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An Optimization model of British Columbia’s Georgia Strait chinook and coho salmon fishery Staley, Michael James 1978

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AN OPTIMIZATION MODEL OF BRITISH COLUMBIA'S GEORGIA STRAIT CHINOOK AND  COHO SALMON FISHERY  by MICHAEL B..Sc, U n i v e r s i t y  A THESIS SUBMITTED  JAMES STALEY of B r i t i s h  Columbia,  IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE O  in THE FACULTY OF GRADUATE STUDIES (Department o f Zoology)  We  accept this to  t h e s i s as conforming  the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA O c t o b e r , 1978  ©  1974  M i c h a e l James S t a l e y ,  1978  In presenting this thesis in partial fulfilment of t h e r e q u i r e m e n t s an advanced degree at the University of B r i t i s h C o l u m b i a , the  I agree  that  Library shall make it freely available for r e f e r e n c e and s t u d y .  I further agree that permission for extensive copying o f t h i s for  thesis  scholarly purposes may be granted by the Head o f my D e p a r t m e n t o r  by his representatives. of  for  It  is understood that c o p y i n g o r p u b l i c a t i o n  this thesis for financial gain shall not be allowed without my  written permission.  Department of The  S?fl o L-Q (',  University of B r i t i s h Columbia  2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date  (KJr  2. •/-  t °i'1  Y  &flSTaBACT  A  computational  multidimensional  procedure  .  for  optimization  m o d e l s i s p r e s e n t e d . The  to  a model o f t h e G e o r g i a S t r a i t s p o r t and  of  Chinook  C Oncorhynchus tshawytscha  salmon. Optimal compared  to  performance, are  current  age  of  near  end  of the The  insignifigant.  zero  must  be  and  However,  fish  and  left  fisheries  ( fi, k i s u t c h  are c a l c u l a t e d  Differences,  population l e v e l s p l a c e d on  coho  large  i s applied  commercial  for these f i s h e r i e s regulations*  structure,  in  inorder harvests  and  form  present  )  and  seasons to  match  a  value  i n the water a t the  season.  computational  proportional thesis  and  procedure  ) and  between t h e o p t i m a l s e a s o n s  minimal  present  seasons  of  to  those  the o p t i m i z a t i o n  requirements  of  the  optimization  are  of t h e model. I n t h e c a s e s t u d y i n t h i s required  t i m e s t h e computer t i m e o f t h e  approximately  model.  eight  to  ten  iii T A B L E O f CONTENTS  T I T L E PAGE  .  .. . i  ABSTRACT  i  T A B L E OF CONTENTS LIST  i  OF T A B L E S  L I S T OF  i i  .....v  FIGURES  ...vii  ACKNOWLEDGEMENTS  x  1.  INTRODUCTION  1  2.  COMPONENTS  8  2.1.  3.  Bioloqy  9  2.1.1.  Life  2.1.2.  Natural  2.1.3.  "Shaker"  2. 1. 4.  Growth  2.2.  History  10  Mortality  ..14  Mortality  15  .  T h e D y n a m i c s Of  16 Fishinq  2.2.1.  Sports  2.2.2.  Commercial E f f o r t  2.2.3.  Catchability  Effort  Effort  ..17  Response  18  Response  30 ....39  2.3.  Controls  43  2.4.  Value  44  2.4.1.  Commercial Fishery  2.4.2.  The  OPTIMIZATION 3.1.  Fish  3.2.  Effort  i  Benefits MODEL  Dynamics  Of The S p o r t  45 Fishery...  46 50 54 .56  iv  4.  5.  6.  3.3.  Controls  3.4.  Revenue  57 ...57  OPTIMIZATION  59  4.1.  Mathematical  4.2.  The  Formulation  Alqorithm  OPTIMIZATION  61  RESULTS  62  5.1.  Findinq  An O p t i m a l  5.2.  Optimal  Policy  5.3.  Increased  5.4.  Size  5.5.  Increased  5.6.  Enhancement  Policy  (Convergence)  AND  Escapement  ....67 69  Sport  Efficiency  71 ..73  CONCLUSION  6.1.  Georgia  6.2.  The  Strait  6.3.  Optimization  ....76  Fishery  76  Methodology  CITED  64 66  Limits  DISCUSSION  LITERATURE  59  And  80 Resource  Manaqement  82 84  APPENDIX  1  89  APPENDIX  2  95  v LIST  T a b l e 1: C u r r e n t C a t c h "' Month.  Table  2:  Initial  and  and  Target  gf'yffilPfcffS.  Effort  Data f o r G e o r g i a  Population  Strait ....  Pq.  41  ....  Pq.  63  Pg.  66  ••• . . . . P q .  74  Sizes.  T a b l e 3: I n t e r m e d i a t e P o l i c i e s f o r C o m p u t a t i o n P o l i c y Under •"Current** C o n d i t i o n s . ,  of  Optimal ....  Table  Table  4:  Optimal  Seasons w i t h  Enhanced  5: a C o m p a r i s o n o f t h e O p t i m a l Other P o l i c i e s .  Coho.  Policy  with  a V a r i e t y of ....  Table  by  Pq.  79  6; P r e d i c t i o n s f r o m t h e G e o r g i a S t r a i t S i m u l a t i o n H o d e l Under t h e A s s u m p t i o n s o f 50 P e r c e n t Shaker m o r t a l i t y i n t h e T r o l l F i s h e r y , 80 P e r c e n t S h a k e r m o r t a l i t y i n t h e S p o r t F i s h e r y and S p o r t E f f o r t B e s p o n s e . .... Pq. 89  T a b l e 7: P r e d i c t i o n s f r o i t h e G e o r g i a S t r a i t S i m u l a t i o n Model Under t h e a s s u m p t i o n s o f 30 P e r c e n t Shaker m o r t a l i t y i n t h e T r o l l F i s h e r y , 30 P e r c e n t S h a k e r m o r t a l i t y i n t h e S p o r t F i s h e r y and S p o r t E f f o r t B e s p o n s e . .... Pq. 90 T a b l e 8: P r e d i c t i o n s from t h e G e o r g i a S t r a i t S i m u l a t i o n Model . Under t h e A s s u m p t i o n s o f 50 P e r c e n t S h a k e r m o r t a l i t y i n t h e T r o l l F i s h e r y , 80 P e r c e n t S h a k e r m o r t a l i t y i n t h e S p o r t F i s h e r y and F i x e d S p o r t E f f o r t P a t t e r n . .... P g . 91 j;  vi Table 9: P r e d i c t i o n s from the Georgia S t r a i t S i m u l a t i o n Model Onder the Assumptions o f 30 Percent Shaker m o r t a l i t y i t the T r o l l F i s h e r y , 30 Percent Shaker m o r t a l i t y i n the Sport F i s h e r y and Fixed Sport E f f o r t P a t t e r n , .... Pg. 92  V i i  L I S T OF FIGURES  F i g u r e 1: G e o r g i a S t r a i t , F r a s e r R i v e r Escapement R i v e r G i l l n e t C a t c h o f C h i n o o k Salmon.  and F r a s e r .... Fg • , 3  :  F i g u r e 2: G e o r g i a S t r a i t , F r a s e r R i v e r E s c a p e m e n t and F r a s e r R i v e r G i l l n e t C a t c h o f Coho Salmon. .... Fq. 4 F i g u r e 3: G e o r g i a S t r a i t T r o l l and S p o r t C a t c h , and a v e r a g e a e i g h t o f C h i n o o k Salmon.  Troll  Effort  • .... Pq. 5 F i g u r e 4: T a g R e c o v e r i e s c f t h e G e o r g i a Salmon. ,  Strait  Coho and C h i n o o k .... P q . 11  F i g u r e 5: Escapement T i m i n g Salmon.  Figure  f o rGeorgia  Strait  6: S i z e a t ftge o f C h i n o o k a n d Coho  C h i n o o k and Coho .  .... Pg. 12  Salmon. • .... P g . 17  F i g u r e 7: E f f o r t and CPUE i n t h e G e o r g i a J a n u a r y t o a p r i l 1968 - 1975.  Strait  Sport  Fishery  .,.v>::,'P';g'.-,;20 ;  F i g u r e 8: E f f o r t and C P U E i n t h e G e o r g i a S t r a i t Kay 1968 - 1975. /  Sport  ;  Fishery  .... Pq. 21 F i g u r e 9: E f f o r t and CPU! i n t h e G e o r g i a J u n e 1968 - 1975.  Strait  Sport  Fishery  ;  .... Pq. 22 F i g u r e 10: E f f o r t a n d CPUE i n t h e G e o r g i a J u l y 1968 - 1975.  Strait  Sport  Fishery  .... P g . 23  viii Figure 11: E f f o r t and CPUE i n the; Georgia S t r a i t Sport F i s h e r y August 1968 - 1975. . .... Pg. 24 F i g u r e 12: E f f o r t and CPUE i n the Georgia S t r a i t S p o r t F i s h e r y September 1968 - 1975. ...• Pg. 25 F i g u r e 13: E f f o r t and CPUE i n the Georgia S t r a i t Sport F i s h e r y October 1968 - 1975. / . ... Pq. 26 F i g u r e 14: E f f o r t and CPUE i n the Georgia S t r a i t Sport F i s h e r y November 1968 - 1975. • .... Pq. 27 F i g u r e 15: E f f o r t and CPUE i n the Geprgia S t r a i t Sport F i s h e r y •.December 1968 - 1975. • .y^.VPg. 28 Figure 16: Batio o f E f f o r t t o CPUE i n t h e Georgia s t r a i t • Fishery. ....  Sport Pq. 29  Figure 17: E f f o r t and CPU! i n t h e Georgia S t r a i t Fisfcery A p r i l 1965 - 1974.  commercial  F i q u r e 18: E f f o r t and CPUE i n the Georqia S t r a i t F i s h e r y May 1 9 6 5 - 1 9 7 4 . ,  commercial  Figure 19: E f f o r t and CPUE i n the Georgia S t r a i t F i s h e r y June 1965 - 1974. r  commercial  F i g u r e 20: E f f o r t and CPOE i n t h e Georgia S t r a i t F i s h e r y J u l y 1965 - 1974.  commercial  F i g u r e 21: E f f o r t and CPUE i n t h e Georgia S t r a i t F i s h e r y August 1965 - 1574.  commercial  .... Pq. 32  .... Pq. 33  .... Pg. 34  .... Pg. 35  .... Pq. 36  ix F i g u r e 22: E f f o r t and CPOE i n t h e G e o r g i a F i s h e r y September 1965 - 1974.:  Strait  commercial Pg.  F i g u r e 23: E f f o r t and CPOE i n t h e G e o r g i a F i s h e r y O c t o b e r 1965 1974.  Strait  commercial ....  Figure  24:  Parameters o f the T r o l l E f f o r t  37  Pg.  38  Response Model., .... Pg.  39  F i g u r e 25: C a t c h a b i l i t y C o e f i c i e n t o f the; G e o r g i a S t r a i t S p o r t F i s h e r y * a s a F u n c t i o n o f t h e ;age o f C h i n o o k and Coho , Salmon. • ^vv.>;*P-g.- 42 F i g u r e 26: C a t c h a b i l i t y C o e f i c i e n t o f the G e o r g i a c o m m e r c i a l F i s h e r y , a s a F u n c t i o n o f t h e Age and Coho Salmon.  F i g u r e 27: L a n d e d P r i c e per Coho Salmon.  Pound  F i g u r e 28: R e c r e a t i o n a l V a l u e o f the Georgia S t r a i t .  Figure  29:  Distribution  Strait of Chinook ....  of T r o l l Caught Chinook •• .... a Boat-Day c f S p o r t  of Bags i n the  43  and Pg.  Effort ....  Georgia  Pg.  Pg.  46 in 48  Strait Fishery. • .... Pg. 52  F i g u r e 30: O p t i m a l S e a s o n s f o r S p o r t and T r o l l F i s h i n g i n t h e G e o r g i a S t r a i t w i t h R e s p e c t t o I n c r e a s e d E s c a p e m e n t and I n c r e a s e d Shadow P r i c e . .... Pq. 68 F i g u r e 31: O p t i m a l S e a s o n s f o r S p o r t and T r o l l F i s h i n g i n the Georgia S t r a i t with Respect t o I n c r e a s e d S i z e Limits;. • .... Pg. 70  F i g u r e 32: O p t i m a l S e a s o n s f o r S p o r t and T r o l l F i s h i n g i n t h e G e o r g i a S t r a i t with Respect to I n c r e a s e d E f f i c i e n c y i n the Sport F l e e t . '• . ... Pq. 72  ACKNOWLEDGEMENTS  I  would l i k e  his  support and encouragement  The  work  and  appreciation  would n o t have  been  durring possible  needed  and  ft.W.  draft  I would  like  understanding  s  (Sandy)  were o f e n o u r m o u s  t h e t a n g l e o f t h o u g h t s . I am i n d e b t e d  A n d e r s o n a n d C a t h y L e w who t u r n e d Finally  by Hr.  insight  t o d e v e l o p t h e p r o c e d u r e a n d D r P.A.  ,  organizing  without the data,  study.  ( A l ) l o o d . > D r . ;D. L u d w i g p r o v i d e d t h e  L a r i c i n s comments on t h e o r i g i n a l in  the course o f t h i s  o f t h e problem provided  A r g u e a n d M r . F.E.A. inspiration  Dr. C . 3 . W a l t e r s , f o r  t o - t h a n k my s u p e r v i s o r .  scrible  t o t h a n k my w i f e  durring  my s t u d e n t  into  typed  help  t o Joan text.  Kathy f o r h e r endurance days.  1  The s h e l t e r e d waters o f B r i t i s h Columbia support v i a b l e commercial  *s G e o r g i a S t r a i t  and spor-t f i s h e r i e s on s t o c k s of  .• c h i n c c k salmon- ioncorhynchus t s h a f ^ t s c h a ) and coho ••salao:n-- iO ,-:J  :  -  kj.sutcb)aln  the 1950s, the commercial  t r o l l fishery  a  caught t h e  majority o f f i s h taken by hook and l i n e l a t h e Georgia S t r a i t * Ten year averages f o r the years 1953 t o 1962, i n c l u s i v e , t h a t the commercial sportsmen  t r o l i e r s caught  show  125*000 C h i n o o k w h i l e  angled 92,700 chinook i n G e o r g i a S t r a i t s  Average  catches on t h e e n t i r e B r i t i s h Columbia.. -.coast. by hook and l i n e :  in  s a l t w a t e r t o t a l l e d 949,100 Chinook  c a t c h e s were 307,200 commercial  a n n u a l l y . Coho average  and 190,800 s p o r t i n t h e  Georgia S t r a i t as compared with a coastwide t o t a l of 3,131,400 echo {Milne 1964).> The  past 15 years have witnessed a dramatic change i n the  distribution  o f c a t c h between the commercial  and s p o r t  fishermen. I n c r e a s e s i n human p o p u l a t i o n , wealth, l e i s u r e and advances i n gear e f f i c i e n c y growth i n e f f e c t i v e  accompanied a s i g n i f i c a n t  sport f i s h i n g  s p o r t c a t c h has r i s e n  time,  e f f o r t . Subsequently, t h e  t o 348,000 C h i n o o k and 464,000 cohoi «  Meanwhile the commercial  t r o l l c a t c h has d e c l i n e d t o 99,000  coho and 181,000 chinook per year. (Arque, C c u r s l e y , and H a r r i s 1977).  lately,  concern  .populations Strait  has  o f c h i n o o k and  stocks to  amount o f e f f o r t estimate  during the  high  have n o t  e x p e n d e d by  fishing  few  years  of the  pressure.  has  produced  an  Georgia  Spawning  the f i s h e r i e s department t o  {A.S.  has  increased  Argue and  i n c r e a s e and  artificially  the  find  significantly  f.£.A. » o o d  p e r s . comm. ) , I t i s t h e p o s i t i o n o f t h e D e p a r t m e n t Fisheries that "this  aany  shown a g e n e r a l d e c l i n e , b u t ,  spawning p o p u l a t i o n s  past  ability  c o h o salmon t h a t make up t h e  withstand  escapement e s t i m a t e s  and  a r i s e n .aBoat t h e  more e f f i c i e n t  of  enumeration  s t a b l e s i t u a t i o n i n the  escapement  trend." The  Fraser Elver g i l l n e t  e s c a p e m e n t , has 1)  and  that  catch,  chinook populations  may  problem i s the  h a v e become a age  indicating  composition  a shift  i n age  age  Historically, majority of the  2 and  dangerous  c h i n o o k has  declined  ( F i g . 3) ,  towards younger  age  {Anon. 1978}.  fish.  They have : a l s o b o r n e t h e to  ensure the  conservation  r e s t r i c t i o n s have taken  season c l o s u r e s - r e s t r i c t i n g (Milne  indication  t h e c o m m e r c i a l t r o l l e r s have c a u g h t  regulations intended c o h o s a l m o n . The  3)  1961)* l i m i t e d  entry  date, the  sport  fishery  bag  limit  r e g u l a t i o n s . How,  the  sport catch  and  the  has  (Fig,  s t r u c t u r e of t h e catch....The  caught  (ocean  of  ( F i g . 2 ) . Another  average weight of a t r o l l  classes  indicator  shown a c o n s i d e r a b l e d e c l i n e i n c h i n o o k  a moderate d e c l i n e i n coho  conservation  as an  fishing  (Mitchell  on  brunt  the of  ofchinook  three  major f o r m s ;  to.summer  and  1977)  s i z e l i m i t s , ;To  and  fall  been s u b j e c t t o s i z e l i m i t gi^en the i n c r e a s e d  concern  and  months  and  to  importance;of  over c o n s e r v a t i o n ,  the  3  CHINOOK  100 100  50 50 ERASER GILINET J  o o o  CATCH  1  I  l_  -1  I  1_  50 50 FRASER ESCAIEMCNT -L  o o z  I  I  J_  -I  1  1_  ->  1-  .1,  X  u u. o  100  15 0  or  UJ  QJ  s Z  100 ERASER PLUS 50  ->  100  CATCH ESCAPEMENT  1  L  , |._  -I  L  -1  L  50  50 50  '952  54  5G  50  I9G0  6  2  64  6G  60  1970  72  74  76  ^ ^ " hi i vv - .o r r o ^i lll nn t ^t ^ C ?a t^c h' o f / ?C fh i n o o k S a l =««pe«,ent and F r a s e r mon. f  e  r  R  i  V  2  r  NUMBERS - OF  C0H0  (xlOOO)  c M <T>  < *NJ • r-i  O (0 H* o — I M h- -C 3 1— tO CU rt CO n rt CU <-) r+ CU O H* rt 1  1  %  o i-h  ii  »-) n CU o W iU o rl  tr  in a cu — I  t—• < s o 1-1 3  • w M o Pi "O (D B <0 3  r+  » •Ti  M  CU cn ID H  o o  O  o o  o o  5  GEORGIA  x  STRAIT  CHINOOK  GEORGIA  STRAIT  AVERAGE  DRESSED  CHINOOK WEIGHT  to  Q 2  CO LU  o  a  CL  C3 >  <  o o  25  CD CO  ><  X to  CHINOOK  CATCH  500 500  o o o X CJ  400 400  Sporl.—.  300  < CJ  .  / 300 /  V  o o  200 200  X O  100 100  19 52  54  56  58  I9G0  G-  •I  1  I  t  64  GG  GO  1970  I  |  72  74  F i g u r e 3: G e o r g i a S t r a i t T r o l l and S p o r t C a t c h , A v e r a g e Weight o f C h i n o o X Salmon.  76  Troll  E f f o r t and " t o r t ana  6  Department of F i s h e r i e s has begun to i n v e s t i g a t e ne* r e g u l a t i o n s f o r the s p o r t fishermen, and changes i n the commercial t r o l l  regulations.  To a s s i s t i n the assessment of new management p o l i c i e s , the author has worked with a team o f s c i e n t i s t s , under the d i r e c t i o n of Dr. C.J. Walters a t the U n i v e r s i t y of B r i t i s h Columbia,  t o develop a computer s i m u l a t i o n model {Wiegert  19.75, Walters 1971, H o l l i n g e t a . l  A  1978) . The model has been  used to t e s t the e f f e c t i v e n e s s o f v a r i o u s r e s t r i c t i o n s on the Georgia S t r a i t Chinook and coho f i s h e r i e s . The  s i m u l a t i o n model i s designed t o p r e d i c t  population  numbers, f i s h i n g e f f o r t , c a t c h , and escapement on a bi-monthly b a s i s f o r a s i n g l e f i s h i n g area r e p r e s e n t i n g  t h e Georgia  S t r a i t . Both i n i t s a t t e n t i o n t o the d e t a i l s of f i s h and fishermen dynamics and t h e extent and  t o which i t mimics r e a l  catch  e f f o r t s t a t i s t i c s from the Georgia s t r a i t , the model  represent  a " r e a l i s t i c " account o f the f i s h e r y . T h i s r e a l i s m  makes t h e model an a t t r a c t i v e t e s t bed f o r new and powerful methods of a n a l y s i s . In p a r t i c u l a r , the model can be used to t e s t p o l i c i e s designed by techniques o f o p t i m i z a t i o n  (Baiters,  Hilfccrn 1978). T h i s t h e s i s c o n t r i b u t e s t o the development of a new computational framework f o r some l a r g e s c a l e management o p t i m i z a t i o n i n the context  resource  problems. The o p t i m i z a t i o n i s embedded  o f the s i m u l a t i o n  the d e t a i l o f t h e s i m u l a t i o n  model and maintains most of  model. The c o u p l i n g o f t h e  o p t i m i z a t i o n model with the s i m u l a t i o n model a f f o r d s the optimization  model a modest degree o f r e a l i s m and, I hope, some  7  degree c f p r a c t i c a l i t y . The  main problem o f t h i s t h e s i s i s t o f i n d optimal  seasons with r e s p e c t  to changing f i s h s t o c k s , e f f o r t  fishing  levels,  p r i c e s , and b e n e f i t s f o r both the s p o r t s and commercial fishermen, while meeting t a r g e t escapement l e v e l s from the f i s h e r i e s . The computed seasons f o r ""current" c o n d i t i o n s , as p r e d i c t e d by t h e s i m u l a t i o n  model, are compared  with  r e g u l a t i o n s now c o n t r o l l i n g the f i s h e r y . Optimal seasons are computed under a v a r i e t y o f assumptions about values of parameters f o r which t h e r e i s a great discussed  are the e f f e c t s o f i n c r e a s e d  populations,  on optimal  deal o f uncertainty, a b u n d a n c e o f some  seasons, as may r e s u l t from the  "Salmonid Enhancement Program" {BacLeod 19 77, L a r k i n The  also  1974).  problems with a n a l y s i s and o p t i m i z a t i o n i n t h i s  e x e r c i s e are not unigue to t h e Georgia S t r a i t f i s h e r y . Host resource  e x p l o i t a t i o n problems are complex and m u l t i -  dimensional i n the e x p l o i t a t i o n regime and i n the o b j e c t i v e s o f management. T h e r e f o r e ,  they present  major d i f f i c u l t i e s f o r  o p t i m i z a t i o n . The methodology developed below i s c a p a b l e of d e a l i n g with most o f the complexity and d i m e n s i o n a l i t y Georgia S t r a i t  o f the  f i s h e r i e s , and may a l s o be u s e f u l f o r other  problems. I hope that the apparent " r e a l i s m " of t h e s i m u l a t i o n model and o p t i m i z a t i o n pressure  model i n c o n j u n c t i o n  f o r the c o n s e r v a t i o n  coho w i l l serve  with the immediate  of Georgia s t r a i t chinook and  t o enhance t h e p r a c t i c a l i t y of t h i s t h e s i s .  8  .  The o p t i m i z a t i o n work t o be d i s c u s s e d i n c h a p t e r  based  upon a s i m u l a t i o n model. At p r e s e n t  describing  the Georgia  Strait  i s no document  model. T h e r e f o r e , t o l a y t h e  foundations f o r the task o f t h i s t h e s i s , to  there  three i s  d e s c r i b e some o f t h e i m p o r t a n t  i t w i l l be  necessary  ingredients o f the simulation  model. T h e r e a r e f o u r m a j o r c o m p o n e n t s jln t h e m o d e l : population  dynamics o f f i s h  migration, e t c . ) ;  (life  history,: ^mortality,  the f i s h  to the fisherien  estimates  p r o b l e m . ;These f o u r » c o m p o n e n t s f o r m r e g u l a t i o n s c a n be d e v e l o p e d i n t u i t i v e context, while world.  The broader  methods now  available,,  management  a k e r n e l around  and t h e n  still  o f how b e n e f i t s  and managers.  T h e r e a r e many more f a c e t s t o t h e a c t u a l  real  growth,  (2) d y n a m i c s .of A±i«kiB$-;:ef fort-;- (3) a s e t o f  c o n t r o l s a v a i l a b l e t o m a n a g e m e n t : (4) flow from  (1)  examined  in a  which  new  broader,  maintaining a resemblance t o t h e  c o n t e x t would  not o v e r t a x  analytic  9  . > 2.1.  Blqioqy  The  b i o l o g y o f t h e p a c i f i c sa1mon ( O n e o r h y n c h u s s p p . > i s  v e r y complex. In s p i t e o f y e a r s there  isstill  relationships. biology  much u n c e r t a i n t y s u r r o u n d i n g  and e a r l y l i f e  known f o r c e r t a i n  stages  of ocean,studies,  about t h e marine stage.  biological  are  very  little i s  The p r o b l e m  addressed  t h e j i i v e n i l e and a d u l t  little  parameters used i n t h i s "solid"  model a b o u t  some i n f o r m a t i o n a b o u t e a c h p a r a m e t e r  of this  t h e model i s a p r o d u c t  there values.  used i n t h e  t o t h e parameter i n  question and, o f t e n concerns geographical which a r e n o t t h e f o c u s  there  which  data t o s u b s t a n t i a t e p a r t i c u l a r  m o d e l e x i s t s , much o f i t i s t a n g e n t a l  in  very  o f coho and chinocfc s a l m o n . A s a conseguencev  are  Although  important  o f some s p e c i e s o f s a l m o n .  t h i s t h e s i s deals e x c l u s i v e l y with  ocean l i f e  some v e r y  A l o t o f i n f o r m a t i o n e x i s t s on t h e r e p r o d u c t i v e  However, due t o t h e d i f f i c u l t y  by  o f work by many i n v e s t i g a t o r s ,  areas  and s p e c i e s  model. Huch o f t h e " d a t a " v  of the experience  used  and "wisdom" o f two  members o f t h e Department o f F i s h e r i e s , A.S. A r g u e and D. A n d e r s o n . T h e s e two g e n t l e m e n i n t e r p r e t e d t h e a v a i l a b l e i n f o r m a t i o n and made i n f o r m e d  estimates  p a r a m e t e r s . I t i s hoped t h a t t h e s e current  s t a t e o f the Georgia  Strait  on many o f t h e  estimates r e f l e c t the Chinook and c o h o  fishery.  10  2.1,1,. s , L i f e ;  History  L i k e the o t h e r commercial are  salmon s p e c i e s , chinook  anadromous. The eggs are l a i d  young f i s h spend the ocean, die.  lakes.  The  some time i n freshwater before m i g r a t i n g t o  When mature, they r e t u r n t o freshwater t o spawn and  I t i s believed  spend  i n r i v e r s and  and coho  that a f r a c t i o n of the chinook  most of t h e i r ocean l i f e  other f i s h spend  and coho  i n c o a s t a l waters while the  t h e i r ocean l i f e  on the h i g h s e a s . Tag r e t u r n s  from h a t c h e r y - r e a r e d f i s h i n d i c a t e t h a t as much as 761 o f the c h i n c c k and 51% o f t h e coho produced in  i n Georgia S t r a i t  Georgia S t r a i t f o r seme period of time  ( F i g . 4)  reside  (Anon.  1 9 7 8 ) . I t i s the p o r t i o n s o f the s t o c k s r e s i d e n t i n the Georgia Strait  which are the s u b j e c t s of t h i s a n a l y s i s ,  Coho eggs are l a i d The  i n the f a l l and  hatch t h e next  spring.  smolts g e n e r a l l y migrate t o the ocean the f o l l o w i n g  where they spend one fall.  spring  winter and, r e t u r n t o spawn the f o l l o w i n g  By the l a t e summer o f t h e i r f i r s t year at sea, Coho are  f i r s t caught by the s p o r t f i s h e r y and, by the next s p r i n g , they are  caught  by the commercial  trollers.  In the model, coho are  assumed t o be r e c r u i t e d t o the f i s h e r y by August 1 (A.*,,Argue p e r s . comm. ) . During the summer and f a l l sea,  of the l a s t year a t  coho move i n t o freshwater t o spawn. The model uses the  t i m i n g of the F r a s e r R i v e r g i l l n e t c a t c h ( F i g , 5) approximate  the m i g r a t i o n t i m i n g (Ledbetter and  Chinook have a more f l e x i b l e l i f e may  to  Hilborn  1978),  h i s t o r y . Ocean m i g r a t i o n  take p l a c e i n t h e s p r i n g through t o f a l l a f t e r h a t c h i n g , or  a f t e r one or two  w i n t e r s i n f r e s h w a t e r . The  model assumes t h a t  11 PERCENTAGE  CATCH  HARVESTED  COHO 1971 Io 1974  u o <t tz UJ o  00  BY  CATCH  REGION  OnOOOS  Cowiehon  Ouolicum  Squornnh  Copilono  or.  UJ  a.  n I3  U.S.  N/C  WCVI  JS/JF  •'  GSC  CHINOOK 1971 Io 197} BR000S Pvnlladg* Otiolicum Copllono UJ  O z  UJ O  tr UJ a.  60  AO  IL I*  3  u.s-  N/C  XL WCVI  U.S.  - UNIIEO  N/C  -  WCVI -  NOMTH  JS/JF  CSC  STATES CENTRAL  WEST C0»ST  B.C.  VAN. IS.  JS/JF - Jonir.TONE STR. - JUAN DC FUCA STR. GSC  - GEORGIA  S1RAIT  COMMERCIAL  6SP  -  STRAIT  SPORT  F i g u r e 4: Tag R e c o v e r i e s Salmon.  GEORGIA  of the G e o r g i a  Strait  Coho and C h i n o o k  12  Sincfeosa UOT^JOCIOJJ  13  c h i n c c k a r e r e c r u i t e d t o the f i s h e r y by the beginning o f October of t h e i r f i r s t  year  at sea. I n general^  takes place during t h e second through f i f t h  maturation  year a t s e a . For  t h i s model, an estimate o f t h e p r o p o r t i o n of f i s h maturing and r e t u r n i n g t o spawn f o r each age c l a s s was needed. An a n a l y s i s of tag r e t u r n s i n the F r a s e r B i v e r g i l l n e t versus the Georgia S t r a i t s p o r t and t r o l l  f i s h e r y l e d t o t h e f o l l o w i n g estimates  (A. fl. Argue pers. comm.,  Argue 1S76) .  Ocean age two  3$ mature  Ocean age t h r e e  4036 mature  Ocean age four  80S mature  Ocean age f i v e  100% mature  As with coho, t h e run t i m i n g o f mature f i s h was estimated from the F r a s e r B i v e r g i l l n e t c a t c h  ( F i g , 5) (Ledbetter and  H i l b c r n 1978). A f e a t u r e more important tendancy f o r Georgia S t r a i t before maturing. Again,  f o r chinook than coho i s the f i s h t o migrate  out o f the S t r a i t  through an a n a l y s i s o f tag r e t u r n s  i n s i d e and o u t s i d e t h e S t r a i t , estimates  o f the net migration  r a t e s from i n s i d e t o o u t s i d e were d e r i v e d (A.H, pers, comm. ) :  Argue  14  Fish  Ocean year  one  40$  Ocean y e a r  two  25%  Ocean  three  .1:5*  Ocean y e a r  four  10S  Ocean y e a r  five  0%  moving o u t s i d e  their  are  2.1.2. - N a t u r a l Natural  mortality of  f i s h and  are  Environmental resulting  are  or  age  natural  gulf  until  relatively  (Ricker  fishing.  is a  very  difficult  include  i s no  (Ricker  information 1976).  mean b i - m o n t h l y  mortality rates  (A. p.  mortality rates  age  three  through f i v e It i s  decrease with  mortality  15  non-catch  only, not  increased model  mortality  comm. *| * .The  days) i n t h e  to  generally  parameters chosen f o r the  Argue p e r s . (per  numbers  confounds experimental e r r o r s ,  salmon o f  1976). The  small  errors.  (1978) e s t i m a t e s were 0.026.  meant t o r e f l e c t n a t u r a l  c a u s e d by  be  the  fisheries.  observation  magnitude  for chincck  that natural  and  sea  f o r which t h e r e  (1960) e s t i m a t e d t h e  0.0175. H e n r y * s  si?e  troll  generally  variability often  mortality rates  thus to  and  prone t o l a r g e  direction  Parker  and  f i s h at  Experiments  i n biases  concerning  thought  gulf sport  ret u r n t o  to  Mortality  process to study.  be  assumed n o t  r a p i d spawning m i g r a t i o n ,  i n v u l n e r a b l e t o the  of  year  model  instantaneous are:  15 Ocean age  1  0.035  for 3  Ocean age  2  0.015  for  12  months  Ocean age  3  0.0C75 f o r 12  months  Ocean age  4  0.0015 f o r  12  months  Ocean age  5  0.0075 f o r 10  months  fiverage Bicker  0.0  11  (1976) e s t i m a t e s t h e . ' i n s t a n t a n e o u s r a t e  ocean m o r t a l i t y  f o r coho t o  The  i n the  v a l u e s used  be  0.04  for a  model f o r n a t u r a l  for 5  Ocean  2  0.02  f o r 10  availiable  soon, through a n a l y s i s  2.1.3.  months months  1960*s  mortality of the  (Walters,  will  likely  many t a g g i n g  be studies  pers.jGomm*).  "Shaker? H o r t a l i t y  Non-catch ocean natural  mortality  m o r t a l i t y and  included  in catch  includes  salmon c a u g h t  are  are:  0.027  estimates of natural  the  period.  mortality alone  0.04  age  non-catch  month  1  Much b e t t e r  conducted during  half  of  Ocean age  Average  during  months  a closed  discarded  boated, or  by  i s made up  mortality  statistics. that  period  dead o r  fishing,  of the  but  second  l e s s than l e g a l  size,  species  i n question.  mortally  injured  - either  caused  by  the  trolling  a v e r a g e s a b o u t one  fish  (Bicker  e f f e c t of  1976). The  components -  f o r the  s h a k i n g them f r c m  Shaker m o r t a l i t y  c a u s e d by  Mortality  are  o f two  killed  g e a r as  various  kind or  fish  being  i t i s hauled  up.  chinook  that  regulation  caught  These  after  f o r coho and  f o r e v e r y two  not  are  boated  changes  on  16 s h a k e r m o r t a l i t y and shaker m o r t a l i t y is  the  effect  r a t e s on  a major c o n c e r n o f t h e  shaker m o r t a l i t y r a t e of 1976). L i t t l e mortality. fish of  empirical  i s assumed t o  In the  model, t h e  be  i t s age  and  growth o f a  Chinook  or  troll  size,  fishery.  from  these  ' 2x2*  Ihe  and  proposed  of  the  time of  year.  shaker  kill  more or  lack  sport  ( F i g . 6)  Marshall  Rinaldi,  was  was  or f i x e d  fleets,  o r no  also  data  Strait  constructed  1976),  Effort  waiters  1976;  inputs  fishing  Clark  i n and  the  out  and  allocation  effort Munro  theoretical  of  empirical basis. Hliborn  (1978) document t h e  the  made u s i n g  Georgia  d y n a m i c models o f  and  a  An e s t i m a t e o f  1976). T h e s e m o d e l s have s t u d i e d  fishing and  of  salmon  seiners  coast.  Their  among f i s h i n g  a r e a s on  the  B r i t i s h Columbia  conclusion  that  the  key  determinant of  is  sport  inexperience  time of c a p t u r e i n the  behavior of c a p i t a l  Ledbetter  {RicJcer  a f i s h i s assumed t o be  coho at s e a  (Argue and  with l i t t l e  changes  8035.  have been s e v e r a l (Gatto,  about  model, a  sportsmen  because of  A length-weight r e l a t i o n  data  Clark  been done on  b e l i e f that  Dynamics o f f i s h i n g  There  1975;  age,  the  shaker m o r t a l i t y r a t e i n  size  of  the  work has  the  model. I n  i s used f o r t r o l l e r s  fishermen  concern. Therefore,  function  50$  assumptions  consequence of r e g u l a t i o n  simulation  It i s a general  than commercial  fishery  on  the  of various  b o a t movement  is  YEARS  18 availability model and of  of f i s h .  A major i n g r e d i e n t o f t h e s i m u l a t i o n  t h e o p t i m i z a t i o n model o f t h i s  fishing  effort  to the  2.2.1. ? S p o r t s E f f o r t Motivation associated the  success  the  c a n be  capture of  c h a n g e t h e amount o f  probable the  t h a t an  fish.  assumed, i n p a r t , t o Consequently,  will  U n d o u b t e d l y , many o t h e r determine fuel  fishing  they  i n c r e a s e i n the average  sport fishery  motivate  an  factors,  t h i n g s , , may  manager d o e s n o t  the  fishermen  Furthermore,  success  leather,  i t is  effort.  success,  holiday  time,  t h e economy, among o t h e r  m o t i v a t i o n of t h e  have j u r i s d i c t i o n  s p o r t s m a n . The  fishery  o v e r t h e economy, n o r  the  e n v i r o n m e n t , „ B e must, t h e r e f o r e , p u r s u e management p l a n s upon r e l a t i o n s h i p s  under h i s c o n t r o l ,  will  per a n g l e r i n  besides fishing  the general s t a t e of  affect  do.  by  be  a change i n  increase in fishing  t h e amount o f s p o r t e f f o r t ,  p r i c e s , and  response  fishing.  number o f s u c c e s s f u l c a p t u r e s e x p e r i e n c e d  likely  i s the  Response  of sport e f f o r t  with  of  thesis  i . e . , /the s u c c e s s  based  of  fishing. The  responsiveness  (CFOE) i s i n d i c a t e d  of s p o r t e f f o r t  i n F i g u r e s 7 through  r e p r e s e n t s c a t c h and  effort  data  areas  1968  (Anon,/B.C. S p o r t s C a t c h  appears  1975  29)  the  f o r one  15.  per  Each  Georgia  effort  graph Strait  month from  Statistics  unit  the  years  1968-1975) . I t  f o r most months t h a t h i g h e r CPUE i s a s s o c i a t e d w i t h  increased e f f o r t . is  13-18, 28,  from  (Statistical to  to catch  simply  F o r t h e s i m u l a t i o n , i t i s assumed t h a t  p r o p o r t i o n a l to r e c e n t success as  measured by  effort CPOE.  Seasonal is  variation  shown i n F i g u r e  indicates greater  that the  i n the  the  the  f o r the  o f the  impacts of  the  success  as  to cancel  relationship fish  Sport  behavior  intended  i n the  effort  cancel  may  any  analysis of this  i n spawning  effort  the s i z e  weighed by  success  of  In the  the  limit  must e x i s t ,  so  escapement./The  upon t h e of  fish  number o f caught i s  t o reduce the c a t c h o f s m a l l  fish  average s i z e of to the  increase  fish  l a r g e r and  caught.  older  fish,  i n spawner e s c a p e  any c o n c i a s i o n s  should  u n c e r t a i n t y i n the r e l a t i o n s h i p of e f f o r t  years  effort  at  but,  high  i s assumed n o t t o s a t u r a t e  l e v e l s of success.  i t has  apparently  ( F i g s 7-15). Unlike  l i c e n c e program, w h i c h l i m i t s  can  increase  t h e s i s i s b a s e d upon ..th«^x^:^l:$cwsii|:??..of  upper l i m i t  participate, who  increase  such  i n c r e a s e , due  model, s p o r t  an  its  to  to  to  fishing.,  reach  recent  i s important  t h a n mere numbers, I n  nuffiAers r a t h e r t h a n w e i g h t . T h e r e f o r e ; be  i s much  s t i m u l a t e enough e f f o r t  that  increase the  intended  may  model i s b a s e d  likely  i n motivating  may  fishermen  of fishermen  increase  r e g u l a t i o n s intended  (size limits)  of the  effort  variation  r e g u l a t i o n changes i n t e n d e d  caught. I t i s very  a case,  set./This  per  winter.  fishermen  included  more i m p o r t a n t  to catch  s i g n i f i c a n t l y . ! , F o r e x a m p l e , an  of the  any  effort  same d a t a  responsiveness  abundance o f f i s h  in  and  16  r a t i o of  summer t h a n t h e  Consideration evaluate  i n the  t h e r e i s no  legal  p a r t i c i p a t e i n sport  not  the  limit  fishing.  Some upper  been r e a c h e d  the commercial  or  fishery  in  with  number o f v e s s e l s a b l e t o the  numbers o f  people  to  H-Q C  EFFORT (BQRT-DRYS)  Ii  1DD.0  C J (TJ CU  15D.D  200.0  IX10  2  3 -J C  Cu  ••  >-| K -< r-n l-h rt O O rl rt "O  6 a  Cu  n 3Pi  o -» -a a co I  3 3" (TJ  C>  O c r m  (TJ O  rl  JQ  V' u>  ro  CO rt M Cu  oo  CD  O 1 rt  W  3" (TJ  ri •<  02  O  Q Q  )  250.D  Q  300.0  c n  rs <r>  EFFORT  01 -< 00  160.0  (BQRT-DRYS)  2D0.D  240.D  CX10  2  )  320  280.0  G CD  o c z  G  n  G  G G G  O  o a  Si  o rvj in CD  CD CD  rj-CD  a  O  I  I—  CD  cc  CD  CD  '—a in.  on a UJa a  CD  04  D.O  0.4  1.2  0.B  1.6  CPUE  F i g u r e 9: E f f o r t and CPDE i n t h e G e c r a i a ^ r i * c „ * J u n e 1968 - 1975. ^ e c r q i a S t r a i t Sport a  2.0  L  Fishery  \  H-  J3  EFFORT  C  n  (TJ  c  C  .  _*  650.D  100.0  J  c  ••  l-ti UJ i-n o 1 M  c  .  -  -J 3  •  6DD.D  2  *  o  "•<  55D.Q  (BQRT-DRYS) ( X 1 0  &i O  Q  C Pi  o  iL) Cl  Q  CD  ™  O TJ CZ m  0  O  I-I  ro  pj  Q  01 rt  G  n ' Oi Hrl  CO •o o 1-1  •  cn  rtT)  Htn nr (I) t-1  -5  zz  G  Q  O  750.0 _J  n c ri  S» fl) C -Q -» C —' (/) •• rt  40.D  EFFORT (BQRT-DRYSJ 60.0 I  80.0  (XiO  I  i  rt -> rh  Hi o> O 00  rt  I  o  -» » tf> & ui n • t3 G ni  G  H-  GG G  rt  IT  tn  -D  o  O  cz m  ii .a pCu  G  co  r»  M &> Hrt CO "D O li rt  ta-  rn H  fr3  G  ro o  3  J  100.0  Q  120.0  X)  EFFORT  C M  16D.D  10 <V  (BQRT-DRYSJ  260.D  360.0  (X10  460, L_  o  G o  G  CD  o  G  TS CZ  G G  rn  G  ro  G Ol  rO O  2  560 _J  XI  C M  o n>  n  EFFORT  ri- •a  80.D  Ot Ul tr «»  (BQRT-DRYS)  100.0  (XIO  120.0  l-l  O  oo ct OJ  _» Oi  n •a  •  G  G  3  r+  3" <I>  CTJ  O T)  O  rn  CJ  n  G G G ro  rill Cu I— ft  in  XI  o  M  cn  rt  •TJ  HW (TJ n <:  93  ro o  G  G  J  140.0  i-h —k if>  i  2  Q  160.0 _J  •  —,  cEg'H  cc o LU  o  CD  | a a. OJ I  0.0  I  0.4  1  0.B  1—  1  CPUE  1.2  F i q u r e 14: E f f o r t and CPUE i n t h e G e o r q i a November 1968 - 1975.  1.6  Strait  Sport  Fisher  (J.  n  c t-i  c n  O ft)  150.0 ° '  0 -»  fD 3 Cr" (D M  EFFORT (BORT-DflYSr U 1 0  Ul ••  230.0 1  3J0.0 I  K l-fi  -» O ri  CTi rt  co  1 a O  O  •  m a  O  (1/  T3  (7)  rn  (D O M  -Q DJ  G  CD  G  CZ  ro  09 G  W  r+  G  M  P J r<+ J  w •n o  r-{ rt  •n  (-•• t/1 tr IT)  M -<  83  ro o  G  J  )  390.0 i  410.0  29  F i q U r  F ish;ry ? e  R  t i 0  °  f  E  f  f  °  r  t  t  0  C  P  U  E  i  n  t  h  e  e-orqia  Strait  80,00 0  70,000  60,000 UJ  7D  CL u  50,000  fx  UJ co 4 0 , 0 0 0 LU LU 5S  O rr LU  30,000  0_  S  20,000  CD  or O 0. co  10,000  F M A M J MONTHS  J A S 0  N  D  Sport  30 There i s a g r e a t d e a l of v a r i a b i l i t y i n the d a t a d e p i c t e d by F i g u r e s 7 through  15. However, p r e d i c t i o n s t h a t i g n o r e d the  behavior of fishermen are s u r e l y more misleading than p r e d i c t i o n s that take some account o f t h i s numerical response process.  2.2.2. » Commercial  E f f o r t Besppnse  M o t i v a t i o n o f the commercial fisherman i s l e s s d i f f i c u l t t o d e f i n e than t h a t o f the r e c r e a t i o n a l fisherman. For the most p a r t , the commercial  fisherman i s out to make money. The more  p o t e n t i a l t o c a t c h f i s h t h e r e i s i n an area, t h e more fishermen w i l l p a r t i c i p a t e . O n l i k e the s p o r t f l e e t , the commercial  fleet  can brave the elements o u t s i d e the s h e l t e r e d waters of Georgia S t r a i t i f the f i s h i n g i s good enough t o warrant the  it.;Therefore,  ccmmercial e f f o r t i n Georgia S t r a i t i s a f f e c t e d by the  abundance o f f i s h i n s i d e , as well as the f i s h i n q o u t s i d e Vancouver  opportunities  I s l a n d and along the north c o a s t . Our concern  i s with the i n s i d e f i s h e r y . T h e r e f o r e , the r e l a t i o n s h i p between e f f o r t and CPOE i s c o n s t r u c t e d with Georgia S t r a i t data a l c n e . F i g u r e s 17 through 23 show e f f o r t and CPOE data i n the G e o r g i a Strait t r o l l fishery for  the years 1968  f o r the months of A p r i l  t o 1975,  through  October  There i s a d e f i n i t e l i m i t to the  number of boats i n the ccmmercial t r o l l f l e e t because  of both  the. l i c e n c e program and the number o f boats that a r e not eguipped t o handle the r i g o r s of the more l u c r a t i v e o u t s i d e f i s h e r y . T h e r e f o r e , the r e l a t i o n s h i p o f e f f o r t to CPOE i s assumed t o s a t u r a t e . F i g u r e 24 i n d i c a t e s the s e a s o n a l v a r i a t i o n  31 in  t h e maximum  level  An  capture  important  used  effort  i n this  model i s t h e t r a d i t i o n a l o n e t h a t  fishing  coefficient  of the f i s h  of the fish  or seasonal  i n t h e summer may be made up c f a  of inexperienced  catchability  in a  The  seasonal changes i n the sport  higher  fishermen than the ardent  fishermen  months, .  coefficients  p h a s e ? m e t h o d o l o g y d e v e l o p e d by m o d e l h a s been u s e d t o r e c o n s t r u c t  f o r c h i n o o k and coho i n t h e G e o r g i a  Average e s c a p e m e n t  by age w e r e u s e d  o f abundance u s i n g  escapement o f t h e o l d e s t peel  of the  as a function of  as well a s time of year.  1975, t h e s i m u l a t i o n  calculation  catch  and C O B p o s i t i o n o f t h e e f f o r t , ,Eor e x a m p l e ,  effort  about  1940). I n t h i s  i s the proportion  be d u e t o e n v i r o n m e n t a l c h a n g e s ,  Osing t h e " c a l i b r a t i o n  Strait.  (Bicker,  C a t c h a b i l i t y i s assumed t o v a r y  may  the winter  Johnson  The a s s u m p t i o n  i s c a u g h t by a s i n g l e u n i t o f e f f o r t  i n the behavior  proportion of  that  and s p e c i e s  efficiency  effort.  i s p r o p o r t i o n a l t o abundance  variability  modeling e x e r c i s e i s  and f i s h i n g  of time,  changes  i s reached.,  of f i s h  available fish  age  i n t h e model and s h o w s ; t h e  p i e c e o f any f i s h e r i e s  model, t h e c a t c h a b i l i t y  unit  assumed  Catchability  coupling  per  effort  o f CPOE a t w h i c h h a l f s a t u r a t i o n o f e f f o r t  2.2.3.  the  troll  fishery according  catch  to start  a backward  b y age and g e a r t y p e .  age c l a s s o f f i s h  was added  The  i n t o the  t o t h e m a t u r a t i o n s c h e d u l e and r u n  timing  discussed  before,,/Progressing  backwards i n t i m e , a t each  period  the catch  and n a t u r a l m o r t a l i t y  a t t h e o l d e s t a g e was  E F F O R T 0.0 O/tn  40.0 _J  80.0 _J  (BOAT _ DAYS) CX10 120.0  1  J  160.0  200.0 _]  210.0 _J  280.0  _)  P-  G b  17  Fish  fu •• i •< w s» m TJ O M n P- rt p(•• -» n o & ji r; "d l  b  a w  ure  b  Q.  G  VT>  P-  .fr  O ft) O rl .C  b  03 rt M Oi  G  A"  b  G pica  Prt n o l-l o p.  E F F O R T  (BOAT _ DAYS)  txio J 1  200.0  300.0 i  400.0  500.0  600.0 J  700.0 _J  800.0 _J  900.0 _J  n c t-i  en.  IT" <T>  b  f ro CD •• H  G  eo.  b  -<  M rf  QJ  rt  -<  n  Ul Cu  I o -» c:  c  rr fl) <D iD O fl  b oi-  I-I  cu  b  b  G  G  n o B 3  ft) I-)  O  e£  E F F O R T  150.0  200.0 J_  (BOAT _ DAYS) IX10 300.0  250.0  1  )  350.0 _l :  100.0  450.0  500.0 _l  P-  J3  C  G Q  Q G  o  n (b M w .  G  tr vO .a tl -< t l Itl L, rh e O 3 l-l (D r« VC  a  OIJ1  G W  1  n  —» rrl  vn  -o 3p.  •  rttr ik C"> m O rt  £.  p. CJ  cn-  b  i/>  r* ii cu  pr»  co •  b  f)  O g =i .D ii  o pCU M  E F F O R T  CBOAT _ DAYS)  (X10 ) 1  210.0  340.0 _J  <MO.O I  S40.0 I  •  6*1.0 I ;  74).0 i  810.0 _J  940.0  _l  Q H-  J3  G  C H (0  tn O m •• M  -<  W  hh  rti C O r->  -< o  pita  a  _,  vC LP  n rt  & a  o> fi  1 <= »a  M  •o o-  .  vO  hn  o  •  rt  ET 01  c:  ro  o ri  J3 HCU  coca  w rt  M  D Hrt  fl O 9  3 111  M  O rCl  E F F O R T  (BOAT _ DAYS)  IX10 J 1  CD  210.0 '  260.0 1  320.0 1  360.0 1  100.0 1  440.0 I  180.0 I  520 I  HJZS a ti (D  H* cn to sr  .  (U  I  -< m  i-ti r-h O tl rt  c -G C tn rt  o  —»  Oi 3 Cu  vO J> n Ln G I HI  G W  . H-  0  •j c rt  •  <a  m o ti  XI  (••>•  o>  Ui rttl 01  M  hi'  o o s  3 ill tl  Ct I-  9t  F i q u r e 22: E f f o r t and CPUF i n the G e o r q i a S t r a i t F i s h e r y September 1965 1974.  commercial  CD  CD  J  CD CD  7.0  1  9.0  1—  11.0  13.0 C P U  15.0 E  I  17.0  19.0  21.0  23.0  E F F O R T  (BOAT _ DAYS)  (X10 ) 1  0 20.0 J  0.0  40.0 40.0 1  60.0 60.0 I  80.0  80.0 l_l  100.0 j_J  120.0 JL  140.  \3  *4  O  °  ~  ~  5  T l (TJ  H"  0) NJ  tr Ui it) M •< t n i-ti O r-h O O rt n O «• tr iii P. '1 3 _»  LP C3  G G Q M  b  G  i H-  c  3  it/ ID  O r-I  J3  w ii  cu  H* r»  n  o a 9 *  ii o  8£  39  Max. troll boat-days per two weeks  A  Half-saturation of troll effort response  <>  5,000  4,000  3,000  3000  1,000  J  F  M  A  M  J  J  A  S  O  N  D  J  MON1HS Fiqure  24:  P a r a m e t e r s o f the T r o l l  Effort  Response  Model.  added t o t h e p o o l , then troll  effort  present  catchability.  t h e p r o p o r t i o n t a k e n by t h e s p o r t and  formed t h e b a s i s f o r t h e c a l c u l a t i o n c f  At the beginning  of t h e y e a r , the e s t i m a t e d  abundance o f t h e o l d e r age c l a s s  represented the r e s i d u a l f o r  the  y o u n g e r age c l a s s and t h e backward c a l c u l a t i o n  for  t h e younger  estimate  o f time  mortality The  age c l a s s e s .  T h i s procedure  varying catchability  schedule  estimates  p r o v i d e s an e x a c t  provided  the n a t u r a l  i s known.  e s c a p e m e n t a n d c a t c h a t a g e used  calculation  continued  i s presented  are presented  i n Table  i n t h e backward  1. T h e r e s u l t i n g  catchability  i n F i g u r e s 25 and 26.  #,-3.,controls A c e n t r a l issue i n the design the  set of admissible controls.  control fishery. kept  There are f i v e  They c a n r e g u l a t e t h e s i z e  number c a u g h t  the gear  o r landed  may be c a u g h t ,  of the f i s h  with which t h e f i s h per t r i p  participation  or the times  in salt  effort,  a r e caught, t h e  when f i s h i n g i s a l l o w e d , / feasible  i s to restrict  for the privilege of f i s h i n g ,  (Sport F i s h  A d v i s o r y Committee  comm. ,;), I n B r i t i s h C o l u m b i a ,  considered  t h a t may be  so a s t o  would be met w i t h c o n s i d e r a b l e d i s a p p r o v a l by  sport fishermen  pers.  strait  w a t e r a n g l i n g . / L i m i t i n g t h e number o f  participants or charging  the  important  ( b a g - l i m i t ) ^ t h e a r e a i n which  One c o n t r o l o p t i o n n o t c o n s i d e r e d  restrict  strategies i s  o p t i o n s open t o t h e managers o f t h e G e o r g i a  i f caught,  fish  o f management  t o be e v e r y  salmon  1977  fishing i s  r e s i d e n t ' s right., L i m i t a t i o n o f  Table 1: Current Catch and ettort Data tor Georaia strait br ilonth. January Sport Zffort Troll Ittort  rebuary  7407. 0.  Sarch  7407. 0.  April  7407. 0.  ray  22961. 1786.  July  June  65921. 1.693.  35179. 3287.  Auqust  September October soveaber Deveaber  169618.  202999.  110362.  37775.  14073.  1560.  2394.  2230.  0.  0.  9629. 0.  Sport CPUI  1.5  1.3  1.11  1.2  1.3  1.1  1.3  1.0  1.0  1.0  1.8  I r o l l CPUI  0.0  0.0  0.0  15.9  15. 5  10.6  19.7  11.3  11.0  0.0  0.0  0.0  0. 0. 127. 202. 4353. 351*. 1966. 1995. 220. 225. Chinook Sport Harvest -eiqht in Pounds Aqe 1 0. 0. 0. Aqe 2 95. 102. 182. Aqe 3 , 21320. 18718. 16164. Aqe 4 17305. 19070. 21041. Aqe 5 3767. 1026. 41 18. Chinock T r c l l Harvest Pieces Aqe 1 0. 0. 0. Aqe 2 0. 0. 0. Aqe 3 0. 0. 0. Aqe 4 0. 0. 0. Aqe S 0. 0. 0. Chinook T r o l l Harvest Sleight in Pounds Aqe 1 0. 0. 0. Aqe 2 0. 0. 0. Aqe 3 0. 0. 0. Aqe 1 0. 0. 0. Aqe 5 0. 0. 0.  0. 517. 6693. 3869. 402.  0. 229U. 15030. 8069. 975.  0. 6372. 1816C. 81C9. 1031.  0. 3S280. 26528. 5020. 1013.  1. 61697. 32776. 6291 . 710.  1. 29737. 12018. 2165. 221.  4. 82CS. 5953. 892. 45..  15. 5582. 2423. 363. 0.  76. 7742. 3374. 208. 0.  0. 517. 33465. 46423. 7397.  0. 2753 . 8717*. 103 )J2. 18423.  0. 10195. 1 19856. 117581. 23191.  1. ' 1. 81144. 172752. 193654. 252375. 77303. 101215. 21378. 16046.  1. 95158. 100951. 36372. 5238.  8. 28719. 51196. 153*2. 1107.  0. 170. 2226U. S793. 170.  0. 655. 50628. 20377. 582.  0. 2334. 24564. 7596.  0. 4990. 1372U. 30 86. 88.  0. 3301. U 191. 813. 84.  0. 8722. 42S5. 1060. 99.  0. 0. 0. 0. •0.  0. 0. 0. 0. 0.  0. 0. 0. 0. o.  0. 0. 2096. 7501. 293412. 162122. 281 01.0. 11C142. 1 1000. 6856.  0. 1596S. 100185. 47524. 1849.  0. 10993. 32 194. 13039. 1932.  0. 29565. 35742. 17603. 2346.  0. 0. 0. 0. 0.  0. 0. 0. 0. 0.  0. 0. 0. 0. 0.  6494. 1 187. 117546. 155865.  5960. 60257.  3400. 19265.  1970. 36S9.  3177. 2600.  Chinook Sport Harvest Pieces 1 1. 2 119. 3 5200. 4 1881. 5 207.  Aqe Age Aqe Aqe Aqe  coho Sport Harvest Pieces 1 0. 0. 2 3701. 2963. Coho Spcrt Harvest Uoiqht in Pounds Aqe 1 0. 0. Aqe 2 3700. 3259.  Aqe Aqe  Coho T r c l l Harvest Pieces Aqe 1 0. Aqe 2 0.  0. 0. coho l r o l l Harvest Weiqht in Pounis Aqe 1 0. 0. Aqe 2 0. 0.  0. S9u. 111320. 69516. 3128.  308.  1. 1  46. 162. 20653. 30194. 21322. - 30366. 6389. 3765. 0. 0.  0. 4444.  0. 16073.  0. 59329.  0. 59625.  0. 5333.  0. 22502.  0. V.2390.  0. 220613.  356. 505448.  2598. 732566.  2990. 283208.  2330. 92472.  1576. 17563.  2859. 12480.  0. 0.  0. 0.  0. 0.  C. C.  0. 67944.  0. 19870.  0. 10944.  0. 0.  0. 0.  0. 0.  C. 0.  C. 0.  0. c.  0. 0.  0. 292159.  0. 93 369.  0. 51437.  0. 0.  0. 0.  0. 0.  COHO  A OH(NOOK  V-\ A June  Years  June  June  /V  June  June  Fiqure 25 C a t c h a b i l t y C o n f i d e n t of the Georqia S t r a i t Sport F i s h e r y , as a Function of the Aqe of Chinook and Coho Salmon.  ro  Fiqure 26 C a t c h a b i l t y C o e f i c i e n t c f the Georgia S t r a i t Comercial F i s h e r y , as a Function of the Aqe of Chinook and Coho Salmon.  COHO -•»-  June  CHINOOK  June  June  June LO  Years  an ccmmercial entire  effort  i s more p a l a t a b l e a n d  for  the  coast.  The  s e t of  follows:  The  controls currently size  limit  three  pounds d r e s s e d  is  bag  no  i s i n effect  limit  f o r the  weight  or  are  commercial  the  commercial  particularly  inlet  and  river  trollers  fishing  fishery.  mouths, are  i s restricted  to the  as  troll  approximately  on  and  i n effect  18  fleet  i s  inches.-There  Many  areas,  closed to  commercial  summer a n d  fall  months. The All  current size  lines  must be  restrictions the  hand  salmon  2±JLt  lalae  The  per  where f i s h i n g  inches f o r sport caught  takes  fish  virtually  place i n marine  year  round.  The  fish.  no waters  bag  limit  and i s  angler-day.  ,  model o u t l i n e d  above produces  performance i n d i c a t o r s .  for,optimization. the  i s 13  r e e l e d . /There a r e  sportsman i s allowed t o  four  of  on  limit  The  value  of  value  of a r e c r e a t i o n a l  Simpler  value  simplification  catch f o r the  commercial  beat-day.  a h o p e l e s s l y complex  used  measures a r e here  troll  i s the  fishery  set  necessary landed  and  the  2.4,1» ,A ''CxfrmfflegGlal^^ftsbery •• • In  t h e m o d e l , i t i s assumed t h e v a l u e  t r o l l e r s i s generated The  commercial  by t h e number o f pounds o f s a l m o n  management a g e n c y may  have more g e n e r a l c o n c e r n s ,  the h e a l t h of t h e p r o c e s s i n g or index  to the  marketing  sector,  landed.  such  but a  good  of t h e  prosperity  c f the e n t i r e  value of the  c a t c h . The  p r i c e p e r pound v a r i e s w i t h t h e t i m e  year  and  the s i z e  An a v e r a g e ( F i g , 27),  The  independent Georgia  of  Strait.  of the  i n the o p t i m i z a t i o n  price  paid f o r a landed  s a l m o n i s assumed t o  the t o t a l Georgia  Columbia,  2±&*£*; Sk£ The  eat  fresh  substitute  The  entire  has  and  significantly  as the outdoor task of putting  represents a Alaska,  California  and  a significantly  caught  fishing,  lower  different who  way  (1974), that  like  the  to  does  i n a 'questionnaire  the e a t i n g o f  ether attributes of  v a l u e on  of  however, i s t h e  experience, i n motivating sport a dollar  price.  i n the sport fishery  Bryan  than  would  lisjijri  f o r o t h e r f o o d . More i m p o r t a n t , act of  local  coast including  a r e many s p o r t f i s h e r m e n  a fish  be  the  i n f l u e n c e on t h e g e n e r a l market  v a l u e . There fish,  influence  However, t h e G e o r g i a S t r a i t  of sport fishermen, concluded  ranked such  c a t c h e s may  B e n e f i t s g f t h e S£o,rt  value of the study  Strait  Washington*'..Oregon, and  sport fishery  generating  number o f s a l m o n l a n d e d from  with the  have l i t t l e  of  fish.  p e r pound i s u s e d  s m a l l c a t c h compared  therefore  landed  price  p r i c e s t o some d e g r e e .  British  i n d u s t r y i s the  as  fish  fishing, fishermen.  recreational  aspects  46  ^'""oho'salulon!  ^  P  °  U  n  °  d  f  T  r  0  1  1  C  u  U  q  h  t  C  h  Average landed price per pound Chinook * Coho o r  2 .00 1.90 1.80  a—A—A—&  1.70 1.60 o  2:  ZD  1.50  O  a.  rr a.  p~J\—A—A—d—A—A—L\—L\—A—  1.40  ui  1.30  co rr <  1.20  .j O  I.I 0  .1  0  J  F  M  MONTHS  A  M  J  J  A  S  O  N  D  i  n  o  "  ™ *  47 of t h e s p o r t denominator of the  fishery  i sdifficult:  I f the fish  g r o u p s , an e q u i v a l e n t  m e t r i c i s needed  b e n e f i t s from t h e s p o r t accounting the costs  r e v i e w s t h e major One fishing  price  of  from  (1966)  approaches t o e v a l u a t i n g  sports  schemes.  (1970)  S t a t e F i s h e r y , I n 1967,  a s k e d t h e g u e s t i o n " F o r what minimum  y o u be w i l l i n g t h e s e l l  depending  o f the  Stevens  was c o n d u c t e d i n t h e W a s h i n g t o n  would  fishery.  The s u g g e s t i o n s range  be w i l l i n g t o pay t o f i s h .  a y e a r " The r e s u l t i n g  trip,  f o r the sport  the r e s o u r c e t o q u e s t i o n s about  o f t h e most i n t e r e s t i n g  Mathews and Brown  for  of using  much a u s e r would  between t h e two u s e r  suggested f o r the e v a l u a t i o n  fishery.  value  accountable i n the value of  a r e t o be a l l o c a t e d  Many methods have been  how  f o r a ccamon  between t h e s p o r t a n d c o m m e r c i a l f i s h e r y . / T h e  commercial f i s h i n g i s r e a d i l y catch.  There i s a need  your r i g h t  t o salmon  fish  v a l u e was $20.Q0-$60.00 p e r f i s h i n g  s t r o n g l y upon t h e a r e a f i s h e d  and t h e q u a l i t y  t h e f i s h i n g e x p e r i e n c e d . I n t h e model o f t h e G e o r g i a S t r a i t  fishery,  t h e v a l u e o f $15.00 i n t h e w i n t e r a n d $25.00 i n t h e  summer p e r b o a t day ( P i g . ,28)  i s used  (Basse a n d P e t e r s o n  1977) . Once a m e t r i c h a s been performance  o f each  must be combined  established  fishery,  into  and t h e one t c be used  t h e numbers f r o m t h e two f i s h e r i e s  an o v e r a l l  measure. The s i m p l e s t  approach  i n t h i s a n a l y s i s i s t o sum t h e d o l l a r  b e n e f i t s f r o m t h e two f i s h e r i e s , transform  f o r measuring the  another approach  t h e b e n e f i t s from a p a r t i c u l a r  function  (Hilborn  and Peterman  fishery,  an added  unit  1977).  fishery  may be t o into  a utility  In t h e case o f the s p o r t  o f s p o r t e f f o r t a t an a l r e a d y  high  48  F i q u r e 28: R e c r e a t i o n a l V, i l u 3 the Georqia Strait.  of  a  Boat-Day  of  Sport  ft 30  5  Q i  §  OQ  I  20  rr o a. CO  ui o  llo  10  UJ  _J  3  J  F  M  MONTHS  A  M  J  S  0  N  D  Effort  in  effort  level  than that the  way  have a q u i t e  same u n i t  i n which  fisheries  of e f f o r t  different  a t a low l e v e l  Baiters  may 1977,  I t i s apparent that  t a k e on  a quite  Keeney and  manaqer  of e f f o r t .  from  the  different  fiaiffa  1976,  affect  that  the study of o p t i m a l p o l i c i e s  form Keeney functions  t h e f o r m o f t h e o p t i m a l p o l i c i e s . I t may  objectives.  c a n be  used t o  Also,  two  the c h o i c e of o b j e c t i v e  will  better  appeal to a  the b e n e f i t s , or u t i l i t y ,  i s combined  ( f l i l b o r n and 1977).  may  also  be  determine  50 3. •/ OPTIMIZATIONMODEL  Much o f t h e p r e s e n t natural  fish  recruitment concept  populations  on o p t i m a l  per r e c r u i t  1958, Ch.,10;  e x p l o i t a t i o n of  h a s been d e v e l o p e d  i s independent o f s t o c k s i z e ,  of y i e l d  19; B i c k e r  theory  (Beyerton  Clark  assuming t h a t  l e a d i n g t o the  and H o l t  1967,- Ch. 18,  1976, Ch.: 8 ) . ^ A n o t h e r  popular  a p p r o a c h i s t o assume t h a t g r o w t h , m o r t a l i t y ,  and r e p r o d u c t i o n  can  change  be p o o l e d  1957; C l a r k  i n t o a gross  1976, Ch./2;  Single-stage stock when l i f e  model  C l a r k , Edward,  recruitment  cycle length i s fixed  u s i n g dynamic  of population  programming, c o n f i r m e d  p o l i c y i s optimal  i n the presence  and F r i e d l a n d e r  models have p r o v e n  {Bicker  (Scheafer  1954). W a l t e r s  that a fixed  1973}.,  useful (1975),  escapement  of environmental  variability.  O t h e r a p p r o a c h e s i n c l u d e s o l v i n g f o r an o p t i m a l  age s t r u c t u r e  given  1974,  an a r b i t r a r y  total  B e d d i n g t o n and T a y l o r simulation harvest  model  schemes  population  (Beddington  1973).Walters  of f i s h  populations,  (1969) d e v e l o p e d and t e s t e d  H o u r s t o n , a n d L a r k i n 1966; H i l b o r n general  various  on t h e model. O t h e r c o n c e r n s h a v e been  about o v e r e x p l o i t a t i o n i n m u l t i p l e stock  s o l u t i o n t o the optimal  structure population  fisheries  1976).To date,  exploitation  when r e c r u i t m e n t  a general  raised  (Paulik> t h e r e i s no  p r o b l e m o f age  depends upon  stock  size;  t  The the  source  "curse  fishery all  o f much o f t h e  of dimensionality*  problem c o n s i d e r e d  1  five  age  r e d u c t i o n i n the  (Bellman  with  1961)  optimization i s  • For  i n t h i s t h e s i s , one  p o s s i b l e combinations of  c o h o and  difficulty  abundance o f two  c l a s s e s of chinook. problem i s needed  the  has age  mixed  to deal c l a s e s of  Unfortunately,  i n order  with  to apply  soiae current  technology., The  simplifications  recruitment  i s constant  used i n the and  model i s t o  that there  e x i s t s an  t a r g e t e s c a p e m e n t abundance f o r e a c h age The  optimization  within  problem  season o p e r a t i o n  fishery  and  maintains  assumes e a c h age  c l a s s o f each s p e c i e s  of a l l the  of the  in  interaction  i n the  limit  of c o n t r o l s with difficult.  The  Optimal seasons w i l l  r e g u l a t i o n s and  coefficients restrictions.  The  from  of the model the  common  analysis of this; fishery  only  under  representing  be  task of  a single  a v a r i e t y of  the a  computational  fishing  be  catchability  possible  done  f o r both  s t u d i e d under v a r i o u s  a v a r i e t y of  is  designing  optimization to  t h i s t h e s i s i s to determine seasons of  fisheries.  plan  i s i n the  a  species.  b e n e f i t from  i s separate  a v a i l a b l e c o n t r o l s . The  complete p o r t f o l i o procedure i s very  only  and  fish.  Another c o m p l i c a t i o n diversity  maximizes t o t a l  optimal  t a r g e t escapement p o p u l a t i o n s .  o t h e r s i n i t s b i o l o g y . The exploitation  initial  c l a s s of each  i s t o d e t e r m i n e an that  assume t h a t  gear  size  52 Bag  limit  c h a n g e s and a r e a c l o s u r e s f o r t h e s p o r t  fishery  a r e n o t c o n s i d e r e d a s c o n t r o l o p t i o n s . F i g u r e 29 shows t h e frequency  o f bags p e r boat-day  f o r sport fishermen  books f o r t h e Department o f F i s h e r i e s ).  A bag l i m i t  to a limit bag  r e d u c t i o n t o one f i s h  o f two a n d one h a l f  c o u l d produce  catch,  o n l y 251 t o 10SS  (Allen  argue  pers.  per a n g l e r - d a y  corresponds  15j£reduction  i n immediate  i n an u l t i m a t e r e d u c t i o n i n c a t c h o f  1955).  The c o n s e q u e n c e o f a s e v e r e b a g  limit  on s p a w n i n g e s c a p e m e n t c o u l d be c o n s i d e r e d m i n i m a l  best,  A l e s s severe  per  bag l i m i t  o f one c h i n o o k ,  a n g l e r - d a y has been suggested  unacceptable  Area  June  23,  1978),  w i t h i n the t o u r i s t peak t o u r i s t  The  total  completely  (Sport F i s h  Advisory  :  r e s t r i c t i o n s on t h e s p o r t f i s h e r m e n ; h a v e been i  d i s c o u n t e d on t h e b a s i s o f t h e  affected  at  ; two s a l m o n  and was f o u n d  by t h e s p o r t f i s h e r m e n  Committee M e e t i n g ,  conm.  p e r boat-da-y..'/This; r e d u c t i o n - i n  an a p p r o x i m a t e  b u t would r e s u l t  (A.f.  who keep l o g  i n e g u i t i e s they  i n d u s t r y . I f some a r e a s  times, the d i s p a r i t y  areas  would be  among  would  were c l o s e d  resort  unacceptable.  o f t h e o p t i m i z a t i o n model: f i s h revenues.  during  operators i n the  f o l l o w i n g s e c t i o n s d e s c r i b e t h e f o u r major  c o n t r o l s , and  generate  dynamics, e f f o r t  components  dynamics,  53  + <3u  -G  Hi •H M-M  •H <Tj  l-l +-> CO  n o a> o  ro  u> x: + > c  •H J) CT  ra  ca  4-1  00  o c  c  •H  < O CD  4-> =3 -Q  •rH l-l -f->  CC O  tn  0_ CO CN  QC  <L>  LU  w  Q_  D  CT  •H  O  ti-  SAVQ-lVOa AO lN30d3d  X  o  I— <  54 y&&k*:,f, l a s h £ n i a i £ s • The  fish  model i s a s t a n d a r d  qhange i n a c l a s s o f f i s h following ordinary dx < i , t ) / d t  during  differential  random e n c o u n t e r model.  The  period  the  k i s g o v e r n e d by  eguation:  = - £ i M i . k ) + (1 < i , k , c ) * < 1-1*1,k,c)) v ( c ) ) u{k,c)E(k,c)gii,k,c) +  Cl(i>krS)  (1?l{i,k,s)v<s})  +  u(k,s)E<k,s)g<i,k,s) ] x ( i , t ) k < t < k+1  , k= 1,..., N . , i=1,.. .7  CD where:  m(i,k) i s t h e sum  rate and  out o f species  G e o r g i a S t r a i t ; ^ .and i during  l ( x , k , c ) .= 1 i f age commercial s i z e  commercial s i z e l(i,k,s) size  =  sport v(c)  size and  timing  for  age  k;  species, f i s h  i i s over  species  fish  i i s under  i  the  and  the  limit;  1 i f age  and  species  fish  0 i f age  and  species  fish  i s over the  sport  sport  sport  sport  shaker  fisheries u (k,s)  fisheries  E ( k , c ) and  i  i s under  the  limit;  v {sj a r e  u(k,c)and  and  and  mature r u n  migration  limit;  l(i,k,s); —  and  period  rate,  limit;  0 i f age  1 (i,k,c) -  of n a t u r a l m o r t a l i t y  mortality  rates for  commercial  respectively;  are t h e  controls  f o r the  r e s p e c t i v e l y during  E(k,s) are  the  effort  period  commercial k;  l e v e l s f o r the  f i s h e r i e s r e s p e c t i v e l y during  and  period  commercial k;  55 g ( i , k , c ) and for  age  and  fisheries x(i,t) time  g(i,k,s) are  s p e c i e s i , i n t h e c o m m e r c i a l and  sport  respectively;  - the  number of  age  and  species i fish  available  - t h e number o f age  and  species i f i s h  present  at  and  species i f i s h  present  at  the beginning x (i,1)  of period  at  k;  - t h e number o f age  the beginning o f the  year;  N - the 2 4 b i - m o n t h l y seven  coefficients  t;  x{i,k)  The  the c a t c h a b i l i t y  periods i n a  c l a s s e s of f i s h  a r e two  year.,  ages o f coho and  five  of  chincox. The of  assumption  o f random e n c o u n t e r  i n f o r m a t i o n on t h e  .fisheries  process  precludes the  model. I n t h e G e o r g i a relatively success  localized  i s a product  different  particular the  sites  fishery,  fishing  1  of the a g g r e g a t i o n of the  be due and  and  c a p t u r e i n most  takes  «hot s p o t s ' . I t i s n o t c l e a r  may  known a b o u t t h e  i n the  to the  fishery  behavior  normally  place  bad  of t h e  assumption  Integrating  fish  or  of  the  of fishermen with the  other  at fish  y ( i , k + 1)-y ( i , k )  oyer  present. Because t h e r e i s  process underlying s u c c e s s f u l capture,  m o d e l . I t i s t h e r e f o r e more p r u d e n t {random  Eguation  at  whether  a r e a s . On  have n o t h i n g t o do  the  number o f t e n u o u s a s s u m p t i o n s r e g u i r e d i n c r e a s e s w i t h  complexity one  Strait  range of s t o c k s i z e s  little the  may  of encounter  tenuous..tack  use o f o t h e r p o s s i b l e f o r m s o f  behavior of f i s h  hand, s u c c e s s  i s guite  1 we  encounter)  than  get:  = -[m{i,k)  •  (l(i,k,c)  many worse  the  t o make ones.  56 •  ( 1 - l ( i , k , c ) ) v ( s ) )u |k,c)E ( k , c ) q ( i , k , c ) •  ( l ( i , k , s ) + ( 1 - 1 ( i , k , s ) ) v (s)) u(k,s) E (k,s)q (i,k,s) 1  (2) where: At  y ( i , k ) = Ln(x ( i , k ) )  this  point,  we  may  define  F(i,k) =  3±2j_  y ( i , k * 1 ) - y (i,k)  Effort The random  encounter  model  instantaneous rate of catch, catch  = effort  Therefore,  catch  (Bicker,  effort,  1940) r e l a t e s  and p o p u l a t i o n  x catchability coefficient  per u n i t e f f o r t  (CPOE) may  x  be  as  fellows:  population written:  CFllE = c a t c h / e f f o r t = c a t c h a b i l i t y c o e f f i c i e n t  x  population  or CPOE = qx Sport  effort  i s assumed  t o be p r o p o r t i o n a l  t o CPOE.  Therefore,  E(k,s)=c(k) W q ( i , k , s ) x ( i , k ) l (i,k,s) i-i  (3) where:  c(k) i s the time v a r y i n q  16, i t may increas  coefficient  be v i e w e d as t h e m a r q i n a l e f f o r t  i n CPOE. C c m m e r c i a l t r o l l  effort  shown i n f i q u r e qenerated  i s assumed  w i t h CPOE. 1 E ( k , c ) = a(k) £ q ( i , k , c ) x ( i , k ) l ( i , k , c ) / r £ q(i,k,c)x (i,k)l(i,k,c) ]  b(k)*  to  by a u n i t saturate  57 <) u  where:  a and b a r e d e p i c t e d  i n Figure  assumed f o r l e g a l s i z e d f i s h  .3.3..  2U  (Note:  response i s  only).  Controls  The  only  c o n t r o l s f o r which . . o p t i m i z a t i o n  t h e s i s a r e t h e seasons o f sport  and t r o l l  i s done i n t h i s  fishing.  u (k,c) = 1 i f c o m m e r c i a l f i s h e r y i s open i n p e r i o d u|k,c) = 0 i f c o m m e r c i a l  fishery i s closed  Therefore:  k;  i n period  k;  u(k,s) = 1 i f s p o r t  f i s h e r i e s f i s h e r y i s open i n p e r i o d  u<k,s)=0 i f s p o r t  fisheries  fishery i s closed  Note t h a t  u=1 d o e s n o t i m p l y t h a t  equations  (3) a n d (4) may p r o d u c e low f i s h i n g  stock  s i z e i s low o r , i n t h e s p o r t  fishing  will  k;  i n period  k.  a c t u a l l y occur; pressure  i f the  f i s h e r y , i f i t i s winter.  levenae  Revenue i s g e n e r a t e d form o f c a t c h Sport  effort  fishery  and i n t h e s p o r t  revenue frcm  the sport  i n terms o f catch.  caught  o f a boat-day  fish  so f o r t h e purpose o f f i s h e r y c a n a l s o be  per boat-day. / T h e r e f o r e ,  the  c a n be assumed t h e same a s t h e  of e f f o r t .  The r e v e n u e e x p r e s s i o n  t o be t h e sum o f t h e components due t o f i s h i n g hand s i d e o f E q u a t i o n 2,  of effort.  The a v e r a g e CPOE i n t h e s p o r t  i s a p p r o x i m a t e l y one f i s h  price of a sport value  f i s h e r y i n the form  i s d e p e n d e n t upon c a t c h ,  optimization, represented  from t h e c o m m e r c i a l f i s h e r y i n t h e  i s taken  on t h e r i g h t  w e i g h t e d by t h e p r i c e and s i z e o f f i s h  58 cau q h t .  1  F(k) = u ( k , c ) E ( k , c ) p ( k , c ) £ 1 ( i , k,c) w ( i , k ) g ( i . k , c ) x <i,k) •  u(k,s)E(k,s) F,k,s)^ 1 (i,k,s)q (i,k,s) x(i,k) (6)  where: k  w(i,k)  i s t h e weight  ( f i g . 6 and l e n g t h  o f age and s p e c i e s  weiqht  i during  relationship);  p(k,c)  i s t h e p r i c e per pound o f c o m m e r c i a l l y  during  period  p(k,s)  i s the p r i c e per f i s h  29) .  k  period  caught  fish  ( F i g 27) ; i n the sport  fishery (Fig.  59 OPTIMIZATION  Pith the optimal  ingredients  c o n t r o l problem  u (k,c) ,u (k,s) ,x ( i , k ) maximizes  R (k)  levels  period  from  after  tarqet  formalized  where:  by  N  The  level  {Equation  not  1)  that  population  depart  dramatically  c o n d i t i o n can  be  d(i) (x(i,N*1)-X(i))  p a r a m e t e r used  to  season  (Kolman and  the  function.  i s the  within  should  later  -  the  chapter,  In a d d i t i o n , the  G(x(i,N+1)) =  problem i s f o r m u l a t e d  multipliers  6).  payoff  tarqet  previous  i=1,...,7  (x(i,N*1))  (X(i)).  i n the  find  k=1,...,n  a terminal  is a  aqainst  i s to  (Equation  levels  X(i)  d(i)  The  defined  o f aqe  and  species i ;  weiqh t h e t e r m i n a l  condition  benefits.  i n the  Trench  method o f  1971,  p.  "Laqranqe"  224;  Clarke  1976,  p.  250).  ILLIJ).  Mathematical  To will  be  ease the carried  = L n x ( i ) , hence expressed  formulation  notation out  and  differentiation,  x(i) =  E X P ( y ( i ) ) . The  p r o b l e m may  then  y (i)  be  as  k=l to  formulation  i n y(i) r a t h e r than x ( i ) . R e c a l l t h a t  N Maximize { £ R (k)  subject  the  +  i  7 2;G} s  l  (8)  60 y ( i , k+ 1)-y ( i , k ) =f (k) 0  k=1,...,N  < u (k,c) ,u (k,.s) < 1 (9)  Ihe  " L a g r a n q i o n " f o r t h i s problem ( C l a r k , 1976) i s : » 7 L = S [ e | k ) - ^ z ( i ) (y (i,k+1) -y ( i , k ) -F ( i , k) 1 + G  ±4 (10) Where: z i s t h e L a q r a n q e m u l t i p l i e r . A necessary u(.,.) u's.  and s u f f i c i e n t  i s that  condition  L must be maximized  D i f f e r e n t i a t i n g with  respect  for optimality  with  respect  of a p o l i c y  t o a l l y ' s and  t o y and r e a r r a n q i n q  terms  produces z ( i , k - 1 ) - z ( i , k ) •= • rlU(k)/dy ( i , k ) 4 z ( i , k )  dF ( i , k ) / d y ( i , k) k=2,...,N (11)  z ( i ,N)  = d G / d y ( i , N+1) (12)  i'rci  Equations  Therefore,  2 and 6, note  t o maximize  L with  that  L i s l i n e a r i n t h e u's.  respect  t o u, t h e f o l l o w i n q  c o n d i t i o n s must be s a t i s f i e d : 7 7. F (k,c) £ w ( i , k ) 1 ( i , k , c ) ^ Z, z ( i , k) r 1 ( i , k, c) «- (1-1 ( i , k, c) ) v (c) 1 u (k, c) = 1  X P |k,c) £ w ( i , k ) l ( i , k , c ) i-l  7  P (k,s) £ w ( i , k ) 1 <i,k,s) l-l 7 P ( k , s ) £ w{i,k) 1 ( i , k , s ) i-l  7  >y £ z ( i , k) [" 1 ( i , k , c ) + | 1 - l ( i , k , c ) ) v(c) 1 l-i u (k , c) = 0' 7  < % z ( i , k)T 1 ( i , k , s ) + (1-1 ( i , k , s ) ) v (s) 1  ^ u (k,s) = 1 7 > % z ( i , k) r 1 ( i ,k, s) + (1-1 ( i , k, s) ) v (s) 1  i-l  u(k,s) = 0 113)  61  U 2. z  The a l g o r i t h m  Some methods e x i s t t o handle t h i s problem.  One c o u l d s o l v e  f o r the seven times 23 x»s and z*s and two times 24 u*s. T h i s approach  would mean s o l v i n g a system o f 370 n o n - l i n e a r  eguations f o r 370 unknowns, and would be p r o h i b i t i v e l y expensive. F o r t u n a t e l y f o r t h i s study, i t was p o s s i b l e t o d e r i v e a much s i m p l e r procedure, s i m i l a r t o " p o l i c y  interation  (Howard, 1960). The procedure i n v o l v e s t h e f o l l o w i n g - steps£ Step 1:  P i c k a s e t of u's.  Step 2:  Solve Eguation 1 forward t o time N u s i n g c u r r e n t  best estimate o f t h e o p t i m a l u* s. Step 3:  Determine  z(N) and solve eguation  (11) backwards  from N t o 1 u s i n g c u r r e n t u*s. Step 4:  U s i n g z*s, determine a new s e t o f  u*s a c c o r d i n g  to e g u a t i o n (13)., Step 5:  I f , during two i t e r a t i o n s , a l l x's, z * s , and u's  remain unchanged, then s t o p ; e l s e go t o Step 2. Ho theory e x i s t s concerning the numerical p r o p e r t i e s o f t h i s a l g o r i t h m . Puteraan and B r u n e l l e  (197j6) have compared  p o l i c y i t e r a t i o n t o the "Newton* method o f n o n - l i n e a r 1  programming. Convergence  o f t h e a l g o r i t h m i s not guaranteed. .,•  However, i f the a l g o r i t h m s t o p s , then a s o l u t i o n t o t h e "Lagrange" problem has been reached and i t i s guaranteed the r e s u l t i n g p o l i c y i s l o c a l l y o p t i m a l .  that  H  62 OPTIMIZATION  The o p t i m i z a t i o n p r o c e d u r e section  requires i n i t i a l  population study  sizes  were t a k e n  population  (X { i H . from  described  i n the  population sizes  (x ( i , 1 ) )  t h e s i m u l a t i o n model.; An  of constant  to start  recruitment  after  structure  o f t h e s i m u l a t i o n model i s l i k e l y  An i m p o r t a n t  s i x years.  values  parameter  {Table  met. D i f f e r e n t i a t i n q Therefore,  d (i)  calculating  left  fish,  then  water. boat fish.  On  than  respect  the best  system  2)  1971).  they  to y(i),  leaves  of z (i)  a r e known  Iqnorinq size  i n the sea i s greater  than  i n t h e s e a , then  the fishermen  X ( i )i s d (i) .  interesting  as t h e "shadow"  the price  i s more  (Eq. 7 ) .  and t h e b a s i s f o r  limits  decision i s t o leave  the contrary, i f the fish  The  a s t h e x ( i , 1) .  and  (13) s t a t e s t h a t i f t h e shadow  the optimal  availiable  Strait.  o f t h e z»s. The z»s h a v e a n  I n economics,  (Intriliqator  mortality,  G with  as a  population  t h e deqree t o which  i s the t e r m i n a l value  the rest  interpretation.  fish  The f i n a l  i n the optimization i s d(i)  The m a q n i t u d e o f d ( i ) d e t e r m i n e s  prices  initial  of "current" conditions i n the Georgia uses these  i n this  an e q u i l i b r i u m p o p u l a t i o n  i s reached  optimization  and target  the simulation then,  structure  estimate  preceding  The p o p u l a t i o n s i z e s u s e d  s t r u c t u r e i s used  conseguence  RESULTS  shaker  price  of a  of the landed  the f i s h  i n the  valuable i n the  should  be a l l o w e d  to  63  TABLE  2.  I n i t i a l  and  tar<jct  p o p u l a t i o n  s i z e s  Coho Ocean  y e a r  1  I n i t i a l  1,800,000  T a r g e t  Ocean  y e a r  2  I n i t i a l  1,080,000  T a r g e t  1 , 0 8 0 , 0 0 0 0  C h i n o o k Ocean  y e a r  1  I n i t i a l  1,300,000  T a r g e t  9 8 0 , 0 0 0  Ocean  y e a r  2  I n i t i a l  980,000  T a r g e t  4 9 0 , 0 0 0  Ocean  y e a r  3  I n i t i a l  490,000  T a r g e t  1 4 2 , 0 0 0  Ocean  y e a r  4  I n i t i a l  142,000  t a r g e t  1 7 , 0 0 0  Ocean  y e a r  5  I n i t i a l  17,000  T a r g e t  2,500  The to  z's  r e p r e s e n t the  be c a u g h t  z's  later  value of l e a v i n g the  when t h e y  are  also i n c l u d e the cost of v i o l a t i n g  valuechosen leaving may  f o r d ( i ) can  a fish  come f r o m  i n the  sea  more v a l u a b l e .  The  t a r g e t escapements.  The  l a r g e r and  be i n t e r p r e t e d  fish  a s the  value  i n t h e water f o r f u t u r e b e n e f i t s . the  offspring  spawning grounds, o r from  i f the f i s h  the  These b e n e f i t s  i s allowed  value of the f i s h  of  to reach  i n next  the  years  catch. For the of  t h e d's  to  be  optimization i n this were n o t  found  by  t h a t t h e d's ccmmercial period  other  should  fishery  of the  available.  independent  Therefore, suitable  means. The be  thesis,  a p p r o a c h used  was  p r o p o r t i o n a l to the landed  of a f i s h  o f age  and  estimates  values to  had  assume  value i n  s p e c i e s i i n the  the  last  year. d { i ) = r p ( i , N , c ) w(i,N) 114)  A search f o r the the  terminal values  0.07  and  tarqet  5.1.  left  an  of r which generated  (X's)  averaqe  a policy  most c l o s e l y r e s u l t e d trivial  discrepancy of  that  met  i n r equal  to  C.71%  the  from  X's.  F i n d i n g an The  five  sclving  O p t i m a l P ^ M c y . iConverqence)  method d e s c r i b e d i n t h e l a s t  very e f f i c i e n t l y or  value  i n a l l cases. Convergence  i t e r a t i o n s o f the equation  computational  section  (1) and  requirement  a l g o r i t h m . The equation  (11)  found  was  solutions  obtained  i n four  calculation included  five  times.  i s equivalent to runninq  This the  65 simulation Table  year  on  an  policy  and  no  optimal used  commercial  computed  policy  fishing.  an a v e r a g e  by t h e  an  average  fishery  17%  t o o few  f o r the  season  o f 0.5%  This policy of  over  fish.  from  too  The  January  few  unchanged and  59%  underharvested  t o o many f i s h .  fish.  The  next  until  The  opened the  March a n d  June  final  left  commercial f i s h e r y  sport  closed  1, l e a v i n g  policy  next  leaving  p o l i c y c l o s e d the  through  the  fisheries a l l  harvested the population  months o f J a n u a r y  commercial f i s h e r y average  included sport f i s h i n g a l l  a l g o r i t h m c l o s e d up b o t h  year around. T h i s p o l i c y  method  f o r ^ c u r r e n t " c o n d i t i o n s . The  i n a l l cases  populations leaving policy  years.  3 shows i n t e r m e d i a t e p o l i c i e s o b t a i n e d a s t h e  converged initial  model e i g h t t o t e n  the  an  the one  sport half  month l a t e r . ./  J5.2..  Optimal  The  first  "best guess"  Policy  optimization result parameter  management w i l l escapement presented  estimates  attempt  levels.  The  i n Table 3,  obtained  and  t o m a i n t a i n c u r r e n t age optimal pclicy  final  current  practice  of A p r i l  opening  f o r coho. 3) The  15  s t r u c t u r e and is  iteration* between t h e 1) The  during the winter.  opens t h e commercial  or  that  f o r t h i s case  c u r r e n t management p r a c t i c e s :  c l o s e s the s p o r t f i s h e r y pclicy  using nominal  and t h e a s s u m p t i o n  There a r e t h r e e major d i f f e r e n c e s policy  was  fishery opening  optimal  June  2)  optimal  The  and  leaves the  policy  optimal  15 as o p p o s e d t o  f o r chinook  policy  optimal  July  the 1  commercial  66  TABLE 3.  Intermediate p o l i c i e s f o r computation o f o p t i m a l p o l i c y under "current" conditions.  FIRST ITERATION Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sept  Oct  Nov  Dec  Sport  11  11  1 1  11  11  11  1 1  1 1  1 1  1 1  1 1  1 1  Troll  11  11  1 1  11  11  11  1 1  1 1  1 1  1 1  1 1  1 1  Average d e v i a t i o n  from t a r g e t p o p u l a t i o n s -• 17%  SECOND ITERATION Jan  F'eb  Mar  Apr  May  Jun  Jul  Aug  Sept  Oct  Nov  Dec  Sport  0 0  0 0  0 0  11  11  11  1 1  1 1  1 1  1 1  1 1  1 1  Troll  0 0  0 0  0 0  0 0  0 0  1 1  1 1  1 1  1 1  1 1  1 1  1 1  Average d e v i a t i o n  from t a r g e t p o p u l a t i o n - .5%  THIRD ITERATION Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sept  Oct  Nov  Dec  Sport  0 0  0 0  0 0  11  11  11  1 1  1 1  1 1  1 1  1 1  1 1  Troll  0 0  0 0  0 0  0 0  0 0  0 1  1 1  1 1  1 1  1 1  1 1  1 1  Average d e v i a t i o n  1 - f i s h e r y open 0 - fishery closed  from t a r g e t p o p u l a t i o n  .71%  67 fishery  open d u r i n g  fishery  c l o s e s i n O c t o b e r . The  d i f f e r e n c e s i s the during the pound  latter  ( F i g . 27)  November and  higher  during the  to harvest The  the in a  optimal  high  year.  per  by a  v a l u e . The  fish  fish,  due  i n the  price  to  when t h e y  was  coipared  decrease  per  growth,  commercial -IfctHL  s  a r e more v a l u a b l e . : . to;curreiit,3seasoES  winter  i n sport  using  sport fishery resulted  b e n e f i t s , which  140,000 d o l l a r i n c r e a s e i n t h e c o m m e r c i a l net  fish  w a t e r d u r i n g t h e e a r l y months  s i m u l a t i o n m o d e l . C l o s i n g the  offset  caught  Both t h e r i s i n g  weight per  value  them l a t e r  140,000 d o l l a r  these  of commercially  f i s h i n the  policy  for  months.; On der •thes«r"'COTrdl'ti©|ri*|  later  b e t t e r t o l e a v e the and  value  increased  c o n t r i b u t e to a very fishery  major r e a s o n  months o f t h e  and  December.,In p r a c t i c e , t h e  change i n v a l u e u s i n g t h e  optimal  was landed  policy  was  insignifigant.  5j.3jt  Increased Much o f t h e  Strait  over  the  were d e v e l o p e d Eguation  i n the  seasons. The  14.  an  fishing using  water a t  the  fish  increased value  stocks. This  of f i s h  left  season. A s e r i e s of optimal values  of the r  shows t h e e f f e c t  t h e end  of the  As r i s i n c r e a s e d , t h e  sport fishery  Georgia  o p t i m i z a t i o n e x e r c i s e has  of  increased  F i g u r e 30  development of the  this  conservation  be i n t e r p r e t e d a s  water a f t e r  fish  impetus f o r the  s i m u l a t i o n model and  from concern can  Escapement •••  i s confined  year  the  concern the  policies  parameter i n  of increased on  in  come  value  optimal  l e n g t h of the seasons  of  a  fishing decrease.  t o t h e summer months when i t has  MONTHS o  z  o  to  Optimum open season j> c_ c_ S£  «9  £ C  n  a a n fOD Ul 1-1 Mo a X) M  01  I—  Cn CU O n> -o & LO < t r*  CO  o oc  ri  M3 &  1—  1  to  0H- ft L.1 C  3- C HO "JO a (A ro 16 • w l-ti  •o o l-l (t n  rf CO D  o  rt  r+ O  I-i 3 Cu  o a M 1) a. ro urr u; O  1  O  TT  0>  "i r--  U M  be  V •o H(3D a fD . G a rta o> (• a  89  69 t h e h i g h e s t v a l u e , and later  months when t h e  commercial  fishing  i s delayed  to  fish  have the h i g h e s t v a l u e v  The  change i n the s p o r t season  where r i s changed f r o m  0.1**  reflect  the  "sguare"  (Fig.  28) . The  than  the c u r v e  is  still  J5.J4  nature  of the s p o r t f i s h e r y  sport fishery  value curve  assumed i n t h i s  to  0.16  curve  smoother  model. However, i t s " r e a l " s h a p e  uncertain.  Size Limits -  A  Optimal limits. limits  f i s h i n g seasons  F i g u r e 31 had  effect  are  upon t h e s p o r t f i s h i n g  kill  the  value of the f i s h e r y . at least  shaker  up  m o r t a l i t y , but  t o 20  The  results  inches,  legal  c o m m e r c i a l f i s h e r i e s , from  d o e s not  sized  t o 20  to the  size  The  fish  contributes to contribute to size  o p t i m a l t o have a  l i m i t s , on  present  of the commercial f i s h e r y  size  season.  show t h a t , f o r  i t i s never  winter sport f i s h e r y , i n c r e a s e d s i z e  expansion  to  harvest of undersized f i s h  the  limits  f o r various  p o l i c i e s . Increased  assumed t o r e s p o n d  o n l y . T h e r e f o r e , the through  were computed  shows t h e r e s u l t i n g  little  sport fishermen  and  abrupt  value  i s surely  the  both the s p o r t  inches allowed  same s e a s o n  as  an  the  sportsman's. While decrease  increasing the  population puzzling. policy not  the s i z e  v a l u e o f r so a s  l e v e l s . The A t 26  results  i n c h e s and  l i m i t , i t was  not t o o v e r s h o o t f o r t h e 26  a value of  i s t o open t h e c o m m e r c i a l  to i n c l u d e a w i n t e r  found  necessary  target  inch size l i m i t  0 f o r r , the  fishery  sports fishery.  the  to  year  are  optimal round,  This policy  but  resulted  in  F i q u r e 3 1 : O p t i m a l S e a s o n s f o r S p o r t and T r o l l I ' i s h i n q i n t h e Georqia S t r a i t with Respect to Increased S i z e L i m i t s .  71 an  a v e r a g e o f 2 1 % t o o many f i s h  i n t h e water a t t h e end o f t h e  year.  Opening both f i s h e r i e s  limit  does n o t v i o l a t e t h e t a r g e t p o p u l a t i o n .  be  negative  the  for this  speculate  species  5,5.  with  a 26 i n c h  size  However, r must  p o l i c y t o be o p t i m a l * / I n t e r p r e t a t i o n o f  shadow p r i c e b e i n g  could  a l l year round  that  negative  i sdifficult.  i t i s an a r t i f a c t  However, one  o f t h e " c u r r e n t " age and  structure.  Increased The  Sport  catchability  Efficiency coefficient  i s t h e most  uncertain  p a r a m e t e r i n t h e model. The u n c e r t a i n t y , a r i s e s b e c a u s e catchability effcrt, and  i s computed  effort  data  of t h e s p o r t  statistics  fleet,  and H a r r i s  c a l c u l a t i o n of catch response  The likely  per u n i t e f f o r t ,  o f the sport  increases  and f u t u r e  the sport c a t c h a b i l i t y i n both  confined year.  fleet  t c do so. T h e r e f o r e ,  uncertainty  allowed  Catch  upon s m a l l  samples  t o be b a d l y  biased  1S77). C a t c h a b i l i t y a l s o e n t e r s  sport  the  catch,  from  into  which t h e s p o r t  i s predicted.  efficiency continue  a r e based  and a r e b e l i e v e d  computed f o r i n c r e a s e d  As  rates,  f o r the commercial f ^  fishing  (Argue C o u r s l e y  effort  mortality  and e s c a p e m e n t , a l l o f which a r e p r o n e t o e r r o r .  However, s p o r t f i s h i n g  the  from n a t u r a l  i s i n c r e a s i n g and w i l l optimal  catchability i n sport  policies  to r e f l e c t  both  efficiency  (Fig. 32).  i n c r e a s e s , t h e amount o f f i s h i n g  f l e e t s i s reduced. Again, the sport  t o t h e summer and t h e c c m m e r c i a l Increased  sport  were  catchability  season i s  s e a s o n t o t h e end o f  r e s u l t s i n both an  F i q u r e 32: o p t i m a l S e a s o n s f o r s p o r t and T r o l l F i s h i n q i n t h e G e o r q i a S t r a i t with Hespect to I n c r e a s e d E f f i c i e n c y i n the Sport Fleet.  73 increase of  any  i n the  u n i t of  increases,  e f f o r t on  the  also increase  amount o f e f f o r t  value to  the  an  increase  f i s h stocks.  of a f i s h  provide  and  left  As  i n the  i n the  sport  water  f o r enough f i s h a t t h e  impact  efficiency  (d(i)) end  must  of  the  season.  56 ±  , Enhancement  X  Enhancement  was  abundance o f t h e of  doubling  the  d r a m a t i c , but policies the  two  the  Say  over harvest. was  8%  most s e v e r l y  The  overfished  c h i n o o k was  the  end  is  i n the  occurring  of  escapement o f coho t o public reaction  the  troll  7)  to  s e c o n d and  The  sport  (155?  and  the  year,  the  a  good i d e a  reflect  deviations from d e s i r e d  Exactly  such  this  a penalty  on  stock  in  to s e l l  high  ages  were  sizes.  the  Overfishing  present type of  than result  excess  these  terminal as  part  target  chinook  large  cf  as C a p i l i n o . J u d g i n g  t o model t h e  terminal  first  year chinook  9 6 1 more c o h o  not  until  vere r e q u i r e d  Georgia S t r a i t , with  hatcheries  was  optimal  1656 r e s p e c t i v e l y ) .  by  effect  season  season  fifth  The  seasons  a v e r a g e d e p a r t u r e from  t o government d e c i s i o n s  i t m i g h t be  (eguation  The  compensated  necessary at the  fish,  significant.  opening of  start  optimal  initial  4).  more f i s h t h a n needed. A l l t h e  were o v e r h a r v e s t e d .  new  was  the  (Tab.  Here s e v e r e r e s t r i c t i o n s i n f i s h i n g  conditions  the  the  and  i n c r e a s i n g the  c l a s s e s o f coho  direction  were t o d e l a y  to o f f s e t  of  age  by  number o f c o h o on  beginning of  July.  represented  w e l l as  from  excess  cost low  term  G  74  T a b l e 4.  Optimal season w i t h enhanced  coho  Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sept  Oct  Nov  Dec  Sport  00  00  00  00  11  11  11  11  11  11  11  11  Troll  00  00  00  00  00  00  11  11  11  11  11  11  D e v i a t i o n from t a r g e t p o p u l a t i o n s Coho 96%  Chinook.  Age 1 -.4%  Age 2 -15%  Age 3 -1%  Average d e v i a t i o n from t a r g e t p o p u l a t i o n - 8%  Age 4 -2%  Age 5 -16%  75 T h i s r e s u l t may Enhanced f i s h ,  hy s t i m u l a t i n g  overexploitation may  have s e r i o u s  o f unenhanced  need t o be more s e v e r e .  opening  implications  fishing effort,  overexploitation  Also,  a poor d e c i s i o n  cause the  stocks.  on f i s h i n g  regarding  by s t i m u l a t i n g  be v e r y c o s t l y  o f unenhanced  may  enhancement,  stocks,.Restrictions  o r c l o s i n g o f any f i s h e r y may,  amounts o f f i s h i n g e f f o r t ,  for  i n terms of  large  the  76 6  Conclusions this the  ; A  can  particular  DXS€"OSSi;0M>.^JD-^.O»fiLqSi&QH.  be  drawn i n t h r e e  fishery,  the computational  of the  determining  main  is  t o see  of  the system about  policies  under a s i m p l e models and  which t h e r e  here,  two  i n pre-spawning  age  stock  policies  coefficient  little  and  examination,  the  stock  parts the  abundance there  abundance. In t h e  are  single  case:  cn  E r r o r s i n a s s e s s i n g the  predicted catch. will  also result  reflects  the  will  result  escapements. T h e r e f o r e ,  square  effect  abundance o f  p o l i c i e s are i n turn  amount o f t i m e t h a t t h e  potential  in a  a  i n large errors i n predicting catch  from a l l c o h o r t s . O p t i m a l c a t c h . The  g*s  (a + bqx) qx  of the  the  to  known a b o u t t h e  Errors i n estimates  to  are  model g u a d a t i c a l l y : t h e  r a t e of c a t c h =  cohort  assumptions  l a r g e u n c e r t a i n t i e s . In  c l a s s e s . On  components which e n t e r t h e  catchability  are  s e t of  and  t h e r e i s u n c e r t a i n t y about a l l the  parameters; t h e r e i s a l s o very fish  management.  p u r p o s e s f o r b u i l d i n g .simpl,e„&o&els  s e n s i t i v e these  model p r e s e n t e d  and  ;;:;  optimal  how  management o f  ..,,.  rSegfogj^s^ One  the  scheme p r o p o s e d ,  importance o f o p t i m i z a t i o n i n resource  - 6.1.  of  areas:  policies  sensitive  f i s h e r i e s are  f o r the c a t c h t o v i o l a t e the  very  closed  target  of c l o s u r e s are  very  77 sensitive The is  to the  unknown q u a n t i t i e s c a t c h a b i l i t y  major c o n c l u s i o n r e g a r d i n g t h e G e o r g i a  t h a t , under t h e assumed  commercial f i s h e r i e s , sport  fishery  particular general  winter  i s optimal. There i s l i t t l e  trend  analysis  i n the  they  fishery  Allen  is likely should  harvested  be  a  fall  a sufficient  different (1)  fishery  the  sport  t e s t e d where a confidence  thesis.  the  However,  the  in  the  a good a s s u m p t i o n . left  during  i n the the  The  water i n  the  more v a l u a b l e  obtained  commercial  fishery.  use  of  l i m i t s may  breeding  Georgia  number o f f i s h  stock,  with  left  summer  l i m i t s as  be  used e i t h e r  Strait in  the  a to  o r t o promote t h e can t a k e  on  maximum  three  forms: The  maximum t o t a l  numbers o f f i s h ,  (2)  The  maximum number o f l a r g e f i s h ;  (3)  The  maximum t o t a l  independent  size;  weight.  and  can  a summer  size  d e s i r e d k i n d , " Maximum c a t c h  and  winter  in  more v a l u a b l e  season best  regulation. "Size  catch of the  Strait  i n both  t o i n s u r e escapement from the  fishing  and  abundance.  a n a l y s i s a l s o shows t h a t s e a s o n c l o s u r e  (1954) d i s c u s s e s t h e  fisheries maintain  being  Dramatic i n c r e a s e s i n the  water a f t e r t h e sport  be  The  used a s a t o o l  fishery.  winter  can  sports fishery. be  used i n t h i s  of s p o r t f i s h e r y  shows t h a t f i s h  so  schedule  t h e r e were; no c a s e s  p r i c e schedule  summer t h a n  price  and  of  78 In t h i s under t h e  a n a l y s i s , the  first  objective  A l l e n concludes a n g l e r s can they  "...  no  be a l l o w e d  fisheries  maintaining It fishery  limit  to take  both  fisheries  benefits  allow  of the  limit  small  commercial  two  fish  fish  fisherman.  The  not  other  c o n d i t i o n s one  between c o m m e r c i a l  that before  Georgia of  for size  can  be  (3)  above. S i z e  and  resource.  is  limits in  For example, a  i n the  sport  fishery  purpose i s to  more v a l u a b l e f o r  more a b u n d a n t  the  fish.  instruments  The  to  current p o l i c i e s of  size  the  stocks,,  does n o t  in either  differ  results  or  i n d i c a t e d that to  value their  g r e a t l y frcm  appearance  must maximize p r e s e n t  sport  the  distributing  aimed a t d i t r i b u t i n g  policy  p o l i c i e s and  in  commercial f i s h e r y  used as  However, t h e  Earlier  limits  p u r p o s e i s t o make a v a i l a b l e t o  a t t r i b u t e near z e r o  current  i n the  p u r p o s e s . One  a t p r e s e r v i n g the  ( T a b l e 5).  b e n e f i t s and  the  s m a l l e r and  practiced policy  performance  w a t e r . The  of  f o r two  The  computed optimum  present  current  reasons  s e a s o n s a p p e a r t o be  and  case,  as,possible  upon t h e b a s i s  t o grow b i g g e r and  i n c r e a s e escapement.  harvest  limits  i n the commercial than  shows s i z e l i m i t s  l i m i t s and  Size  mechanisms f o r  users  s p o r t s m e n more o f t h e  analysis  operate  be a p p l i e d so  many f i s h  However, t h e  are i n f a c t  more s m a l l e r the  as  should  o b j e c t i v e resembling  between t h e  larger size allows  t h a t one  w i t h an  i s assumed t o  stocks..  i s conservation.  operated  the  size  have been d e f e n d e d  breeding  i s true  fishery  (maximum number). I n s u c h a  d i e from n a t u r a l causes".  Strait  the  sport  within  to stocks resulting  fisheries,  match  season  left  in  the  allocation  have e v o l v e d  due  to  79 T a b l e 5.  A comparison o f the o p t i m a l p o l i c y w i t h a v a r i e t y policies.  Chinook Escapement  Policy  Coho Escapement  of other  T r o l l landed Value  S p o r t landed Value  (1) Present  seasons  34,879  124,861  $2,300,000  $12,640,000  seasons  36,577  124,660  $2,440,000  $12,500,000  49,572  177,390  $2,900,000  $ 8,180,000  50,000  149,000  $1,400,000  $12,000,000  (2) Optimal (3) Optimal seasons w i t h 20" s i z e l i m i t both s p e c i e s , both fisheries (4) P r e s e n t seasons 20" s p o r t chinook size limit. T r o l l e f f o r t cons t a n t a t 40% p r e s e n t maximum  80 political  and  economic  pressures  v a l u e of s p o r t versus commercial is  likely  these  frcm  groups.  f i s h e r i e s used  a m a n i f e s t a t i o n of t h e s e  The  relative  in this  thesis  p r e s s u r e s . By s u b m i t i n g  p r e s s u r e s t h e management has  maximizing  both  put  foreward  to  an o b j e c t i v e o f  present b e n e f i t s r a t h e r than conserving  f o r the  future. The  f o c u s of t h i s t h e s i s has  management o f t h e G e o r g i a development of s e a s o n a l annual  g o a l s has  The  been p r e s e n t e d .  objectives,  §±2x  The The  from  time  and  fishery.  i s right  The  d y n a m i c s from  from  any  for  i f t h e r e i s no  can  reach s i o i l a r  a long  time  f o r the  t o meet  goals  been t h e s u b j e c t o f  and this  the f i s h e r y , i t s perspective,  d e s i g n methods can  form  p r e d i c t i o n s and  of a n a l y s i s must be  reasonable  and  intuitive  c o n c l u s i o n s , then  upon t h e computed  most t e c h n i g u e s  of  answer. C o n v e r s e l y , pclicy  trappings.  c o m p u t e r becomes n e c e s s a r y  becomes t o o  approached  policies  intuitively p a t h by  clear,  which  one  be  reasonable  results  d e s i g n c o u l d , i n h i n d s i g h t , have  without  The  be  g r e a t doubt s h o u l d  been d e v e l o p e d  and  A technigue  l o n g term  f o r a look at  evaluation of p o l i c y  unlikely  within-season  Methodology  generated  frcm  have n o t  s e v e r a l p o i n t s o f view. The  placed  the  management p l a n s d e s i g n e d  ccnseguence of p o l i c i e s analysis.  Strait  been  the mathematical  cumbersome f o r p e n c i l  t h a t t h e human a l o n e c a n  seguence o f s t e p s i n a f i n i t e  and find  and  computational  when t h e a r i t h m e t i c  paper.  Furthermore,  the r i g h t  p e r i o d o f time  i t is  combination to arrive  at a  81 c o r r e c t and reasonable A promising  s o l u t i o n to a managementproblem.  approach to p o l i c y design and a n a l y s i s i s  s i m u l a t i o n modeling. Modeling  a l i e n s the s y n t h e s i s of data  known processes with the not so- w e l l known and processes. The  known and  and  guessed a t  the u n c e r t a i n are glued together to  form a dynamic r e p r e s e n t a t i o n of the " r e a l " system. A l a b o r a t o r y world i s created i n t o which one can make management i n t e r v e n t i o n s and  observe  predicted results. Alternate p o l i c i e s  can be evaluated f o r t h e i r performance i n the model world without  r i s k s of damaging the r e a l world. There are s e v e r a l  ways to use a s i m u l a t i o n model f o r p o l i c y design. One  method  i n v o l v e s the use of the s i m u l a t i o n model to e x h a u s t i v e l y s e a r c h f o r best c o n t r o l p o l i c i e s  (Peterman 1975,  1977). Others  use  more formal o p t i m i z a t i o n techniques on s i m p l e r models and  then  apply the c o n t r o l p o l i c i e s to the l a r g e r models  (Winkler  B o i l i n g and  in this thesis  Dantzig  1978). The method presented  preserves a l l of the components of the s i m u l a t i o n with  1 975,  the  e x c e p t i o n of a longer term p e r s p e c t i v e , and even l o n g term e f f e c t s are p a r t i a l l y  accounted  f o r through  of d e s i r e d t e r m i n a l stock s i z e s .  the  specification  A formal optimization  technique i s used on the complex and d e t a i l e d s i m u l a t i o n model. T h i s f a c t makes the d e s c r i b e d methodology a most powerful o p t i m i z a t i o n procedure and  f o r d e a l i n g with l a r g e s c a l e , complex,  multidimensional models. The Georgia S t r a i t problem was  procedure.  The computation was  a good t e s t bed f o r the  very e f f i c i e n t , r e q u i r i n g  more computing r e s o u r c e s than the s i m u l a t i o n model. computational  requirements  The  are o n l y p r o p o r t i o n a l , not  little  82 geometrical such the  to the  a s dynamic  programming  d e s c r i b e d method w i l l  management  6 3±  The  final  optimization resource  s y s t e m s has  ali. 1978).  process  of  gaps i n cur  how  allows  us  great  resource  with  used  of  simplified  importance way  s y s t e m s . The  a particular  how  way.  we  should  I f the  value  example, t h e  the  sensitivity  c l o s u r e s t o u n c e r t a i n t i e s about that increased  p r e - s p a w n e r abundance  Georgia  value  the  i n w h i c h we  Strait  salmon  o b j e c t i v e function i s unacceptable,  of  value  p o l i c y generated then  resources.  complex  model under a  behave i f we  optimal  may  identify  the outputs  o p t i m i z a t i o n of a simple  o b j e c t i v e shows us  of  to  o f u n c e r t a i n t i e s and  Another f u n c t i o n of o p t i m i z a t i o n i s to we  great  modeling  extension  abundance s u g g e s t s  i n c r e a s e the b e n e f i t s of the  A  as an  h a r v e s t i n g and  u n c e r t a i n t i e s a b o u t how  operates.  model  o f season fish  (Holling  when e x t r a p o l a t i n g t h e  H i l b o r n 1 9 7 8 ) . For  and  of  of behavior  b e l i e v e the world  r e s p e c t t o the  the o p t i m a l p o l i c y  p r o p r i e t y of  help i n p o i n t i n g to  understanding  to judge the  ( H a l t e r s and  understanding  we  Optimization  harvest e f f i c i e n c y  in  that  Management  M o d e l s , however, a r e o n l y  world.  of ignorance world  other  management p r o b l e m s . M o d e l i n g  been o f  o f c a u t i o n must be real  p r o v e u s e f u l on  Resource  i n resource  c h a r a c t e r i z a t i o n s of  the  methods  1975). I t i s hoped  area of d i s c u s s i o n r e l a t e s t o the  u n c e r t a n t i e s and  deal  (Walters  model l i k e  problems.  O p t i m i z a t i o n and  A  Si  d i m e n s i o n a l i t y of the  particular the  world  under  the o p t i m i z a t i o n  one  83 exercise  h a s d e m o n s t r a t e d a d i s c r e p a n c y between t h e e x p l i c i t  statement world. the  way b e n e f i t s f l o w  component o f t h e v a l u e  major c o n c e r n  before  of the resource.  Strait  assumption  has been t h a t a  fishery.  Past  policies  a  have  o f t h e s p o r t s m a n . Many p e o p l e  the fishermen's  accept  union,  fishery  some o f t h e b u r d e n o f c o n s e r v a t i o n and t h a t  of the commercial  discrepancy  between t h e s t a t e d v a l u e s y s t e m and a r e a l  has b e e n  may a l s o a r i s e  benefits  with  from  a d d i t i o n a l amenity  value o f the f i s h . employment  the  at small catch  Thus, a value  or u t i l i t y ,  o v e r and  T h e s e v a l u e s may be and p r e d o m i n a t e t h e  levels.  may h e l p t o c l e a r l y  behavior  i s unacceptable.  or t r a d i t i o n ,  O p t i m i z a t i o n c a n be used Modeling  trcller  pinpointed f o r r a t i o n a l d i s c u s s i o n . D i s p a r i t i e s  above the landed associated  argue,  fishermen  elimination  system  fish  always  would  that the sport  and  fish  t h e complete e l i m i n a t i o n o f t h e commercial  any c c n t r c l  o f some  F o r example,  i s a l w a y s more v a l u a b l e t h a n  by t h e c c m m e r c i a l  particularly should  o r by an o m i s s i o n  o f c a t c h between t h e c c m m e r c i a l  A critical  c a u g h t by a s p o r t s m a n  suggested  u n c e r t a i n t y , about  t o t h e managers o f t h e G e o r g i a  sport f i s h e r i e s .  caught  through  from a r e s o u r c e  f i s h e r i e s i s the allocation the  and t h e way i n which we v a l u e t h e  Such d i s c r e p a n c i e s c a n a r i s e  critical one  o f o u r v a l u e system  of a r e s o u r c e  i n an s i m i l a r define areas  way t o m o d e l s . c f u n c e r t a i n t y about  system. O p t i m i z a t i o n  then  helps to  d e f i n e u n c e r t a i n t i e s and c o n f l i c t s a b o u t how t h e b e n e f i t s o f resource  systems a r e p e r c e i v e d .  84 LITERATURE  CITED  A l l e n , K.R. 1954. F a c t o r s a f f e c t i n g the e f f i c i e n c y of r e s t r i c t i v e r e g u l a t i o n s i n f i s h e r i e s management. 1. S i z e l i m i t s New Z e a l a n d J o u r n a l o f S c i e n c e a n d T e c h n o l o g y S e r . B. 3 5 ( 6 ) : 4 9 8 - 5 2 9 . A l l e n , K.R. 1955. F a c t o r s a f f e c t i n g the e f f i c i e n c y of r e s t r i c t i v e r e g u l a t i o n s i n f i s h e r i e s management. 11-baq l i m i t s New Z e a l a n d J o u r n a l o f S c i e n c e a n d T e c h n o l o g y , S e r . B. 36 ( 1) : 3 0 5 - 3 3 4 . Anon.  1978. 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Anim.  budworta Analysis,  89 APPENDIX  The  r e s u l t s and  predictions  are  numerous and  varied.  has  t a k e n on two  forms.  used  extensively  various  specific  i n a tabular  model p r e d i c t i o n s  of a c t i o n s  sport  under  effort  are pursued  predictions  1 9 7 7 ) have been  o t h e r form  form.  response.  of  Tables 4 through  assumptions  other than s p o r t  extreme  the a f f e c t o f some season  p r e s e n t a s e t of i n d i c a t o r s which and o f i n t e r e s t t o the  of  Within the t a b l e s  t o t e s t t h e model u n d e r  admissible  important  model  a v a r i e t y of  extreme  to determine  regulations  The  in d e t a i l  management a c t i o n s and  tables  simulation  of t h e  ( P e t e r man,  of c o n t r o l a c t i o n s .  been t o examine  m o r t a l i t y and  variety  the l a r q e  presentation  Nomograms  nanagement a c t i o n s  7 illustrate shaker  has  from  t o a l l o w managers t o o b s e r v e t h e e f f e c t s o f  combinations  presentation  The  J  closures.  are thought  people i n v o l v e d  to  The be  in decision  making. Escapement of spawners i s t h o u g h t importance find  a t p r e s e n t . One  a policy that  return  them t o h i s t o r i c a l  Indicators CPUE and  mortality  double  and  escapement l e v e l s ,  listed.  was  to  or a t l e a s t  levels.  o f the c o m m e r c i a l  f i s h e r y are c a t c h ,  p r e s e n t e d f o r the s p o r t the average  utmost  managers' o b j e c t i v e s  a v a r i e t y o f a t t r i b u t e s o f monetary  i n d i c a t o r s are  are  would  o f the  t o be of  weight  value. S i m i l a r  fishery.  of chinook  effort,  Shaker  i n both  fisheries  a  'JO  The  first  management a c t i o n  model p r e d i c t i o n s under c u r r e n t to  be an a c c u r a t e  evaluate  departures.  regulations escapement fishery.  (rows would  This  outside the  require  caught  percent  would  size  of s p o r t  throuqh action sport  fish  Actions  limit  four  that  and f i v e  salmon.  are increased  Action  i s from  i n Georqia outside  eiqht  cauqht  fifteen  throuqh fish.  fishery.  trollers  boats  Strait  Action  size  forty  which  and t h a t  eleven  limits  percent  would  from  sixty  the i n s i d e i n the s i z e  i s an i n c r e a s e  of the other  of  choose t o  the other  of the season. A c t i o n s  a one c h i n o o k  was  i n s i d e and  ten are increases  are combinations  simulates  extreme  s i x i s meant t o e m u l a t e a  and be e x c l u d e d  o f chinook. f o r p a r t  fourteen  which t o  of d o u b l e d  the o b j e c t i v e  I t i s assumed t h a t  maximum e f f o r t  exclusively  from  represent  the o b j e c t i v e  intended  complete e l i m i n a t i o n of the s p o r t  Island.  operate  the  I t i s not  the basis  actions  of movement o f c o m m e r c i a l  observed  limit  three  1-3). Note t h a t  Vancouver  fishery.  b u t , t o form  The n e x t  Actions  commercially  restriction  regulations.  p r e d i c t i o n suggests  unreasonable. on  account,  on t h e t a b l e s r e p r e s e n t s  i n the  twelve  actions.  per day baq l i m i t  Finally i n the  Table  6: P e d i c t i o n s f r o m t h e G ^ o r q l a S t r a i t • S i n u l a t i o n M o d e l U n d e r t h e A s s u m p t i o n s c f SO P e r c e n t S h a k e r m o r t a l i t y i n t h e T r o l l F i s h e r y , 80 P e r c e n t S h a k e r m o r t a l i t y i n t h e S p o r t F i s h e r y and Sport E f f o r t Response. ZKOICATCM rcUl  JZ  C  fc c  •mortality t r o l l " o n a U ty » p o r t  v E  5"  w  c  o  xlO  ~ -  *10  3  321.  (2) ho [ t o l l  12.  1-2.  (')  Troll  24," ch:[nook  (S)  Troll  26" th [nook  39.  (8) Sport 20" both i p t - e l c .  (9) Sp.>rt CO" c M n o o k  "2.  _  «  J . " -  •46. .1.  (10) Sport 21" el.lnook <11)  Sport 2i" C h i n o o k Oct 1 to June 1  "  »o7~  (6) T r o l l e f f o r t c o m t . n t • t 4 0 1 of p r .  (14)  S ^ o r t 70" C h i n o o k T r o l l *an« 6 Sport 70" chinook T r o l l i»oe » • 7  04.7  b«i-ll.lt  U  xlO  3  '294,.  .s ^  >  • •c o a —  " i. o  *"  -1 _  xlO  3  156.  171.  6 3."  B«;  1  (114.  «7.  65.  9 1.  178.  I H .  321. 2C6.  "  -««. 2«2. is:.-  5  iro.  '  138".  !7.  ^  •5C77-14,9.—1.3:  "'•  176.  ,  7  -  268.  - •«,.-—  0  21.  _  o.  -  13.  1  1  a  c -3  TlX  TTJ7  2 11.  0.  fi  .0 '  0  . o~ "  1. 9  C.  .05.  0.  41.  7(1  113.  0.'  " tr.  5  o—  ilO  5  13.0  956.  589.  7.15  5.4,5  0.  0.  1. 7d  0.0  231.  121.  8. 26  6. m  10.  7C7.  1.22  664..  556.  CO  6 . 30  0.  0.  0.0  7.63  52 .  1 0 . 90  5.6S  0.  0.  331.  S52.  693 .  1. 13  2 . 20 '  14..  3  0.0  13.3  1 . 1 <4 *1 1 . «  <4 .  1. 2  1. 3  13«.  83 2 .  3 S 4 4 .  4.79.  71».  1. 17  U.  1. 14  1. S  12  1.  B05.  351.  ".53.  703.  1.  n.  15.  2.5  2.6  1  ^  iT  271  2.8  K ) .  IS.  14,.  }.,  9.--15.  14-  1 44.  1.3  1.6 2..  1 )5.  .  2  5  n  )6.  j  "  1. -  150.  1  . 7  2. 5  .4)2.  6  '•'  8  "  1 34.. 130.  159.  575.- 16 ..  7  7  "  _  2  «,  S J  101.  2  «  1.  "  " °  .  2 0 * .  6 2 3 .  6«8.  114.5.  22 1.  114  0. 75  5 .77  13.6  910.  573.  7.67  5.69  13.5  9 17.  57 1.  4. 65  !.«.;  1435.  64.2.  1. 05  12.  ' -  " -  4,77. 6757 1,26.  630.  1. 01  lToi 1.03  10,7.  ,1.1  0.90  630.  6  12.35'  5.9.  0  126.  701.  3)2.  0  1  use.  e..  611. 512. 0.97  -  202.  5  1.11  696.  33 2.  xlO  1  HIS.  1 0 . TU U. T S.  3  1 105.  7  12.0 ...1.  11.9  12. 0  14.76.  124,6.  c  5  6  ,  j^J"  623. 906.  66 2.  l.i  7.65  7.;5  967.  12.52  832.  7.83  c  « . <~ i;  679.  4 4 55 .  1  uu  < r  3 0 0 .  -  u  c ^ c ^ ' ^ S "  395.  J  v. -  -5.  0.  91U.  0.  " S.  t! V.  ,10  Jot7  O >  0  r u - o JZ c w i-J > s ^r >-j * i —o^ = w u-« -  s —  =3  U  O  —  w  U i.  o k -  U  1. 6 " 105.  -  "  571  > -  «  t . .7  "1  u  ' 9.  0 c "1  J< c  t-»  1 4. 0..0  - 2 . .0  10.  9.  0, .0  "o  0.  9.  ' -  172. " " 5 7 . "  " 1  i.  ;10>  ^  ,  ~-  C vi _  —  v  o c i />  3  6~."~  -  273.  C17.  126."  "  b.' B6.  131.  133.  2 2.  IS.  13'..  >•-.  H «  0.  ' 0.  "  -J  t-  0.  o."~ "  ^  -37.  xlO  0.  ~ 1 2 « 7 ~ 10 7 . "  (12) Sport 20" c h i n o o k T r o l l 26" C h i n o o k (13)  •  130.  , 5 3  J7.  -c  3  _a  <•c _  -* o H O <->  «50.~  "39„7  .  ( I ) T r o l l J . . n . 1 Chinook Jul, 1  xlO  3  e  Ul  _4 u  u  JTJ  73.  (3) No f p o r t ( U !n.ry Ko t r o l l f i t ]" r r  o i-  0  ^  (1) Ko . p o r t i"l« h e r , f l a lh . r r  I-  n  o O  o  —  *S  « w  J=  MA;JICEMN"T ACTIONS  K u  C  a J* a o  Troll  1 1 .53  6 . 3 3  9 . 03  825.  7.62  9.22  7344.  7.55  5.40  no • ~  I  0  0 0  >-  0  5 Chinook.  J  _  I'  c  t  tr  •: I  iJ  Escapement  Coho  Escapement  Total  Troll  Catch  I l l s  TI h'  •-I H  in  o  c 3 DJ  cr  iI  ! i!  Chinook. T r o l l  I'M  Coho T r o l l  I-I  1  Catch  Troll  Net  V*l  Land  Value  (/>  lO  •c  r-l <r. •»  c  n  3 UJ TJ  ,-t  o  t"h C  n  j  i  I  : 2'  (1  T r o l l Value Boat-Day  i  Catch  Sport  Catch  Sport  Sport  Catch  Effort  Cl'PE  I I I  -J •  i2  Value  C M n u o k Sl.nLcr MoriAllty Coho S h . i l r r r l o r i a l It y Aviiap.c Vclr.dt T r o l l Chlncxk  A v c r « r . ' ^V(|;ht S p o r t Chinook. -  Z6  w c  ft) D. r—  n, - t HO 3  tr.  rr  ri  H O  O TJ  Ui  If tr  (C  3 O IO  UJ o  n  CU  t l  J3  O 3  •pr  m  IU r-l  r-l  HCU  ai  it.  o r-l  o  (p 3  B O l-l r-l' cu I-. H-  n  CO rt M CU  CO o ill  rl  >.  CO H-  n  m  -<  r-l  3 C  l- a  3  n  M  r t s r  r-l rt D>  (-••  1  Sport  •'  13  CO  • Coho S p o r t  M  n re o  'JO  Sport  Chinook  ,v M  >  rt m rn  Total  Sr  a .  r=j  u  I I  r t  CJ  Effort  Troll  !r l  H  -<  Troll  I  re  Catch  -J  a-  a.  r t O  .t CO r ) •< O r-l I-.rt ti  O Q. (0  Table  8: P e d i c t i c n r , f r c t n t h e G e o r q i a . S t r a i t S i m u l a t i o n Kodel Under t h e A s s u m p t i o n s c t 50 P e r c e n t S h a k e r rccrT-dlity i n Troll Fishery, 80 Percent Shaker m o r t a l i t y i n the Sport Fishery and Fixed Spcrt Effort Pattern.  Coors«rcial T r o l l  Korea 11 ty  the  V*ighn  l M i \\ \\ 11 i, ii ti 11  h i i i 1 I ! Ii I  i i •KAKACDtZXT ACTIONS  (0)  Fraacnt  <1) Ho « p o r t  flihtry  (2) Ko t r o l l  fi  (3) Ko » ? o r t Ko t r o l l  flihtry  (5) T r o l l »  xio  3  33.  122.  2  ""71.  32T.  350.  5».  ils.  b"i  1337  36.  xlO  »io  3  3  xlO  3  15*7  3  0  ~  201.""156.  57  '~  ~  '22.  ~  y  •1  oT  ~  ^°  ^  2  1  xlO  5  i  xlO  3  ^  1.6  2 11.'  °-°  °^  6 0 . " "123."  xl0  3  « °-  iTTJ  iVTi  °-  '.''»  0.0  TTV.  in.  6  ^  356.  so..  xlO  S  135;  ( 3 .  '• 6  (7) T r o l l J J u l y 1 coho *?t<:i**  (9) Sport 20" chinook (10) Sport 24" chinook (in sport :< (12) Sport 20" chinook T r o l l 26" chinook  3 2 . " ' 12l'."~ 176i  0  E5.'  92.  2  "".''-6 " l 0 5 .  "  1 2 2 . " 2 5 0 . " ' 16  122."' 250.  13. "  1.3  1.5  . - I - — - L - ' " : - . " : _ J _ "3.  113.  "133".  -*  ' '  n  >  2  " l 9 . " 13.  : _ _ . l . . _ ' _  1  ""ee.  ,  /  120.  9  813. " 3 t « .  _  -  '•  '"•  2  2  J  ;  -  620. aaa  " 3 .  i  353. ie]  ' 3 9.  18  3.  2  2.3  '1  '-j,'  '-  1-3  3  11. ' i _ ' i L 7iJ7772!I:~!"777J":JJ!il_^l: ! 2-2  2-1  729.  s  1.12  3  201.  nm  121.  5.3,,  3  8.26  6.  1.  r r r — T o — m —  rrr  0.  0. 0.0  7.6o"  «».'io.» s.6» 13. 1 1 1 63. 5  7 0 3 . 1 2 . 33  ""  13.1  523.  5.1,"  s.,. 576.'  7.66  5.91  1 22.  0  8  723.  -  258.  ;  139.  703.  " 217.  7  366."  ATT  ,J1  - "70  2M  -  729.  0.89  '"•  7  2  9  -  086." 7 2 9 .  729  10.1 1 7 K .  952.  "7.  »»" »»!i"'""v~,.H  -  066. 7 2 9 .  ll-ll:..ll__.!l_.l  1-  1.12  729  365.  2  -* '"• " - '"•  2.2  729.  " - - '-' a5  xlO  7  7  069.  SI I i ! J  3  - - "- "- <>•" ».i i ^ . .m. ^".v  2  9  160. '""90.  7  1 l'_'1__'1_1*- '°13.  J1J..:..".;_J!!;...:!_J:;.J^_J3o".  5  8  .~J.-i.AlliJ.tl:..2::...l"~ '30.  6  f,  sTT . j . . . ]  0. 2.20 0.0  -------:..-l'i..":.._°. :  (6) T r o l l e f f o r t at 401  Amy bag-Halt  xlO  3  "3 S i .  t  ch  (9) Sport 20" both  xlO  -^---.--!:-A'i_'.'i.J. i.J. :_.^11' " - ° - " - I - "- '•"  (A) T r o l l 24" ch M  «IO'  i i i I I il  0.59  j  -  i  3  0. 97  13.1 1290.  758.  '7.55  ^-i~T^IZ7~TII7"7I.«o 10. 1  165..  523.  7 . 72  6.23  6  . 3 3  8.99  7771.7.7" ,7 .."TI-r-Trr - °-" '77,37."7,7"777~7,7  I s  3; S  "1 !  1 M  A  Chinook. F s c a p e u c n c  t  i  Coho  Escapcaent  tr  hrt>  si  ii  Total Ttoll  Catch  ia  **1  CZu •• Chinook T r o l l  Catch  • ll>  ! i  CO  n Coho T r o l l  Catch  a> W I  O  I  ;  Effort  Troll  CUPE  Troll  Net  Troll  Und  I I  I'll i  Troll  ! I  £r ID ri  Value  M  O  In  c W  UJ T! !-t o  a .  Ul n a ~c (tl  o  l-l rt  O ii)  rn  ft  rr. M O  O  M  rt  rn  <l  O i-ti  3  -  rt H-  -<  X Value  T r o l l Value Boat-Day  Cl UJ  Total  Sport  Caich  Sport  Coho S p o r t  Sport  i -  I  1  I  Catch  F.ffort  Spnrt CUl'F. t  I  -I  O  I  c  I  I -  Sport  Value  Coho Sh.iker HnrlalUy Avi-r.ir-.r V.*l ,|,e T r o l l Chinook r  i  i  r  ?c  (D  O n n  'Oi rt rr  Avcrnpi- Uelf.l't Sport C h i n o o k  o  pDJ  ;B  LO I-I  rt  ll)  ' i  in  M  rt in i~ tr  p rt  t—' m h' ;v 1+ t)  LO  1-1 C  H  3  3  1—i  O M rr PJ  CJ  rr  3" (L  00  n O  •I rt  M M-  rt I-ICl  3  rtrt o Mn m  •<  rt (T)  ^6  ID O  it-  g  '-<  Chhu-ofc r.hakrr M o r t a l 11y  i •  i  rt  •  I  I l»  Catch  o  tr n Cu •XI J 3  n  Chinook  t/l  hr, O  -  0  ^•  %  (0  I ul  i .-  i  3 c  APPENDIX 2  The Lagrange system in one dimension: Max Y, U  R(y  z  k-1  u  •  K  k  )+ G  N + l  Subject to the constraint of the state dynamics equation:  k l  y  =  +  +  F ( y  k'  u  k  }  Maximi ze the "Lagrangion" with respect to Y(y^:k=l'.. .N+1) U(u :k=l...N+1). k  N Max L = E [R(Y »u ) - Z ( y Y U k1 k  k  k  k + 1  - y  k  - F{y ,  _  5  Maximize over Y: dL dy  =  d R / d y  k  k  dG/dy  +  Z  k  +  Z  - Z  N+1  k  d p  /  d y  k " k-1 Z  N  Set equal to zero:  k-1  Z  Z  N M  =  Z  k  +  d R / d y  k  +  Z  k  d F / d y  k  = dG/dy . N+1 J M  Maximize over U: R and F are assumed l i n e a r in U therefore u,k •= Umax(l) ,, . or Umm • (0)' v  k  U|<  })]  and  96  The Lagrangion system has three sets of simultaneous equations:  y  k l +  - h  +  F(  V  y-,  Z  k - 1  = Z  k  k>  . .  u  k  N  =  K  -'  N  = y*  + dR/dy + Z Z  k  = dG/dy  = Umax or Umin  k  dF/dy  k  . . k = 1...N  N+1  k = 1...N  

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