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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 JAMES STALEY B..Sc, U n i v e r s i t y o f B r i t i s h Columbia, 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE O i n THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1978 © Michael James S t a l e y , 1978 In presenting this thesis in partial fulfilment of the r e q u i r e m e n t s for an advanced degree at the University of British Columbia, I agree t h a t the Library shall make it freely available for r e f e r e n c e and study . I further agree that permission for extensive copying o f t h i s t h e s i s for scholarly purposes may be granted by the Head o f my Department o r by his representatives. It is understood that c o p y i n g o r p u b l i c a t i o n o f this thesis for financial gain shall not be allowed without my written permission. Department of S?fl o L-Q (', The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date (KJr 2. •/- t °i'1 Y & f l S T a B A C T . A computational procedure f o r o p t i m i z a t i o n o f l a r g e m u l t i d i m e n s i o n a l models i s presented. The procedure i s a p p l i e d to a model of t h e Georgia S t r a i t s p o r t and commercial f i s h e r i e s of Chinook C Oncorhynchus tshawytscha ) and coho ( fi, k i s u t c h ) salmon. Optimal seasons f o r these f i s h e r i e s are c a l c u l a t e d and compared to c u r r e n t r e g u l a t i o n s * D i f f e r e n c e s , i n form and performance, between the o p t i m a l seasons and present seasons are minimal and i n s i g n i f i g a n t . However, i n o r d e r t o match present age s t r u c t u r e , p o p u l a t i o n l e v e l s and h a r v e s t s a value of near zero must be placed on f i s h l e f t i n the water a t the end of the season. The computational requirements of the o p t i m i z a t i o n are p r o p o r t i o n a l t o those of the model. In the case study i n t h i s t h e s i s the o p t i m i z a t i o n r e q u i r e d approximately e i g h t to ten times the computer time of the model. TABLE Of CONTENTS i i i T I T L E PAGE . . . . i ABSTRACT i i TABLE OF CONTENTS i i i LIS T OF TABLES . . . . . v L I S T OF FIGURES . . . v i i ACKNOWLEDGEMENTS x 1. INTRODUCTION 1 2. COMPONENTS 8 2.1. B i o l o q y 9 2.1.1. L i f e H i s t o r y 10 2.1.2. N a t u r a l M o r t a l i t y ..14 2.1.3. " S h a k e r " M o r t a l i t y 15 2. 1. 4. G r o w t h . 1 6 2.2. The D y n a m i c s Of F i s h i n q E f f o r t ..17 2.2.1. S p o r t s E f f o r t R e s p o n s e 18 2.2.2. C o m m e r c i a l E f f o r t R e s p o n s e 30 2.2.3. C a t c h a b i l i t y ....39 2.3. C o n t r o l s 43 2.4. V a l u e 44 2.4.1. C o m m e r c i a l F i s h e r y 45 2.4.2. The B e n e f i t s Of The S p o r t F i s h e r y . . . 46 3. OPTIMIZATION MODEL 50 3.1. F i s h D y n a m i c s 54 3.2. E f f o r t .56 i v 3.3. C o n t r o l s 57 3.4. Revenue ...57 4. OPTIMIZATION 59 4.1. M a t h e m a t i c a l F o r m u l a t i o n 59 4.2. The A l q o r i t h m 61 5. OPTIMIZATION RESULTS 62 5.1. F i n d i n q An O p t i m a l P o l i c y (Convergence) 64 5.2. O p t i m a l P o l i c y 66 5.3. I n c r e a s e d Escapement ....67 5.4. S i z e L i m i t s 69 5.5. I n c r e a s e d S p o r t E f f i c i e n c y 71 5.6. Enhancement ..73 6. DISCUSSION AND CONCLUSION ....76 6.1. G e o r g i a S t r a i t F i s h e r y 76 6.2. The Methodology 80 6.3. O p t i m i z a t i o n And R e s o u r c e Manaqement 82 LITERATURE CITED 84 APPENDIX 1 89 APPENDIX 2 95 LIST gf'yffilPfcffS. v Table 1: C u r r e n t Catch and E f f o r t Data f o r Georgia S t r a i t by "' Month. .... Pq. 41 Table 2: I n i t i a l and Target P o p u l a t i o n S i z e s . .... Pq. 63 Table 3: Intermediate P o l i c i e s f o r Computation of Optimal P o l i c y Under •"Current** C o n d i t i o n s . , .... Pg. 66 Table 4: Optimal Seasons with Enhanced Coho. ••• . . . . Pq. 74 Table 5: a Comparison of the Optimal P o l i c y with a V a r i e t y of Other P o l i c i e s . .... Pq. 79 T a b l e 6; 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 Hodel Under the Assumptions of 50 Percent Shaker m o r t a l i t y i n the T r o l l F i s h e r y , 80 Percent Shaker m o r t a l i t y i n the Sport F i s h e r y and Sport E f f o r t Besponse. .... Pq. 89 Table 7: P r e d i c t i o n s f r o i the Georgia S t r a i t S i m u l a t i o n Model Under the assumptions of 30 Percent Shaker m o r t a l i t y i n 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 Sport E f f o r t Besponse. .... Pq. 90 Table 8: P r e d i c t i o n s from t h e Georgia S t r a i t S i m u l a t i o n Model . Under the Assumptions of 50 Percent Shaker m o r t a l i t y i n the T r o l l F i s h e r y , 80 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 . j; .... Pg. 91 v i Table 9: Predictions from the Georgia S t r a i t Simulation Model Onder the Assumptions of 30 Percent Shaker mortality i t the T r o l l Fishery, 30 Percent Shaker mortality i n the Sport Fishery and Fixed Sport E f f o r t Pattern, .... Pg. 92 V i i LIST OF FIGURES Fi g u r e 1: Georgia S t r a i t , F r a s e r River Escapement and Fra s e r River G i l l n e t Catch o f Chinook Salmon. : .... Fg • , 3 Fi g u r e 2: Georgia S t r a i t , Fraser River Escapement and F r a s e r R i v e r G i l l n e t Catch of Coho Salmon. .... Fq. 4 Fig u r e 3: Georgia S t r a i t T r o l l and Sport Catch, T r o l l E f f o r t and average a e i g h t of Chinook Salmon. • .... Pq. 5 Figu r e 4: Tag Recove r i e s c f the Georgia S t r a i t Coho and Chinook Salmon. , .... Pq. 11 Fig u r e 5: Escapement Timing f o r Georgia S t r a i t Chinook and Coho Salmon. . .... Pg. 12 Figu r e 6: S i z e a t ftge o f Chinook and Coho Salmon. • .... Pg. 17 Fi g u r e 7: 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 January to a p r i l 1968 - 1975. .;,.v>::;,'P';g'.-,;20 Fig u r e 8: E f f o r t and C P U E i n t h e Georgia S t r a i t Sport F i s h e r y Kay 1968 - 1975. / .... Pq. 21 Fi g u r e 9: E f f o r t and CPU! i n the Georgia S t r a i t Sport F i s h e r y June 1968 - 1975. ; .... Pq. 22 Fi g u r e 10: 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 J u l y 1968 - 1975. .... Pg. 23 v i i i Figure 11: E f f o r t and CPUE i n the; Georgia S t r a i t Sport Fishery August 1968 - 1975. . .... Pg. 24 Figure 12: E f f o r t and CPUE in the Georgia S t r a i t Sport Fishery September 1968 - 1975. ...• Pg. 25 Figure 13: Ef f o r t and CPUE i n the Georgia S t r a i t Sport Fishery October 1968 - 1975. / . ... Pq. 26 Figure 14: E f f o r t and CPUE i n the Georgia S t r a i t Sport Fishery November 1968 - 1975. • .... Pq. 27 Figure 15: E f f o r t and CPUE i n the Geprgia S t r a i t Sport Fishery •.December 1968 - 1975. • .y^.VPg. 28 Figure 16: Batio of Effort to CPUE i n the Georgia s t r a i t Sport • Fishery. .... Pq. 29 Figure 17: E f f o r t and CPU! in the Georgia S t r a i t commercial Fisfcery A p r i l 1965 - 1974. .... Pq. 32 Fiqure 18: E f f o r t and CPUE in the Georqia S t r a i t commercial Fishery May 1965-1974., .... Pq. 33 Figure 19: E f f o r t and CPUE i n the Georgia S t r a i t commercial Fishery June 1965 - 1974. r .... Pg. 34 Figure 20: Ef f o r t and CPOE i n the Georgia S t r a i t commercial Fishery July 1965 - 1974. .... Pg. 35 Figure 21: Ef f o r t and CPUE i n the Georgia S t r a i t commercial Fishery August 1965 - 1574. .... Pq. 36 i x F i g u r e 22: E f f o r t and CPOE i n the Georgia S t r a i t commercial F i s h e r y September 1965 - 1974.: Pg. 37 F i g u r e 23: E f f o r t and CPOE i n the Georgia S t r a i t commercial F i s h e r y October 1965 - 1974. .... Pg. 38 F i g u r e 24: Parameters o f the T r o l l E f f o r t 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; Georgia S t r a i t Sport F i s h e r y * as a F u n c t i o n of t h e ;age o f Chinook 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 of the Georgia S t r a i t commercial F i s h e r y , as a F u n c t i o n of the Age of Chinook and Coho Salmon. .... Pg. 43 F i g u r e 27: Landed P r i c e per Pound of T r o l l Caught Chinook and Coho Salmon. •• .... Pg. 46 F i g u r e 28: R e c r e a t i o n a l Value of a Boat-Day c f Sport E f f o r t i n the Georgia S t r a i t . .... Pg. 48 F i g u r e 29: D i s t r i b u t i o n of Bags i n the Georgia S t r a i t F i s h e r y . • .... Pg. 52 F i g u r e 30: Optimal Seasons f o r Sport 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 to Increased Escapement and Increased Shadow P r i c e . .... Pq. 68 F i g u r e 31: Optimal Seasons for Sport 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 Increased S i z e Limits;. • .... Pg. 70 Figure 32: Optimal Seasons f o r Sport 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 to Increased E f f i c i e n c y i n the Sport F l e e t . '• . ... Pq. 72 ACKNOWLEDGEMENTS I w o u l d l i k e t o -thank my s u p e r v i s o r . D r . C . 3 . W a l t e r s , f o r h i s s u p p o r t a n d e n c o u r a g e m e n t d u r r i n g t h e c o u r s e o f t h i s s t u d y . The work w o u l d n o t h a v e been p o s s i b l e w i t h o u t t h e d a t a , i n s i g h t and a p p r e c i a t i o n o f t h e p r o b l e m p r o v i d e d by H r . ft.W.s (Sandy) A r g u e a n d Mr. F.E.A. ( 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 i n s p i r a t i o n n e e d e d t o d e v e l o p t h e p r o c e d u r e and Dr P.A. L a r i c i n , s comments on t h e o r i g i n a l d r a f t were o f en o u r m o u s h e l p i n o r g a n i z i n g 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 t o J o a n A n d e r s o n a n d C a t h y Lew who t u r n e d s c r i b l e i n t o t y p e d t e x t . F i n a l l y I w o u l d l i k e t o t h a n k my w i f e K a t h y f o r h e r e n d u r a n c e and u n d e r s t a n d i n g d u r r i n g my s t u d e n t d a y s . 1 The sheltered waters of B r i t i s h Columbia *s Georgia S t r a i t support viable commercial and spor-t f i s h e r i e s on stocks of .• chincck salmon- ioncorhynchus tshaf^tscha) and coho ••salao:n---iOa,-:J: k j . s u t c b ) a l n the 1950s, the commercial t r o l l f i s h e r y caught the majority of 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 for the years 1953 to 1962, i n c l u s i v e , show that the commercial t r o l i e r s caught 125*000 Chinook while sportsmen angled 92,700 chinook i n Georgia S t r a i t s Average catches on the en t i r e B r i t i s h Columbia..:-.coast. by hook and l i n e i n saltwater t o t a l l e d 949,100 Chinook annually. Coho average catches were 307,200 commercial and 190,800 sport i n the 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 d i s t r i b u t i o n of catch between the commercial and sport fishermen. Increases i n human population, wealth, l e i s u r e time, and advances i n gear e f f i c i e n c y accompanied a s i g n i f i c a n t growth i n e f f e c t i v e sport f i s h i n g e f f o r t . Subsequently, the sport catch has ri s e n to 348,000 Chinook and 464,000 cohoi « Meanwhile the commercial t r o l l catch has declined to 99,000 coho and 181,000 chinook per year. (Arque, Ccursley, and Harris 1977). l a t e l y , concern has a r i s e n .aBoat t h e a b i l i t y of the aany .populations of chinook and coho salmon t h a t make up the Georgia S t r a i t stocks to withstand h i g h f i s h i n g pressure. Spawning escapement e s t i m a t e s have not shown a g e n e r a l d e c l i n e , but, the amount o f e f f o r t expended by the f i s h e r i e s department t o f i n d and estimate spawning p o p u l a t i o n s has i n c r e a s e d s i g n i f i c a n t l y d u r i n g the past few years {A.S. Argue and f.£.A. »ood pers. comm. ), I t i s the p o s i t i o n o f the Department of F i s h e r i e s t h a t " t h i s i n c r e a s e and more e f f i c i e n t enumeration has produced an a r t i f i c i a l l y s t a b l e s i t u a t i o n i n the escapement t r e n d . " The Fraser E l v e r g i l l n e t c a t c h , as an i n d i c a t o r of escapement, has shown a c o n s i d e r a b l e d e c l i n e i n chinook ( F i g , 1) and a moderate d e c l i n e i n coho ( F i g . 2 ) . Another i n d i c a t i o n t h a t chinook p o p u l a t i o n s may have become a dangerous c o n s e r v a t i o n problem i s the age s t r u c t u r e of the catch....The average weight of a t r o l l caught chinook has d e c l i n e d ( F i g . 3) , i n d i c a t i n g a s h i f t i n age composition towards younger age c l a s s e s (ocean age 2 and 3) {Anon. 1978}. H i s t o r i c a l l y , the commercial t r o l l e r s have caught the m a j o r i t y o f t h e f i s h . They have :also borne the brunt of r e g u l a t i o n s i n t e n d e d to ensure t h e c o n s e r v a t i o n o f c h i n o o k and coho salmon. The r e s t r i c t i o n s have taken on t h r e e major forms; season c l o s u r e s - r e s t r i c t i n g f i s h i n g to.summer and f a l l months (Milne 1961)* l i m i t e d e n t r y ( M i t c h e l l 1977) and s i z e l i m i t s , ;To date, the s p o r t f i s h e r y has been s u b j e c t t o s i z e l i m i t and to bag l i m i t r e g u l a t i o n s . How, g i ^ e n the i n c r e a s e d importance;of the s p o r t c a t c h and the concern over c o n s e r v a t i o n , the 3 C H I N O O K o o o o o z X u u. o or UJ QJ s Z 100 50 50 100 100 50 50 ERASER GILINET CATCH J 1 I l_ FRASER ESCAIEMCNT -L I I J _ ERASER CATCH PLUS ESCAPEMENT -> 1 L , |._ -I 1 1_ -I L -1 I 1_ -> 1- .1, -1 L '952 54 5G 50 I9G0 6 2 64 6G 60 1970 72 74 76 100 50 50 15 0 100 50 50 ^ ^ " i v o r ^ l n ^ ^ ? ^ ' f / ? f e r R i V 2 r =««pe«,ent and F r a s e r hiv-.r o i l l n t t C a t c h of Chinook Salmon. c M <T> < NJ * • r-i O (0 H* o I—1 M h-1 -C 3 1— tO CU rt CO n rt CU <-) r+ CU O H* rt % o i-h i i »-) n CU o W tr iU o rl 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 NUMBERS - OF C0H0 ( x l O O O ) o o O o o o o 5 GEORGIA S T R A I T CHINOOK x CO LU a C3 > < CO >-< t o Q 2 o CL o o CD X t o o o o X CJ < CJ V o o X O 25 500 400 300 200 100 GEORGIA STRAIT CHINOOK AVERAGE DRESSED WEIGHT 19 52 54 56 58 I9G0 G-CHINOOK CATCH Sporl.—. / . / • I 1 I t I | 64 GG GO 1970 72 74 76 500 400 300 200 100 F i g u r e 3: Georgia S t r a i t T r o l l and Sport Catch, T r o l l E f f o r t and Average Weight o f ChinooX Salmon. " t o r t ana 6 Department of Fisheries has begun to investigate ne* regulations for the sport 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 of s c i e n t i s t s , under the dir e c t i o n of Dr. C.J. Walters at the University of B r i t i s h Columbia, to develop a computer simulation model {Wiegert 19.75, Walters 1971, Holling et a.l A 1978) . The model has been used to test the effectiveness of various 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 simulation model i s designed to predict population numbers, f i s h i n g e f f o r t , catch, and escapement on a bi-monthly basis f o r a single f i s h i n g area representing the Georgia S t r a i t . Both i n i t s attention to the d e t a i l s of f i s h and fishermen dynamics and the extent to which i t mimics rea l catch and 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 of the fishery. This realism makes the model an a t t r a c t i v e test bed f o r new and powerful methods of analysis. In p a r t i c u l a r , the model can be used to test p o l i c i e s designed by techniques of optimization (Baiters, Hilfccrn 1978). This thesis contributes to the development of a new computational framework for some large scale resource management optimization problems. The optimization i s embedded i n the context of the simulation model and maintains most of the d e t a i l of the simulation model. The coupling of the optimization model with the simulation model affords the optimization model a modest degree of realism and, I hope, some 7 degree cf p r a c t i c a l i t y . The main problem of thi s t h e s i s i s to find optimal f i s h i n g seasons with respect to changing f i s h stocks, e f f o r t l e v e l s , prices, and benefits for both the sports and commercial fishermen, while meeting target 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" conditions, as predicted by the simulation model, are compared with regulations now c o n t r o l l i n g the fishery. Optimal seasons are computed under a variety of assumptions about values of parameters for which there i s a great deal of uncertainty, also discussed are the e f f e c t s of increased abundanceof some populations, on optimal seasons, as may r e s u l t from the "Salmonid Enhancement Program" {BacLeod 19 77, Larkin 1974). The problems with analysis and optimization i n t h i s exercise are not unigue to the Georgia S t r a i t f i s h e r y . Host resource exploitation problems are complex and multi-dimensional i n the expl o i t a t i o n regime and i n the objectives of management. Therefore, they present major d i f f i c u l t i e s for optimization. The methodology developed below i s capable of dealing with most of the complexity and dimensionality of the Georgia S t r a i t f i s h e r i e s , and may also be useful for other problems. I hope that the apparent "realism" of the simulation model and optimization model i n conjunction with the immediate pressure for the conservation of Georgia s t r a i t chinook and coho w i l l serve to enhance the p r a c t i c a l i t y of t h i s thesis. 8 . The o p t i m i z a t i o n work to be d i s c u s s e d i n ch a p t e r t h r e e i s based upon a s i m u l a t i o n model. At present there i s no document d e s c r i b i n g the Georgia S t r a i t model. T h e r e f o r e , t o l a y the foundations f o r the task o f t h i s t h e s i s , i t w i l l be necessary t o d e s c r i b e some of t h e i m p o r t a n t i n g r e d i e n t s o f the s i m u l a t i o n model. There a r e f o u r major components jln the model: (1) p o p u l a t i o n dynamics of f i s h ( l i f e h i s t o r y , : ^ m o r t a l i t y , growth, m i g r a t i o n , e t c . ) ; (2) dynamics .of A±i«kiB$-;:ef fort-;- (3) a s e t of c o n t r o l s a v a i l a b l e t o management: (4) estimates of how b e n e f i t s flow from the f i s h t o the f i s h e r i e n and managers. There are many more f a c e t s t o the a c t u a l management problem. ;These four»components form a k e r n e l around which new r e g u l a t i o n s can be developed and then examined i n a broader, i n t u i t i v e c o n t e x t , while s t i l l m aintaining a resemblance t o the r e a l world. The broader context would not overtax a n a l y t i c methods now a v a i l a b l e , , 9 . > 2.1. B l q i o q y The b i o l o g y of the p a c i f i c sa1mon (Oneorhynchus spp. > i s ver y complex. In s p i t e o f years o f work by many i n v e s t i g a t o r s , t h e r e i s s t i l l much u n c e r t a i n t y surrounding some very important r e l a t i o n s h i p s . A l o t of i n f o r m a t i o n e x i s t s on the r e p r o d u c t i v e b i o l o g y and e a r l y l i f e stages of some s p e c i e s o f salmon. However, due to the d i f f i c u l t y of oc e a n , s t u d i e s , very l i t t l e i s known f o r c e r t a i n about the marine stage. The problem addressed by t h i s t h e s i s d e a l s e x c l u s i v e l y with the j i i v e n i l e and a d u l t ocean l i f e of coho and chinocfc s a l m o n . A s a conseguencev t h e r e are b i o l o g i c a l parameters used i n t h i s model about which there are very l i t t l e " s o l i d " 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 v a l u e s . Although some i n f o r m a t i o n about each parameter used i n the model e x i s t s , much o f i t i s t a n g e n t a l to the parameter i n qu e s t i o n and, o f t e n concerns g e o g r a p h i c a l areas and s p e c i e s which are not the focus o f t h i s model. vHuch o f the " d a t a " used i n the model i s a product of the experience and "wisdom" of two members of the Department o f F i s h e r i e s , A.S. Argue and D. Anderson. These two gentlemen i n t e r p r e t e d the a v a i l a b l e i n f o r m a t i o n and made informed e s t i m a t e s on many of the parameters. I t i s hoped t h a t t h e s e e s t i m a t e s r e f l e c t the c u r r e n t s t a t e o f the Georgia S t r a i t Chinook and coho f i s h e r y . 10 2.1,1,. s;, L i f e History Like the other commercial salmon species, chinook and coho are anadromous. The eggs are l a i d in r i v e r s and lakes. The young f i s h spend some time i n freshwater before migrating to the ocean, When mature, they return to freshwater to spawn and die. I t i s believed that a f r a c t i o n of the chinook and coho spend most of th e i r ocean l i f e i n coastal waters while the other f i s h spend t h e i r ocean l i f e on the high seas. Tag returns from hatchery-reared f i s h indicate that as much as 761 of the chincck and 51% of the coho produced in Georgia S t r a i t reside i n Georgia S t r a i t for seme period of time (Fig. 4) (Anon. 1978). I t i s the portions of the stocks resident i n the Georgia S t r a i t which are the subjects of t h i s analysis, Coho eggs are l a i d i n the f a l l and hatch the next spring. The smolts generally migrate to the ocean the following spring where they spend one winter and, return to spawn the following f a l l . By the l a t e summer of t h e i r f i r s t year at sea, Coho are f i r s t caught by the sport f i s h e r y and, by the next spring, they are caught by the commercial t r o l l e r s . In the model, coho are assumed to be recruited to the fishery by August 1 (A.*,,Argue pers. comm. ). During the summer and f a l l of the l a s t year at sea, coho move into freshwater to spawn. The model uses the timing of the Fraser River g i l l n e t catch (Fig, 5) to approximate the migration timing (Ledbetter and Hilborn 1 9 7 8 ) , Chinook have a more f l e x i b l e l i f e history. Ocean migration may take place i n the spring through to f a l l a f t e r hatching, or a f t e r one or two winters i n freshwater. The model assumes that 11 P E R C E N T A G E C A T C H H A R V E S T E D B Y C A T C H REG ION u o <t t-z UJ o or. UJ a. 00 C O H O 1971 Io 1974 OnOOOS Cowiehon Ouolicum Squornnh Copilono U.S. I 3 n N/C WCVI JS/JF •' GSC UJ O z UJ 60 O tr UJ a. AO CH INOOK 1971 Io 197} BR000S Pvnlladg* Otiolicum Copllono 3 u.s-I* IL X L N/C WCVI JS/JF CSC U.S. - UNIIEO STATES N/C - NOMTH CENTRAL B.C. WCVI - WEST C0»ST VAN. IS. JS/JF - Jonir.TONE STR. - JUAN DC FUCA STR. GSC - GEORGIA S1RAIT COMMERCIAL 6SP - GEORGIA STRAIT SPORT F i g u r e 4: Tag R e c o v e r i e s of the Georgia S t r a i t Coho and Chinook Salmon. 12 Sincfeosa UOT^JOCIOJJ 13 chincck are recruited to the fi s h e r y by the beginning of October of th e i r f i r s t year at sea. In general^ maturation takes place during the second through f i f t h year at sea. For thi s model, an estimate of the proportion of f i s h maturing and returning to spawn for each age class was needed. An analysis of tag returns i n the Fraser Biver g i l l n e t versus the Georgia S t r a i t sport and t r o l l fishery led to the following estimates (A. fl. Argue pers. comm., Argue 1S76) . Ocean age two 3$ mature Ocean age three 4036 mature Ocean age four 80S mature Ocean age fi v e 100% mature As with coho, the run timing of mature f i s h was estimated from the Fraser Biver g i l l n e t catch (Fig, 5) (Ledbetter and Hilbcrn 1978). A feature more important for chinook than coho i s the tendancy f o r Georgia S t r a i t f i s h to migrate out of the S t r a i t before maturing. Again, through an analysis of tag returns inside and outside the S t r a i t , estimates of the net migration rates from inside to outside were derived (A.H, Argue pers, comm. ) : 14 Ocean year one 40$ Ocean year two 25% Ocean year t h r e e .1:5* Ocean year f o u r 10S Ocean year f i v e 0% F i s h moving o u t s i d e are assumed not t o re t u r n t o the g u l f u n t i l t h e i r r a p i d spawning m i g r a t i o n , and thus t o be r e l a t i v e l y i n v u l n e r a b l e t o the g u l f s p o r t and t r o l l f i s h e r i e s . 2.1.2. - N a t u r a l M o r t a l i t y N a t u r a l m o r t a l i t y o f f i s h at sea i s a very d i f f i c u l t process to study. Experiments g e n e r a l l y i n c l u d e s m a l l numbers of f i s h and are prone t o l a r g e o b s e r v a t i o n e r r o r s . Environmental v a r i a b i l i t y o f t e n confounds experimental e r r o r s , r e s u l t i n g i n b i a s e s f o r which t h e r e i s no i n f o r m a t i o n concerning d i r e c t i o n or magnitude (Ricker 1976). Parker (1960) estimated t h e mean bi-monthly non-catch m o r t a l i t y r a t e s f o r c h i n c c k salmon of age t h r e e through f i v e t o be 0.0175. Henry*s (1978) e s t i m a t e s were 0.026. I t i s g e n e r a l l y thought t h a t n a t u r a l m o r t a l i t y r a t e s decrease with i n c r e a s e d s i ? e and age (Ricker 1976). The parameters chosen f o r the model are meant to r e f l e c t n a t u r a l m o r t a l i t y o n l y , not m o r t a l i t y caused by f i s h i n g . (A. p. Argue p e r s . comm. *| * .The i n stantaneous n a t u r a l m o r t a l i t y r a t e s (per 15 days) i n the model a r e : 15 Ocean age 1 0.035 f o r 3 months Ocean age 2 0.015 f o r 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 0.0 11 B i c k e r (1976) e s t i m a t e s the .'instantaneous rate of non-catch ocean m o r t a l i t y f o r coho t o be 0.04 f o r a h a l f month p e r i o d . The values used i n the model f o r n a t u r a l m o r t a l i t y a l o n e a r e : Ocean age 1 0.04 f o r 5 months Ocean age 2 0.02 f o r 10 months Average 0.027 Much b e t t e r e s t i m a t e s o f n a t u r a l m o r t a l i t y w i l l l i k e l y be a v a i l i a b l e soon, through a n a l y s i s of the many t a g g i n g s t u d i e s conducted d u r i n g the 1960*s (Walters, pers.jGomm*). 2.1.3. "Shaker? H o r t a l i t y Non-catch ocean m o r t a l i t y i s made up of two components -n a t u r a l m o r t a l i t y and m o r t a l i t y caused by f i s h i n g , but not i n c l u d e d i n c a t c h s t a t i s t i c s . M o r t a l i t y of the second kind i n c l u d e s salmon caught that are l e s s than l e g a l s i z e , or caught durin g a c l o s e d p e r i o d f o r the s p e c i e s i n question. These f i s h are d i s c a r d e d dead or m o r t a l l y i n j u r e d - e i t h e r a f t e r being boated, or by shaking them frcm the gear as i t i s hauled up. Shaker m o r t a l i t y caused by t r o l l i n g f o r coho and chinook averages about one f i s h k i l l e d f o r every two t h a t are boated (Bicker 1976). The e f f e c t o f v a r i o u s r e g u l a t i o n changes on 16 shaker m o r t a l i t y and the e f f e c t of v a r i o u s assumptions about shaker m o r t a l i t y r a t e s on the consequence of r e g u l a t i o n changes i s a major concern o f the s i m u l a t i o n model. In the model, a shaker m o r t a l i t y r a t e o f 50$ i s used f o r t r o l l e r s {RicJcer 1976). L i t t l e e m p i r i c a l work has been done on s p o r t shaker m o r t a l i t y . I t i s a general b e l i e f t h a t sportsmen k i l l more f i s h than commercial fishermen because of i n e x p e r i e n c e or l a c k of concern. T h e r e f o r e , the shaker m o r t a l i t y r a t e i n s p o r t f i s h e r y i s assumed t o be 8035. In the model, t h e s i z e o f a f i s h i s assumed to be a f u n c t i o n o f i t s age and the time of year. An e s timate o f t h e growth o f a C h i n o o k or coho at sea ( F i g . 6) was made using data on the s i z e , age, and time of capture i n the Georgia S t r a i t t r o l l f i s h e r y . A length-weight r e l a t i o n was a l s o c o n s t r u c t e d from these data (Argue and M a r s h a l l 1976), ' 2x2* Ihe Dynamics o f f i s h i n g E f f o r t There have been s e v e r a l dynamic models of f i s h i n g e f f o r t proposed (Gatto, R i n a l d i , and waiters 1976; C l a r k and Munro 1975; C l a r k 1976). These models have s t u d i e d the t h e o r e t i c a l behavior of c a p i t a l or f i x e d i n p u t s i n and out of f i s h i n g f l e e t s , with l i t t l e or no e m p i r i c a l b a s i s . H l i b o r n and L e d b e t t e r (1978) document the a l l o c a t i o n of salmon s e i n e r s among f i s h i n g areas on the B r i t i s h Columbia coast. T h e i r c o n c l u s i o n i s t h a t the key determinant of boat movement i s Y E A R S 18 a v a i l a b i l i t y of f i s h . A major i n g r e d i e n t o f the s i m u l a t i o n model and the o p t i m i z a t i o n model of t h i s t h e s i s i s the response of f i s h i n g e f f o r t t o the success of f i s h i n g . 2.2.1. ? Sports E f f o r t Response Mot i v a t i o n of s p o r t e f f o r t can be assumed, i n p a r t , to be a s s o c i a t e d with the capture of f i s h . Consequently, a change i n the number of s u c c e s s f u l c a p t u r e s experienced by fishermen w i l l l i k e l y change the amount o f f i s h i n g they do. Furthermore, i t i s probable t h a t an i n c r e a s e i n the average success per a n g l e r i n the s p o r t f i s h e r y w i l l motivate an i n c r e a s e i n f i s h i n g e f f o r t . Undoubtedly, many other f a c t o r s , b e s i d e s f i s h i n g s u c c e s s , determine the amount of s p o r t e f f o r t , l e a t h e r , h o l i d a y time, f u e l p r i c e s , and the g e n e r a l s t a t e of the economy, among other things,, may a f f e c t the motivation of the sportsman. The f i s h e r y manager does not have j u r i s d i c t i o n over the economy, nor the environment,„Be must, t h e r e f o r e , pursue management plans based 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 , i.e., /the success o f f i s h i n g . The r esponsiveness of s p o r t e f f o r t to catch per u n i t e f f o r t (CFOE) i s i n d i c a t e d i n F i g u r e s 7 through 15. Each graph r e p r e s e n t s c a t c h and e f f o r t data from the Georgia S t r a i t ( S t a t i s t i c a l areas 13-18, 28, 29) f o r one month from the years 1968 t o 1975 (Anon,/B.C. S p o r t s Catch S t a t i s t i c s 1968-1975) . I t appears f o r most months that higher CPUE i s a s s o c i a t e d with i n c r e a s e d e f f o r t . For the s i m u l a t i o n , i t i s assumed t h a t e f f o r t i s simply p r o p o r t i o n a l to r e c e n t success as measured by CPOE. Seasonal v a r i a t i o n i n the r a t i o o f e f f o r t to c a t c h per e f f o r t i s shown i n F i g u r e 16 f o r the same data s e t . / T h i s v a r i a t i o n i n d i c a t e s that the responsiveness of the fishermen i s much gr e a t e r i n the summer than the winter. C o n s i d e r a t i o n o f the behavior of fishermen i s important to e v a l u a t e the impacts of r e g u l a t i o n changes intended t o i n c r e a s e the abundance o f f i s h s i g n i f i c a n t l y . ! , F o r example, an i n c r e a s e i n the success of the fishermen may s t i m u l a t e enough e f f o r t so as to c a n c e l any intended i n c r e a s e i n spawning escapement./The r e l a t i o n s h i p i n c l u d e d i n the model i s based upon the number of f i s h caught. I t i s very l i k e l y that the s i z e of f i s h caught i s more important i n m o t i v a t i n g e f f o r t than mere numbers, In such a case, r e g u l a t i o n s intended t o reduce the c a t c h o f s m a l l f i s h ( s i z e l i m i t s ) may i n c r e a s e t h e average s i z e of f i s h caught. Sport e f f o r t may i n c r e a s e , due to the l a r g e r and o l d e r f i s h , and c a n c e l any intended i n c r e a s e i n spawner escape a n a l y s i s o f t h i s t h e s i s i s based upon ..th«^x^:^l:$cwsii|:??..of nuffiAers r a t h e r than weight. T h e r e f o r e ; any c o n c i a s i o n s should be weighed by the 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 t o success of f i s h i n g . , In the model, s p o r t e f f o r t i s assumed not t o s a t u r a t e or reach an upper l i m i t a t high l e v e l s of success. Some upper l i m i t must e x i s t , but, i t has apparently not been reached i n r e c e n t years ( F i g s 7-15). Unlike the commercial f i s h e r y with i t s l i c e n c e program, which l i m i t s the number of v e s s e l s a b l e to p a r t i c i p a t e , t h e r e i s no l e g a l l i m i t t o the numbers of people who can p a r t i c i p a t e i n sport f i s h i n g . H -- Q C Ii C J (TJ CU 3 - J C • • Cu >-| K -< r-n l-h rt O O rl rt Cu 3 Pi " O n o -» -a a co I 3 3 " (TJ C> (TJ O rl J Q V' u> CO rt M Cu EFFORT (BQRT-DRYS) IX10 2 ) 1DD.0 15D.D 200.0 250.D 300.0 6 Q a Q Q O c r m ro oo O 1 rt CD W 3" (TJ ri •< O 02 c n rs <r> 01 -< 00 EFFORT (BQRT-DRYS) C X 1 0 2 ) 160.0 2D0.D 240.D 280.0 320 G CD o c z n G G G G G O o a S i o rvj in CD rj-CD a I I— cc CD '—a in. on a UJa a 04 D.O 0.4 O CD CD CD 0.B 1.2 CPUE CD CD 1.6 2.0 F i g u r e 9: E f f o r t and CPDE i n the G e c r a i a ^ r a i * c „ * L June 1968 - 1975. ^ e c r q i a S t r a i t S p o r t F i s h e r y \ H-J3 C n (TJ c C . * "•< o c • • _* l-ti UJ i-n o 1 M c . --J 3 &i • O C Pi ™ O TJ iL) CZ Cl m O I-I pj 01 r t n ' Oi H-rl CO • •o o 1-1 rt-T) H-tn nr (I) t-1 -5 EFFORT (BQRT-DRYS) (X10 2 J 55D.Q 6DD.D 650.D 100.0 o CD r o cn O 750.0 _J Q Q Q G 0 Q G zz n c ri S» fl) C -Q -» C —' (/) •• rt rt -> rh Hi o> O 00 I r t -» » tf> & ui n • t3 G ni H-rt IT tn -D o i i . a p -Cu co r» M &> H-rt CO "D O li rt ta-rn H EFFORT (BQRT-DRYSJ 40.D 60.0 80.0 I I o O cz m ro o ( X i O 3 J 100.0 i 120.0 G G G G G G Q fr3 X) C M 10 <V EFFORT (BQRT-DRYSJ 16D.D 260.D 360.0 ( X 1 0 2 460, L_ 560 _J o G o CD o TS CZ r n G G G G ro G G O l rO O XI C M o n> n ri- •a Ot Ul tr «» l-l i-h —k if> O oo ct i OJ _» Oi n •a • G 3 r+ 3" <I> CTJ CJ O n r i -l l Cu I — f t in XI o M r t •TJ H-W (TJ n <: E F F O R T ( B Q R T - D R Y S ) ( X I O 2 J 80.D 100.0 120.0 140.0 O T) r n ro cn ro o 160.0 _J G G G G G G Q 93 • — , cEg'H o cc | CD o L U a a . OJ I I 1 1 1 — 0.0 0.4 0.B 1.2 1.6 CPUE F i q u r e 14: E f f o r t and CPUE in the Georqia S t r a i t Sport F i s h e r November 1968 - 1975. (J. n c t-i O ft) 0 -» fD Ul 3 •• Cr" (D K M l-fi -» O ri CTi rt co 1 a O O • m a (1/ (7) (D O M -Q DJ W r+ M PJ rJ-< + w •n o r-{ r t •n (-•• t/1 tr IT) M -< c n EFFORT (BORT-DflYSr U 1 0 J ) 150.0 2 3 0 . 0 3 J 0 . 0 3 9 0 . 0 ° ' 1 I i CD O T3 CZ rn ro ro o 410.0 G G 09 G G G 83 29 F i q U r F e i s h ; r y R ? t i 0 ° f E f f ° r t t 0 C P U E i n t h e e-orqia S t r a i t Sport 80,00 0 70,000 60,000 UJ 7D CL u 50,000 fx UJ co LU LU 5S O rr LU 0_ 40 ,000 30,000 S 20,000 CD or O 0. co 10,000 F M A M J J A S 0 N D MONTHS 30 There i s a great deal of v a r i a b i l i t y i n the data depicted by Figures 7 through 15. However, predictions that ignored the behavior of fishermen are surely more misleading than predictions that take some account of this numerical response process. 2.2.2. » Commercial E f f o r t Besppnse Motivation of the commercial fisherman i s l e s s d i f f i c u l t to define than that of the recreational fisherman. For the most part, the commercial fisherman i s out to make money. The more potential to catch f i s h there i s i n an area, the more fishermen w i l l participate. Onlike the sport f l e e t , the commercial f l e e t can brave the elements outside the sheltered waters of Georgia S t r a i t i f the f i s h i n g i s good enough to warrant it.;Therefore, the ccmmercial e f f o r t i n Georgia S t r a i t i s affected by the abundance of f i s h i n s i d e , as well as the f i s h i n q opportunities outside Vancouver Island and along the north coast. Our concern i s with the inside fishery. Therefore, the rela t i o n s h i p between e f f o r t and CPOE i s constructed with Georgia S t r a i t data alcne. Figures 17 through 23 show e f f o r t and CPOE data i n the Georgia S t r a i t t r o l l fishery for the months of A p r i l through October for the years 1968 to 1975, 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. licence program and the number of boats that are not eguipped to handle the r i g o r s of the more l u c r a t i v e outside fis h e r y . Therefore, the r e l a t i o n s h i p of e f f o r t to CPOE i s assumed to saturate. Figure 24 indicates the seasonal variation 31 i n the maximum t r o l l e f f o r t assumed i n the model and shows;the l e v e l of CPOE a t which h a l f s a t u r a t i o n of e f f o r t i s reached., 2.2.3. C a t c h a b i l i t y An important p i e c e o f any f i s h e r i e s modeling e x e r c i s e i s the c o u p l i n g of f i s h and f i s h i n g e f f o r t . The assumption about capture used i n t h i s model i s the t r a d i t i o n a l one t h a t c a t c h per e f f o r t i s p r o p o r t i o n a l t o abundance (Bicker, 1940). In t h i s model, the c a t c h a b i l i t y c o e f f i c i e n t i s the p r o p o r t i o n of t h e a v a i l a b l e f i s h t h a t i s caught by a s i n g l e u n i t of e f f o r t i n a u n i t of time, C a t c h a b i l i t y i s assumed t o vary as a f u n c t i o n of age and s p e c i e s of the f i s h as w e l l a s time of year. The v a r i a b i l i t y may be due to environmental changes, se a s o n a l changes i n the behavior o f t h e f i s h or sea s o n a l changes i n the e f f i c i e n c y and C O B p o s i t i o n of the e f f o r t , ,Eor example, s p o r t f i s h i n g e f f o r t i n t h e summer may be made up c f a high e r p r o p o r t i o n of i n e x p e r i e n c e d fishermen than the ardent fishermen of the winter months, . Osing the " c a l i b r a t i o n phase? methodology developed by Johnson 1975, the s i m u l a t i o n model has been used t o r e c o n s t r u c t c a t c h a b i l i t y c o e f f i c i e n t s f o r chinook and coho i n the Georgia S t r a i t . Average escapement by age were used to s t a r t a backward c a l c u l a t i o n of abundance using c a t c h by age and gear type. The escapement of the o l d e s t age c l a s s o f f i s h was added i n t o the pe e l f i s h e r y a c c o r d i n g to the maturation schedule and run t i m i n g d i s c u s s e d before,,/Progressing backwards i n time, at each p e r i o d the c a t c h and n a t u r a l m o r t a l i t y at the o l d e s t age was E F F O R T 0.0 O / t n b A" b pi-ca 40.0 _J 80.0 _J (BOAT _ DAYS) CX10 1 J 120.0 160.0 200.0 _] 210.0 _J 280.0 _) P-b ure 17 Fish fu •• b i •< w s» m TJ O M n P- rt p-(•• -» n o & a G ji r; w "d l b Q . VT> P-G G G .fr O ft) O r l .C 03 rt M Oi P-rt n o l-l o p. 200.0 E F F O R T 300.0 i 400.0 (BOAT _ DAYS) txio1 J 500.0 600.0 J 700.0 _ J 800.0 _ J 900.0 _ J en. b eo. b G n c t-i IT" <T> f ro CD •• H -< M rf QJ rt -< n c Ul Cu I o -» c: rr fl) b <D iD O fl oi-b I-I cu b G G n o B 3 ft) I-) O e£ 150.0 E F F O R T (BOAT _ DAYS) I X10 1 ) 200.0 250.0 J_ 300.0 350.0 _l : 100.0 450.0 500.0 _ l G Q Q G G o G W c n -b co • b P-J3 C n (b M w . tr vO . a t l -< t l Itl L, rh e O 3 l-l (D r« a VC O-IJ1 n 1 —» rrl vn -o p. 3 • rt-tr ik C"> m O rt £. p. CJ i/> r* i i cu p-r» f) O g =i .D i i o p-CU M 210.0 E F F O R T CBOAT _ DAYS) (X101 ) 340.0 <MO.O S40.0 • 6*1.0 74).0 _ J I I I ; i 810.0 _ J 940.0 _ l Q G o a M p i -ta •o o -o co-ca H-J3 C H (0 tn O m • • M -< W hh rti C O r-> n -< r t _, & vC a o> LP f i 1 »a <= . hn vO • r t ET 01 c: ro o r i J3 H-CU w r t M D H-r t f l O 9 3 111 M O r -Cl CD E F F O R T (BOAT _ DAYS) IX101 J 210.0 260.0 320.0 360.0 100.0 440.0 180.0 520 ' 1 1 1 1 I I I o G W 0 M hi' H-JZS a t i (D H* cn to sr . (U I -< m i-ti r-h c O -G t l C rt tn rt Oi 3 —» Cu vO J> n Ln G I HI . H-• j c rt • <a m o ti X I (••>• o> Ui rt-t l 01 o o s 3 ill t l Ct I-9t Fiqure 22: E f f o r t and CPUF i n the Georqia S t r a i t commercial Fishery September 1965 - 1974. CD CD CD J CD 1 1 — 7.0 9.0 11.0 15.0 I 17.0 13.0 C P 19.0 21.0 23.0 U E *4 \3 M b E F F O R T (BOAT _ DAYS) 0 40.0 60.0 80.0 J 1 I l_l j _ J JL (X101 ) 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140. O ° 5 ~ ~ T l (TJ H" 0) NJ t r U i it) M •< t n i-ti O r-h O O r t n O «• t r i i i P. '1 3 _» LP C3 G i G H -Q c 3 G it/ ID O r-I J3 w ii cu H* r» n o a 9 * ii o 8£ 3 9 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 F i q u r e 24: MON1HS Parameters of the T r o l l E f f o r t Response Model. added t o the p o o l , then the p r o p o r t i o n taken by the s p o r t and t r o l l e f f o r t present formed t h e b a s i s f o r the c a l c u l a t i o n c f c a t c h a b i l i t y . At the beginning of the year, the estimated abundance of the 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 younger age c l a s s and the backward c a l c u l a t i o n c o n t i n u e d f o r the younger age c l a s s e s . T h i s procedure provides an exact estimate of time v a r y i n g c a t c h a b i l i t y provided the n a t u r a l m o r t a l i t y schedule i s known. The escapement and c a t c h a t age used i n the backward c a l c u l a t i o n i s presented i n Table 1. The r e s u l t i n g c a t c h a b i l i t y estimates are presented i n F i g u r e s 25 and 26. #,-3.,controls -A c e n t r a l i s s u e i n the de s i g n of management s t r a t e g i e s i s the s e t of a d m i s s i b l e c o n t r o l s . There are f i v e important c o n t r o l o ptions open t o the managers of the Georgia s t r a i t f i s h e r y . They can r e g u l a t e the s i z e of the f i s h t h a t may be kept i f caught, the gear with which the f i s h a r e caught, the number caught or landed per t r i p ( b a g - l i m i t ) ^ the area i n which f i s h may be caught, or the times when f i s h i n g i s a l l o w e d , / One c o n t r o l o p t i o n not co n s i d e r e d f e a s i b l e i s t o r e s t r i c t p a r t i c i p a t i o n i n s a l t water a n g l i n g . / L i m i t i n g the number o f p a r t i c i p a n t s or c h a r g i n g f o r the p r i v i l e g e of f i s h i n g , so as to r e s t r i c t e f f o r t , would be met with c o n s i d e r a b l e d i s a p p r o v a l by the s p o r t fishermen (Sport F i s h Advisory Committee 1977 pers. comm. ,;), In B r i t i s h Columbia, salmon f i s h i n g i s co n s i d e r e d t o be every 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 rebuary Sarch Apr i l ray June Sport Zffort 7407. 7407. 7407. 22961. 65921. 35179. T ro l l I t tort 0. 0. 0. 1786. 1.693. 3287. Sport CPUI 1.5 1.3 1.11 1.2 1.3 1.1 I r o l l CPUI 0.0 0.0 0.0 15.9 15. 5 10.6 Chinook Sport Harvest Pieces 0. A q e 1 1. 0. 0. 0. 0. A g e 2 119. 127. 202. 517. 229U. 6372. A q e 3 5200. 4353. 351*. 6693. 15030. 1816C. A q e 4 1881. 1966. 1995. 3869. 8069. 81C9. A q e 5 207. 220. 225. 402. 975. 1031. Chinook Sport Harvest -eiqht in Pounds 0. 0. 0. A q e 1 0. 0. 0. A q e 2 95. 102. 182. 517. 2753 . 10195. A q e 3 , 21320. 18718. 16164. 33465. 8717*. 1 19856. A q e 4 17305. 19070. 21041. 46423. 103 )J2. 117581. A q e 5 3767. 1026. 41 18. 7397. 18423. 23191. Chinock T r c l l Harvest Pieces A q e 1 0. 0. 0. 0. 0. 0. A q e 2 0. 0. 0. 170. 655. 2334. A q e 3 0. 0. 0. 2226U. 50628. 24564. A q e 4 0. 0. 0. S793. 20377. 7596. A q e S 0. 0. 0. 170. 582. 3 0 8 . Chinook Tro l l Harvest Sleight in Pounds A q e 1 0. 0. 0. 0. 0. 0. A q e 2 0. 0. 0. S9u. 2096. 7501. A q e 3 0. 0. 0. 111320. 293412. 162122. A q e 1 0. 0. 0. 69516. 281 01.0. 11C142. A q e 5 0. 0. 0. 3128. 1 1000. 6856. coho Sport Harvest Pieces 0. A q e 1 0. 0. 0. 0. 0. A q e 2 3701. 2963. 4444. 16073. 59329. 59625. Coho Spcrt Harvest Uoiqht in Pounds A q e 1 0. 0. 0. 0. 0. 0. Aqe 2 3700. 3259. 5333. 22502. V.2390. 220613. Coho T r c l l Harvest Pieces Aqe 1 0. 0. 0. 0. 0. C. Aqe 2 0. 0. 0. 0. 0. C. coho l r o l l Harvest Weiqht in Pounis Aqe 1 0. 0. C. C. 0. 0. Aqe 2 0. 0. 0. 0. c. 0. July Auqust September October soveaber Deveaber 169618. 202999. 110362. 37775. 14073. 9629. 1560. 2394. 2230. 0. 0. 0. 1. 1 1.3 1.0 1.0 1.0 1.8 19.7 11.3 11.0 0.0 0.0 0.0 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. 1. ' 81144. 193654. 77303. 21378. 1. 172752. 252375. 101215. 16046. 1. 95158. 100951. 36372. 5238. 8. 28719. 51196. 153*2. 1107. 46. 20653. 21322. -6389. 0. 162. 30194. 30366. 3765. 0. 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. 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. 1 187. 117546. 6494. 155865. 5960. 60257. 3400. 19265. 1970. 36S9. 3177. 2600. 356. 505448. 2598. 732566. 2990. 283208. 2330. 92472. 1576. 17563. 2859. 12480. 0. 67944. 0. 19870. 0. 10944. 0. 0. 0. 0. 0. 0. 0. 292159. 0. 93 369. 0. 51437. 0. 0. 0. 0. 0. 0. COHO V-\ A -A OH(NOOK / V June Years June June June June Fiqure 25 Catchabilty C o n f i d e n t of the Georqia S t r a i t Sport Fishery, as a Function of the Aqe of Chinook and Coho Salmon. ro Fiqure 26 Catchabilty Coeficient cf the Georgia S t r a i t Comercial Fishery, as a Function of the Aqe of Chinook and Coho Salmon. COHO -•»- CHINOOK June June Years June June LO an c c m m e r c i a l e f f o r t i s more p a l a t a b l e and i s i n e f f e c t f o r t h e e n t i r e c o a s t . The s e t o f c o n t r o l s c u r r e n t l y i n e f f e c t a r e a s f o l l o w s : The s i z e l i m i t f o r t h e c o m m e r c i a l t r o l l f l e e t i s t h r e e p o u n d s d r e s s e d w e i g h t o r a p p r o x i m a t e l y 18 i n c h e s . - T h e r e i s no bag l i m i t on t h e c o m m e r c i a l f i s h e r y . Many a r e a s , p a r t i c u l a r l y i n l e t a n d r i v e r m o u t h s , a r e c l o s e d t o c o m m e r c i a l t r o l l e r s and f i s h i n g i s r e s t r i c t e d t o t h e summer a n d f a l l m onths. The c u r r e n t s i z e l i m i t i s 13 i n c h e s f o r s p o r t c a u g h t f i s h . A l l l i n e s must be hand r e e l e d . /There a r e v i r t u a l l y no r e s t r i c t i o n s on where f i s h i n g t a k e s p l a c e i n m a r i n e w a t e r s and t h e s p o r t s m a n i s a l l o w e d t o f i s h y e a r r o u n d . The b a g l i m i t i s f o u r s a l m o n p e r a n g l e r - d a y . 2±JLt l a l a e , The m o d el o u t l i n e d a b o v e p r o d u c e s a h o p e l e s s l y c o m p l e x s e t o f p e r f o r m a n c e i n d i c a t o r s . S i m p l e r v a l u e m e a s u r e s a r e n e c e s s a r y f o r , o p t i m i z a t i o n . The s i m p l i f i c a t i o n u s e d h e r e i s t h e l a n d e d v a l u e o f t h e c a t c h f o r t h e c o m m e r c i a l t r o l l f i s h e r y a n d t h e v a l u e o f a r e c r e a t i o n a l b e a t - d a y . 2.4,1» ,A ''CxfrmfflegGlal^^ftsbery •  • In the model, i t i s assumed the value to the commercial t r o l l e r s i s generated by the number o f pounds o f salmon landed. The management agency may have more g e n e r a l concerns, such as the h e a l t h of t h e p r o c e s s i n g or marketing s e c t o r , but a good index of the p r o s p e r i t y c f the e n t i r e i n d u s t r y i s the landed value of the catch. The p r i c e per pound v a r i e s with the time of year and the s i z e of the f i s h . An average p r i c e per pound i s used i n the o p t i m i z a t i o n ( F i g , 27), The p r i c e paid f o r a landed salmon i s assumed t o be independent of the t o t a l number of salmon landed from the Georgia S t r a i t . Georgia S t r a i t catches may i n f l u e n c e l o c a l p r i c e s t o some degree. However, the Georgia S t r a i t r e p r e s e n t s a s m a l l c a t c h compared with the e n t i r e coast i n c l u d i n g A l a s k a , B r i t i s h Columbia, Washington*'..Oregon, and C a l i f o r n i a and would t h e r e f o r e have l i t t l e i n f l u e n c e on the g e n e r a l market p r i c e . 2±&*£*; Sk£ B e n e f i t s g f the S£o,rt l i s j i j r i The s p o r t f i s h e r y has a s i g n i f i c a n t l y d i f f e r e n t way of generating value. There are many s p o r t fishermen who l i k e t o eat f r e s h f i s h , and a f i s h caught i n t h e s p o r t f i s h e r y does s u b s t i t u t e f o r other food. More important, however, i s the value of the act o f f i s h i n g , Bryan (1974), i n a 'questionnaire study of s p o r t fishermen, concluded t h a t the e a t i n g of f i s h ranked s i g n i f i c a n t l y lower than ether a t t r i b u t e s o f f i s h i n g , such as the outdoor experience, i n m o t i v a t i n g s p o r t fishermen. The task of p u t t i n g a d o l l a r value on the r e c r e a t i o n a l aspects 46 ^ ' " " o h o ' s a l u l o n ! ^ P ° U n d ° f T r 0 1 1 C u U q h t C h i n o " ™ * o 2: ZD O a. rr ui a. co rr < .1 .j O 0 2 .00 1.90 1.80 1.70 1.60 1.50 1.40 1.30 1.20 I.I 0 Average landed price per pound Chinook * r Coho o a—A—A—& p~J\—A—A—d—A—A—L\—L\—A— J F M A M J J A S O N D MONTHS 47 of the s p o r t f i s h e r y i s d i f f i c u l t : There i s a need f o r a ccamon denominator between the s p o r t and commercial f i s h e r y . / T h e value of commercial f i s h i n g i s r e a d i l y accountable i n the value of the c a t c h . I f the f i s h are t o be a l l o c a t e d between the two user groups, an e q u i v a l e n t m e t r i c i s needed f o r the spo r t f i s h e r y . Many methods have been suggested f o r the e v a l u a t i o n o f the b e n e f i t s from the s p o r t f i s h e r y . The su g g e s t i o n s range from accounting the c o s t s of using the resource t o q u e s t i o n s about how much a user would be w i l l i n g t o pay t o f i s h . Stevens (1966) reviews the major schemes. One of the most i n t e r e s t i n g approaches t o e v a l u a t i n g s p o r t s f i s h i n g was conducted i n the Washington S t a t e F i s h e r y , I n 1967, Mathews and Brown (1970) asked the g u e s t i o n "For what minimum p r i c e would you be w i l l i n g t he s e l l your r i g h t t o salmon f i s h f o r a year" The r e s u l t i n g v alue was $20.Q0-$60.00 per f i s h i n g t r i p , depending s t r o n g l y upon t h e area f i s h e d and the q u a l i t y of the f i s h i n g experienced. In the model of the Georgia S t r a i t f i s h e r y , the value o f $15.00 i n the winter and $25.00 i n the summer per boat day (Pig. ,28) i s used (Basse and Peterson 1977) . Once a metric has been e s t a b l i s h e d f o r measuring the performance of each f i s h e r y , the numbers from the two f i s h e r i e s must be combined i n t o an o v e r a l l measure. The s i m p l e s t approach and the one t c be used i n t h i s a n a l y s i s i s t o sum the d o l l a r b e n e f i t s from the two f i s h e r i e s , another approach may be to tra n s f o r m the b e n e f i t s from a p a r t i c u l a r f i s h e r y i n t o a u t i l i t y f u n c t i o n ( H i l b o r n and Peterman 1977). In the case of the s p o r t f i s h e r y , an added u n i t of s p o r t e f f o r t a t an alre 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, the G e o r q i a S t r a i t . i l u 3 of a Boat-Day o f S p o r t E f f o r t i n ft 30 5 Q i § OQ rr o a. CO ui o ll-o UJ _J 3 I 20 10 J F M A M J S 0 N D MONTHS e f f o r t l e v e l may have a q u i t e d i f f e r e n t appeal to a manaqer than t h a t same u n i t of e f f o r t at a low l e v e l of e f f o r t . A l s o , the way i n which the b e n e f i t s , or u t i l i t y , from the two f i s h e r i e s i s combined may t a k e on a q u i t e d i f f e r e n t form ( f l i l b o r n and B a i t e r s 1977, Keeney and fiaiffa 1976, Keeney 1977). I t i s apparent t h a t the c h o i c e of o b j e c t i v e f u n c t i o n s w i l l a f f e c t the form of the o p t i m a l p o l i c i e s . I t may a l s o be t h a t the study of o p t i m a l p o l i c i e s can be used to determine b e t t e r o b j e c t i v e s . 50 3. •/ OPTIMIZATIONMODEL Much of the present t h e o r y on o p t i m a l e x p l o i t a t i o n of n a t u r a l f i s h p o p u l a t i o n s has been developed assuming t h a t r e c r u i t m e n t i s independent o f s t o c k s i z e , l e a d i n g t o the concept of y i e l d per r e c r u i t (Beyerton and Holt 1967,- Ch. 18, 19; Bic k e r 1958, Ch.,10; C l a r k 1976, Ch.: 8).^Another popular approach i s t o assume t h a t growth, m o r t a l i t y , and r e p r o d u c t i o n can be pooled i n t o a gross model of po p u l a t i o n change (Scheafer 1957; C l a r k 1976, Ch./2; C l a r k , Edward, and F r i e d l a n d e r 1973}., S i n g l e - s t a g e s t o c k r e c r u i t m e n t models have proven u s e f u l when l i f e c y c l e l e n g t h i s f i x e d {Bicker 1954). Walters (1975), u s i n g dynamic programming, confirmed t h a t a f i x e d escapement p o l i c y i s optimal i n the presence of environmental v a r i a b i l i t y . t Other approaches i n c l u d e s o l v i n g f o r an optimal age s t r u c t u r e given an a r b i t r a r y t o t a l p o p u l a t i o n (Beddington 1974, Beddington and T a y l o r 1 9 7 3 ) . W a l t e r s (1969) developed a g e n e r a l s i m u l a t i o n model of f i s h p o p u l a t i o n s , and t e s t e d v a r i o u s harvest schemes on the model. Other concerns have been r a i s e d 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 s t o c k f i s h e r i e s (Paulik> Hourston, and L a r k i n 1966; H i l b o r n 1976).To date, t h e r e i s no ge n e r a l s o l u t i o n t o the o p t i m a l e x p l o i t a t i o n problem of age s t r u c t u r e population when r e c r u i t m e n t depends upon stock s i z e ; The source o f much o f the d i f f i c u l t y with o p t i m i z a t i o n i s the "curse o f d i m e n s i o n a l i t y * 1 (Bellman 1961) • F o r the mixed f i s h e r y problem c o n s i d e r e d i n t h i s t h e s i s , one has to d e a l with a l l p o s s i b l e combinations of abundance o f two age c l a s e s of coho and f i v e age c l a s s e s of chinook. U n f o r t u n a t e l y , soiae r e d u c t i o n i n the problem i s needed i n order to apply c u r r e n t technology., The s i m p l i f i c a t i o n s used i n the model i s t o assume t h a t r e c r u i t m e n t i s c o n s t a n t and t h a t there e x i s t s an i n i t i a l and a t a r g e t escapement abundance f o r each age c l a s s of each s p e c i e s . The o p t i m i z a t i o n problem i s to determine an optimal plan of w i t h i n season o p e r a t i o n t h a t maximizes t o t a l b e n e f i t from the f i s h e r y and maintains t a r g e t escapement p o p u l a t i o n s . The model assumes each age c l a s s o f each s p e c i e s i s separate from the others i n i t s b i o l o g y . The o n l y i n t e r a c t i o n i s i n the common e x p l o i t a t i o n of a l l the f i s h . Another c o m p l i c a t i o n i n the a n a l y s i s o f t h i s ; f i s h e r y i s the d i v e r s i t y of the a v a i l a b l e c o n t r o l s . The task o f d e s i g n i n g a complete p o r t f o l i o of c o n t r o l s with a s i n g l e computational procedure i s very d i f f i c u l t . The o n l y o p t i m i z a t i o n t o be done i n t h i s t h e s i s i s to determine seasons of f i s h i n g f o r both f i s h e r i e s . Optimal seasons w i l l be s t u d i e d under v a r i o u s s i z e l i m i t r e g u l a t i o n s and under a v a r i e t y of c a t c h a b i l i t y c o e f f i c i e n t s r e p r e s e n t i n g a v a r i e t y of p o s s i b l e gear r e s t r i c t i o n s . 52 Bag l i m i t changes and area c l o s u r e s f o r the s p o r t f i s h e r y are not c o n s i d e r e d as c o n t r o l o p t i o n s . F i g u r e 29 shows the frequency of bags per boat-day f o r s p o r t fishermen who keep l o g books f o r the Department o f F i s h e r i e s (A.f. argue pers. conm. ). A bag l i m i t r e d u c t i o n to one f i s h per angler-day corresponds t o a l i m i t o f two and one h a l f per boat-da-y..'/This; r e d u c t i o n - i n bag c o u l d produce an approximate 1 5 j £ r e d u c t i o n i n immediate c a t c h , but would r e s u l t i n an ultimate r e d u c t i o n i n c a t c h of only 251 to 10SS ( A l l e n 1955). The consequence of a severe bag l i m i t on spawning escapement c o u l d be considered minimal a t best, A l e s s severe bag l i m i t of one chinook, ; two salmon t o t a l per angler-day has been suggested and was found completely unacceptable by the s p o r t fishermen (Sport F i s h A d v i s o r y Committee Meeting, June 23, 1978 ) , : Area r e s t r i c t i o n s on t h e s p o r t fishermen; have been i d i s c o u n t e d on the b a s i s o f t h e i n e g u i t i e s they would generate w i t h i n the t o u r i s t i n d u s t r y . I f some areas were c l o s e d d u r i n g peak t o u r i s t times, the d i s p a r i t y among r e s o r t o p e r a t o r s i n the a f f e c t e d areas would be unacceptable. 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 the f o u r major components of the o p t i m i z a t i o n model: f i s h dynamics, e f f o r t dynamics, c o n t r o l s , and revenues. 5 3 u -G Hi •H M--M •H <Tj l-l +-> CO + <3-n o a> o u> x: +-> c •H J) CT ra ca 4-1 o c c •H 4-> =3 - Q •rH l-l -f-> tn C N <L> w D CT •H ti-ro 00 < O CD CC O 0_ CO QC LU Q_ X O o I— < SAVQ-lVOa AO lN30d3d 54 y&&k*:,f, l a s h £ n i a i £ s • The f i s h model i s a standard random encounter model. The qhange i n a c l a s s of f i s h d u r i n g p e r i o d k i s governed by the f o l l o w i n g o r d i n a r y d i f f e r e n t i a l eguation: dx < i , t ) / d t = -£iMi.k)+ (1 <i,k,c)*< 1-1*1,k,c)) v(c)) u { k , c ) E ( k , c ) g i i , k , c ) + C l ( i > k r S ) + (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 the sum o f n a t u r a l m o r t a l i t y r a t e , m i g r a t i o n r a t e out o f Georgia S t r a i t ; ^ .and mature run t i m i n g f o r age and s p e c i e s i d u r i n g p e r i o d k; l ( x , k , c ) .= 1 i f age and s p e c i e s , f i s h i i s over the commercial s i z e l i m i t ; 1 ( i , k , c ) - 0 i f age and s p e c i e s f i s h i i s under the commercial s i z e l i m i t ; l ( i , k , s ) = 1 i f age and s p e c i e s f i s h i i s over the s p o r t s i z e l i m i t ; l ( i , k , s ) ; — 0 i f age and s p e c i e s f i s h i i s under the s p o r t s i z e l i m i t ; v(c) and v {sj are shaker m o r t a l i t y r a t e s f o r commercial and s p o r t f i s h e r i e s r e s p e c t i v e l y ; u(k,c)and u (k,s) are the c o n t r o l s f o r the commercial and s p o r t f i s h e r i e s r e s p e c t i v e l y during p e r i o d k; E(k,c) and E(k,s) are the e f f o r t l e v e l s f o r the commercial and s p o r t f i s h e r i e s r e s p e c t i v e l y during p e r i o d k; 55 g ( i , k , c ) and g ( i , k , s ) are the c a t c h a b i l i t y c o e f f i c i e n t s f o r age and s p e c i e s i , i n the commercial and s p o r t f i s h e r i e s r e s p e c t i v e l y ; x ( i , t ) - the number of age and s p e c i e s i f i s h a v a i l a b l e a t time t ; x{i,k) - the number of age and s p e c i e s i f i s h present at the beginning o f p e r i o d k; x (i,1) - the number of age and s p e c i e s i f i s h present at the beginning o f the year; N - the 2 4 b i - m o n t h l y p e r i o d s i n a year., The seven c l a s s e s of f i s h are two ages of coho and f i v e of chincox. The assumption o f random encounter i s g u i t e tenuous..tack of i n f o r m a t i o n on the process of encounter and capture i n most . f i s h e r i e s precludes the use o f other p o s s i b l e forms o f the model. In the Georgia S t r a i t f i s h e r y , f i s h i n g t a k e s p l a c e at r e l a t i v e l y l o c a l i z e d «hot spots' 1 . I t i s not c l e a r whether success i s a product of the a g g r e g a t i o n of the f i s h or o f d i f f e r e n t behavior o f f i s h i n the f i s h e r y areas. On the other hand, success may be due to the behavior of fishermen a t p a r t i c u l a r s i t e s and may have nothing to do with the f i s h oyer the range of stock s i z e s normally present. Because t h e r e i s l i t t l e known about the process u n d e r l y i n g s u c c e s s f u l c a p t u r e , the number o f tenuous assumptions r e g u i r e d i n c r e a s e s with the complexity of the model. I t i s t h e r e f o r e more prudent to make one bad assumption {random encounter) than many worse ones. I n t e g r a t i n g Eguation 1 we get: y ( i , k + 1)-y (i,k) = -[m{i,k) • ( l ( i , k , c ) 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 where: y (i,k) = Ln(x (i,k) ) At t h i s p o i n t , we may d e f i n e F ( i , k ) = y ( i , k * 1 ) - y (i,k) (2) 3±2j_ E f f o r t The random encounter model ( B i c k e r , 1940) r e l a t e s i nstantaneous r a t e o f c a t c h , e f f o r t , and p o p u l a t i o n as f e l l o w s : catch = e f f o r t x c a t c h a b i l i t y c o e f f i c i e n t x p o p u l a t i o n T h e r e f o r e , c a t c h per u n i t e f f o r t (CPOE) may be w r i t t e n : C F l l E = 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 p o p u l a t i o n or CPOE = qx Sport e f f o r t i s assumed to be p r o p o r t i o n a l to CPOE. T h e r e f o r e , 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 c o e f f i c i e n t shown i n f i q u r e 16, i t may be viewed as the marqinal e f f o r t qenerated by a u n i t i n c r e a s i n CPOE. Ccmmercial t r o l l e f f o r t i s assumed to s a t u r a t e with CPOE. 1 E(k,c) = a(k) £ q ( i , k , c ) x ( i , k ) l ( i , k , c ) / r b(k)* £ q ( i , k , c ) x ( i , k ) l ( i , k , c ) ] 57 <u) where: a and b are d e p i c t e d i n F i g u r e 2U (Note: response i s assumed f o r l e g a l s i z e d f i s h o n l y ) . .3.3.. C o n t r o l s The only c o n t r o l s f o r which ..optimization i s done i n t h i s t h e s i s are the seasons o f s p o r t and t r o l l f i s h i n g . T h e r e f o r e : u (k,c) = 1 i f commercial f i s h e r y i s open i n pe r i o d k; u|k,c) = 0 i f commercial f i s h e r y i s c l o s e d i n p e r i o d 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 k; u<k,s)=0 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 c l o s e d i n p e r i o d k. Note that u=1 does not imply t h a t f i s h i n g w i l l a c t u a l l y occur; equations (3) and (4) may produce low f i s h i n g pressure i f the stock s i z e i s low o r , i n the s p o r t f i s h e r y , i f i t i s winter. levenae Revenue i s generated from the commercial f i s h e r y i n the form of c a t c h and i n the s p o r t f i s h e r y i n the form of e f f o r t . Sport e f f o r t i s dependent upon c a t c h , so f o r the purpose of o p t i m i z a t i o n , revenue frcm the s p o r t f i s h e r y can a l s o be represented i n terms of catch. The average CPOE i n the s p o r t f i s h e r y i s approximately one f i s h per boat-day. /Therefore, the p r i c e of a s p o r t caught f i s h can be assumed the same as the value of a boat-day of e f f o r t . The revenue e x p r e s s i o n i s taken to be the sum o f the components due to f i s h i n g on the r i g h t hand s i d e of Equation 2, weighted by the p r i c e and s i z e of f i s h 58 cau qht. 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: w(i,k) i s the weight of age and species i during p e r i o d k ( f i g . 6 and l e n g t h weiqht r e l a t i o n s h i p ) ; p(k,c) i s the p r i c e per pound of commercially caught f i s h during p e r i o d k ( F i g 27) ; p(k,s) i s the p r i c e per f i s h i n the sport f i s h e r y ( F i g . 29) . 59 O P T I M I Z A T I O N P i t h the i n g r e d i e n t s d e f i n e d i n the p r e v i o u s c h a p t e r , the o p t i m a l c o n t r o l problem i s to f i n d u (k,c) ,u (k,s) ,x (i,k) k=1,...,n i=1,...,7 {Equation 1) t h a t maximizes R (k) (Equation 6 ) . In a d d i t i o n , the p o p u l a t i o n l e v e l s a f t e r p e r i o d N (x(i,N*1)) should not depart d r a m a t i c a l l y from t a r q e t l e v e l s ( X ( i ) ) . The l a t e r c o n d i t i o n can be f o r m a l i z e d by a t e r m i n a l payoff f u n c t i o n . G(x(i,N+1)) = - d ( i ) ( x ( i , N * 1 ) - X ( i ) ) where: X(i) i s the t a r q e t l e v e l of aqe and s p e c i e s i ; d ( i ) i s a parameter used to weiqh the t e r m i n a l c o n d i t i o n a q a i n s t the w i t h i n season b e n e f i t s . The problem i s formulated i n the method of "Laqranqe" m u l t i p l i e r s (Kolman and Trench 1971, p. 224; C l a r k e 1976, p. 250). ILLIJ). Mathematical f o r m u l a t i o n To ease the n o t a t i o n and d i f f e r e n t i a t i o n , the f o r m u l a t i o n w i l l be c a r r i e d out i n y ( i ) r a t h e r than x ( i ) . R e c a l l t h a t y (i) = L n x ( i ) , hence x(i) = E X P ( y ( i ) ) . The problem may then be expressed as N 7 Maximize {£ R (k) + 2;G} k=l i s l (8) s u b j e c t to 60 y ( i , k+ 1)-y (i,k) =f (k) k=1,...,N 0 < u (k,c) ,u (k,.s) < 1 (9) Ihe "Lagranqion" f o r t h i s problem (Clark, 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 the Laqranqe m u l t i p l i e r . A necessary and s u f f i c i e n t c o n d i t i o n f o r o p t i m a l i t y of a p o l i c y u(.,.) i s that L must be maximized with respect to a l l y's and u's. D i f f e r e n t i a t i n g with r e s p e c t to 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)/dy ( i , k) k=2,...,N (11) z ( i ,N) = dG/dy(i, N+1) (12) i ' r c i Equations 2 and 6, note that L i s l i n e a r i n the u's. There f o r e , to maximize L with res p e c t to u, the 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 7 P |k,c) £ w (i,k) l ( i , k , c ) >y £ z ( i , k) [" 1 ( i , k , c ) + | 1 - l ( i , k , c ) ) v(c) 1 i-l l-i u (k , c) = 0' 7 7 P (k,s) £ w (i,k) 1 <i,k,s) < % z ( i , k)T 1 (i,k,s)+ (1-1 (i,k,s) ) v (s) 1 l- l ^ u (k,s) = 1 7 7 P(k,s) £ w{i,k) 1 (i,k,s) > % z ( i , k) r 1 (i ,k, s) + (1-1 ( i , k, s) ) v (s) 1 i-l i-l u(k,s) = 0 113) 61 Uz 2. The algorithm Some methods exist to handle t h i s problem. One could solve for the seven times 23 x»s and z*s and two times 24 u*s. This approach would mean solving a system of 370 non-linear eguations for 370 unknowns, and would be p r o h i b i t i v e l y expensive. Fortunately for t h i s study, i t was possible to derive a much simpler procedure, similar to "policy i n t e r a t i o n H (Howard, 1960). The procedure involves the following - steps£ Step 1: Pick a set of u's. Step 2: Solve Eguation 1 forward to time N using current best estimate of the optimal u* s. Step 3: Determine z(N) and solve eguation (11) backwards from N to 1 using current u*s. Step 4: Using z*s, determine a new s e t o f u*s according to eguation (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 stop; else go to Step 2. Ho theory exists concerning the numerical properties of t h i s algorithm. Puteraan and Brunelle (197j6) have compared policy i t e r a t i o n to the "Newton*1 method of non-linear programming. Convergence of the algorithm i s not guaranteed. .,• However, i f the algorithm stops, then a solution to the "Lagrange" problem has been reached and i t i s guaranteed that the r e s u l t i n g policy i s l o c a l l y optimal. 62 OPTIMIZATION RESULTS The o p t i m i z a t i o n p r o c e d u r e d e s c r i b e d i n t h e p r e c e d i n g s e c t i o n r e q u i r e s i n i t i a l p o p u l a t i o n s i z e s (x ( i , 1)) a n d t a r g e t p o p u l a t i o n s i z e s (X { i H . The p o p u l a t i o n s i z e s u s e d i n t h i s s t u d y were t a k e n f r o m t h e s i m u l a t i o n model.; An i n i t i a l p o p u l a t i o n s t r u c t u r e i s u s e d t o s t a r t t h e s i m u l a t i o n t h e n , a s a c o n s e g u e n c e o f c o n s t a n t r e c r u i t m e n t an e q u i l i b r i u m p o p u l a t i o n s t r u c t u r e i s r e a c h e d a f t e r s i x y e a r s . The f i n a l p o p u l a t i o n s t r u c t u r e o f t h e s i m u l a t i o n m o d el i s l i k e l y t h e b e s t a v a i l i a b l e e s t i m a t e o f " c u r r e n t " c o n d i t i o n s i n t h e G e o r g i a S t r a i t . The o p t i m i z a t i o n u s e s t h e s e v a l u e s { T a b l e 2) a s t h e x ( i , 1) . An i m p o r t a n t p a r a m e t e r i n t h e o p t i m i z a t i o n i s d ( i ) ( E q . 7 ) . The m a q n i t u d e o f d ( i ) d e t e r m i n e s t h e d e q r e e t o w h i c h X ( i ) i s met. D i f f e r e n t i a t i n q G w i t h r e s p e c t t o y ( i ) , l e a v e s d ( i ) . T h e r e f o r e , d ( i ) i s t h e t e r m i n a l v a l u e o f z ( i ) a n d t h e b a s i s f o r c a l c u l a t i n g t h e r e s t o f t h e z»s. The z»s h a v e a n i n t e r e s t i n g i n t e r p r e t a t i o n . I n e c o n o m i c s , t h e y a r e known a s t h e "shadow" p r i c e s ( I n t r i l i q a t o r 1 9 7 1 ) . I q n o r i n q s i z e l i m i t s a n d s h a k e r m o r t a l i t y , s y s t e m (13) s t a t e s t h a t i f t h e shadow p r i c e o f a f i s h l e f t i n t h e s e a i s g r e a t e r t h a n t h e p r i c e o f t h e l a n d e d f i s h , t h e n t h e o p t i m a l d e c i s i o n i s t o l e a v e t h e f i s h i n t h e w a t e r . On t h e c o n t r a r y , i f t h e f i s h i s more v a l u a b l e i n t h e b o a t t h a n i n t h e s e a , t h e n t h e f i s h e r m e n s h o u l d be a l l o w e d t o f i s h . 63 T A B L E 2 . I n i t i a l a n d t a r < j c t p o p u l a t i o n s i z e s C o h o O c e a n y e a r 1 I n i t i a l 1 , 8 0 0 , 0 0 0 T a r g e t 1 , 0 8 0 , 0 0 0 O c e a n y e a r 2 I n i t i a l 1 , 0 8 0 , 0 0 0 T a r g e t 0 C h i n o o k O c e a n y e a r 1 I n i t i a l 1 , 3 0 0 , 0 0 0 T a r g e t 9 8 0 , 0 0 0 O c e a n y e a r 2 I n i t i a l 9 8 0 , 0 0 0 T a r g e t 4 9 0 , 0 0 0 O c e a n y e a r 3 I n i t i a l 4 9 0 , 0 0 0 T a r g e t 1 4 2 , 0 0 0 O c e a n y e a r 4 I n i t i a l 1 4 2 , 0 0 0 t a r g e t 1 7 , 0 0 0 O c e a n y e a r 5 I n i t i a l 1 7 , 0 0 0 T a r g e t 2 , 5 0 0 The z's r e p r e s e n t the value of l e a v i n g the f i s h i n the sea to be caught l a t e r when they are l a r g e r and more v a l u a b l e . The z's a l s o i n c l u d e the c o s t o f v i o l a t i n g t a r g e t escapements. The v a l u e c h o s e n f o r d ( i ) can be i n t e r p r e t e d as the value of l e a v i n g a f i s h i n t h e water f o r f u t u r e b e n e f i t s . These b e n e f i t s may come from the o f f s p r i n g i f the f i s h i s allowed to reach the spawning grounds, or from the value of the f i s h i n next years c a t c h . For the o p t i m i z a t i o n i n t h i s t h e s i s , independent estimates of the d's were not a v a i l a b l e . T h e r e f o r e , s u i t a b l e v a l u e s had to be found by other means. The approach used was t o assume t h a t the d's should be p r o p o r t i o n a l to the landed value i n the ccmmercial f i s h e r y of a f i s h of age and s p e c i e s i i n the l a s t p e r i o d of the year. d { i ) = r p ( i , N , c ) w(i,N) 114) A search f o r the value of r which generated a p o l i c y t h a t met the t e r m i n a l values (X's) most c l o s e l y r e s u l t e d i n r equal to 0.07 and l e f t an averaqe t r i v i a l d i s crepancy of C.71% from the t a r q e t X's. 5.1. F i n d i n g an O p t i m a l P ^ M c y . iConverqence) The method d e s c r i b e d i n the l a s t s e c t i o n found s o l u t i o n s very e f f i c i e n t l y i n a l l cases. Convergence was obtained i n four or f i v e i t e r a t i o n s o f the a l g o r i t h m . The c a l c u l a t i o n i n c l u d e d s c l v i n g equation (1) and equation (11) f i v e times. T h i s computational requirement i s e q u i v a l e n t t o runninq the 65 s i m u l a t i o n model e i g h t to ten years. Table 3 shows i n t e r m e d i a t e p o l i c i e s o b tained as the method converged on an optimal p o l i c y f o r ^ c u r r e n t " c o n d i t i o n s . The i n i t i a l p o l i c y used i n a l l c a s e s i n c l u d e d sport f i s h i n g a l l year and no commercial f i s h i n g . T h i s p o l i c y underharvested the p o p u l a t i o n s l e a v i n g an average of 59% too many f i s h . The next p o l i c y computed by the a l g o r i t h m c l o s e d up both f i s h e r i e s a l l year around. T h i s p o l i c y over harvested the p o p u l a t i o n l e a v i n g an average 17% too few f i s h . The next p o l i c y c l o s e d the s p o r t f i s h e r y f o r the months of January through March and c l o s e d the commercial f i s h e r y from January u n t i l June 1, l e a v i n g an average of 0.5% too few f i s h . The f i n a l p o l i c y l e f t the s p o r t season unchanged and opened the commercial f i s h e r y one h a l f month l a t e r . ./ J5.2.. Optimal P o l i c y The f i r s t o p t i m i z a t i o n r e s u l t obtained was using nominal or "best guess" parameter estimates and the assumption t h a t management w i l l attempt to maintain c u r r e n t age s t r u c t u r e and escapement l e v e l s . The o p t i m a l p c l i c y f o r t h i s case i s presented i n Table 3 , f i n a l i t e r a t i o n * There are t h r e e major d i f f e r e n c e s between the o p t i m a l p o l i c y and c u r r e n t management p r a c t i c e s : 1) The o p t i m a l p o l i c y c l o s e s the s p o r t f i s h e r y d u r i n g the winter. 2) The o p t i m a l p c l i c y opens the commercial f i s h e r y June 15 as opposed t o the c u r r e n t p r a c t i c e of A p r i l 15 opening f o r chinook and J u l y 1 opening f o r coho. 3) The o p t i m a l p o l i c y l eaves the commercial 66 TABLE 3. Intermediate p o l i c i e s for computation of optimal p o l i c y under "current" conditions. FIRST ITERATION Jan Feb Mar Apr May Jun J u l Aug Sept Oct Nov Dec Sport 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T r o l l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Average deviation from target populations -• 17% SECOND ITERATION Jan F'eb Mar Apr May Jun Ju l Aug Sept Oct Nov Dec Sport 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T r o l l 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 deviation from target population - .5% THIRD ITERATION Jan Feb Mar Apr May Jun J u l Aug Sept Oct Nov Dec Sport 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T r o l l 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 deviation from target population .71% 1 - f i s h e r y open 0 - fi s h e r y closed 67 f i s h e r y open during November and December.,In p r a c t i c e , the f i s h e r y c l o s e s i n October. The major reason f o r these d i f f e r e n c e s i s the h i g h e r value of commercially caught f i s h d u r i n g the l a t t e r months o f t h e year. Both t h e r i s i n g p r i c e per pound ( F i g . 27) and i n c r e a s e d weight per f i s h , due t o growth, c o n t r i b u t e to a very high value per f i s h i n the commercial f i s h e r y d u r i n g the l a t e r months.; On der •thes«r"'COTrdl'ti©|ri*| - I f c t H L s b e t t e r t o leave the f i s h i n the water d u r i n g the e a r l y months and to h a r v e s t them l a t e r when they are more valuable.:. The optimal p o l i c y was c o i p a r e d to;curreiit,3seasoES u s i n g the s i m u l a t i o n model. C l o s i n g the winter s p o r t f i s h e r y r e s u l t e d i n a 140,000 d o l l a r decrease i n s p o r t b e n e f i t s , which was o f f s e t by a 140,000 d o l l a r i n c r e a s e i n the commercial landed value. The net change i n value u s i n g the optimal p o l i c y was i n s i g n i f i g a n t . 5j.3jt Increased Escapement •• Much of the impetus f o r the development of the Georgia S t r a i t s i m u l a t i o n model and t h i s o p t i m i z a t i o n e x e r c i s e has come from concern over c o n s e r v a t i o n o f the f i s h s t o c k s . T h i s concern can be i n t e r p r e t e d as an i n c r e a s e d v a l u e of f i s h l e f t i n the water a f t e r the f i s h i n g season. A s e r i e s of optimal p o l i c i e s were developed using i n c r e a s e d values of the r parameter i n Eguation 14. F i g u r e 30 shows t h e e f f e c t of i n c r e a s e d value of a f i s h i n the water a t the end of the year on the o p t i m a l f i s h i n g seasons. As r i s i n c r e a s e d , the l e n g t h of the seasons decrease. The s p o r t f i s h e r y i s c o n f i n e d to the summer months when i t has MONTHS o z o Optimum open season to j> c_ c_ S£ «9 £ C n M a a fD n O Ul 1-1 M o a X) 01 I — Cn CU O n> -o & LO <t r* M-CO ri 3 & o 1—1 o to c C ft H- 0-L.1 3- C H- a O "JO (A ro 16 • w l-ti •o o (t l-l n rf CO D r+ o O rt I-i 3 Cu o a M a. 1) 0> 1 ro O u- TT rr u; "i O r--U M •o V (D H-3 a fD . G a r t -a o> a (• be 89 69 the h i g h e s t v a l u e , and commercial f i s h i n g i s delayed to the l a t e r months when the f i s h have the h i g h e s t valuev The abrupt change i n the s p o r t season where r i s changed from 0.1** to 0.16 r e f l e c t the "sguare" nature of the s p o r t f i s h e r y value curve ( F i g . 28) . The s p o r t f i s h e r y value curve i s s u r e l y smoother than the curve assumed i n t h i s model. However, i t s " r e a l " shape i s s t i l l u n c e r t a i n . J5.J4A S i z e L i m i t s -Optimal f i s h i n g seasons were computed f o r v a r i o u s s i z e l i m i t s . F i g u r e 31 shows the r e s u l t i n g p o l i c i e s . Increased s i z e l i m i t s had l i t t l e e f f e c t upon the s p o r t f i s h i n g season. The s p o r t fishermen are assumed t o respond t o l e g a l s i z e d f i s h o n l y . T h e r e f o r e , the harvest o f undersized f i s h c o n t r i b u t e s t o the k i l l through shaker m o r t a l i t y , but does not c o n t r i b u t e to the value of the f i s h e r y . The r e s u l t s show t h a t , f o r s i z e l i m i t s a t l e a s t up t o 20 inches, i t i s never o p t i m a l to have a winter s p o r t f i s h e r y , i n c r e a s e d s i z e l i m i t s , on both the s p o r t and commercial f i s h e r i e s , from present to 20 i n c h e s allowed an expansion of the commercial f i s h e r y to the same season as the sportsman's. While i n c r e a s i n g the s i z e l i m i t , i t was found necessary to decrease the value of r so as not to overshoot t a r g e t p o p u l a t i o n l e v e l s . The r e s u l t s f o r the 26 i n c h s i z e l i m i t are p u z z l i n g . At 26 i n c h e s and a value of 0 f o r r , the o p t i m a l p o l i c y i s to open the commercial f i s h e r y the year round, but not to i n c l u d e a winter s p o r t s f i s h e r y . T h i s p o l i c y r e s u l t e d i n F i q u r e 31: O p t i m a l Seasons f o r S p o r t and T r o l l I'ishinq i n t h e G e o r q i a S t r a i t w i t h Respect t o I n c r e a s e d S i z e L i m i t s . 71 an average of 21% too many f i s h i n the water at the end of the year. Opening both f i s h e r i e s a l l year round with a 26 i n c h s i z e l i m i t does not v i o l a t e the t a r g e t p o p u l a t i o n . However, r must be negative f o r t h i s p o l i c y to be o p t i m a l * / I n t e r p r e t a t i o n of the shadow p r i c e being n e g a t i v e i s d i f f i c u l t . However, one co u l d s p e c u l a t e t h a t i t i s an a r t i f a c t of the " c u r r e n t " age and s p e c i e s s t r u c t u r e . 5,5. Increased Sport E f f i c i e n c y The c a t c h a b i l i t y c o e f f i c i e n t i s the most u n c e r t a i n parameter i n the model. The u n c e r t a i n t y , a r i s e s because c a t c h a b i l i t y i s computed from n a t u r a l m o r t a l i t y r a t e s , c a t c h , e f f c r t , and escapement, a l l of which are prone t o e r r o r . Catch and e f f o r t data f o r the commercial f ^ However, sp o r t f i s h i n g s t a t i s t i c s are based upon s m a l l samples of the s p o r t f i s h i n g f l e e t , and are b e l i e v e d to be badly b i a s e d (Argue Coursley and H a r r i s 1S77). C a t c h a b i l i t y a l s o e n t e r s i n t o the c a l c u l a t i o n of c a t c h per u n i t e f f o r t , from which the s p o r t e f f o r t response i s p r e d i c t e d . The e f f i c i e n c y o f t h e s p o r t f l e e t i s i n c r e a s i n g and w i l l l i k e l y continue t c do so. T h e r e f o r e , o p t i m a l p o l i c i e s were computed f o r i n c r e a s e d s p o r t c a t c h a b i l i t y to r e f l e c t both u n c e r t a i n t y and f u t u r e i n c r e a s e s i n s p o r t e f f i c i e n c y ( F i g . 32). As the s p o r t c a t c h a b i l i t y i n c r e a s e s , the amount of f i s h i n g allowed i n both f l e e t s i s reduced. Again, the s p o r t season i s con f i n e d t o the summer and the ccmmercial season t o the end of the year. Increased s p o r t c a t c h a b i l i t y 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 Seasons 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 w i t h Hespect to I n c r e a s e d E f f i c i e n c y i n the S p o r t F l e e t . 73 i n c r e a s e i n the amount of e f f o r t and an i n c r e a s e i n the impact of any u n i t of e f f o r t on the f i s h s t o c k s . As s p o r t e f f i c i e n c y i n c r e a s e s , the value of a f i s h l e f t i n the water ( d ( i ) ) must a l s o i n c r e a s e t o provide f o r enough f i s h at the end of the season. 5±6X , Enhancement Enhancement was r e p r e s e n t e d by i n c r e a s i n g the i n i t i a l abundance of the two age c l a s s e s o f coho (Tab. 4). The e f f e c t of doubling the number of coho on the optimal seasons was not dramatic, but the d i r e c t i o n was s i g n i f i c a n t . The o p t i m a l p o l i c i e s were to delay the opening of the s p o r t season u n t i l the beginning o f Say and s t a r t the t r o l l season the f i r s t c f J u l y . Here severe r e s t r i c t i o n s i n f i s h i n g vere r e q u i r e d i n part to o f f s e t over h a r v e s t . The average departure from t a r g e t c o n d i t i o n s was 8% more f i s h than needed. A l l the chinook ages were overharvested. The second and f i f t h year chinook were the most s e v e r l y o v e r f i s h e d (155? and 1656 r e s p e c t i v e l y ) . O v e r f i s h i n g of the chinook was compensated by 9 6 1 more coho present than necessary at the end o f the year, E x a c t l y t h i s type of r e s u l t i s new o c c u r r i n g i n the Georgia S t r a i t , with l a r g e excess escapement of coho t o h a t c h e r i e s such as C a p i l i n o . Judging from p u b l i c r e a c t i o n to government d e c i s i o n s to s e l l these excess f i s h , i t might be a good i d e a to model the t e r m i n a l c o s t term G (eguation 7) to r e f l e c t a p e n a l t y on high as w e l l as low deviations from d e s i r e d t e r m i n a l stock s i z e s . 74 Table 4. Optimal season with enhanced coho Jan Feb Mar Apr May Jun J u l Aug Sept Oct Nov Dec Sport 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 T r o l l 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 Deviation from target populations Coho Chinook. Age 1 Age 2 Age 3 Age 4 Age 5 96% -.4% -15% -1% -2% -16% Average deviation from target population - 8% 75 T h i s r e s u l t may have s e r i o u s i m p l i c a t i o n s f o r enhancement, Enhanced f i s h , hy s t i m u l a t i n g f i s h i n g e f f o r t , may cause the o v e r e x p l o i t a t i o n of unenhanced s t o c k s , . R e s t r i c t i o n s on f i s h i n g may need to be more severe. A l s o , a poor d e c i s i o n r e g a r d i n g the opening or c l o s i n g of any f i s h e r y may, by s t i m u l a t i n g l a r g e amounts of f i s h i n g e f f o r t , be very c o s t l y i n terms of o v e r e x p l o i t a t i o n of unenhanced s t o c k s . 76 6 A ;DXS€"OSSi;0M>.^JD-^.O»fiLqSi&QH. C o n c l u s i o n s can be drawn i n t h r e e areas: the management of t h i s p a r t i c u l a r f i s h e r y , the computational scheme proposed, and the importance o f o p t i m i z a t i o n i n resource management. - 6 . 1 . rSegfogj^s^ ;:;..,,. One of the main purposes f o r b u i l d i n g .simpl,e„&o&els and determining o p t i m a l p o l i c i e s under a simple set of assumptions i s t o see how s e n s i t i v e these models and p o l i c i e s are to parts of the system about which there are l a r g e u n c e r t a i n t i e s . In the model presented here, 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 l i t t l e known about the abundance of f i s h i n pre-spawning age c l a s s e s . On examination, there are two components which enter t h e model g u a d a t i c a l l y : the c a t c h a b i l i t y c o e f f i c i e n t and the stock abundance. In the s i n g l e stock case: r a t e of c a t c h = (a + bqx) qx E r r o r s i n estimates of the g*s w i l l r e s u l t i n a square e f f e c t cn p r e d i c t e d c a t c h . E r r o r s i n a s s e s s i n g the abundance of a cohort w i l l a l s o r e s u l t i n l a r g e e r r o r s i n p r e d i c t i n g c a t c h from a l l c o h o r t s . Optimal p o l i c i e s are i n t u r n very s e n s i t i v e to the c a t c h . The amount o f time t h a t the f i s h e r i e s a r e c l o s e d r e f l e c t s the p o t e n t i a l f o r the c a t c h t o v i o l a t e t a r g e t escapements. T h e r e f o r e , the p o l i c i e s of c l o s u r e s are very 77 s e n s i t i v e 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 and abundance. The major c o n c l u s i o n r e g a r d i n g the Georgia S t r a i t f i s h e r y i s t h a t , under the assumed p r i c e schedule i n both the sport and commercial f i s h e r i e s , t h e r e were; no cases t e s t e d where a winter s p o r t f i s h e r y i s o p t i m a l . There i s l i t t l e c o n f i d e n c e i n the p a r t i c u l a r p r i c e schedule used i n t h i s t h e s i s . However, the g e n e r a l trend of s p o r t f i s h e r y being more valuable i n the summer than i n the winter i s l i k e l y a good assumption. The a n a l y s i s shows t h a t f i s h should be l e f t i n the water i n the winter so they can be harvested d u r i n g the more v a l u a b l e summer s p o r t s f i s h e r y . The a n a l y s i s a l s o shows t h a t season c l o s u r e can be used as a t o o l t o i n s u r e escapement from the Georgia S t r a i t f i s h e r y . Dramatic i n c r e a s e s i n t h e number of f i s h l e f t i n the water a f t e r the f i s h i n g season best obtained with a summer sp o r t f i s h e r y and a f a l l commercial f i s h e r y . A l l e n (1954) d i s c u s s e s the use o f s i z e l i m i t s as a f i s h e r i e s r e g u l a t i o n . " S i z e l i m i t s may be used e i t h e r t o maintain a s u f f i c i e n t breeding s t o c k , or to promote the maximum c a t c h of the d e s i r e d k i n d , " Maximum c a t c h can take on three d i f f e r e n t forms: (1) The maximum t o t a l numbers of f i s h , independent of s i z e ; (2) The maximum number o f l a r g e f i s h ; and (3) The maximum t o t a l weight. 78 In t h i s a n a l y s i s , the s p o r t f i s h e r y i s assumed to operate under the f i r s t o b j e c t i v e (maximum number). In such a case, A l l e n concludes "... no s i z e l i m i t should be a p p l i e d so t h a t a n g l e r s can be allowed to take as many f i s h a s , p o s s i b l e before they d i e from n a t u r a l causes". S i z e l i m i t s i n the Georgia S t r a i t f i s h e r i e s have been defended upon the b a s i s of maintaining breeding s t o c k s . . I t i s true that one of the reasons f o r s i z e l i m i t s i n the f i s h e r y i s c o n s e r v a t i o n . However, the commercial f i s h e r y i s operated with an o b j e c t i v e resembling (3) above. S i z e l i m i t s i n both f i s h e r i e s are i n f a c t mechanisms f o r d i s t r i b u t i n g b e n e f i t s between the two users of the resource. For example, a l a r g e r s i z e l i m i t i n the commercial than i n the s p o r t f i s h e r y a l l o w s more s m a l l e r f i s h f o r two purposes. One purpose i s to allow the s m a l l f i s h to grow big g e r and more v a l u a b l e f o r the commercial fisherman. The other purpose i s t o make a v a i l a b l e to the sportsmen more of the s m a l l e r and more abundant f i s h . The a n a l y s i s shows s i z e l i m i t s can be used as instruments to i n c r e a s e escapement. However, the c u r r e n t p o l i c i e s of s i z e l i m i t s and seasons appear t o be aimed at d i t r i b u t i n g the harvest and not at p r e s e r v i n g the stocks,, The computed optimum p o l i c y does not d i f f e r g r e a t l y frcm the present p r a c t i c e d p o l i c y i n e i t h e r appearance or performance (Table 5). E a r l i e r r e s u l t s i n d i c a t e d t h a t to match c u r r e n t c o n d i t i o n s one must maximize present w i t h i n season b e n e f i t s and a t t r i b u t e near zero value to stocks l e f t i n the water. The c u r r e n t p o l i c i e s and t h e i r r e s u l t i n g a l l o c a t i o n between commercial and s p o r t f i s h e r i e s , have evolved due t o 79 Table 5. A comparison of the optimal p o l i c y with a v a r i e t y of other p o l i c i e s . Chinook Coho T r o l l landed Sport landed P o l i c y Escapement Escapement Value Value (1) Present seasons 34,879 124,861 $2,300,000 $12,640,000 (2) Optimal seasons 36,577 124,660 $2,440,000 $12,500,000 (3) Optimal seasons 49,572 177,390 $2,900,000 $ 8,180,000 with 20" size l i m i t both species, both f i s h e r i e s (4) Present seasons 50,000 149,000 $1,400,000 $12,000,000 20" sport chinook siz e l i m i t . T r o l l e f f o r t con-stant at 40% present maximum 80 p o l i t i c a l and economic pressures frcm both groups. The r e l a t i v e v a lue of s p o r t versus commercial f i s h e r i e s used i n t h i s t h e s i s i s l i k e l y a m a n i f e s t a t i o n of these pressures. By submiting t o these pressures the management has put foreward an o b j e c t i v e of maximizing present b e n e f i t s r a t h e r than c o n s e r v i n g f o r the f u t u r e . The focus of t h i s t h e s i s has been the within-season management of the Georgia S t r a i t f i s h e r y . A technigue f o r the development of seasonal management plans designed to meet annual g o a l s has been presented. The l o n g term g o a l s and ccnseguence of p o l i c i e s have not been the s u b j e c t of t h i s a n a l y s i s . The time i s r i g h t f o r a look at the f i s h e r y , i t s o b j e c t i v e s , and dynamics from a long time p e r s p e c t i v e , §±2x The Methodology The e v a l u a t i o n of p o l i c y design methods can be approached from s e v e r a l p o i n t s of view. The p r e d i c t i o n s and p o l i c i e s generated from any form of a n a l y s i s must be i n t u i t i v e l y c l e a r , f o r i f t h e r e i s no reasonable and i n t u i t i v e path by which one can reach s i o i l a r c o n c l u s i o n s , then g r e a t doubt should be placed upon the computed answer. Conversely, reasonable r e s u l t s frcm most technigues of p c l i c y design c o u l d , i n h i n d s i g h t , have been developed without the mathematical and computational t r a p p i n g s . The computer becomes necessary when the a r i t h m e t i c becomes too cumbersome f o r p e n c i l and paper. Furthermore, i t i s u n l i k e l y t h a t the human alone can f i n d the r i g h t combination and seguence o f s t e p s i n a f i n i t e p e r i o d of time t o a r r i v e a t a 81 correct and reasonable solution to a managementproblem. A promising approach to policy design and analysis i s simulation modeling. Modeling aliens the synthesis of data and known processes with the not so- well known and guessed at processes. The known and the uncertain are glued together to form a dynamic representation of the " r e a l " system. A laboratory world i s created into which one can make management interventions and observe predicted results. Alternate p o l i c i e s can be evaluated for 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 several ways to use a simulation model for policy design. One method involves the use of the simulation model to exhaustively search for best c o n t r o l p o l i c i e s (Peterman 1975, 1977). Others use more formal optimization techniques on simpler models and then apply the control p o l i c i e s to the larger models (Winkler 1 975, Boiling and Dantzig 1978). The method presented in t h i s thesis preserves a l l of the components of the simulation with the exception of a longer term perspective, and even long term e f f e c t s are p a r t i a l l y accounted for through the s p e c i f i c a t i o n of desired terminal stock sizes. A formal optimization technique i s used on the complex and detailed simulation model. This fact makes the described methodology a most powerful optimization procedure for dealing with large scale, complex, and multidimensional models. The Georgia S t r a i t problem was a good test bed for the procedure. The computation was very e f f i c i e n t , requiring l i t t l e more computing resources than the simulation model. The computational requirements are only proportional, not 82 g e o m e t r i c a l to the d i m e n s i o n a l i t y of the model l i k e methods such as dynamic programming (Walters 1975). I t i s hoped t h a t the d e s c r i b e d method w i l l prove u s e f u l on other resource management problems. 6 A3± O p t i m i z a t i o n and Resource Management The f i n a l area of d i s c u s s i o n r e l a t e s t o the p r o p r i e t y of o p t i m i z a t i o n i n resource management problems. Modeling of resource systems has been o f great help i n p o i n t i n g to u n c e r t a n t i e s and gaps i n cur understanding of behavior ( H o l l i n g S i a l i . 1 9 7 8 ) . Models, however, are only s i m p l i f i e d c h a r a c t e r i z a t i o n s of how we b e l i e v e the world o p e r a t e s . A great d e a l of c a u t i o n must be used when e x t r a p o l a t i n g the model t o the r e a l world. O p t i m i z a t i o n as an extension of the modeling process allows us to judge the importance of u n c e r t a i n t i e s and of ignorance with r e s p e c t t o the way i n which we value the world ( H a l t e r s and H i l b o r n 1 9 7 8 ). For example, the s e n s i t i v i t y of the o p t i m a l p o l i c y o f season c l o s u r e s t o u n c e r t a i n t i e s about harvest e f f i c i e n c y and f i s h abundance suggests t h a t i n c r e a s e d understanding of h a r v e s t i n g and pre-spawner abundance may i n c r e a s e the b e n e f i t s o f the Georgia S t r a i t salmon res o u r c e s . 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 i d e n t i f y u n c e r t a i n t i e s about how we v a l u e the outputs of complex systems. The o p t i m i z a t i o n of a simple model under a p a r t i c u l a r o b j e c t i v e shows us how we should behave i f we value the world i n a p a r t i c u l a r way. I f the o p t i m a l p o l i c y generated under one o b j e c t i v e f u n c t i o n i s unacceptable, then the o p t i m i z a t i o n 83 e x e r c i s e has demonstrated a d i s c r e p a n c y between the e x p l i c i t statement o f our value system and the way i n which we value the world. Such d i s c r e p a n c i e s can a r i s e through uncertainty, about the way b e n e f i t s flow from a r e s o u r c e or by an omission of some c r i t i c a l component of the value of the reso u r c e . For example, one major concern to the managers of the Georgia S t r a i t f i s h e r i e s i s the a l l o c a t i o n of c a t c h between the ccmmercial and the sport f i s h e r i e s . A c r i t i c a l assumption has been t h a t a f i s h caught by a sportsman i s always more v a l u a b l e than a f i s h caught by the ccmmercial f i s h e r y . Past p o l i c i e s have always suggested the complete e l i m i n a t i o n of the commercial f i s h e r y b e f o r e any c c n t r c l of the sportsman. Many people would argue, p a r t i c u l a r l y the fishermen's union, t h a t the s p o r t fishermen should accept some o f the burden of c o n s e r v a t i o n and that e l i m i n a t i o n of the commercial t r c l l e r i s unacceptable. Thus, a dis c r e p a n c y between the s t a t e d value system and a r e a l value system has been 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 may a l s o a r i s e from a d d i t i o n a l amenity or u t i l i t y , over and above the landed value o f the f i s h . These values may be a s s o c i a t e d with employment or t r a d i t i o n , and predominate the b e n e f i t s at s m a l l c a t c h l e v e l s . O p t i m i z a t i o n can be used i n an s i m i l a r way to models. Modeling may h e l p to c l e a r l y d e f i n e areas c f u n c e r t a i n t y about the behavior of a resource 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 about how the b e n e f i t s o f resource systems are p e r c e i v e d . LITERATURE CITED 84 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 o f 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 and T e c h n o l o g y Ser. B. 35(6) : 498-529. A l l e n , K.R. 1955. F a c t o r s a f f e c t i n g t h e 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 and T e c h n o l o g y , S e r . B. 36 ( 1) : 305-334. Anon. 1978. Working paper summary on b a c k g r o u n d i n f o r m a t i o n r e g a r d i n g t h e s t a t u s o f c h i n o o k and coho s t o c k s f o r s p o r t f i s h a d v i s o r y committee m e e t i n g June 23, 1978. Dept. Of F i s h e r i e s and E n v i r o n m e n t Canada. Anon. 1967 - 1975. Salmon s p o r t f i s h i n g c a t c h s t a t i s t i c s f o r t h e t i d a l w a t e r s of B r i t i s h C o l u m b i a . Dept. Of F i s h e r i e s and E n v i r o n m e n t Canada. A r g u e , A.W. 1976. P r e l i m i n a r y i n f o r m a t i o n f r o m 1973 and 1974 C a n a d i a n c h i n o o k and coho c a t c h s a m p l i n g and mark r e c o v e r y programs. F i s h and M a r i n e S e r v . , E n v i r o n m e n t Canada, T e c h n i c a l R e p o r t S e r i e s No. PACT-.76-9 . 32 pp. A r q u e , A.W., j . C o u r s l e y , and G.D. H a r r i s . 1977. P r e l i m i n a r y r e v i s i o n o f and Juan de Fu.ca S t r a i t t i d a l salmon s p o r t c a t c h s t a t i s t i c s 1972 t o 1976, based on head r e c o v e r y program d a t a . F i s h and M a r i n e S e r v . , E n v i r . Canada T e c h . Kept. S e r i e s No. PACT-77-16. Argue, A.W. and D.E. M a r s h a l l . 1976. S i z e and age o f c h i n o o k and coho salmon f o r s u b d i v i s i o n s o f t h e S t r a i t o f G e o r g i a t r o l l f i s h e r y 1 966. F i s h and Marine S e r v . , E n v i r . Canada, T e c h . Rept. S e r i e s No. PACT-76-18. 175 pp. B e d d i n g t o n , J.R. 1974. Aqe s t r u c t u r e , sex r a t i o , and p o p u l a t i o n d e n s i t y i n t h e h a r v e s t i n q of a n i m a l p o p u l a t i o n s . J . A p p l . E c o l . 11: 915-924. B e d d i n g t o n , J.R. and D.B. T a y l o r . 1973. O p t i m a l a g e - s p e c i f i c h a r v e s t i n q of a p o p u l a t i o n . B i o m e t r i c s 29:801-809. B e l l m a n , R. 1957. Dy.na.mic P r o g r a m m i n P r i n c e t o n U n i v e r s i t y P r e s s , P r i n c e t o n , New J e r s e y . 340 pp. . 85 Beverton, O.J.H. and S.J. Ho l t . 1967. On The Dynamics gf Ex£l2ii.2.d F i s h Populations.. U.K. Min. A g r i c . F i s h . , F i s h . Invest. Ser. 2, 19: 1-533. Bryan, R.C. 1974. The dimensions of a s a l t - w a t e r s p o r t f i s h i n q t r i p , o r what do people look f o r i n a f i s h i n q t r i p besides f i s h ? F i s h and Marine Serv,, Euvir. Canada Tech. Rept. S e r i e s No. PACT-74-1. C l a r k , C.W. 1976. Mathematical Bioecongmics.. The o p t i m a l Sl^nacjement of renewable resouucesj. John Wiley and Sons, New York, New York. 352 pp. C l a r k , C, W. , G. Edwards, and M. F r i e d l a n d e r . 1 973 . Beverton-l i o l t model of a commercial f i s h e r y : Optimal dynamics. J . F i s h . Res. Board Can. 30: 1629-1640. C l a r k , C.W. and G.R. Munro. 1976. Renewable resources and e x t i n c t i o n ; The consequences of i r r e v e r s i b i l i t y . Resource paper No. 2, Dept. Of Economics, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C. 21 pp. Gatto, M., S. R i n a l d i , and C. Walters. 1976. A predator-prey modal f o r d i s c r e t e time commercial f i s h e r i e s . Appl. Math. Model. 1: 67-76. Henry, K.A. 1978. Estimating n a t u r a l and f i s h i n q m o r t a l i t i e s of chinook salmon, Qnc^r hy, nchus tshawy_tscha*. In The Ocean, Based On Recoveries Of Marked F i s h . Fish B u l l . 76 { 1) : 45-51 . H i l b o r n , R. 1976. Optimal e x p l o i t a t i o n of m u l t i p l e s t o c k s by a common f i s h e r y : A new methodoloqy. J. F i s h . Res. Board Can. 33(1): 1-5. H i l b o r n , R. and R.M. Peterman. 1977. Chanqinq management o b j e c t i v e s . In: P a c i f i c Salmon x Management For Pegp.le.j_ D.V. E l l i s , ed. Western g e o g r a p h i c a l s e r i e s 13: 68-98. U n i v e r s i t y of V i c t o r i a Press, V i c t o r i a , B.C. 320 pp. H i l b o r n , R. and C.J. Walters. 1977. D i f f e r i n g goals of salmon management on the Skeena River. J. F i s h . Res. Board Can. 34 (1) : 64-72. H i l b o r n , R. and M. Ledbetter. 1978. An a n a l y s i s of the B r i t i s h Columbia purse s e i n e f l e e t : Dynamics of movement. Submitted to J . F i s h . Res. Board Can. H o l l i n g , C. S. , ed. 1978, Adaptive Environmental Assessment And Management.. John Wiley and Sons, New York. In press. l i o l l i n q , C S . and G. B. Dantziq. 1978. Determining optimal p o l i c i e s f o r ecosystems. Manage. S c i . In press. 86 Howard, R. 1960. DYnamic Programming. And. Markov P r o c e s s e s ^ The MIT P r e s s , Cambridge, Mass. I n t r i l i g a t o r , M.D. 1971. M a t h e m a t i c a l O p t i m i z a t i o n And Economic Theory.. P r e n t i c e - H a l l (Enqlewood C l i f f s , N.J.) J o h n s o n , F.C. 1975. A model f o r salmon f i s h e r y r e g u l a t o r y a n a l y s i s . S e c ond I n t e r i m R e p o r t . N a t i o n a l Bureau o f S t a n d a r d s , NBSIR 75-745. Kolmon, B. And W.F. T r e n c h . 1971. E l e m g n t a r y Hultiva_ri__.t__.le C a l c u l u s ^ , Academic P r e s s . New Y o r k . Keeney, R.L. 1977. A u t i l i t y f u n c t i o n f o r e x a m i n i n g p o l i c y a f f e c t i n g salmon on the Skeena R i v e r . J . F i s h . Res. B o a r d Can. 34(1) : 49-6 3. Keeney, R.L. and H. R a i f f a . 1976. D e c i s i o n s With Mu-lti-__>l-e O b j e c t i v e s j. P r e f e r e n c e s And V a l u e T r a d e o f f s . . J o h n W i l e y and Sons, New York. 56 9 pp. L a r k i n , P. A. 1 974. P l a y i t a g a i n Sam - an e s s a y on salmon enhancement. J . F i s h . Res. Board Can. 31 ( J ) : 1434-1456. L e d b e t t e r , M, and R. H i l b o r n . 1978. N u m e r i c a l o v e r v i e w o f . salmon run t i m i n g s . F i s h and M a r i n e Serv. E n v i r . Canada, T e c h n i c a l Rept. S e r . I n P r e s s . MacLeod, J.R, 1977, Enhancement t e c h n o l o g y : a p o s i t i v e s t a t e m e n t . I n P a c i f i c § a l m o n x Management __or Pe.g£l-__t D. V. E l l i s , ed. Western g e o g r a p h i c a l S e r i e s 13: 137-147. U n i v e r s i t y o f V i c t o r i a P r e s s , V i c t o r i a , B.C. 320 pp. Masse, W.D. and K . P e t e r s o n . 1977. E v a l u a t i o n of i n c r e m e n t a l r e c r e a t i o n a l b e n e f i t s from s a l m o n i d enhancement. M a n u s c r i p t , E c o n o m i c s B r a n c h o f Dept. Of F i s h e r i e s and E n v i r o n m e n t , Canada. Mathews, S.A. and G.S. Brown. 1970. Economic e v a l u a t i o n o f t h e 1967 s p o r t salmon f i s h e r y of W a s h i n g t o n . Wash. Dept. Of F i s h . , T e c h n i c a l Rept... No, 2. M i l n e , D.J. 1964. The c h i n o o k and coho salmon f i s h e r i e s c f B r i t i s h C o l u m b i a . B u l l . F i s h . Res. Board Can. No. 142. 46 pp. M i t c h e l l , S. 1977. H i n d s i q h t r e v i e w s : The B r i t i s h C o l u m b i a l i c e n s e program. I n : P a c i f i c Salmon^ Management For P e o p l e ^ D.V.. E l l i s , ed. Western g e o g r a p h i c a l s e r i e s .13: 148-186. U n i v e r s i t y o f V i c t o r i a P r e s s , V i c t o r i a , B.C. 320 pp. P a r k e r , R.R. 1960. C r i t i c a l s i z e and maximum y i e l d f o r c h i n o o k salmon i o n c o r j i ^ n c h u s tsha.wy_tschaj.__ J . F i s h . Res. Board Can. 17: 199-210. 87 P a u l i k , G.J., A.S. H o u r s t o n , and P.A. L a r k i n . 1967. E x p l o i t a t i o n o f m u l t i p l e s t o c k s by a common f i s h e r y . J . f i s h . Res. Board Can. 2 4 ( 12 ) : 2527-2537. Peterman, R.M. 1.975. New t e c h n i q u e s f o r p o l i c y e v a l u a t i o n i n e c o l o q i c a l s y s t e m s : methodoloqy f o r a c a s e s t u d y o f P a c i f i c salmon f i s h e r i e s . J . F i s h . Res. Board Can. 3 2 ) 1 1 ) : 2179-2188. Peterman, R.M. 1977. G r a p h i c a l e v a l u a t i o n c f e n v i r o n m e n t a l management o p t i o n s : examples from a f o r e s t - i n s e c t p e s t s y s t e m . E c o l . Model. 3: 133-148. Puterman, M.L. and S.L. B r u n e l l e . 1976. On t h e c o n v e r g e n c e o f p o l i c y i t e r a t i o n i n s t a t i o n a r y dynamic programming. F a c u l t y of Commerce, U n i v e r s i t y of B r i t i s h C o l u m b i a Workinq p a p e r No. 392. B i c k e r , W.E. 1940. R e l a t i o n o f " C a t c h p e r u n i t e f f o r t " t c abundance and r a t e o f e x p l o i t a t i o n . J . F i s h . Res. B o a r d Can. 5 :43-70. R i c k e r , W.E. 1954. S t o c k and r e c r u i t m e n t . J . F i s h . Res. E o a r d Can. 1 1 (5) : 559-623 . P i c k e r , W.E. 1 958. Handbook Of Commutations F o r 3i ° l 2 a i£sll S t a t i s t i c s Of. F i s h Po_pula t i on Sj. B u l l . F i s h . Res. B o a r d Can. No. 1 19. 300 pp. ~ R i c k e r , W.E. .1976. Review of t h e r a t e o f growth and m o r t a l i t y o f P a c i f i c salmon i n s a l t water and n o n c a t c h m o r t a l i t y c a u s e d by f i s h i n g . J . F i s h . Res. Board Can. 3 3 ( 7 ) : 1 483 -1524. S t e v e n s , J.B. 1966. R e c r e a t i o n a l b e n e f i t s from water p o l l u t i o n c o n t r o l . Water R e s o u r c e s R e s e a r c h 2 ( 2 ) : 167-182. W a l t e r s , C . J . 1969. A g e n e r a l i z e d computer s i m u l a t i o n model f o r f i s h p o p u l a t o n s t u d i e s . T r a n s . Amer. F i s h . Soc. 98: 505-512. W a l t e r s , C . J . 1971. Systems e c o l o q y : t h e s y s t e m s a p p r o a c h and m a t h e m a t i c a l models i n e c o l o g y . I n ; Fundamen.ta.ls o f E c o l o s i l i . E.P. Odum, ed . W. B, S o unders Co., T o r o n t o , O n t a r i o . W a l t e r s , C . J . 1975. O p t i m a l h a r v e s t s t r a t e g i e s f o r s a l m on i n r e l a t i o n t o e n v i r o n m e n t a l v a r i a b i l i t y and u n c e r t a i n p r o d u c t i o n p a r a m e t e r s . J . F i s h . Res. Board Can. 3 2 ( 1 0 ) : 1777-1785. W a l t e r s , C.J. and R. H i l b o r n . 1978. E c o l o q i c a l o p t i m i z a t i o n and a d a p t i v e management. Annu. Rev. E c o l . S y s t . 9. In p r e s s . 88 Wieqert, R.G. 1 975. Simulation models of ecosystems. Anim. Rev. Ecol. Syst. 6: 311-338. Winkler, C. 1975. An o p t i m i z a t i o n technique f o r the budworta f o r e s t - p e s t model. Int e r . Inst. For Appl. Syst. A n a l y s i s , Laxenburq, A u s t r i a , RM-75-11. 89 APPENDIX J The r e s u l t s and p r e d i c t i o n s from the l a r q e s i m u l a t i o n model are numerous and v a r i e d . The p r e s e n t a t i o n of the p r e d i c t i o n s has taken on two forms. Nomograms (Peter man, 1977) have been used e x t e n s i v e l y to allow managers to observe the e f f e c t s of various combinations of c o n t r o l a c t i o n s . The other form of p r e s e n t a t i o n has been to examine in d e t a i l a v a r i e t y of s p e c i f i c nanagement a c t i o n s i n a t a b u l a r form. Tables 4 through 7 i l l u s t r a t e model p r e d i c t i o n s under extreme assumptions of shaker m o r t a l i t y and sport e f f o r t response. Within the t a b l e s a v a r i e t y of a c t i o n s are pursued to t e s t the model under extreme management a c t i o n s and to determine the a f f e c t of some ad m i s s i b l e r e g u l a t i o n s other than s p o r t season c l o s u r e s . The t a b l e s present a set of i n d i c a t o r s which are thought to be important and of i n t e r e s t t o the people i n v o l v e d i n d e c i s i o n making. Escapement of spawners i s thought to be of utmost importance at present. One of the managers' o b j e c t i v e s was to f i n d a p o l i c y t h a t would double escapement l e v e l s , or at l e a s t r e t u r n them to h i s t o r i c a l l e v e l s . I n d i c a t o r s of the commercial f i s h e r y are c a t c h , e f f o r t , CPUE and a v a r i e t y of a t t r i b u t e s of monetary value. S i m i l a r i n d i c a t o r s are presented f o r the sport f i s h e r y . Shaker m o r t a l i t y and the average weight of chinook i n both f i s h e r i e s are l i s t e d . 'JO The f i r s t management a c t i o n on the t a b l e s r e p r e s e n t s the model p r e d i c t i o n s under c u r r e n t r e g u l a t i o n s . I t i s not intended to be an accurate account, but, to form the b a s i s from which to eval u a t e departures. The next three a c t i o n s represent extreme r e g u l a t i o n s (rows 1-3). Note that the o b j e c t i v e of doubled escapement would r e q u i r e complete e l i m i n a t i o n of the sport f i s h e r y . T h i s p r e d i c t i o n suggests that the o b j e c t i v e was unreasonable. A c t i o n s four and f i v e are i n c r e a s e d s i z e l i m i t s on commercially caught salmon. A c t i o n s i x i s meant to emulate a r e s t r i c t i o n of movement of commercial t r o l l e r s i n s i d e and o u t s i d e Vancouver I s l a n d . I t i s assumed that f o r t y percent of the observed maximum e f f o r t i s from boats which would choose to operate e x c l u s i v e l y i n Georqia S t r a i t and that the other s i x t y percent would f i s h outside and be excluded from the i n s i d e f i s h e r y . Actions eiqht throuqh ten are i n c r e a s e s i n the s i z e l i m i t of sport cauqht f i s h . A c t i o n eleven i s an i n c r e a s e i n the s i z e l i m i t of chinook. f o r part of the season. A c t i o n s twelve throuqh f o u r t e e n are combinations of the other a c t i o n s . F i n a l l y a c t i o n f i f t e e n s imulates a one chinook per day baq l i m i t i n the sport f i s h e r y . T a b l e 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 a n d S p o r t E f f o r t R e s p o n s e . ZKOICATCM r c U l T r o l l •mortality t r o l l " o n a U ty »por t MA;JICEMN"T ACTIONS C JZ fc C K c v u a E w 5" *S J* « I- -* a w o o - H O c o n e J= o o -c o O i - <-> — 0 Ul U t-.s _4 u _a ^ u v > • " o >- w r u - o — c • o a i. c - o U s JZ o = w c *" c — o i/> i. k- i. — w i > s ^ > * i — u-« <- -1 " C 0 « - =3 O -J r -j ^ -•c - J >•- . v i J< c U U > u u «. <~ _ _ — _ c "1 o — v. - u i; ~- " 1 a c 0 t! " " c ^ c ^ ' ^ S " H « t-» -3 O V. tr. S. < r x l O 3 *10 3 x l O 3 x l O 3 x l O 3 x l O 3 ;10> , 1 0 5 i l O 1 x l O 5 ~ - ^ JTJ 571 T lX TTJ7 Jot7 - 5 . 6 7 9 . 1.11 13 .0 956 . 5 8 9 . 7.15 5.4,5 (1) Ko .por t i"l« her , 7 3 . 3 2 1 . « 5 0 . ~ ' 2 9 4 , . 156. 2 2 . _ 2 1 . 14 . fi 2 11. 0 . 0 . 0 . 0 . 1. 7d 0 . 0 2 3 1 . 121 . 8. 26 6 . m (2) ho [ t o l l f l a l h . r r 12. 1 - 2 . • 0 . 0 . 0 . o. 1 0 , .0 0 . .0 0 . 9 1 U . . 0 5 . 5 1 0 . 7 C 7 . 1 .22 14.. 3 664.. 556. C O 6 . 30 (3) No f p o r t ( U ! Ko t r o l l f i t ] n .ry " r r . "39„7 o."~ " ' 0 . b.' C-- 0 . " o . 0 ' 0 . o~ " C. 0 . 0 . ' 0 . 0 . 2 . 20 ' 0 . 0 0 . 0 . 0 . 0 7 . 6 3 ( ' ) T r o l l 24," ch: [nook 39 . " 1 3 0 . 171 . I S . B 6 . 1 7 . 1 0 . - 2 . .0 1. 9 113. 7(1 41. 3 3 1 . S 5 2 . 6 9 3 . 1. 13 1 3 . 3 1 126. 6 5 2 . 1 0 . 90 5 . 6 S (S) T r o l l 26" th [nook »o7~ ~ 1 2 « 7 ~ 10 7 . " 6 3 . " B « ; 1 6~."~ 9. " t . .7 1. 6 " 105. 3 9 5 . 3 0 0 . 4  55 . 6 9 6 . 1 . 1 <4 * 11 . « use. 7 0 1 . 1 2 . 3 5 ' 5 .77 (6) T r o l l e f fo r t • t 4 0 1 of pr. c o m t . n t " 2 . 13'.. 1 3 1 . (114. « 7 . 9 . 1 <4 . 1. 2 1. 3 13« . 83 2 . 3S44. 4.79. 7 1 » . 1. 17 13 .6 9 1 0 . 5 7 3 . 7 . 6 7 5 . 6 9 (I) T r o l l J . .n . 1 J u l , 1 Chinook _ « J . - " 126." 178 . " 6 5 . 9 1. 13 . " 1 U . 1. 14 1. S 12 1 . B 0 5 . 351 . ".53. 7 0 3 . 1. 114 1 3 . 5 9 1 7 . 57 1. 4. 65 ! . « . ; (8) Sport 20" both i p t - e l c . (9) Sp.>rt CO" cMnook (10) Sport 21" el.lnook < 1 1 ) Sport 2i" Chinook Oct 1 to June 1 (12) Sport 20" chinook T r o l l 26" Chinook ( 1 3 ) S ^ o r t 70" C h i n o o k T r o l l *an« 6 ( 1 4 ) Sport 70" chinook T r o l l i»oe » • 7 •46. I H . 321. 2C6. " 5 - u - J - 1 33 2. 1 )5. 159. 114.5. 0. 75 e . . 1 0 , 7 . c 5 6 , j^J" .1. -««. 2«2. is:.- iro. n . 15 . 2.5 2.6 1 )6. 575.- 16 .. 611. 512. 0.97 , 1 . 1 HIS. 623. l.i , 5 3 - ^ i T 271 2 . 8 K ) . . 4 ) 2 . 101. 3 ) 2 . 5 . 9 . 0 . 9 0 1 0 . T U T U . S . 9 0 6 . 7 .65 1 1 . 5 3 J 7 . 133 . 2 7 3 . 176. ! 7 . I S . 14,. } . , 2 . 5 n j 6 7 7 _ 2 « 1. 1 4 3 5 . 64.2. 1. 05 12 . 3 1 105. 66 2. 7 . ; 5 6 . 3 3 ^ ^ ^ ' • ' " 8 " " 2 " " ° - ' - 0 0 " - 7 9 6 7 . 12.52 9 . 03 • 5 C 7 7 - 1 4 , 9 . — 1 . 3 : - • « , . - — 9 . - - 1 5 . 1.3 1. - 150. « , S J . 2 0 * . 6 3 0 . 1. 01 1 2 . 0 . . . 1 . 832 . 7 .83 " ' • ' , 7 - , 0 ' - 1 4 - 1.6 1 . 7 1 34.. 6 2 3 . 2 0 2 . 4,77. 6757 lTo i 1 1 . 9 14.76. 8 2 5 . 7 .62 9 . 2 2 04.7 b«i - l l . l t - 3 7 . 138". 2 6 8 . 172. " " 5 7 . " ' 9. 1 44. 2 . . 2 . 5 130. 6 « 8 . 22 1. 1 ,26. 6 3 0 . 1.03 12 . 0 124,6. 7344. 7 . 5 5 5 . 4 0 no • ~ 0 0 0 >- 0 I 5 J i J I l l s i I ! r l I 1 _ I' c t •: I j i I : 2' i ! i ! I 'M I I I I - J I • i 2 Chinook. Escapement Coho Escapement T o t a l T r o l l C a t ch Chinook. T r o l l C a t ch Coho T r o l l C a t ch T r o l l E f f o r t T r o l l Net V * l u T r o l l Land Value T r o l l Va lue Boat-Day T o t a l Sport Ca tch Chinook Sport Ca tch Coho Sport Ca tch Sport E f f o r t Sport Cl'PE Sport Va lue CMnuok Sl.nLcr M o r i A l l t y Coho Sh. i l r r r l o r i a l It y Avi iap.c Vclr.dt T r o l l Chlncxk Avcr«r . ' - ^V(|;ht Sport Chinook. tr T I •-I c h ' H 3 - J in o D J • ' c r a -re H 1 3 I-I ft) -< r t D . S r r — CJ (/> n , - t a . lO > H -r- l M O <r. w 3 •c •» c c 3 n U J T J t r . ,-t o r r r i H O r=j O TJ ,v t"h M Ui If C n tr n re o (C (1 3 r t O 'JO U J IO m CO o o r n r - l n CU t l J 3 O •pr m H -3 IU r - l CU ai r - l o it. ( p CO • B 3 r t O n M l - l CU r - l ' CO cu o r l I-. ill H- >. CO n m H --< r - l 3 C l - 1 - 3 M a n a. r - l r t r t r t (-•• s r D> O . t CO r ) •< O O Q . r - l I-.- ( 0 r t t i Z6 T a b l e 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 K o d e l U n d e r 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 t h e T r o l l F i s h e r y , 8 0 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 a n d F i x e d S p c r t E f f o r t P a t t e r n . Coors«rcial T r o l l •KAKACDtZXT ACTIONS (0) Fraacnt <1) Ho «po r t f l i h t r y (2) Ko t r o l l f i (3) Ko » ? o r t f l i h t r y Ko t r o l l (A) T r o l l 24" ch (5) T r o l l » M ch (6) T r o l l e f fo r t at 401 (7) T r o l l J Ju ly 1 coho (9) Sport 20" both *?t<:i** (9) Sport 20" chinook (10) Sport 24" chinook (in sport :< Korea 11 ty V * i g h n (12) Sport 20" chinook T r o l l 26" chinook Amy bag-Halt l M i 11 \\ h \\ 11 i i i, f, ii ti i i i i i 1 I ! Ii I 1 i i I I i l SI I i ! J « I O ' x l O 3 x i o 3 »io3 x l O 3 x l O 3 0 5 x l O 3 x l O 3 x l O 3 x l 0 S x l O 3 x l O 3 3 3 . 122 . 2 36 . 15*7 ~ ' ~ ~ y ~ 2 ^ ^ « 6°- iTTJ iVTi sTT . j . . 7 . 3 ] 5.3,, ""71 . 32T . 3 5 0 . 2 0 1 . " " 1 5 6 . ' 2 2 . • 1 1.6 2 11. ' 5 » . ils. b"i 57 oT ° - ' . ' ' » 0 . 0 201 . 1 2 1 . 8.26 6 . 1 . ~ ^° °-° °^  ^ 356. so.. TTV. i n . n m r r r r r r — T o — m — 1337 "3 S i . 0. 2.20 0.0 0. 0. 0.0 7.6o" -^---.--!:-A'i_'.'i.J.ti.J.0:_.^11' "2- 6°5- "7- I9- 7"- '•" «».'io.» s.6» '• " "".''-6 " l 0 5 . _ 8 1 3 . " 3 t « . 069. 7 2 9 . 1.12 13 . 1 1 1 63. 7 0 3 . 1 2 . 33 5 . 1 , " 6 0 . " "123 . " 135; ( 3 . -------:..-l'i..":.._°.6: 1 l'_'1__'1_1*- 8'°- "a5- 729- '-'s 5"" s.,. 3 2 . " ' 12 l ' . "~ 176i E5.' 9 2 . 13 . 13. " 1.3 1.5 120. 620 . 353. 3 6 5 . 7 2 9 . 1.12 13 .1 5 2 3 . 5 7 6 . ' 7 .66 5 .91 .~J.-i.AlliJ.tl:..2::...l"~ 2-* aaa- ie]- 2"- 7"- <>•" ».i i^. .m. ^ ".v ' 3 0 . 122 ." 2 5 0 . " ' 16 ' 9 ' n > 2 - 2 2 - i " 3 . ' 3 9. 18 3. 366." 7 2 9 . 0 . 8 9 10 .1 1 7 K . 9 5 2 . "7. J 1 J . . : . . " . ; _ J ! ! ; . . . : ! _ J : ; . J ^ _ J - J ;-* '"• " 2- '"• A T T- »»" »»!i"'""v~,.H 3o". 1 2 2 . " ' 2 5 0 . 160. '""90. " l 9 . " 13 . 2 . 2 2 .3 1 22. 7 2 3 . 258. 066. 7 2 9 . 0 . 5 9 13 .1 1290. 7 5 8 . '7.55 6 .23 . - I - — - L - ' " : - . " : _ J _ 1 : _ _ . l . . _ ' , _ '1 ' - j , ' 0 8 - ; " - ' " • 7 2 9 - j - i 3 -^i~T^IZ7~TII7"7I.«o 6 . 3 3 / ' • ' " • ' - 3 1-3 139. 7 0 3 . 217. 086." 7 2 9 . 0. 97 10. 1 1 6 5 . . 5 2 3 . 7 . 72 8 .99 " 3 . 1 1 3 . "133". ""ee. l l - l l : . . l l _ _ . ! l _ . l 11. ' i _ ' iL 7771.7.7" ,7 .."TI-r-Trr 7iJ7772!I:~!"777J":JJ!il_ l^: ! 1 - 2 - 2 2 - 1 ,J1- 70"- 2 M- 729- °-" '77,37."7,7"777~7,7 I s i ; i .-i -- i -i • i i I O I I ' l l ! i I I I u l I 1 I I l» t I I O I c I - I I -i r "1 ! A M t 1 i s i i i ! I 3 ; S Chinook. Fscapeucnc Coho Escapcaent T o t a l T t o l l Ca tch Chinook T r o l l Ca tch Coho T r o l l Catch T r o l l E f f o r t T r o l l CUPE T r o l l Net Va lue T r o l l U n d Value T r o l l Value Boat-Day T o t a l Sport C a i c h Chinook Sport Ca t ch Coho Sport Ca tch Sport F.ffort Spnrt CUl'F. Sport Value Chhu-ofc r.hakrr Mortal 11y Coho Sh.iker H n r l a l U y Avi-r.ir-.r V.*lr,|,e T r o l l Chinook Avcrnpi- Uelf.l't Sport Chinook **1 CO n tr h-rt> i a CZu •• • ll> a> W 0 3 £ r r t c ID ^ • H -r i M O - < I n % c W X (0 U J T ! r r . a . o !-t M O Ul n a O ~c (tl o M r n r t l - l O r t i i ) O <l 3 i - t i r n f t Cl U J ID h r , t / l o O O tr n n Cu •XI J3 r t ? c (D p -O n DJ n ' O i ;B LO r t g r t r r o i t - I-I l l ) ' i in M r t in p -i~ tr r t • t—' m h ' ; v LO 1+ t) '-< 1-1 C H 3 1—i 3 O CJ M r t r r r r I-I-3" PJ Cl ( L M 3 M -00 rt rt n •< o O • I M - m r t n r t (T) ^6 APPENDIX 2 The Lagrange system in one dimension: Max z R(y u ) + G Y, U k-1 K • k N + l Subject to the constraint of the state dynamics equation: y k + l = + F ( y k ' u k } Maximi ze the "Lagrangion" with respect to Y(y^:k=l'.. .N+1) and U(uk:k=l...N+1). N Max L = E [R(Y k»u k) - Z k ( y k + 1 - y k - F{y k, U | <})] Y 5 U k_1 Maximize over Y: dL dy k = d R / d y k + Z k + Z k d p / d y k " Zk-1 dG/dy N + 1 - Z N Set equal to zero: Zk-1 = Z k + d R / d y k + Z k d F / d y k ZM = dG/dyM . N JN+1 Maximize over U: R and F are assumed l inear in U therefore u, •= U ,, . or U • (0) k max(l) mm v ' 96 The Lagrangion system has three sets of simultaneous equations: y k + l - h + F(V uk> . . k = K - ' N y-, = y * Z k - 1 = Z k + dR/dyk + Z k dF/dy k . . k = 1 . . .N Z N = dG/dy N + 1 = Umax or Umin k = 1...N 

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