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? 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