Estimating abundance, fishing mortality and migration rates by area

Transcription

Estimating abundance, fishing mortality and migration rates by area
SCRS/97/84
Estimating abundance, fishing mortality and migration rates by area, using the spatial VPA
methodology. Application to yellowfin tuna in eastern and western Atlantic
MAURY O
*
+*, -
.
/ 0 &1&
(1)
, GASCUEL D
2
(1)
, FONTENEAU A.
,& 1
!
"
'
1
#
#
$
&
%
$
%
$
%
#
$
(
*
"
#
"
#
, $
-
#
$) %
$
$
'
#
10
!"
#0
"
'
'
'
"
0
.....
3
#
$
....
"
:
B
'
0
4"
# 56678#
2
0
+
'
!"
'
9
'
566< -3
'
4..8 /
' 0
4!
566@ - /
0
..# 8 :
'#
4:
( 566> ?
;
0 '#
# '
566< - 3
3
566= -
'
4..8
'
$
/
0
'
566< - A
0
0
"
3
'
566< 0
#
0
'
#
1
0
'
#
0
'
1
1
0
!"
2(("1
'
0
"
'
'
' !" 3
$
'
'
0
4?
'
/
C2/ 4C
#
/
'
566> 1
'2
2
'
0
/
' 0
'
$
/
0
$% & ' & (
()
%"
("1(& &"()
INTRODUCTION
#
"
! " #"
" #)&
!"
%
$
(2)
'
2
'
/'
8
!"
'
4
C
1. DATA AND MÉTHOD
1
?
2
':
;
0
(# 566<8 ;
' $
5#
=
D#
D # +5
−4
+ , 5# 8
D#
5#
D#
3D# =
D#
+ , D#
D#
45− + 5D # 8 +
+ , D# 8
+ , 5#
5#
0
5#
'
45−
45−
−4
5#
−4
5
5
5
5#
+ , 5# 8
1#
) 1#
D#
−4
5#
+ , D# 8
+ , 5# 8
478
+ D5#
2#
'
2#
5
D
8
-35#
3D#
? D# #
-15D#
'
$' 1
0
#
0
(D#
$
#
'
3
35#
3D#
1#
′ =
0
8
2
0
95#
9D# # 0
4? 5# # ? D# # 35# # 3D# # 15D#
1D5# 8
'
? 5#
? D#
' 1
'
' !"
:'
'
F
4#
4#
=
#
5#
=
#
with Ns,t and qs,t , the fish number and the catchability in the unit surface ds during
time t.
Contrary to the catchability qt, the assumption that the coefficient q’t is spatially
constant at a given time t can be done. Then, catch per unit effort in each zone i at
time t can be expressed as follow:
D
4
0
) 2#
) 2#
) 1#
(2)
#
'
458
(5#
$
'
0
'
2#
The catchability per surface unit q’t is defined as being equal to the local CPUE Us,t
divided by the local density Ds,t , both calculated on a unit surface ds during time t :
0
'0
E
1#
=
324
1
2#
=
5 78
H
+ 5D #
1D5# #
' $
/'
=
4
0
(1)
+ , D# 8
D
-? 5#
−4
5
9
)#
$
8
D#
D
D
D#
45− + D5# 8 +
9D# #
95#
#
H
5#
35# =
458
0
#
=
F
1#
$
−4
=
5# +5
#
#
'
H
'
#0
4!
:
#
/# #
0
:
'
( 4566> 8 1
$
0
56=>#
# 56G58
#0
0
=
4D8
1.1. The spatial VPA methodology
0
458
'
=
#
5# )#
3#
=
)#
)#
with fs,t the effort in the elementary surface ds at time t.
With the assumption of spatial homogeneity of fish density in each zone i (Ds,t=Di,t),
the previous equation can be simplified:
324
#
=
#
5# =
=
#
with Ni, t, , the number of fish in zone i at
#
#
time t. Such a simplification could be made at the global stock level only under the
generally false hypothesis of equality of fish densities in all zones at a given time t :
324
3
=
=
)
3#
=
)#
(5
#
)#
)
.
)#
B
'
4<8 0 4
1#
8=
495# I9D# )9 JK8# '
31# 4 , 1# +
− 4 1#
1# 41 −
1#
8
+ , 1# 8
8
+
32# 4 , 2# +
− 4 2#
2# 41 −
2#
8
+ , 2# 8
8
−
458
3 4, +
41 − − 4
H
1.2. Extending the method to several fleets
8
+, 8
8
=0
3
'
478# ? 5# # ? D# # (5# # (D#
(
'
0
3
' !"
+
4<8
'0
'
'!
(
#
478
3D# 9 $#
4566<8 E
35#
9D#
95#
'
458
1D5# : '
458
1
'
0
15D#
2
#
'
415D# # 1D5# 8
1D5#
)
4( H
0
15D#
8 3
#
0
H
8 0
'
4 0
8
, 4
80
'
#
1 4
'
4
# 56GK-,
(# 5665 -A
3
# 566<8
1D5#
$
E
#
15D#
0H
0
4=8
1 5D#
J5
'
#
'
3D#
+ 5D # = 5 + + ′5D #
+ 5D # = 5
+ D5# = 5
+ D5# = 5 + + ′ D5#
1 D5#
3
3
=
/#
478
H
0
) #2#
2# ) #1#
' $
1#
=
#2#
3#L#
"
#1#
'
L4
478
'
=
5#
=
5#
=
5#
5# D #
4@8
#D #
) 5#D #
) 5#5#
D#
4@8 H
5#5#
) #D #
) #5#
D#
9L#8
#5#
'
9 0#
4, # 1 D5# 8 2
4, # 1 5D# 8
0
$ '
1# #
1D5# 1
1D5# 1)5 3
1D5# H
+ 12# =
0
H
2# + 1
+
0
,
(# 566< -!
# 566@8#
'#
4A
?
#
458
H
#D #
15D# 1
H 15D# 1)5
15D#
4=8
1#
− 4 2# + , 2# 8
D#
#5#
#
4>8
2#
) #D #
) #5#
D#
=
D# #
5#
=
D#
) D#
) 5#
#
5# #
#
=
5#
D#
) D#
) 5#
35# #
35#
#
#
4 5 − 18
− 4 1# + , 1# 8
+
4<8
4>8
'
'
+ 21# = 5
2 15D# ≤ , 4⇔1F5D# ≤ K0
1D5#
15D#
'
8# '
1.3. Application to Atlantic yellowfin tuna
1
#
0
' 0
"
"
0
5#
0
L
?
'
'
0
2(("1
"
'C
' 0
0
:
0
"
'
1
$
!"
'
4K)5)D)78
4566<8 0
0
'
)
L
0
4C
(# 566D8
#
4<)=I8 0 2(("1
56G...)566
0
!"
0
'2(("1 0
(
56G)566
'
'
4
0
?
/
"
# 56678
'
# 566<8 2
3
' 0
'
=M$=M
0
'
45=K
7KK
' =M
8 0
0
' 0
4
58 1
0
0
0
0
C2/4
rap150
1,5
1
0,5
1
2
3
4
5
6
7
8
9
10
11
time (months)
0
#
/
rap300
2
0
4788 /
1
4/0
western surface / eastern surface
2,5
# 0
fig 1. Surfaces ratio for both threshold levels.
4/0
'#
0
0
2(("1
56=@)5667
E
0
(
# 566D#
0
1
2. RESULTS
0
'
2.1. Global and local fishing mortalities
=M$=M
=M$=M
0
F
# 566=8
"
2.2. Fish numbers in each zone and migration rates
12
25000000
100
moy%N1
moy%N2
90
effectifs relatifs moyens
effectifs
20000000
15000000
N1
N2
N
10000000
5000000
0
0
4
8
12
16
20
24
trimestres
80
70
60
50
40
30
20
10
0
0
5000000
4
8
12
16
20
24
trimestres
4500000
4000000
effectifs
3500000
3000000
N1
2500000
N2
N
2000000
3. DISCUSSION AND CONCLUSION
..."
'
43
1500000
'
!"
# 566< 8
'
'
'
1000000
500000
0
12
16
20
24
/
"
43
trimestres
!"
8
$
?
'
$
!"
...
4:
'
8
'
3
'
45668
'
F
'
0
'
N
C
'
1
43
(
0
?
0
(!B+
0
'
'
# 5668 N
#
0
'
0
#
'
# 56678
4/
O
'0
(!B+
0
1 '
'
(# 56>6 -;
566>8 1
4
'
F
1
' F
8
0
566>8 :
1
'
# 56G> -;
E
'
4
E
4;
'
'
')
#
# 566D -C
' F#
#
#
'
' F#
'
9
#
4?
0
'
'
4C
(# 566>
'
,
# 566>8
Q
0
'
( 566>
8 2
0
'
P
# 566<8
'
R
4!
2
'
'
0
!"
0
'
/
8 4?
'
/;",S/ 4/
# 566>8
0
'
C
4
F
#
%
:
O T;# / T;
'2
#
#
3U # " ;
56=>
D# H==7
'
$
3
# O/1 ?
+# " 3
4+
C
4+
C
6
1
'
'
C
( 5& (
'
"
/
0
H
1
( 733 +#
!" C
( 5& (
1
( 733 +#
566>
F
H
2(("1#
/'
2(("1
4D8#
"V
#T
$
566@
+ 566= ,'
%
O
8
"
# 1,?
#, C
6
/'
, 566< B
$
$
H ?
'
566>
2
$
566< /
D
5665 "
"
#! !
0
H
#
"
H
2
'
'# E ; : '
!
(# H 7>=)76=
"# , C
RÉFERENCES
3
?
" 566< 1
2(("1
"
4D8# /(O/P
67P
<D# D5=)D5G
3
:
F;
F"
8
(
1
# 5)7L
" 566< /
3
F
#
$
"
/(O/P
67P
<7# D5=)D5G
0
' '
(
566> 3
O :# O C !
0
(
3
*( & ("
56>6 "
'
3 V
,
0
'
)
"
( 733 +#
$
( E # ? ?
'
( ' !#
3
0
,S
F
(
8
1
( 5& (
H
'
#
"
T)( 566@ 1
"
CONCLUSION
;"
1
:
!"
'
'
4?
'
2(("1
"
4D8# /(O/P
67P
<5# DK<)DKG
#
'
' '
'
8
0
0
'
4(
# 566D -C
E
(
#
4+
H >D7)>77
1
# 5D> I
#1 ,
8
2(("1#
L
6
+ 1
$
566@ W
V
"V # T
8
"
# +9/")
"
566@ 2
P
& H
+ 3
( 8(
(
C
,# " 3
#( (
4+
566D ?
6
8
"
$
( 9 /(
+
!
" +# , / :
!
3 566> /
$(
+9CO+3
;
#
O# ( T E
'
;
'
3
O# ( T E
566D W
'(
!# " 3
( 8(
(
(
"# T (
C
(9+U #
?
?
3
4/
?
?
L
(
E
/
4
3" $
5 O /
P
5
11
8
*)
$
#, !
0
?
'
/
,S
/
H
'
'
'
B
H
5K /
)
O
T +#
? ,
56@< "
(2+? 5==H 5=D)5@7
?
! 566< /
/
!
#
!"
(? 566>P
,,HK6# >!
" 56GK ,
!
'
/;",S/
/
0
8 2(+/ "
566> +
" , 566K ,'
! # 5=7
:
TO # , " 3
'
56G5 ,'
<=
;"
(? 566>P HKG# G
2(+/"
?
/
566> /
'
' #, C
/
5KG)5D5
# 566<
' #, C
E ;# / " 1
( 1
B
'!
66<
D=<
O
2(+/ "
( ? 566<P
,H5<
'# E 1
566< +
#: ! 3
/
' 566< 9
(
)
*+
!
!
#
(
!
#
(
# 566< "
# T? L 0
( + 566@ "
; # =>K
!
/
7D@
!"
2(("1 0
0
1
56G> "
'
A
566< B
/(O/P
6<P
>D
H 5==)5>D
C
0
!
/
/0
/
/0
E
# 5667
# 566D
(11 #
#

Documents pareils