THE CATCH PROCESS (continued)
In our previous derivation of the relationship between CPUE and fish abundance we assumed that
all the fishing units and all the fish were spatially homogeneous.
Now we explore what happens
when this is not the case.
Spatial Effects on CPUE
Fish and fishing gear will almost never be uniformly distributed over the fishing grounds.
How does
this affect the relationship between CPUE and abundance?
Suppose there are two fishing areas, A and B, and no interchange of fish between them.
The
timeaveraged abundance for both areas combined is
This is a simple extension of the
timeaveraged abundance that we
explored in the Catch1 lecture.
avN
A_B
t
( )
1
t
0
t
u
N
A
u
( )
N
B
u
( )
+
( 29
⌠
⌡
d
⋅
=
The integral of a sum is
the sum of the integrals.
=
1
t
0
t
u
N
A
u
( )
⌠
⌡
d
0
t
u
N
B
u
( )
⌠
⌡
d
+
⋅
=
avN
A
t
( )
avN
B
t
( )
+
CPUE
A
t
( )
q
A
CPUE
B
t
( )
q
B
+
=
from CPUE = q·avN
If
q
A
= q
B
= q , then
q avN
A_B
t
( )
⋅
CPUE
A
t
( )
CPUE
B
t
( )
+
=
and in general
CPUE
A
CPUE
B
+
C
A
f
A
C
B
f
B
+
=
C
A
C
B
+
f
A
f
B
+
≠
To combine catch and effort data from different areas we should take the sum of the individual
ratios of catch over effort;
we should NOT take the ratio of the sum of the catch over the sum of
the effort, although that is what people commonly do.
Here is a hypothetical numerical example with
N
A
(0) = N
B
(0) = 1000 that illustrates the point.
M
0.1
=
/yr
q
0.01
=
/yr
f'
A
10
=
units
f'
B
30
=
units
Suppose that after three months (1/4 yr) of fishing we have the following:
Area A:
C
A
24.4
=
f
A
2.5
=
CPUE
A
9.75
=
Area B:
C
B
71.4
=
f
B
7.5
=
CPUE
B
9.52
=
Combined:
C
A_B
95.8
=
f
A_B
10.0
=
CPUE
A_B
9.58
=
The sum of the CPUE values is
CPUE
A
CPUE
B
+
19.27
=
. The sum of the catches (total catch)
over the sum of the effort (total effort) is
CPUE
A_B
9.58
=
.
The ratio of the total catch over the total effort is equivalent to the weighted average fish density per
area, with the "weight" for each area equal to the fishing effort.
FW431/531
Copyright 2008 by David B. Sampson
Catch3  Page 44
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View Full DocumentPopulation B
Location
Fish Density
Population A
Location
Σ
C
Σ
f
Σ
f
C
f
⋅
1
Σ
f
⋅
=
What is a weighted average?
We want our measure of CPUE to be proportional to the total timeaveraged abundance, not the
average (with respect to area) timeaveraged abundance.
The quantity (
Σ
C)/(
Σ
f) may or may not
be proportional to the timeaveraged abundance.
It will depend on the distribution of fishing effort
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 Fall '09
 Fishing, Recreational fishing, fishing effort, David B. Sampson

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