338 
Abstract— A learning curve analysis 
is applied to model the change in effort 
units with time by the commercial fish- 
ery for Atlantic cod (Gadus morhua ) in 
the Barents Sea. The results indicate 
that fishing efficiency has increased and 
that the adjusted commercial catch per 
unit of effort (CPUE) is more strongly 
related with stock abundance. 
Manuscript accepted 1 1 October 2000. 
Fish. Bull. 99:338-342 (2001). 
Adjustment of commercial trawling effort 
for Atlantic cod, Gadus morhua, due to 
increasing catching efficiency 
Are Salthaug 
Institute of Marine Research 
Nordnesgaten 50 
PO Box 1870 
N-5817 Bergen 
Norway 
E-mail address: ares@imr.no 
Fishing fleets and individual fishing 
vessels are expected to increase their 
efficiency with time owing to techno- 
logical improvements. This is a ser- 
ious problem when a time series of com- 
mercial catch per unit effort (CPUE) is 
used to measure trends in fish stock 
abundance ( Gulland, 1983 ). A standard 
effort unit will gradually remove a 
greater proportion of the stock, and the 
CPUE corresponding to a given fish stock 
abundance will increase. Commercial 
effort units should, therefore, be adjusted 
to account for gradual changes in catch- 
ability (Gulland, 1983). 
A learning curve describes how unit 
costs decline as organizations gain 
experience in production (Argot and 
Epple, 1990). The general form of the 
learning curve is given by 
y = ax~ b , ( 1 ) 
where y = the number of direct labor 
hours required to produce 
the xth unit; 
a = the number of labor hours 
required to produce the first 
unit; 
x = the cumulative number of 
units produced; and 
b = the parameter measuring 
the rate at which labor 
hours are reduced as cumu- 
lative output increases (Ar- 
got and Epple, 1990). 
If a learning curve is used to describe a 
fishery, the labor hours required to pro- 
duce the xth unit can be translated into 
the effort required to catch a certain 
fraction of the fish stock, termed effort 
per stock fraction ( epsf ). Time, instead 
of cumulative catch, is assumed to be 
a better measure of x because fisher- 
men learn even if stock abundance and 
catches are low. In this study, appro- 
priate learning curves are fitted to the 
decrease in epsf with time for vessels 
in the Norwegian bottom trawler fleet 
in the fishery for Atlantic cod ( Gadus 
morhua). Effort is then adjusted by 
using the fitted learning curve, to gen- 
erate CPUE-indices that better reflect 
fish stock abundance. 
Materials and methods 
To calculate the effort per stock fraction 
( epsf) for a given vessel, effort is divided 
by the ratio of catch and fishable stock 
biomass (stock fraction caught) in a 
given time period: 
where B ? = the estimated weight of 
fishable biomass; and 
e = the total effort and c is the 
total catch (weight) during 
the time period. 
The catch and effort data should be 
independent from the estimate of B f . 
Some catch composition criteria should 
also be introduced to increase the prob- 
ability that the vessels were part of 
the targeted fishery during the period. 
Note that epsf is the inverse of catch- 
ability. 
By inserting epsf for y and time (t) for 
x in Equation 1, then 
