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EcoTroph (ET): a trophic level based software for assessing the impacts of fishing on aquatic ecosystems. Gascuel, Didier; Tremblay-Boyer, Laura; Pauly, Daniel 2009

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ISSN 1198-6727  Fisheries Centre Research Reports 2009 Volume 17 Number 1  EcoTroph (ET): a trophic level based software for assessing the impacts of fishing on aquatic ecosystems  Fisheries Centre, University of British Columbia, Canada  !  ! " '  , --.  #$  & & " $( (  /)  "  % ') *+  #  Fisheries Centre Research Reports 17(1) 2009 ECOTROPH (ET): A TROPHIC LEVEL BASED SOFTWARE FOR ASSESSING THE IMPACTS OF FISHING ON AQUATIC ECOSYSTEMS  D. Gascuel (1), L. Tremblay-Boyer (2) and D. Pauly (2)  CONTENTS  Page  Director’s Foreword ............................................................................. 1 Abstract ................................................................................................ 2 Introduction ......................................................................................... 3 PART I – The trophic level based model: theoretical approach ............. 5 1.  Building the model: principles, assumptions and equations .................................................5 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8.  2.  Learning from the model: some generic rules of the ecosystem functioning .................... 24 2.1. 2.2. 2.3. 2.4. 2.5. 2.6.  3.  Simulation of a virtual ecosystem: method .................................................................................24 Impact of transfer efficiency and flow kinetics on unexploited biomass ...................................26 Impact of fishing on biomass....................................................................................................... 27 Catch simulations ........................................................................................................................ 30 Dynamic model: impact of fishing on ecosystem stability ......................................................... 33 Concluding remarks on the theoretical approach....................................................................... 35  The Catch Trophic Spectrum Analysis (CTSA) ...................................................................37 3.1. 3.2. 3.3.  4.  Origin of the model ........................................................................................................................ 5 EcoTroph: general principles ........................................................................................................ 6 EcoTroph: biomass and flow equations ...................................................................................... 10 EcoTroph and Ecopath: first comparison ................................................................................... 12 Flow kinetic equation ................................................................................................................... 14 Top-down control and biomass input control ............................................................................ 17 Catch equation and accessibility................................................................................................. 20 From steady-state to time- dynamic modelling ..........................................................................22  From EcoTroph to the CTSA ....................................................................................................... 37 Testing the method on simulated data ....................................................................................... 38 Application to real case studies ................................................................................................... 41  Conclusion: the trophic level based approach..................................................................... 42  PART II - ECOTROPH: A new tool in the EwE family ........................... 43 1.  General information ............................................................................................................ 43 1.1. 1.2. 1.3.  2.  Structure of the EcoTroph routines: ...........................................................................................43 Installation of the plug-in ............................................................................................................44 Additional information ................................................................................................................ 45  ET-Transpose: looking at an Ecopath model using EcoTroph ........................................... 45 2.1. 2.2. 2.3. 2.4.  What is it used for? ...................................................................................................................... 45 How it works................................................................................................................................. 45 How to use it .................................................................................................................................49 Example of application ................................................................................................................ 52  3.  ET-CTSA: estimating input parameters of EcoTroph ..........................................................53 3.1. 3.2. 3.3. 3.4.  4.  ET-Diagnosis: using EcoTroph for simulation and global diagnosis ................................. 60 4.1. 4.2. 4.3. 4.4.  5.  What is it used for? ...................................................................................................................... 53 How it works ................................................................................................................................ 54 How to use .................................................................................................................................... 55 Example of application ............................................................................................................... 60 What is it used for? ..................................................................................................................... 60 How it works ................................................................................................................................ 61 How to use it................................................................................................................................. 61 Example of application: ............................................................................................................... 64  ET-Dynamic: using EcoTroph with time series .................................................................. 65 5.1. 5.2. 5.3. 5.4.  What is it used for? ...................................................................................................................... 65 How it works ................................................................................................................................ 66 How to use it................................................................................................................................. 66 Example of application ................................................................................................................ 71  Acknowledgments ............................................................................... 73 References .......................................................................................... 73 Appendix I – A Non-continuous simulation of EcoTroph .................... 77 Appendix II – Estimating transfer efficiency from catch data ............. 80  (1) Université Européenne de Bretagne, Agrocampus Ouest Pôle Halieutique / Aquatic and fisheries sciences centre, UMR Ecologie et Santé des Ecosystèmes, 65 Route de Saint Brieuc, CS 84215, 35042 Rennes, France –  Didier.Gascuel@agrocampus-ouest.fr (2) University of British Columbia, Fisheries Centre, AERL, 2202 Main Mall, Vancouver BC, V6T 1Z4, Canada l.boyer@fisheries.ubc.ca; d.pauly@fisheries.ubc.ca  A Research Report from the Fisheries Centre at UBC, with support provided by The EU project TrophMod MOIF-CT-2006-38767, and The Pew Charitable Trusts (Philadephia, USA) through the Sea Around Us Project. 82 pages © Fisheries Centre, University of British Columbia, 2009  Fisheries Centre Research Reports are abstracted in the FAO Aquatic Sciences and Fisheries Abstracts (ASFA) ISSN 1198-6727  1  B  "  "  #C  '  #  /  =  $  % $%  "2  6  , #  ,  $  %  " , " $%, 2  5 A  @ ,  , $ B  5  #  %  = , , 5 ,  &  4  $%  "  &  $  , 6  1  B  "  "  #C  )  #  ,  C 2 , ,4  , $  5 ,7 "  /  ,8 6  6  ,# D  6  6 6  E D 2 %  4 ,8  , ,  E "  "  ,; % 47  7  E B#7EB 2  #  7  ,  # 55 /  "  "& !," , " ,  , ,  "  " C  2C F: ( & + 4) "  C  ,8  "  F8  C F:  , 6 D  %  (  4  7 D ,  ( -:+) D ( 8  + 'A  "  , 5 , "  ,  1  B  "  "  #C  6  0  #  ,G  D 2 "  2  , .  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B(τ)  τ + ∆τ  B(τ) ⋅ dτ  M1  τ  0 $  1  ),  )  B = Φ ⋅ ∆t  M-  ∆  τ  $  0  -  )  τ+∆τ,  , ,  ,5 2  ,  6  ,  $1*  )'  7 # )0 "?! . )+ "  6 ,.  6  6 I  6  ,$  , 7  6 6  ,  ψτ  I  ψ(τ) = µ(τ) + ϕ(τ) = ,  µ(τ)  1 ⋅ dΦ(τ ) Φ(τ) dτ  ψ τ µ(τ)  ϕτ  M/ 6  ϕτ !"', 8  ϕτ  1  B  "  "  #C  µ(τ),  $τ,  =τ,  ')  #  ψτ, µτ  , 5  ϕτ).  ,.  2  " /  , 7 # )0 "?! . )+  Φ(τ+ ∆τ) = Φ(τ) ⋅ exp[ - (µ τ + ϕ τ ) ⋅ ∆τ ] 6 "µτ  ( 4  M(  7  ,  S0  2  ϕτ  ,  %  G' H 5  '+//D #  A  '+3/  G'  ,  %  # '++) *,**,'= I'++' ,  *,'* #  7  %  (  '++-  Φτ  6  P τ, τ+∆τQ  s = ∆τ  Φτ = 1 ⋅ Φ(τ) ⋅ exp[-(µτ+ϕτ) ⋅ s] ⋅ ds ∆τ s = 0  Φ τ = Φ(τ) ⋅  $8  M3  1 - exp[-(µτ+ϕτ) ⋅ ∆τ] (µτ+ϕτ) ⋅ ∆τ  ) &)43 +,  M+  )4 . 37 & . )'4 &-)+ 6 ,5  6  # τ <  τK', 5  τ τK' $ , - , 6  ,  T # τK' O 6  @'  ⋅ !⋅  "',  7 ,. 6 ),: "  6 P τ, τ+∆τ] #τ H Φ τ · ∆ τ  , M'*  1  B  "  "  #C  '0  #  = P τ, τ+∆τQ  ,& Φ(τ)  τ  6  6  Φ(τ) = - dP dτ  M'' #τ  Y=F.B  P  τ.  Mo.B  U  Q  Predation M2.B  R  P  Growth  Trophic level:  τ  τ  τ+1  Boxe:  i  j  j  :!&" 6 2 4 # =)⋅ HT . T τ τK' # '++) ,  6  ) ∆τA∆ H #A #A  τ =*⋅  "  +  < &  ;  $⋅ HN , %  6 M')  τ  P τ, τ+∆τ],  #A  τ  #A  6 6,  = ,5 τ  "  6  2  . $ &A  ,  ϕτ  ( $τ  µτ. ;A  τK',  S',/ , N =*·  ,$  Pτ+1 = Pτ ⋅ exp [- (F+ Mo + U/B+ R/B) ⋅ ∆t ] (  ;  &  $ = M'0  ')  µ = Mo + U/B + R/B = Mo⋅B + U + R ∆τ/∆t P  M'1  1  B  "  "  #C  '1  #  5 , &  "  =*  ,7 H=*K=)  =)  2 6 =  2 F  # "*27  C  ,  2 )4 . 3  ) &)43  +9"?! . )+  "+"& # . &! . !&" 7  =  %  ""  6 .  #  #  6  %<D TA  6  ""  !  !  ""  "#. )+ 34 ". 0""+' +4 & '". "& #  Φ)  #  Φ H " #A τ, H Φ A #A  τ  #  #A  $  $  F R5  F  µ,  τA  $ ? 6  C  #A H τA  ϕτ) µ)  $  CR  # H Φ · ∆τ H ∆τA∆  $τ H ϕτ · ∆τ/∆t  µ H = · K & K ; A# B  "  % 6  . ,8  #A  TA  6 2 ,% TA  6 ,#  , 6  , ,  $6  # )0 9+". - "?! . )+ $6$  3")&". - # 44&) 3 , 5  2  I  2  "  6  , , 6  $  "  4  ,  " , %  " I  ,  2  , ,  "  "  ,  2  ,.  1  B  "  "  #C  '-  #  ( )**3 , #A  !  U %  6  ' ('3  --  #A  ,  ∆τA∆  τ  6  θ  = )*,) L (τ " 0,)/) · 6 *,*1' L θ  ∆τA∆  M'-  ')"( !⋅  *,'"*,0 !⋅  "'  $ ,/ ,$ -U %  "'  0  7,0  5,0  -a-  6,0  29 °C 25 °C 20 °C 15 °C 10 °C 5 °C 0 °C  5,0 4,0 3,0 2,0  T rop h ic level (T L )  Speed of the flow (TL.year-1)  ,  4,5 4,0 3,5 3,0  -b-  2,5 2,0  1,0  1,5  0,0  1,0  2,0  2,5  3,0 3,5 4,0 Trophic level (TL)  :!&" A "  4,5  5,0  0  2  1  2  3 4 Time (year)  5  6  7  , )**3  D  ,  5 ,  '0  " 6  d = a ⋅ −b dt  M'/  '/ ∆τ ,  " '/ 5  t=  1 ⋅ a ⋅ (b+1)  [  dt = 1 ⋅ b ⋅ d a  6  b +1  ]  M'( τ  6  −1  M'3  τ, 5  ' τ,  6  '+  1  = [1 + a ⋅ (b+1) ⋅ t ] b+1 I ,  τ  M'+ 6  / )-U %  1  B  "  "  #C  '/  #  '-  = [1 + 86.0 ⋅ exp(0.041 ⋅ θ) ⋅ t ] 6 I  0.235  M)* $ $ , / , $ 1 0,) 1,0  2  )* ',F  , , C  )-U %  , . 0,-  '  $6*  ?! . )+)7. 3" 7 # )0 9+". -  )  ,  4& . - # 44&) 3+ &"7 "&"+ " . !. )+ ∆τA∆  ', : ,  I ∆τA∆  ,7 6 ∆τ/∆  5 ;  #A  # 6  , ,  , , 8  '+('  " " )**' , 4 (  1  )**3 , 5 6 4 C  #A  D F  #  55  "  D  #A  F  ; ∆τ/∆ H ΦτA τ⋅∆τ  "  C  # )  2  ;  55 D , ,  D  '-  ,4 6  '  /,  P τ, τ+∆τQ,  #A  ;  $  2  ,  ; #A HV 7  '+(' , #A V : '+-(D & 2 '+(" : '+-/D # '++3 6 2 6 # C '+3* 6 , , = H *,+3- L G *,/-10 L !  , ,  # 2  "*,)(+ L  θ *,1/01,  '++3 =  ( , τ –1.72 L 6 *,*-0 L θ ,  #A H= τ θ &) H *,0(, #A H ),-/ L τ  ,  6  "*,(3  '$  D  D 2 #A L G*,(* L 6 *,*)*Lθ &) H *,/3D #A H ',3+ L G &) H /0 , '- ,  '/) 6  6  2 #A H ),0' L  τ  θ  1  B  "  $61  "  #C  '(  #  3 +:" +. 3" 7 # )0 9+". - ,!" . )7 -3+:  5  2 ,% $  -,  , ,%  $ ,  =)  "  =* $ ,T  2  #  ,  5  6 , ,  ∆ = F+M ∆t )' #A ',  V  $A  M)' 7 E $K=  '+('  )4(,)0+ )+. &)# +, )'  , ,  +4!. )+. &)#  2  , :  6  6 6  "  6  A ,  $A$  3" . )4(,)0+ )+. &)#"?! . )+ ( ,  F ,%  F  "  , 8  "  " 6 )'  (  )  5  τ  )**-  "  )  Bpred γ + (1-α τ) ⋅ M ref,τ Bpred,ref  M))  )  (∆∆τt ) = (BP ) = α ⋅ M ⋅ (BB τ  ,4 , ,  "  τ  2 C  2  M τ = α τ ⋅ M ref,τ ⋅  C  "  ref,τ  pred pred,ref  )  γ  + (1-α τ) ⋅ M ref,τ + Fτ  M)0  µτ  " , S',-,0  ,%  6  2 ,  ∆τ/∆  µτ,  "  1  B  "  ∆τA∆ τ  #A  =  "  #C  '3  #  τD  6  τ  ,τ  τ  6  D  6  ,  D ,  A , D ,5 =  τ  τK' ατ  6  = * αH*  τ, αH'  K$ ,% γ :  τK*,3  '  τK',0  ,τ  " " ∆τ/∆ H  " 0D  *  γH '  , 5 55  ' , 4 '  :  "  '+/- , = 8  W  '++0D 8  , '++(  $  1,  )0  γ γ ∆τ = P = M ref ⋅ 1 + α ⋅ Bpred - Bpred,ref +F ∆t B B pred,ref γ  :  τ  2  =  2  M)1 D  ()  Bpred γ - Bpred,ref ∆τ = P = P - Fref ⋅ 1 + α ⋅ ∆t B B ref B pred,ref γ  γ  +F  M)-  ), ,  )  (,7  α  γ  ) ∆τ/∆  #A , :  6  6  =)  1  ,: α  8 =)A=,  = W  '++0  =)  =  1  B  "  1,  "  #C  '+  #  =  " , ,  ,  $A*  3" "?! . )+)7 )'  +4!. ( )+. &)#  7  , , ),  ,  2 "  F ),  '  , C, 8  "  (  Φ(2) = Φ(1) ⋅ exp(-µτ)  ,,)/  Φ(1) = (1 − ) ⋅ Φ ref (1) + β  ⋅ Φ ref (1) ⋅ Btot Btot, ref  6  M)(  6  Φ  "  ' τ≥)  ' ,  βH *  I ,8  F  "  ' ,8  F  6  1  M2 =  β  ,% <  "  C  ,  "  γH'  5  5  C  A  , M = α ⋅ Bpred + 1 - α M ref Bpred,ref  ))  a ⋅V⋅ Bpred Bprey  8  ( '++(  V=  v⋅Bprey 2⋅v + a ⋅Bpred B  M2 = 5  , a .v.Bpred 2.v + a.Bpred =A=  M 2ref =  a .v.Bpred,ref 2.v + a.Bpred,ref  X =)A=)  2 =)  =  =  = =)  6  =)  α≈  2 .v = 2⋅V 2⋅v + a⋅Bpred Bprey  5  " BH  A), αH*  α , 5  ' "  D H '  " I  ,  1  B  $;  "  "  #C  .3"?! . )+ +, $ ;$  3"  "  )*  #  -# .  .3"?! . )+  %  Nτ  ,  6  , , 1 1 ϕτ Yτ = t =0 dY ⋅ dt = t =0 ⋅ ∆Φ ⋅ dt dt ϕτ +µτ  ∆Φ  M)3 P τ, τ+∆τQD  ,  7  6 NA τ τ + ∆τ  dY ⋅ dτ = ∆τ ϕτ ⋅ Φ(τ+s) ⋅ ds s =0 dτ  Yτ = τ  M)+  ϕτ  / 5  ))  φτ  )0  6  τ  Yτ = ϕ τ ⋅ Φ τ ⋅ ∆τ  M0*  Yτ = ϕ τ ⋅ Bτ ⋅ ∆τ ∆t  M0*  0*  6 $τ  NτA τ, Fτ  ,5  $τ  = ϕ τ . ∆τ ∆t  M0'  0'  $τ  ϕτ  &  6  -  ϕτ  -  ,  ,  )3  ∆Φ = Φ(τ) ⋅ [1 - exp (-(µτ+ϕτ) ⋅ ∆τ)] )3  7  +  7  )+  Yτ =  ϕτ  µτ+ϕτ  ∆Φ = Φ(τ) - Φ(τ+ ∆τ) E  ,  ϕτ Yτ = ⋅ Φ(τ) ⋅ [1 - exp (-(µτ+ϕτ) ⋅ ∆τ)] , ϕτ +µ τ Yτ = ϕτ ⋅ Φτ ⋅ ∆τ 0* , (  ∆τ  Yτ = s =0 ϕτ ⋅ Φτ ⋅ exp (-(µτ+ϕτ) ⋅ ∆τ) ⋅ ds  ⋅ Φτ ⋅ [1 - exp (-(µτ+ϕτ) ⋅ ∆τ)] , &  +  0*  1  B  "  "  #C  $  )'  #  6  Yτ = ϕ τ ⋅ Pτ = ϕ τ ⋅ Bτ ⋅ (P/B)τ = Fτ ⋅ Bτ  M0)  ϕτ  0) $τ  $ ;*  "  -# . +,  ,  .3 '!#. )+  $  2 , ,  0* 7 Rτ 7 ( '++/  6  4τ  τ Rτ H τ,4τ , 7 Rτ , .  P τ, τ+∆τ]. Τ  S0  %  4τ , ,  4τ  8  4  ,  2  , 6  ΦR  τHΦ  ,τ , 4  M00  τ  (  µ*τ = Ln  Φ*ref,τ ⋅ 1 - ϕ*ref,τ Φ*ref,τ+ ∆τ ∆τ  ϕ*ref,τ =  M01  ϕref,τ  ,  Sref,τ  ϕ∗τ,  Φ*2 = Φ*ref,2 ⋅ Φ 2 = Φ 2 ⋅ Sτ Φ ref,2  M0-  Φ*τ+ ∆τ = Φ*τ ⋅ exp[-(µ*τ + ϕ*τ) ⋅ ∆τ]  M0/  µ∗τ  ,7 6 6 , 4  F  ,5 '+-(  "  C F  :  6  C  1  B  "  "  #C  µ∗τ ,7  ))  #  6 0),  '  )  )  ,  % , 0*  Yτ = ϕ*τ ⋅ Φ*τ ⋅ ∆τ  ,,,0(  $  )  Bτ  = Φ τ ⋅ ∆τ ∆τ/∆t  B*τ  M03  = Φ*τ ⋅ ∆τ ∆τ/∆t  M03  5 ,8  ϕR  $τ,  τ  ∆τ/∆ ,?  . 4τ  $=  , τ  S) #  55  "  ,  &)' . " , ( .. ". ). '"(, + '- '),"# # +: 6 "  "  ,  6 " , 4,5  , 5  τ  4,0  *,' , τ+∆τ  ∆,  ∆  ,  (  ∆C ,  ,  3,5 3,0 2,5  " *,'  Trophic level (TL)  " ∆τ  2,0 0  0,5  1  1,5  2  2,5  Time (year)  ∆τE$ , :!&" ;2 ∆ H *,'  2  S',0,0  3  1  B  "  "  #C  )0  #  2  ∆τ' = ∆t' ⋅ ∆τ ∆t  M0+  " Φ)  % "  )( , 2  A "  ,  "  2  , (  $  Φ τ+ ∆τ', t + ∆t' = Φ τ,t ⋅ exp[ - (µ τ + ϕ τ, t ) ⋅ ∆τ' ]  M1*  Bτ,t = Φ τ,t ⋅ ∆τ' ∆τ'/∆t'  M1'  ∆τC/∆ C  2  )- , )"  2  1' ,  $  Yτ,t = ϕ τ, t ⋅ Φ τ,t ⋅ ∆τ' = ϕ τ, t ⋅ Bτ,t ⋅ ∆τ' ∆t'  M1)  , 5  2 ϕτ  Φτ µτ A  +,  $τ ατ  "  1'  τ  /,  γ  β, 5  "  . +:  ? %  1)  1*  K∆ C  1)  K∆ C, 7  1* ,  4  7  6 S0 , ∆  7 *,'  , 2  ,:  6 $  1*  Φτ +  10 i =1 ∆τ' i , t +10⋅∆t'  = Φτ,t ⋅ exp  6,  [  10  i =1 - (µ τ i  + ϕ τ i ) ⋅ ∆τ' i  ] ,  ∆τC  µτ  ϕτ  '*  1  B  "  "  #C  )1  #  , 5 ,B  6 6  , 7  " ,  00 τ  0(  , #  )  "  #  55  ,  *  " &++:7 &)' . 3" '),"# )'" :"+"&- &!# " 7 7 !+ . )++:  )!." )  . "'  5 6 6  , -1  *$  '!#. )+)7 5&. !# " ) . "' '". 3), *$$  )'')+7 " . !&"  5 6 , A  "  " Biomass flow (t.TL.year )  D  6  ,  High efficiencies  120  Reference  100  Low efficiencies  80 60 40 20 0  '**  )  '*Y  , , &+ 7 "& "7 7 -"+ 6 "µ H *,'* *,*(  D *,'-  , ,  5  3,5  4,0  4,5  5,0  Slow transfers  4  Reference Fast transfers  3  Accumulation  2 1 0 2,0  2,5  3,0  3,5  4,0  4,5  5,0  Trophic level (TL)  :!&" =(  I D  3,0  Trophic level (TL)  ,  )**- D  (  6  2,5  -1  '*** Φ  Flow kinetics (TL.year )  2,0  +. -# - . )+ Φ '  ,  ,$  2  1  B  "  "  #C  )-  #  ( $ ,3  , 2 '-U %, 4 )-U %  # )0 9+". -  ', 7 2  $ , 3 τH0,*  "  F  F  *$*  "  αH*,/  C  C,  +4!. ( )+. &)# )( C,  "  ,  "  )4(,)0+ )+. &)# αH* F " C )'  "  6  *,-,  6 βH*  F  "  βH*,1  C  '!#. )+ . "4  $  6  6  , I ,  2  4 1,0  ,!  0,8  $ +, 4τ  τ-*  -* Y :  '+-(  E E ,  Selectivity  * '  0,6 0,4  TL50=2.5 TL50=3.0 Refer.  0,2  TL50=3.5 TL50=3.0 low S  0,0 2,0  τ-* H 0,*D τ-* H ),-  τ-* H 0,$  2,5  4,0  4,5  :!&" B( 4 6  +,  , $R  3,5  Trophic level (TL)  $ " , 5  3,0  *  )  $R $τ H $R 4τ ,  0'  ϕτ = F* ⋅ Sτ ∆τ/∆t 7  E' = 0,-  M10 6  ϕmoy ϕmoy + µ ϕ  -,*,  M11  5,0  1  B  "  "  #C  )/  #  $ τ ZH 0,- ,  , $  6 , ,  Φ 1(t) = Φ 1 ⋅ ε 1(t)  µ(t) = µ ⋅ ε 1(t)  or  M1"  -* 6 6  6 -'  $R  6  , $ ''  D , ,  ε *,) "', $  ε'  ε2  -*  /'  '**  ε  ,B ε'  '**  ,  , ε2  *,'  *,)  '  0* ,  **  '4 .)7. &+ 7 "&"7 7 -"+  +,7 # )0 9+". - )+!+"<4# ). ", )' 5  40  High efficiencies  2  Biomass (t)  Reference 30  6 ,  Low efficiencies  20  , $ , '*  10  , $ I  0 2,0  2,5  3,0  3,5  4,0  4,5  5,0  Trophic level (TL) 40  Biomass (t)  " @  ,  Slow transfers Reference Fast transfers Accumulation  30  , % $ $ ,  2  '*  ,  20  I  , $  10  < 0 2,0  2,5  3,0  3,5  4,0  4,5  ,  5,0  Trophic level (TL)  :!&" $> ( 5 2 6  , , 6  F7 $ , '* , $  2  C 2  1  B  "  "  #C  , #  6  " 6 "  , 6  *1  )(  #  ,  '4 .)77 -3+:)+ )'  6 $ , '' , ? 6  2 6  ,4 ,  =  ,5 C  6  F  "  $ , '' ,$ τ-* H ),-,  -*Y  , $ Z+* Y  0,-, 4 6  D " 5  F  C  "  C  Z $H*,)  "'  ,  "  , 6 "  $ , ''  , = 6  6 ,  τ-* H 0,*"0,- , 5  6  , " 6  ,  1  B  "  "  #C  1,0  total biomass  25 20  Relative biomass  Biomass per trophic class (t)  30  Increasing fishing effort  15 10  0,6  TL50=2.5  0,4  TL50=3.0 TL50=3.5  biomass of predators  0,0  2,0  2,5  3,0  3,5  4,0  4,5  0,0  5,0  30  0,5  1,0  1,5  2,0  1,0  total biomass  25 20  Relative biomass  Biomass per trophic class (t)  0,8  0,2  5 0  Increasing fishing effort  15 10  0,8 0,6  TL50=2.5 TL50=3.0 TL50=3.5  0,4 biomass of predators  0,2  5 0  0,0  2,0  2,5  3,0  3,5  4,0  4,5  5,0  0,0  30  0,5  1,0  1,5  2,0  TL50=2.5  1,0  TL50=3  25  Relative biomass  Biomass per trophic class (t)  )3  #  Increasing fishing effort  20 15 10 5  TL50=3.5  0,8 0,6 0,4 0,2  0 2,0  2,5  3,0  3,5  4,0  4,5  0,0  5,0  0,0  0,5  Trophic level (TL)  1,0  -1  1,5  2,0  Fishing mortality (year )  :!&" $$ 2 5 I 6  ,  F  "  " D  C  " "  '  D ,  $ , ') " , $ , ') ,  ,5  F  C  ,  B  "  8  "  #C  2  )+  #  " 6  $ , ''  , D ,  F  "  "  C  , :  7 Accessible biomass (t)  1  Increasing fishing effort  6 5 4 3 2 1  6  0 2,0  2,5  3,0  ,  4,0  4,5  5,0  Trophic level (TL)  ?  F  C  " "  250  , 5 ,5  2  200  , 2 "  Biomass (t)  " %  3,5  , , " "  " , 5  150  Unexploiotable biomass 100  Exploitable biomass  50 0 0,0  E  0,5  , ?  1,0  1,5  2,0  -1  Fishing mortality (year )  :!&" $* 2 % 6 6  2 ,  6 F  "  C  Biomass per troph.class (t)  , 25 20  :  15  E B  5  ( '++( "  2 ,  0 2  Biomass per troph.class (t)  C , 5  10  2,5  3  3,5 4 Trophic level (TL)  4,5  5  7  25  , 5  "  20 15  '0  τ-* H 0,,  10 5  ,  0 2  2,5  3  3,5  4  4,5  5  Trophic level (TL)  :!&" $1 2 4 ,4  6  %  $ ,  1  B  "  "  #C  0*  #  $ , '0 8  6 F  "  ,  "  , 5  C  , 2  =  ,  , : D 0 ,5 ϕ/(ϕ+µ) ,  6 , 7 ,  I  , 2  # " 1( $H*  $H)  F  2 C  " ) . "' )+. &)#  ,  & '". "&5 # !"  . ).  "µ τ H *,*( "µ τ H *,'*  "  "µ τ H *,'7 7 " .)7. &+ 7 "&9+". 4 " & $  @>  '-1,*  ((,*  )-0,*  '((,'  (*,*  0-(,)  )'),'  -+,1  '+',3  '++,'  '*0,3  )1*,*  )0*,*  +-,3  00',/  )(/,*  30,)  03',)  )-),-  //,)  )-0,*  '((,'  (*,*  '/(,+  ')0,+  (0,3  50 = 2.7 TL50 50 = 3.0 TL50  -1  Catches (t.year )  60  " 6  , ,  τ-*,  6 ?  6 "  $ , ')  6 "  6 $ , '1  6  " ,! # )' C  @* " &($  . ).  )**,*  .3 '!#. )+ 5  $H*  ,  7 7 " .)7. &+ 7 "&"7 7 -"+ " "µ τ H *,*( " "µ τ H *,'* "µ τ H *,'-  *8  , $H) A  "'  50 = 3.5 TL50  40  20  0 0,0  0,2  0,4  0,6  0,8  1,0  Pseudo exploitation rate 3  4  F  C  #  # AA  [  , , ****)/+0,  A ,  A  )***D A  :!&" $8 ( 6 C  6 F ,  "  B  "  "  #C  I  ,  5 2  F= 6  4  N  " 6  ,  ,? $  '1  τ-* H 0,- $=4  % *,+ , 5  τ H ),"' $ , '- ,  $=4  '1  6  ϕτ H '  TL50=2.5 50  τ-* H 0,*  τ-* H ),,5  !"'  60  6  N  N  "  τ-* H ),-  "'  -1  , $ $ H *,-  "'  ,  TL50=3.0 TL50=3.5  40 30 20 10  %  0 0,0  D  -1  Catches (t.year )  , 5 ,  " !-*H0,* ,  TL50=3.0 TL50=3.5  40 30 20  0  , ,  0,0  2  0,5  1,0  1,5  TL50=2.5  50 -1  Catches (t.year )  )*Y, " ,. I ,  2,0  Fishing mortality F  60  ,%  "  2,0  10  '*Y  "  1,5  50  " $ , '-  1,0  Fishing mortality F  TL50=2.5  , 5  0,5  60  ,5  $ , '-  6  ,  , $ µτ H ),0 !"', 7 $=4 N  "'  6 C =4 N , $ $ 6  '  ? $τ H )  0'  #  Catches (t.year )  1  TL50=3.0 TL50=3.5  40 30 20 10 0 0,0  8  1,0  1,5  Fishing mortality F  $ , ,  '/  0,5  :!&" $6 2  6  ,  "  " "  2,0  1  B  "  "  #C  0)  #  6 $ , '/ $H*,) 0,-,  ,4 6  ,5 -  "'  $H*,0  6 1,-  "'  $H*,3  "'  <  , ,4  %  ( )**- )**/ ,  <  Catch per TL (t.year-1)  2  ,  3,0  3,0  2,0  2,0  1,0  1,0  0,0 2,0  2,5  3,0  3,5  4,0  4,5  Y3  I  '  2,8  Mean biomass TL  Y4.5  Y5  0  0,5  1  1,5  2  Fishing mortality (year-1)  % D  Y4  0,0  5,0  Trophic level  :!&" $A 2 4  Y3.5  D $H*,) F  CD !-*H0,*  "  TL50=3.5  7  TL50=3  2,7  TL50=2.5  2,6  $ , '( , .  2,5  #  2,4  (  F  '++3  C ,  2,3 0,0  0,5  1,0  1,5  2,0  Fishing mortality (year-1)  Mean catch TL  4,0  $ , '( ,  TL50=3.5 TL50=3 TL50=2.5  3,5  $ ,  '(  ,  "  3,0  2,5 0,0  0,5  1,0  1,5  D  2,0  Fishing mortality (year-1)  ,  :!&" $; ( = D 2 2  " "  ,  "  2  ,  1  B  "  *6  "  #C  00  #  + '- '),"#'4 .)77 -3+:)+" )  . "' . # .  ;  $ ,  '3 ,  ' , -'  0* Y  "  ,:  1 6  ,5  I  , 0,-  Total biomass (t)  300  200  , 4 ,  100  ?  Accessible biomass (t)  0 1  11  21  31  41  51  61  71  81  11  21  31  41  51  61  71  81  91  41  51  61  71  81  91  100  50  0 1  Trophic classes  Catches (t.year -1)  40  >3.98 3.22/3.98 2.73/3.22 2.33/2.73  20  2.0/2.33  0 1  11  21  31  Year of simulation  :!&" $=( 4 $R H '  "'D  ε' H *,)  ε) H *D  91  1 -,  1  B  "  "  #C  01  #  Coefficient of variation  0.25  " " $ ,'+ , $ )  1, ,  2  0.20 0.15 0.10  Fished  0.05  Unfished  0.00 TL2  I  TL3  TL4  TL5  Trophic class  , :!&" $B " "  Ouput variablity (C.V.)  ε' H *,)  Unfished biomass Fished acc. biom  \*,**' 6  )* , $  Unfished acc. biom  0.2  $ ,  '  0.1  $ , )* 0.0 0.00  0.05  0.10  0.15  0.20  0.25  0.30  D $ , )*  Acc. biom  1.4  , ,  Input variability sigma(ε 1 )  C.V. ratio (Fished/unfish.)  $R H 'D  7  Fished biomass  0.3  4  ε) H *  , $ $R H ' '- Y  Biomass  "'  1.3  -* Y, 1.2  , 1.1  7 ,  1.0 0.0  0.2  0.4  0.6  0.8  5  1.0  Fishing mortality (year-1)  :!&" *> ( #  ,  , 0*  ε) H * ,  2  $R H '  , ? D  0* ε) ,  \*,**' $ , )* ε'  ,  "  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1  B  "  "  #C  0/  #  ,4  2  , ,W  )**1 , 5  6  )0 )**1  )**3 , 7  $ 2 ,  "  "  & 2 '+(-  +,  " ,5 , ,  I 6  ,  I 6 % %  , ,  D  , , &  "  , )**( ,  6 , )**( , 4 .  5  , '+/+  I %  '++-  6  , 7  6 .  '+/+ D  ,5 , 6 , . , 4 ,5  6 %  :  #  '++3 ,  )**' , , ,7  "4  I  , )**)D %  , )**/ ,  # . , ,  2  I ,#  2  " , ,7  "  , $ 6  ,  +  . I ,  "  F  6C  1  B  "  "  #C  0(  #  . 2  ,? , 6  2 #  C #  )**- , 5  6  6,$ F  6 ( '++3 )**) # , ,  2 6  ,  6 ,  1  3"  1$  .3 &)43- 4" . &!'  &)'  $>  +# -  ) &)43. ). 3"  5  " ,5 6,  6  " S',' , 7 <  2 "  #  " B#7D  7  F  C 6  ,5 '+/-  2 B  %  7  #  '+()  ,  P τ, τ+∆τQ  5 K∆ A), W  Φ(τ) ⋅ e −µτ ⋅ ∆τ / 2  M1/  W  K∆ A)  Φ(τ+ ∆τ) ⋅ e  µτ ⋅ ∆τ / 2  Yτ = Φ(τ) ⋅ e  −µτ ⋅ ∆τ / 2  Φ(τ) = Φ(τ+ ∆τ) ⋅ e  M1/  − Φ(τ+ ∆τ) ⋅ e µτ ⋅ ∆τ/2  µτ ⋅ ∆τ  M1(  + Yτ ⋅ e µτ ⋅ ∆τ/2  W, , #  C  M13 %  2" τ+∆τ  7 τ  C #  '+() ,  Nτ, $  (  Φ(τ) - µτ ϕτ = 1 ⋅ Ln ∆τ Φ(τ+1) '*  13  M1+ %  )**3D  )**1 ,  1  B  "  5  "  #C  2  03  #  τ  2 ) ,% ) ,:  S',0,0  '-  ,  6  "  )-  ()  2  2  γ  ∆τ = P = P ⋅ 1 + α ⋅ Bpred - Bpred,v ∆t B B v B pred,v γ  "  γ  +F  M-*  #A  6  '- , $ 6  0' , 5  ΕΦ τ =  6  ϕτ ϕτ+µτ  M-'  µτ  Nτ α  5  γ  F  α  " C  2 τ+∆τ  τ  τ 6 -'  , (∆τ/∆ )τ  13  1+  )  $τ -*  0'  Φ(τ) ΕΦτ , τ (∆τ/∆ )τ  , #A Φ(τ)  D  (∆τ/∆ )τ,  τ  1*  , ϕτ  (∆τ/∆ )τ  ,  " . +:. 3" '". 3),)+ '!#. ",, . 8  , , % 47, = ,  1*$  )+5"&:"+ " 4&)4"&. " )7. 3"  5  "2  E W  ,4 ,  6  E '+/'  % 47  2  "  ,  $ µτ H ),0  -* *,1D  *,-  6 "µτ H *,'* D '-U %D  2 "  "'  % 47 *,)  '  "',  'α τ-* H 0,* ,  Biomass per troph.class (t)  1  B  "  "  #C  0+  #  100.0  7  10.0  *,-  % 47  ,  1.0  0.1  $ , )' , . F  0.0 2.0  2.5  3.0  3.5  4.0  4.5  5.0  C  5.5  2  1.0  ,  -1  Fishing loss rate (TL )  6  $  0.8 0.6  ,  0.4 0.2  ,  0.0 2.0  2.5  3.0  3.5  4.0  4.5  5.0  5.5  ) ,  -1  Fishing mortality (year )  1.0 0.8  7  0.6  ,  0.4  5  6  0.2  % 47, $ "  0.0 2.0  2.5  3.0  3.5  4.0  4.5  Trophic level (TL)  5.0  5.5  1, % 6  :!&" *$ @ 5 % 47 ,  ,  D D  6,  1**  "+ . 5.. )+4!.4 & '". "&  7  , , D #A  #  55  "4 " 2  % 47, 8  ,4  " ,.  % 47 , % 47  * 5  ),',' "  2 $  2  2  " 3 *,/  F  6  C  6 "' $R H *,% 47  2 "  , ? " D ,$ τ-* H 0,* , ,  1  B  "  2  "  #C  1*  #  % 47  , % 74 C  F % 47 ( &+ 7 "&"7 7 -"+ Fishing mortality (year )  1.8 -1  ( &+ 7 "&9+". -  Low TE  1.6  High TE  1.2  Input values  0.6  0.6  0.4  0.4  0.2  0.2  Bottom-up  1.0 0.8 0.6 0.4 0.2  0.0  0.0  2  2.5  3  3.5  4  4.5  2  5  2.5  100.00  3.5  4  4.5  Fast Kinetics Fast Kinetics Slow kinetics  3  3.5  4  5  Bottom-up Bottom-up 10.0  Top-Down0.6 Top-Down0.6  1.0  1.0  0.1  0.1  0.10  4.5  Trophic level (TL)  Slow kinetics  Low TE  1.00  2.5  100.0  High TE 10.0  2  5  High TE Low TE 10.00  3  Trophic level (TL)  100.0  1000.00 -1  Top-Down0.6  0.8  Input values Fast Kinetics  0.0  Flow per tro.class (t.TL.year )  ( )(,)0+ )+. &)#  Slow kinetics  0.8  Input values  1.4  ,  0.01 0.0  0.0  0.00 2  2.5  3  3.5  4  4.5  2  5  2.5  3  3.5  4  4.5  2  5  2.5  3  3.5  4  4.5  5  Biomass per trophic class (t)  Trophic level (TL) High TE  100  40  Slow kinetics  High TE Low TE  80  40  Bottom-up  Slow kinetics Fast Kinetics  30  Low TE  Bottom-up Top-Down0.6  30  Fast Kinetics  Top-Down0.6  60 20  20  10  10  40 20 0  0 2  2.5  3  3.5  4  4.5  5  0 2  2.5  Trophic level (TL)  3  3.5  4  4.5  5  2  2.5  :!&" ** ( 4  3  3.5  4  4.5  5  Trophic level (TL)  Trophic level (TL)  % 47 2  "  , , E  ,4 % 47  E  ,  % 47 "  6  $ , )) , 5 "  "  , ?  ,  5  "  $ , )) α H *,1 )-Y  " '*Y, ?  ! ,  , 8  % 47 "  αH*  " -Y  α H *,/ ,  1  B  "  "  #C  1'  #  2 $ ,)) '-U %  2 -  ,7  )-U %  -*Y  ,. 2  "  '*U % 2  ,7  % 47 ( '-Y  '*Y  , $ ,))  '**Y  , 6 ,  $ 2 %  % 47 '  ,  ) % 47 , B#7  5  @  , . 2 % 47  =  ,, 5  2 ,5 2  % 47 !' "  11  , =  2 6  44# - . )+. )&" #  6 I  ) #  , 55  ,  " . !,"  % 47  " ,  www.fishbase.org  , 5  $ ,4 !  "  ,  ,  ,  !  % 47  ,7 , , #  ( )**'  , , G  4  )**3D %  ,  )**3 , ,5 "4 8  #  55  1( , % 47 2  I  6 αH*,1  ,7  '*Y % 47  6 S0,1 ,  " #  55  1  B  "  "  #C  1)  #  .  % 47 ,8  ,7  2 , 7 ,$ E  2  E  6 , )**3 6  2 6  #A  C F 6 C ,5 "  ,  2  I  ,7  % 47  6  " 2  ,  $  % 47  %  7  2  " % 47  ,7  2"  < 6  ,=  8  ,  )+ # !)+ . 3" . &)43- # "5"# $  ", 44&) 3  )*  " 6  4 '+(- , 4 6  '+-1 '+-(  : "  ,  , , & 2  '+-(  '+-1 , 4 :  "  '+-(D & 2 '+(2 ,5  2 7  %  7%  6  ,  % 8 , )***D %  8  8 , '++3 )**1 ,  # '++) , '++(  2  A #  " "  , 6  )**) , .  " 6 , 5  D B  / %  " !  )**(  6  ,  1  B  "  "  #C  10  #  (  # /  55  " ,  6  "  "  ,8  "  ,8 F8  C C F:  "  2C  F:  C  6  "  ,7 , #  ,#  $  " ,  "+"& #+7 )&' . )+  $$  . &! . !&" )7. 3"  ) &)43&)!. +"  I ( 2  +  $ , )0 ,  # "  6 ,  "=  "  "% 47,  :!&" *1 (  ) &)43&)!. +" ( & + 4) "  ,.  6  5  1  B  "  "  #C  11  #  , =  "  A  "  , %  (  4  7  ,  6  "% 47  ,  "= , ,4  ( -:+) "=  " *  (  "  + 'A  -, ,  , 5 C "  $*  )  6  I  ,  + .# #. )+)7. 3" 4# !:(+  ,4 , ,B  8 " , !  / ,  " ^  , ,  %  ,  ,  , ^ ^  5 %A# "Z . C 2 " "  ,  , " ,  , ,  , $  A "Z # " 2 .G,  8  /A , .  /  F  C  " 2  6F "  #  I  " ,  "Z  "Z  $ , )1 ,  @ :!&" *8 2 #  1  B  $1  "  "  #C  1-  #  ,,. )+ #+7 )&' . )+ $1$  +:" )7. &)43- # "5"# +. 3" &" !# . " '  ' ,&  )  (  *,'  6 /  -,+ ,B  ( "  S ',/,' , $1*  . ! ",+. 3" ' +! # / 7 :!&"  )-  , )**3 %?4: CE  E '+3-  ,, % ? , )**(  $ V  )**1, =  4 != '+3- )**1 01  2  :  , , )1 ,#  #A  TA  _  )**1  ,  ,,.  ,  *  ( & + 4) " # ))9+: . +  *$  )4 . 3'),"#! +:  ) &)43  3 .- .! ",7 )&D " , S ',1 , ,B  "  2 , "  2 "  ,5  " , 7  "  " I  **  C  )0 .0)&9 I  6  ,  "  ,  "  1  B  "  "  #C  1/  #  "4 A  F  A  "4  6C  ,  # '  6 N,  )  #A #H #A  6  "4  N  R  #  6 ,  6  ,  A , 6F  "4  C  ,  0 )  6 ,  2 ),  1  A  , ,  , -  .  2 , "  F=  C  I 1  "  ,  "  1  B  "  "  #C  $ %& "4 %  #  6 %4  4  , 4  6  F ),*  /,+  1(  #  6 C ,  4  4,  %4 ',  *,' "4 ,  ! ,G  % A ,  !?  !  , 3" .+, &, ,"5-. )+ , 5  C  %  2  ,;  "  4 !  . 3")&". - #'),"# " F4  ,  C  $ ! H4 , ?  F4  R  !"*,*-  C  )- , 4  !  *,*-  *,*(, .+, &,,"5-. )+)7" . ' . " )7. &)43- # "5"# 7 &)' 6 % # '++) 6  )4 . 3'),"# , "4  "  , !  ? % ,$  6 6  !  ,%  6 !  6  I  ,?  2 6  ,  ' +! # # ,"7 +" :' $  ,  ,  [[[[[[[[[[[[[[[[[[[ " 3+- #+). " 5  )  0  ,  6  " !  ,5 !·!?  !  !  %  "4 !  A  5  " !  ? !?  ! ,  6  % F4  % C,  " ,4  6 ,  ,  1  B  "  $  "  #C  )-  13  #  "4 ,  01 $ , )- , $  !  ),-(  1 % ),/, !  ),D  % $ , )- , I  I  ,  4  $ , )- ,  ( 4  )' 7 )&" 3 4" " )& :& )!4% '" +  Small zooplankton  Biomass (T/Km2)  Turtles 3  Benthos Mullets+  2  Bonga Sardinella+  1  Large zooplankton Crustacea  0 2  2,5  3  3,5  4  …  4,5  Trophic level TL  ( ):( )& ' #,-. & -!. )+ . 3")& ". - #'),"#  Biomass distribution (%)  0,8  0,6  0,4  S param. = 0.075  0,2  0,0 2  3  4  5  Trophic level TL  ( )'  Biomass (T/Km2)  2,5  . & )43- 4" . &!'% !+" $B=6  Large zooplankton Cephalopods  2,0  Crustacea 1,5  Mullets+ Seabream+  1,0  Sardinella+ 0,5  Bonga  …  0,0 2  2,5  3  3,5  4  4,5  5  5,5  Trophic level TL  :!&" *6 (  "4 2  , , D ,!  6  1  B  "  "  #C  6D , I 2  4  # "8  1+  #  D  4 D  "7 +. )+ )7. 3" 5 &- # " 4&" "+. ",+  (  +. # "  4  )  #  . "' )'  ')!+.)7 )' . &)43- # "5"#+  "  -# ". )7 -3"&"  . 3 .4 " &  " . 3&)!:3"  G  4"",)7. 3" )' . &)43- # "5"#  7 # )0 4  %  ')!+.)7 )' "<. & . ",7 &)' . 3" " ) . "' 7 -3+: &)4)&. )+)7. 3" )' 7 -3+:  $ 7  &)4)&. )+)7. 3" " - ,5"&. ", 7 -3+:  3  +:. 3&)!:3. 3"  7 # )0 . 3 .- ,5"&. ", -# " )'  7 # )0 . 3.  &  ;  ')!+.)7)&: +- ' . . "&4&" "+.+. 3" " ) . "' . &)43- # "5"#  7  2,  `  ',0,'  R`  )'"))  a`  ,  b`Ab  !,  N`  ,  ',0  "'  ',-  "'  ',(  "'  c`  !"'  ',0,)D ',(,'  cR`  !"'  ',(,)  !"'  ',0,)  ?  &)4)&. )+)7. 3" )' 7 # )0 # ) . ." 3 . &)43- # "5"#,!" . ),:" . )+%"< &". )+%".  d`  $  &)4)&. )+)7. 3" )' )7" . 3 .- &"')5", 7 -3+:  dR`  "'  ',(,'  $`  "'  ',(,)  7  &)4)&. )+)7. 3" 7 -3+:  "  3. &)43- # "5"#  -# " )'  &)4)&. )+)7" 3. &)43- # "5"# / " -# ". )7 -3+:  4  &"')5", )'  . 3.  5"& :" . '" ..9" +!+.)7 )' 4&),! ", .. 3" 7 & .. &)43- # "5"#. )&" 3 :5"+. &)43- # "5"# %)&% 5"& :" :" )7. 3" )' 4&" "+. ." 3. &)43- # "5"#  *1  ',(,)  b  ',-,'  )0 . )! " .  #  &  1/ " "  %  E # # F 2 % % 1 /<  E & 1 /<  1 (D 1 %  %  G H  # F !  / F  #  % # 1 /& F 2 G % G ( /  % % % G  7 %  ( 1 /&  1/ #  "=  ,5  " "4  7  " /  # "  (  " " 1  4`  4  .  6;  "= 6  '  ! 6  " )  $ , )/ , 7 6 (,  -,!  "4 0  ,  1  B  "  "  #C  :!&" *A ( .  E =  -*  #  E  "  F7  F7 2  F%  C  C  C "  " 4  $ , )( , ?  ,  "  =  ,4 2  6  "  "  ,  :!&" *;( .  ;  F7  E 7  4  E  "  F;  C  C,  H *,*( , ;  F;  "  C F7 "  C F.  6C  ,$  , 2  1  B  "  F%  "  #C  C  ,  "  " % 2  -'  #  F#  "  C  ,  F=  C  $ , )3 2  "  ,  :!&" *=( 6 " F4  F#  4 $ , )+  F7 F#  , #  F#  C  C  C F#  C  ,  I  C  C  F#  C  A < 6  ,, , ,  "  ,? 4  2  ,  7 " $ , )+  ,  "  6  < 6  I A  ,  1  B  "  "  #C  -)  #  0.7 0.6  Biomass  0.5 0.4 0.3 0.2 0.1 0 2  3  4  5  6  Trophic level  :!&" *B( 7  F#  C  6  *8  " ,  < 6  < '4# " )7 44# - . )+ $  3  " , )**3 ,  $ D  2 1 %  #%  '+3$ , 0* $ , 4  )**1 , D 6  , ,!  , ,  " "  D  !Z1,* $ , 0* ,5  !  1 6 ,  B  "  "  #C  -0  #  Biomass per trophic class (T/Km2)  !+" $B=6  !+" *>>8  3.0  3.0  2.5  2.5  2.0  2.0  1.5  1.5  1.0  1.0  0.5  0.5  0.0  0.0 2.0  2.5  3.0  3.5  4.0  4.5  5.0  2.0  5.5  2.5  3.0  3.5  Catches (T/Km 2)  Small scale fishery Fish.mortality 1985  0.3  0.4 0.2 0.2 0.1  0.0  0.0 3.0  3.5  5.0  4.0  4.5  5.0  0.4  0.6  Small scale fishery Fish.mortality 2004  0.3  0.4 0.2 0.2 0.1  0.0  5.5  0.0 2.0  2.5  3.0  3.5  Trophic level TL  4.0  4.5  5.0  '+3-  )**1  "  D D  (  1$  5.5  Trophic level TL  :!&" 1> ( 7  1  0.6  Industrial fishery Catches (T/Km ) -1) Fishing mortality (year  Industrial fishery  2.5  4.5  Guinea 2004  Guinea 1985 0.4  2.0  4.0  Large zooplankton Cephalopods Crustacea Bathy-dem invert.eaters Bathy-dem pred.eaters S. demersal invert.eaters ML demers. invert.eaters SM demersal pred.eaters L. demersal pred.eaters Soles+ Grunts+ Mullets+ Sea catfish Seabream+ Royal threadfin Giant Afr. threadfin Lesser Afr. threadfin Other croakers Bobo croaker Sardinella+ Ethmalosa Horse mackerels+ Carangids Barracudas+ Large pelagics Sharks+ Rays+ Sea birds Turtles Dolphins Whales 5.5  I  2  ,  " . 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" 6  , )**1 , %  $ , 10 , , )**1 4 _ ( )**1 , Z' $ , 10 , 2  I 4  , )**1D !  )**1 , 1.0  100.00  10.00  Biomass per trophic class (t/Km2)  Biomass per trophic class (t/Km2)  Biomass trophic spectra Increasing fishing efforts  1.00  0.10  0.01  Catch trophic spectra 0.8  0.6 Increasing fishing efforts  0.4  0.2 0.0  2.0  2.5  3.0  3.5  4.0  4.5  5.0  2.0  2.5  3.0  Relative change in biomass  3.0  3.5  4.0  4.5  5.0  Trophic level TL  Relative catch in the trophic class  Relative biomass in the trophic class  Trophic level TL  TL 5.0 TL 4.5 TL 4.0 TL 3.5 TL 3.0  2.0  1.0  Relative change in catch  3.0  TL 3.0 TL 3.5 TL 4.0 TL 4.5 TL 5.0  2.0  1.0  0.0  0.0 0.0  1.0  :!&" 81 ( 4 , )**1  2.0 3.0 Fishing effort multiplier  4.0  0.0  5.0  1.0  2.0  3.0  4.0  5.0  Fishing effort multiplier  F 6  ,5  C  , ,  ,  6 6$  (  + '- ! +:  ) &)430. 3. '" "&"  3 .- .! 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"  , " ,=  6  ,  7  ,5 '*  '+++  )**)  ,  2 ,  1  B  "  ()  #  )  100,00  ) 0,8 0,6 0,4  1985 2004  0,2 0,0 2,0  2,5  3,0  3,5  4,0  Biomass trophic spectra  2  Catch trophic spectra  1,0  Biomass per trophic class (t/Km  2  Biomass per trophic class (t/Km  "  #C  4,5  10,00  1,00  0,10  1985 2004  0,01 2,0  5,0  2,5  3,0  Biomass (t/Km 2)  3,0  12 9  2,0  6 1,0  Acc.Biom. Pred.Biom. Catch  3 0 1985  1990  1995  2000  0,0 2005  Catch (t/an/Km2)  Change in total biomass & catch  15  3,5  4,0  4,5  5,0  Trophic level TL  Relative biomass per trophic class  Trophic level TL  Relative change in biomass  1,0 0,8 0,6 0,4  3,5 4,0 4,5  0,2  5,0 5,5  0,0 1985  :!&" 6$ 2 :  1990  '+3D  '+3-  1995  )**1  )**1  2000  2005  ,% , " ,  $ 6  " ,5  ,  ,$ 2  2 , , 8  %  " , " ,  1  B  "  "  #C  (0  #  H  6 ;  = 46  % $  % 4  B  7  4,=, G  7  &,&, '+(', &  7  "4  = % $ =.5$"% ")**/"03(/( , 7 ; # < $ % 2 47;# ,! 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TE accounts for individual energy losses due to respiration, digestion, excretion, etc., as well as losses due to non-predatory mortality, e.g. when individuals are not being consumed because they are protected from predation or because consumers are saturated, such as may happen during phytoplankton blooms (Cushing 1973). TE is thus a general measure of an ecosystem’s efficiency at transferring energy from low to high trophic levels. In EcoTroph, the decline of production between trophic levels is modelled as a declining exponential function, with TE representing the proportion of production left over a transfer of one TL unit. In other words: Production(TLn+1) = Production(TLn)×exp(log(TE)) In EcoTroph, most especially in the catch trophic spectrum analysis (CTSA), results are very sensitive to the value of TE (see § 3.2.2 in main text). Also, in marine ecology and in fisheries science in general, TE is an essential parameter involved in answering a number of important questions, such as the fraction of total primary production that is used by fisheries (Pauly and Christensen 1995), the effects of fishing at an ecosystem scale (Libralato et al. 2008), or the energy used by different groups of fish (Jennings et al. 2008). An average value of TE=10% is obtained for marine ecosystems in general (Pauly and Christensen 1995), which, perhaps surprisingly, also seems to apply to other systems (Morowitz 1991) However, the average value estimated by Pauly and Christensen (1995) masks a great variability between ecosystem types (Pauly and Christensen 1993; Jarre-Teichmann and Christensen 1998). Thus, having access to ecosystem-specific estimates of TE would greatly contribute to our understanding of ecosystem functioning and its interaction with fishing. Here, we elaborate on a method previously presented in Pauly and Palomares (2005) to estimate the transfer efficiency of an ecosystem based on time-series of catch and TL data. This method assumes that, for a given ecosystem, the proportion of production exploited at each trophic level is constant, so that we would expect total catches to decrease with increasing mean TL of the catch at a rate that is proportional to TE (see Fig. A4). Assuming that production declines exponentially with trophic levels (as modelled in EcoTroph), the relationship between the mean trophic level of the catch and the log(catch) is thus linear, and the TE can be Figure A4 - Illustration of the rationale behind the extracted from the slope as TE=10b , where b is the estimation of TE from mean TL/catch time-series. If slope and the mean trophic level is the explanatory the proportion of production exploited is constant between TLs, catch should decline with increasing TL variable. at a rate proportional to TE, reflecting the concurrent decline in production by TL.  For this method to work optimally, the total catch/mean TL time-series used need to have sufficient contrast in the mean TL of the catch, and not be affected by major changes in the effort patterns of the underlying fleet. Moreover, the catch must come from the same ecosystem (or a relatively small region); otherwise an observed increase of the catch could reflect a geographic expansion of the fleet (Bhathal and Pauly 2008). If dealing with catch data from larger regions (e.g. FAO areas, as in Pauly and Palomares  80  1  B  "  % '0+,  B, 8  % %  =, # 4 ?  % _  5,  #, 4  4, 4  4  ,5 , %  5  ,  ,  ?  ] _ 6_  .  ,4  "B  , !  l $, 5  #  4  $  _  k  _ ] _ !  C:  _  % , 0)@00,  , % ,  _  6_  ]  _  6  j -]  E _, 5  4 , !  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B  (/  #  , %  ,$  ,=  G, # , '++(, , '** ')-"'01,  , '++(, 4 , ( '0+"'(),  " 6  "  B, '++3, ,  7,  7, #  , ) -0+"--1,  , )**1, =  ,$ ,7  #  !  ,  $  ,-  1  B  "  "  #C  2  I  ((  #  (  . <  S',),0 ,  $  %  8 0  , 7  0,*"0,0 $ , 7'  , 5 2  #A  #  6  6  !0  ,7 0, 7 1,0  6  .+, &,  ) &)43'),"#  Vulner. Biomass vB Selectivity  5  0,8  4  0,6  3  0,4  2 0,2  1 0  0,0 2  2,5  3  3,5  4  4,5  5  5,5  6  P/B  3 2 1  Flow \ trophic class (t.year-1)  Speed of the flow (TL.year-1)  100,0  4  0  1,0  0,1  0,0  2,0  2,5  3,0  3,5 4,0 Trophic level (TL)  4,5  5,0  2,0  20  Catch per TL (t.year-1)  Biomass per trophic class (t)  Flow P 10,0  B 15  10  5  2,5  3,0  2,5  3,0  3,5 4,0 Trophic level (TL)  4,5  5,0  3,0  2,0  1,0  0,0  0 2,0  2,5  3,0  3,5  4,0  4,5  2,0  5,0  Trophic level (TL)  :!&"  3,5  4,0  4,5  5,0  Trophic level  $27  2 ,  #A  1  B  "  "  #C  5  (3  #  $ , 7) 2  6  ,  ,5  6  <  ,7 ! 1,*"1,0  ' 1,* ! 0,*"0,0  6 #A  1,0  ,  7  ),7 ",  ) &)43'),"#  1,0  6  Φ τ +1 = φτ . exp(-ϕ-µ)  Vulner. Biomass vB Selectivity  5  0,8  4  0,6  3  0,4  2 0,2  1 0  0,0 2  2,5  3  3,5  4  4,5  5  5,5  6  Flow \ trophic class (t.year-1)  Speed of the flow (TL.year-1)  100,0  4  P/B  3 2 1  3,0  3,5 4,0 Trophic level (TL)  4,5  1,0  0,1  5,0  20  Catch per TL (t.year-1)  Biomass per trophic class (t)  2,5  10,0  0,0 2,0  0 2,0  Flow P  B 15  10  5  2,5  3,0  3,5 4,0 Trophic level (TL)  4,5  5,0  3,0  2,0  1,0  0,0  0 2,0  2,5  3,0  3,5  4,0  4,5  2,0  5,0  3,0  3,5  4,0  4,5  5,0  Trophic level  Trophic level (TL)  :!&"  2,5  * 2 7  2 ,  #A  1  B  "  "  #C  (+  #  0,0, ? $ ,70  ,  8  < ,  1,0  8,0  Standard EcoTroph  0,8  6,0  0,6 4,0  2,0  0,0  0,4  Catches  0,2  R.Total.Biom  0,0 0,0  0,5  1,0  1,5  R.Access.Biom  2,0  Fishing mortality F  8,0  1,0  Modified EcoTroph  0,8  6,0  0,6 4,0 0,4  R.Total.Biom  2,0  0,2  0,0  0,0 0,0  0,5  1,0  1,5  Fishing mortality F  :!&"  Catches  1 2%  2,0  R.Access.Bio m  EcoTroph: a trophic level based software, Gascuel, Tremblay-Boyer and Pauly  APPENDIX II - ESTIMATING TRANSFER EFFICIENCY FROM CATCH DATA  Transfer efficiency (TE) represents the proportion of the production of lower trophic levels that is transferred to higher trophic levels (see § 1.3.2 in main text). TE accounts for individual energy losses due to respiration, digestion, excretion, etc., as well as losses due to non-predatory mortality, e.g. when individuals are not being consumed because they are protected from predation or because consumers are saturated, such as may happen during phytoplankton blooms (Cushing 1973). TE is thus a general measure of an ecosystem’s efficiency at transferring energy from low to high trophic levels. In EcoTroph, the decline of production between trophic levels is modelled as a declining exponential function, with TE representing the proportion of production left over a transfer of one TL unit. In other words: Production(TLn+1) = Production(TLn)×exp(log(TE)) In EcoTroph, most especially in the catch trophic spectrum analysis (CTSA), results are very sensitive to the value of TE (see § 3.2.2 in main text). Also, in marine ecology and in fisheries science in general, TE is an essential parameter involved in answering a number of important questions, such as the fraction of total primary production that is used by fisheries (Pauly and Christensen 1995), the effects of fishing at an ecosystem scale (Libralato et al. 2008), or the energy used by different groups of fish (Jennings et al. 2008). An average value of TE=10% is obtained for marine ecosystems in general (Pauly and Christensen 1995), which, perhaps surprisingly, also seems to apply to other systems (Morowitz 1991) However, the average value estimated by Pauly and Christensen (1995) masks a great variability between ecosystem types (Pauly and Christensen 1993; Jarre-Teichmann and Christensen 1998). Thus, having access to ecosystem-specific estimates of TE would greatly contribute to our understanding of ecosystem functioning and its interaction with fishing. Here, we elaborate on a method previously presented in Pauly and Palomares (2005) to estimate the transfer efficiency of an ecosystem based on time-series of catch and TL data. This method assumes that, for a given ecosystem, the proportion of production exploited at each trophic level is constant, so that we would expect total catches to decrease with increasing mean TL of the catch at a rate that is proportional to TE (see Fig. A4). Assuming that production declines exponentially with trophic levels (as modelled in EcoTroph), the relationship between the mean trophic level of the catch and the log(catch) is thus linear, and the TE can be Figure A4 - Illustration of the rationale behind the extracted from the slope as TE=10b , where b is the estimation of TE from mean TL/catch time-series. If slope and the mean trophic level is the explanatory the proportion of production exploited is constant between TLs, catch should decline with increasing TL variable. at a rate proportional to TE, reflecting the concurrent decline in production by TL.  For this method to work optimally, the total catch/mean TL time-series used need to have sufficient contrast in the mean TL of the catch, and not be affected by major changes in the effort patterns of the underlying fleet. Moreover, the catch must come from the same ecosystem (or a relatively small region); otherwise an observed increase of the catch could reflect a geographic expansion of the fleet (Bhathal and Pauly 2008). If dealing with catch data from larger regions (e.g. FAO areas, as in Pauly and Palomares  80  1  B  "  "  #C  3'  #  )**-  $ $  # 8 != $ , 7- ,  6 %  % I  $  ,  " "  $  "  6  ,  8  !=  )**3 , 4 % 4 - 2 ! # < *,! ,A! , 8 *,,  4  W  ( )**1  TLy=Σi(TLi×Yiy)/Σi(Yiy) N  !  " , 8 *,*3) !A ,  2#  4  #  *,'*' $ , 7- ,  W  ,  '*Y 6 )**, %  ,7 C $ %  *,*/)  6 4  %  " 6 , "  6 , !  2  6 6  2  ,: , ,  6  6 !, " ,  4  1  B  :!&" 6 ( A!=  "  "  #C  3)  #  "  !  , ! !D  6  ,  != D  ! ,# ,  

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