THE CATCH PROCESS (continued)
In our previous derivation of the relationship between CPUE and fish abundance we assumed that
all the units of fishing were equivalent.
Now we explore what happens when they are not.
Fishing Power
Suppose there are two boats fishing simultaneously on the same grounds, but they are not equally
effective at catching fish.
For example, one boat might be using a larger net than the other or it
might have a more powerful engine so that it can tow at a faster speed.
Suppose boat A removes
fish at instantaneous rate q
A
and boat B removes fish at instantaneous rate q
B
.
The following
equations apply.
They are simple extensions of the differential equations for N and C.
dN
dt
M
q
A
+
q
B
+
(
29

N
⋅
=
==>
N t
( )
N 0
(
) exp
M
q
A
+
q
B
+
(
29

t
⋅
⋅
=
dC
A
dt
q
A
N
⋅
=
==>
C
A
t
( )
q
A
N 0
(
)
⋅
1
exp
M
q
A
+
q
B
+
(
29

t
⋅

M
q
A
+
q
B
+
⋅
=
dC
B
dt
q
B
N
⋅
=
==>
C
B
t
( )
q
B
N 0
(
)
⋅
1
exp
M
q
A
+
q
B
+
(
29

t
⋅

M
q
A
+
q
B
+
⋅
=
Let
Z = ( M + q
A
+ q
B
), and divide the two catch equations by t to get equations for the observed
catch rates.
Each boat's catch rate is its own CPUE value.
C
A
t
( )
t
q
A
N 0
(
)
⋅
1
exp
Z
(
)

t
⋅
[
]

Z t
⋅
⋅
=
CPUE
A
t
( )
=
q
A
avN t
( )
⋅
=
C
B
t
( )
t
q
B
N 0
(
)
⋅
1
exp
Z
(
)

t
⋅
[
]

Z t
⋅
⋅
=
CPUE
B
t
( )
=
q
B
avN t
( )
⋅
=
We can combine the two sets of equations to show the relationship between the observed catch
rates.
CPUE
A
t
( )
q
A
avN t
( )
=
CPUE
B
t
( )
q
B
=
==>
CPUE
A
t
( )
CPUE
B
t
( )
q
A
q
B
=
The ratio of the catch rates will be the same as the ratio of the catchability coefficients.
Notice that the catch rates will be different unless
q
A
= q
B
.
If we ignored the differences between the two boats in their inherent fishing abilities, it might appear
that the two boats were fishing on different populations. This becomes a special problem when we
apply the notion of catchperuniteffort to catches by an entire fishing fleet.
If the composition of
the fleet changes over time, then changes that we observe in the CPUE might be due to changes in
the fleet's fishing ability rather than to changes in fish abundance.
One solution to this problem is to calibrate the boats against each other and calculate
CPUE
in
terms of a
standard unit of fishing effort
.
We can do this if we know the
fishing power
of each
boat.
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 Fall '09
 Fishing, Overfishing, Logistic function, Recreational fishing, David B. Sampson

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