Standardisation of commercial CPUE

A. Salthaug*, O.R. GodùInstitute of Marine Research, PO Box 1870, Nordnes, N-5817 Bergen, Norway

Received 2 November 1999; received in revised form 20 March 2000; accepted 8 April 2000

Abstract

A model for standardisation of ®shing power for individual vessels in a commercial ®shing ¯eet is developed. Catch rates of

vessels are compared when they are ®shing close together in time and space, and their ®shing power relative to a standard

vessel is calculated. The model is applied to a logbook data base from the Norwegian bottom trawler ¯eet, and effects of

varying model parameters are explored. Relative ®shing power from the model are correlated with the vessel's length and

engine power. The model seems to be robust when varying catch composition criteria, minimum number of comparisons

required and standard vessel. # 2001 Elsevier Science B.V. All rights reserved.

Keywords: Fishing power; Effort standardisation; Commercial data; CPUE

1. Introduction

When using catch per unit effort (CPUE) from a

commercial ®shing ¯eet as an index of ®sh stock

abundance or density, the measure of one unit effort

has to be equal for different vessels (Gulland, 1983).

Individual ®shing vessels often tend to show large

differences in ®shing power, i.e. their CPUE for the

de®ned effort unit will differ when ®shing on the same

density of ®sh at the same time and place (Beverton

and Holt, 1957). The effort in CPUE observations

from different vessels should, therefore, be standar-

dised or adjusted to the same level.

Factors most likely to cause differences in ®shing

power between vessels are size, engine power, skipper,

age of vessel and differences in ®shing technology

(Gulland, 1983). Differences in vessel-generated noise

may also be important (EngaÊs et al., 1991). A vessel's

®shing power also differs for different species and for

sub-groups within the same species, and the ®shing

power may vary with season. This is so because

different groups of marine organisms have different

spatial distributions and totally different behaviour in

relation to the ®shing gear, which also may vary

seasonally (FernoÈ and Olsen, 1994). Over time, the

®shing power of vessels is expected to change due to

technological improvements (Gulland, 1983). Indivi-

dual vessels are also expected to have different plans

for making these improvements, thereby having dif-

ferent pace in enhancing ®shing power.

A realistic measure of ®shing power for commercial

®shing vessels should be obtained when the vessels

target the species of interest. In today's multi-species

®sheries, the skipper's target species often change

rapidly because of prices, quotas and catch regula-

tions. Different vessels may also target different spe-

cies within the same time period. The catch

composition may, however, be used as an indicator

of the vessel's actual target species (see, e.g., Ketchen,

Fisheries Research 49 (2001) 271±281

* Corresponding author. Tel.: �47-55-23-86-73;

fax: �47-55-23-86-87.

E-mail address: ares@imr.no (A. Salthaug).

0165-7836/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 5 - 7 8 3 6 ( 0 0 ) 0 0 2 0 4 - 6

1964), but such measures are not suf®cient for deter-

mining the skipper's intentions.

The traditional approach when standardising com-

mercial CPUE is to analyse factors that cause differ-

ences in ®shing power, model the ®shing power

according to these factors, and then adjust the effort

in individual CPUE observations according to the

model (see, e.g., Gulland, 1956; Beverton and Holt,

1957; Gavaris, 1980; Kimura, 1981; Hilborn and

Walters, 1992; Large, 1992; Kulka et al., 1996). In

this work, instead of making a model with variables

in¯uencing ®shing power, we estimate the actual

relative ®shing power of individual vessels in a ¯eet

by comparing their ef®ciency directly on the ®shing

grounds. This approach is similar to an intercalibration

approach used to compare research vessels (see, e.g.,

Wilderbuer et al., 1998). Estimates of relative ®shing

power between vessel pairs are subsequently used to

estimate each vessel's ®shing power relative to one

particular vessel termed standard vessel.

The model is applied to a commercial dataset from

the Norwegian bottom trawler ¯eet. Relative ®shing

power of individual vessels is compared with some

vessel characteristics, and the effects of varying some

important parameters in the model is explored.

2. Material and methods

2.1. Model description

The model is based on methods described in Gul-

land (1956) and Beverton and Holt (1957) who com-

pared CPUE from pairs of vessels when they were

®shing at the same time and place. For a given ¯eet

and for a given species or sub-group, the relative

differences in ®shing power are estimated between

as many vessel pairs as possible. These estimates are

then used to calculate each vessel's ®shing power

relative to a chosen standard vessel. The relative ®shing

powers between two arbitrary individual vessels are

termed local power factors, and the ®shing powers

between the standard vessel and other vessels, relative

to the standard vessel, are termed global power factors.

Using a vessel's global power factor, the applied effort

can be converted to effort units of the standard vessel.

When two vessels have recorded catches close in

time from the same area the probability that they were

®shing on the same density of ®sh under equal envir-

onmental conditions is assumed to be high. A single

estimate of relative ®shing power between the vessels

can then be made by taking the ratio of their CPUEs,

and this is de®ned as a comparison. A time±space cell

for a comparison has to be de®ned, i.e. the maximum

difference in time and distance between the two

vessels when their CPUEs are compared. Some catch

composition criteria can also be made to increase the

probability that the vessels were trying to catch the

same species. The expression for local power factor,

relative to one of the two vessels, is given by

Pik � medianCPUEij

CPUEkj

� �; j � 1; . . . ; n; n � l (1)

where Pik is the local power factor of vessel i relative

to vessel k, CPUEij and CPUEkj are their respective

catch per unit effort during comparison j, n the number

of comparisons used and l the minimum number of

comparisons required to estimate a local power factor

between the two vessels.

The median as an estimator is not heavily affected

by wild values of the CPUE ratios. The mean of the

CPUE ratios cannot be used since vessel i (in Eq. (1))

will be favoured if the vessels are equally ef®cient (in

this case since the expected ratio is larger than 1), due

to the asymmetry in the distribution of ratios.

The standard vessel should be a particularly active

vessel during the entire period of analysis with a high

number of comparisons with the other vessels in the

¯eet. It is important not to choose a vessel which has

undergone signi®cant changes, e.g. rebuilding. This

may change the vessel's ®shing power, and an impor-

tant assumption concerning the standard vessel is that

its ®shing power remains constant throughout the

analysed period. When calculating the global power

factors vessels are grouped into three different levels

according to the possibility of estimating local power

factors directly or indirectly in relation to the standard

vessel. Fig. 1 gives a precise de®nition of what the

different levels imply. For vessels at level 2 the

calculation of the global power factor Fj�2� is done

by averaging products of local power factors:

Fj�2� � 1

n

Xn

i�1

Pi Pij (2)

where n is the number of vessels at level l with

272 A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281

estimated local power factors in relation to vessel j (at

level 2), Pi the local power factor of vessel i relative to

the standard vessel and Pij the local power factor of

vessel j relative to vessel i.

Vessels in the ¯eet that are missing at level 2 can be

related to the standard vessel to obtain a global power

factor Fk�3� at level 3 as follows:

Fk�3� � 1

n

Xn

j�1

Fj�2� Pjk (3)

where n is the number of vessels at level 2 (see Fig. 1)

with estimated local power factors in relation to vessel

k, Fj�2� the global power factor of vessel j and Pjk the

local power factor of vessel k (at level 3) relative to

vessel j.

Since the relative ®shing power between vessels in a

¯eet changes with time, it is important to divide longer

time periods into shorter ones and to estimate local

and global power factors within each of these shorter

periods.

2.2. Application of the model

2.2.1. Dataset

The commercial ®shing data used in the application

of the model is a logbook data base from the Norwe-

gian bottom trawler ¯eet. The logbooks have been

collected and recorded by the Norwegian Directorate

of Fisheries since 1971. Each individual record includes

vessel, date, species, catch (kg), summarised duration

(h) of all the trawl hauls the recorded date, position

according to the area-location scheme used by the

Directorate of Fisheries (Fig. 2), length of the vessel

(m) and engine sizes (hp). The size of the geographical

locations are indicated in Fig. 2, and it should be noted

that the size of the location varies (between 1 and 28 in

longitude and 0.5 and 18 in latitude). If a vessel operated

in different locations on the same day, the Directorate of

Fisheries recorded the location with the largest trawl

catch. Only records from the period 1981±1996 are used

due todifferences in the recordingproceduresduring the

period 1978±1980. The selected area and time period

contain around 225 000 records having catches of cod.

CPUE and the weight fraction of cod in the catch are

calculatedforeach record.CPUE isexpressed inkg hÿ1.

Records containing zero catch are very rare due to the

summation of all the trawl hauls during each day. Zero

values in CPUE observations from a vessel give very

limited information of the ®shing power relative to

another vessel, and these records are therefore removed

from the data.

2.2.2. Standardisation

The ratio of two vessels' CPUEs is calculated when

the same statistical location (Fig. 2) is recorded on the

Fig. 1. The principle of how the local power factors between individual vessels (showed as lines) are used to estimate their global power

factors in relation to a standard vessel using Eqs. (2) and (3). Vessels at level 1 have obtained a local power factor (Pi) directly in relation to the

standard vessel, vessels at level 2 have obtained a local power factor (Pij) in relation to vessels at level 1 and vessels at level 3 have obtained

local power factors (Pjk) in relation to vessels at level 2. The grey and white coloured vessels did not obtain a local power factor directly in

relation to the standard vessel.

A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281 273

same day (comparison in a time±space cell). Because

®shing power is likely to differ among species, only

records with cod catches are used. Most of the com-

parisons are done on north-east Arctic cod, but occa-

sionally the catches were of cod from the North Sea

and Norwegian coast. The ®shing power is assumed to

be independent of cod stock identity.

To establish vessel standardisation, a set of data

selection criteria (like catch composition, standard

vessel, minimum number of comparisons behind a

local power factor, and duration of standardisation

period) needs to be de®ned. Robust ®gures, emerging

from an early data exploration, were used as the basis

for the standardisation. At a later stage, the effect of

varying some of these factors will be studied in more

detail. The minimum number of comparisons required

to estimate a local power factor is set at 10. As catch

composition criteria only records where the weight

fraction of cod exceeds 15% are used, and this thresh-

old is termed the quali®cation level (Ketchen, 1964).

With this threshold it is assumed that both vessels

target cod during a comparison. A too high quali®ca-

tion level may lead to signi®cant loss of observations.

The standard vessel is set to be the vessel having the

highest number of comparisons with other vessels

during the analysed time period of 16 years. Standar-

disation of the ¯eet is done in four separate time

periods (each of 4 years), and the same standard vessel

is used for the whole period. It is then assumed that the

relative ®shing power between the vessels is fairly

constant during a period of 4 years. Shorter time

periods reduced the availability of comparisons too

much in some periods. Vessels that were rebuilt or

given a new registration number during the period are

treated separately before and after the change.

Many works (e.g. Beverton and Holt, 1957) show

that vessel and engine size explain much of the

variation in ®shing power, the larger and more power-

ful vessels being more ef®cient. To evaluate the global

power factors in this work, linear regression analysis

Fig. 2. Original statistical area-location scheme for the Barents Sea used by the Norwegian Directorate of Fisheries. The north-east Atlantic is

similarly divided into areas.

274 A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281

between vessel length and power factor and between

engine size and power factor are carried out. The

measurement procedures for gross tonnage changed

gradually during the analysed period and is thus not

used. The frequency distribution of some vessel's

ratios from comparisons with the standard vessel is

explored to evaluate the method used for estimation of

local power factors and to give a visual impression of

the uncertainty in these.

2.2.3. Effects of varying parameters

The most important parameters used in this appli-

cation which may affect the values of local and

thereby global power factors are: the chosen standard

vessel, the quali®cation level and the minimum num-

ber of comparisons required to estimate a local power

factor between two vessels (l in Eq. (1)). Some effects

of varying these parameters are analysed here. The

model is now applied to data from the last time period

(1993±1996), both in view of high ®shing activity in

this period and to obtain results from the `̀ current''

situation in the ®shery.

To explore the variation in global power factors for

individual vessels when using different standard ves-

sels, global power factors are calculated in relation to

20 different standard vessels. Thus each vessel in the

¯eet obtains 20 or 19 (for standard vessels) different

global power factors. These global power factors are

again adjusted to the level of one of the 20 standard

vessels. This vessel is called the basic standard vessel

and it is chosen randomly from the 20 standard

vessels. Adjusted global power factors for standar-

dised vessels in the ¯eet are given by

Fjk� � Fjk Fks (4)

where Fjk� is the adjusted global power factor between

vessel j and standard vessel k, Fks the global power

factor of standard vessel k relative to the basic stan-

dard vessel s and Fjk the original global power factor

between vessel j and standard vessel k.

The standard vessels are the 20 trawlers with the

highest number of cod records during the period.

Quali®cation level is set at 15% and minimum number

of comparisons required to estimate a local power

factor is set at 10. For each vessel the coef®cient of

variation in the Fjk�s is calculated, and the distribution

of these is explored. The coef®cient of variation CVj in

global power factors for vessel j is given by

CVj � 100 sj

�1=n�Pnk�1Fjk

� (5)

where sj is the standard deviation of Fjk� for vessel j

and n the number of different standard vessels.

The effect of varying the minimum number of

comparisons required to estimate a local power factor

is investigated for eight vessels, relative to an active

standard vessel, during the same period and with the

same quali®cation level as above. Values of the local

power factors are plotted against increasing numbers

of comparisons used in the calculation (l in Eq. (1)).

The comparisons are taken chronologically from the

start of the time period.

To analyse the effect of using different quali®cation

levels, the global power factors of 10 randomly chosen

vessels are calculated using different quali®cation

levels. An active standard vessel is used, and the

minimum number of comparisons required to estimate

a local power factor is set at 10.

Decreases in the total number of standardised ves-

sels when increasing the minimum number of com-

parisons required to estimate a local power factor and

when increasing the quali®cation level are also

explored.

3. Results

3.1. Standardisation

The global power factors are correlated with the

length and engine power of the vessels (Table 1 and

Fig. 3). A linear model based on length generally

explains more of the variation in relative ®shing power

than a linear model with engine power, except in the

period 1989±1992 where a model with engine power is

slightly better. In the periods 1985±1988 and 1993±

1996, the correlations between engine power/length

and relative ®shing power of the vessels are higher

than in the two other periods. This is also the two

periods with the highest number of active trawlers, and

the abundance of north-east Arctic cod were also high

in both of these periods. The slopes of the regressions

are all signi®cantly different from zero (P<0.0001)

and they vary between time periods. There are, how-

ever, no clear trends in the value of the slope from the

A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281 275

®rst to the last period. Outliers may have a large effect

on estimates of the slope, and it is not the purpose of

this work to establish explanatory models for ®shing

power. It was possible to standardise most of the

CPUE observations containing cod catches, with the

lowest proportion in 1989±1992. This was also the

period with the lowest number of active trawlers and

with the highest number of vessels standardised at

level 3. The distributions of the analysed CPUE ratios

relative to the standard vessel (Fig. 4) used in Eq. (1)

are generally skewed to the right with occasionally

very large and small (near zero) values.

Table 1

Results of linear regressions between global power factors (dependent variable) and length (m) and engine power (hp) of the vessels in each of

the four analysed time periodsa

Period Length±power

factor

Horsepower±power

factor

No. of

standardised

ships (n)

No. of ships

standardised

at level 3

Fraction (%)

of records

standardisedr2 Slope r2 Slope

1981±1984 0.30 0.015 0.17 0.0002 113 5 95.09

1985±1988 0.69 0.024 0.56 0.0003 169 2 96.84

1989±1992 0.47 0.040 0.54 0.0005 104 32 84.78

1993±1996 0.78 0.023 0.61 0.0002 134 8 96.82

a The total number of standardised vessels, number of vessels standardised at level 3 and the fraction of the total number of cod records

standardised are shown for each period.

Fig. 3. Global power factors in relation to length for all the standardised vessels in the four analysed time periods. Linear regression lines are

shown, and some results of the regression analysis are given in Table 1.

276 A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281

3.2. Effects of varying parameters

With a few exceptions, the choice of standard vessel

does not seem to have a large effect on the values of

the global power factors (Fig. 5). The mean and

median of the coef®cient of variation of the estimated

adjusted global power factors are 8.67 and 3.88%,

respectively. The frequency plot in Fig. 5 does not

Fig. 4. Frequency plot of the CPUE ratios relative to the standard vessel from three randomly chosen vessels in the period 1993±1996. The

values of the three bars in the right corner of the figure are 9.3, 37.3 and 13.5, respectively.

Fig. 5. Frequency plot of 135 individual vessels' coefficient of variation (CVj) in adjusted global power factors (Fjk�) when using 20 and 19

different standard vessels.

A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281 277

change signi®cantly when using different basic stan-

dard vessels. The number of comparisons required in

the calculations to stabilise the value of the local

power factors varies, but it seems to be around 10

for most of the analysed vessels (Fig. 6). When

varying the quali®cation level, the values of global

power factors are fairly stable except for very low

levels (near 0%) and for levels above 70% (Fig. 7).

When increasing the quali®cation level and the mini-

mum number of comparisons required to estimate a

Fig. 6. The change in value of local power factors for eight vessels (different symbols) relative to a standard vessel when increasing the

number of comparisons required in the estimation of the factor (l in Eq. (1)). The comparisons are taken chronologically from the start of the

time period (1993±1996).

Fig. 7. Trends in the values of 10 randomly chosen vessels' global power factors when changing the qualification level (each vessel has its

own symbol).

278 A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281

local power factor, a limited number of vessels are lost

as they do not meet the requirements (Fig. 8).

4. Discussion

4.1. Model

The spatial distribution of marine organisms is

highly patchy (Pennington, 1996), and an appropriate

time±space cell for a comparison of two vessels'

®shing power depends on the degree of patchiness

in the spatial distribution of the analysed species.

Often the possibility for obtaining appropriate time±

space cells will be limited by the quality of the catch

information and the spatial and temporal resolution of

the commercial catch data. The model requires a

certain amount of temporal and spatial information

from individual vessels' catches. Even when both

vessels are ®shing within the same de®ned time±space

cell there is a certain probability that they are ®shing

on completely different densities of ®sh. This is the

reason why the CPUE ratios from comparisons

between two vessels generally become skewed (see,

e.g., Gulland, 1956) with occasionally very large and

very small (near zero) values. If estimators for differ-

ences in ®shing power which make use of all the

CPUE ratios are applied (as in, e.g., Gulland, 1956;

Beverton and Holt, 1957; Wilderbuer et al., 1998),

occasionally very large and very small values could

have a large effect on the estimator. Therefore, the

median of the ratios is considered to be the most

appropriate estimator of the relative ®shing power

between two ®shing vessels.

A critical assumption in this model is that the

®shing power of the standard vessel remains constant

throughout the analysed time period. Another simpli-

fying assumption is that the local power factors

between pairs of vessels remain constant within the

time period. These assumptions are probably always

violated to a certain extent. Fishing vessels normally

increase their ef®ciency with time due to technologi-

cal improvements, and the rate of improvement may

differ among vessels. Systematic changes in the ®sh-

ing power of the standard vessel will bias the CPUE

indices based on standardised data. If the ef®ciency of

the standard vessel increases with time, this will cause

a gradual increase in catchability. Current differences

in ®shing power between two vessels may also be

dependent on conditions such as water depth, type

Fig. 8. The reduction in the number of standardised vessels in the period 1993±1996 when (a) increasing the minimum number of

comparisons required for estimating a local power factor, and (b) increasing the qualification level. In (a) a qualification level of 15% is used,

and in (b) the minimum number of comparisons required for estimating a local power factor is set at 10.

A. Salthaug, O.R. Godù / Fisheries Research 49 (2001) 271±281 279

of ground and weather conditions. Effects of the

dynamical changes in ®shing power between vessel

pairs are reduced if the ¯eet is standardised within

shorter time periods. The reduction in the length

of these periods may, however, be limited by data

availability.

Though not quanti®ed, the uncertainty in the values

of global power factors that are obtained at level 3 may

be large, and these vessels are probably not very active

in the time period when the standardisation is done. If

the effort in the ¯eet on levels 1 and 2 is suf®cient for

estimating abundance, then level 3 vessels should be

removed.

4.2. Application of the model

Because of the resolution of the analysed dataset,

the smallest time±space cell for a comparison is not

very precise, and so are the catch composition esti-

mates. Vessels can be far apart in time and distance

when their CPUEs are compared. Still the resolution is

high enough for many comparisons to be made during

a time period of 4 years. Even though zero catches are

removed from the standardisation process, these

observations may be important when calculating

CPUE indices.

The results of regressions between global power

factors and engine power/length of the vessels show

that these characteristics probably explain much of the

differences in relative ®shing power. Other studies

also show that engine power and size of vessels or

vessel classes in trawl ®sheries for gadoids are linearly

related to ®shing power (e.g. Beverton and Holt, 1957;

Westrheim and Foucher, 1985), and the regressions in

this work may indicate that our model for estimation

of relative ®shing power would work well. One of the

reasons why a model with length generally becomes

better than a model with engine power for explaining

relative ®shing power can be that length has a higher

resolution in this dataset. Length and engine power are

of course highly correlated. The correlations are

strongest and the slopes become more equal in the

two periods with the largest number of active trawlers

and highest stock abundance. The number of compar-

isons between vessels is probably high in these periods

due to high ®shing activity, and thus the estimates of

the power factors are more precise. The reasons why

larger and more powerful trawlers are more ef®cient

are probably higher towing speed, larger size of the

trawl and heavier gear which improve the stability of

trawl performance.

When using high quali®cation levels, observations

are lost and the number of comparisons are reduced.

This results in a lower number of local power factors, a

lower number of standardised vessels and possibly

more uncertainty in the values of global power factors.

A too low quali®cation level will, however, cause the

inclusion of trawl hauls for which the target species is

different from cod, and some quali®cation level larger

than zero is probably necessary. The minimum num-

ber of comparisons required to estimate a local power

factor can be estimated visually by making plots as in

Fig. 6. If this number is set too high, it will however

result in too few comparisons.

5. Conclusion

The relatively simple model developed here seems

to be a robust method for estimating the relative

®shing power of individual ®shing vessels. Instead

of trying to analyse the complex set of factors causing

differences in catching ef®ciency, the actual ®shing

power of the vessels can be estimated by direct

comparisons of the vessels on the ®shing grounds.

A certain amount of spatial and temporal information

about the vessel's catching operations is however

required. The effects of varying the quali®cation level,

minimum number of comparisons, and standard vessel

should be explored for each dataset the model is

applied to.

Acknowledgements

We wish to thank Dag Tjùstheim and Michael

Pennington for correcting the manuscript and the

Norwegian Directorate of Fisheries for providing us

the data. The project was ®nancially supported by the

Norwegian Research Council (NFR).

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