to significantly affect estimates of CPUE 
(Ketchen, 1964). To avoid vessels that did not take active 
part in the cod fishery, only vessels with at least 10 ob- 
servations where more than 50% cod were present in a 
given year were used in the calculation of the fleet’s aver- 
age epsf. Only cod records from north of 67°N were used 
because this latitude is the limit of the distributional area 
for Atlantic cod along the Norwegian coast. 
Changes in yearly epsf were analyzed and estimates of 
the parameters in the learning curve were made at the 
vessel level and at the fleet level (average epsf) in the pe- 
riod 1971-99. Only one vessel was active during the whole 
period without being rebuilt, and this vessel was chosen 
for analysis at the vessel level. 
The trawl fishery for Atlantic cod in the Barents Sea has 
existed since about 1920, but the Norwegian trawler fleet 
did not significantly participate in this fishery until after 
the end of the Second World War. Year one in the learning 
process for the Norwegian trawler fleet is therefore set at 
1946. In the present study, sufficient data for estimating 
learning curves exist only from 1971, which is a limited 
part of the time period in which the Norwegian fishery has 
existed. This causes the year 1972, the first year where it 
is possible to estimate epsf , to become year 27 in the learn- 
ing process. 
A time series of CPUE for Atlantic cod of the Barents 
Sea was calculated by using the same catch and effort da- 
ta as above, and yearly effort was adjusted (Eq. 4) to the 
level of 1972 by using the estimated learning curve on the 
fleet level. Only records containing more than 20% cod (in 
weight) were used. CPUE was set as total catch divided by 
total effort in the period from July in year t — 1 to June in 
year t. 
Results 
The estimates of annual epsf showed a decreasing trend 
with time both at the fleet level and at the vessel level 
(Fig. 1, A and C). The slope and intercept of the fitted 
regression line at the fleet level (Fig. IB) were 1.742 and 
14.272, respectively, and the correlation given as the r 2 - 
value was 0.50. At the vessel level the values of the slope 
and intercept (Fig. ID) were 1.538 and 13.334, respectively 
and r 2 was 0.55. The estimated a was 1895039.044 at the 
fleet level and 714722.761 at the vessel level. The slopes of 
the two regression lines were significantly different from 
zero (P<0.0001), but the two regression lines were not sig- 
nificantly different from each other (P>0.05) . 
The time series of annual CPUE became much more 
similar to the biomass estimate from VPA when effort was 
adjusted (Fig. 2), especially in the first and last part of the 
time period. In the middle of the period (after 1980) the 
trend in adjusted CPUE suddenly became different from 
that of biomass estimates from VPA, and CPUE values 
were much higher than biomass in relation to the ratio in 
the first and last part of the period for some years. 
