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Decision theory as a tool in sockeye salmon management of the Babine system Sheehan, Stephen W. 1976

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DECISION THEORY AS A TOOL IN SOCKEYE SALMON MANAGEMENT OF THE BABINE SYSTEM by STEPHEN W. SHEEHAN B.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of I n t e r d i s c i p l i n a r y Studies ( C i v i l Engineering and Commerce) We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1976 © Stephen W. Sheehan, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r ee t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y pu rpo se s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t ten pe rm i ss ion . Department o f I n t e r d i s c i p l i n a r y The U n i v e r s i t y o f B r i t i s h Co l umb i a 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date August 1, 1976 ABSTRACT A procedure f o r applying the concepts of Bayesian d e c i s i o n theory to salmon management i s presented and i l l u s t r a t e d w i t h an a p p l i -c a t i o n to the Babine system sockeye salmon f i s h e r y i n B r i t i s h Columbia. The p a r t i c u l a r d e c i s i o n considered i s the recommended escapement to aim f o r i n a given year. The Babine f i s h e r y i s described and the d e c i s i o n theory concepts are o u t l i n e d . The procedure involves d e f i n i n g the r e l a t i o n s h i p between the recommended spawning escapement and the number of adults r e t u r n i n g i n the c y c l e year i n p r o b a b i l i s t i c terms; d e f i n i n g the u t i l i t y , that i s the r e l a t i v e d e s i r a b i l i t y of various s i z e s of catch; and computing the t o t a l expected u t i l i t y of both the catch i n the current year and the spawning returns a s s o c i a t e d w i t h a l t e r n a t i v e values of the recommended escapement. The escapement w i t h the maximum expected u t i l i t y should be chosen and recommended. i i i TABLE OF CONTENST Page ABSTRACT • i i TABLE OF CONTENTS 1 1 1 LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGMENTS v i i CHAPTER 1 INTRODUCTION . . . . 1 2 THE BABINE LAKE AND RIVER SYSTEM 4 3 USE OF DECISION THEORY 11 R e l a t i o n s h i p Between Escapement and Number of Adults Returning i n the Next Cycle 12 4 COMPONENT RELATIONSHIPS OF THE SOCKEYE SALMON LIFE CYCLE 16 R e l a t i o n s h i p Between the Chosen Escapement and the A c t u a l Escapement 16 R e l a t i o n s h i p Between the A c t u a l Escapement and the P o t e n t i a l Egg De p o s i t i o n 18 The R e l a t i o n s h i p Between the P o t e n t i a l Egg De p o s i t i o n and the Number of Fry 21 R e l a t i o n s h i p Between the Number of Fry and the Number of Smolts 25 R e l a t i o n s h i p Between the Numbers of Smolts and Adults . . 30 Combining the Component R e l a t i o n s h i p s 33 i v Page CHAPTER 5 UTILITY 35 I n t r o d u c t i o n 35 U t i l i t y of the Current Year's Catch 35 Expected U t i l i t y of the Escapement 38 The T o t a l Expected U t i l i t y of the Current Year's Run . . 38 Computing the Recommended Escapement w i t h the Maximum To t a l Expected U t i l i t y 39 6 DISCUSSION 41 7 FUTURE DEVELOPMENT 43 BIBLIOGRAPHY 44 V LIST OF TABLES Page TABLE 2.1 Babine Lake T o t a l Sockeye Production 1949 - 67 . 10 (Fence Counts - Indian Catch) 3.1 Babine System Sockeye Salmon F i s h e r , P r o b a b i l i t y R e l a t i o n s h i p Between Chosen Escapement and Number of Returning Adults 15 v i LIST OF FIGURES Page FIGURE 2.1 Skeena and Babine River Systems Showing Locations of Major Spawning Streams on Babine Lake 5 2.2 Location of the Babine River Counting Fence on the Lower Babine River. Nilkitkwa Lake and Upper Babine River l i e between the fence and Babine Lake . . . . 6 2.3 Fulton Spawning Channel No. 1 7 2.4 Fulton River with inset of Babine Lake 8 3.1 Recommended Escapement vs Number of Returning Adults . 13 4.1 Relationship Between the Recommended Escapement and the Actual Escapement 17 4.2 Relationship Between the Actual Escapement and the Potential Egg Deposition 19 4.3 Relationship Between the Potential Egg Deposition and the Number of Fry 22 4.4 Relationship Between the Number of Fry and the Number of Smolts 26 4.5 Relationship Between the Numbers of Smolts and Adults . 31 5.1 Catch - Number of Sockeye Salmon vs U t i l i t y Points . . 37 5.2 Total Expected U t i l i t y vs Recommended Escapement . . 40 v i i ACKNOWLEDGMENTS The author i s very g r a t e f u l to h i s supervisor, P r o f e s s o r Samuel 0. R u s s e l l , f o r h i s constant encouragement and a v a i l a b l e guidance i n the development of t h i s t h e s i s . S p e c i a l thanks are extended to members of the P a c i f i c B i o l o g i c a l S t a t i o n , e s p e c i a l l y Mr. Howard Smith, Mr. Fred W i t h l e r , and Dr. Don A l d e r d i c e who sup p l i e d that data and r e -viewed the a n a l y s i s . The author would a l s o l i k e to thank h i s colleague, Mr. Gunther Brox, f o r h i s comments and a s s i s t a n c e ; Mr. Richard Higgins and Mr. Robert H. Owen f o r a s s i s t a n c e i n developing the computer program; Mr. Richard Brun who prepared the drawings; and Miss Kathie Cook who typed t h i s t h e s i s . CHAPTER 1 INTRODUCTION Fi s h e r y management i s d i f f i c u l t under almost any circumstances and p a r t i c u l a r l y so i n the case of sockeye salmon which spend part of t h e i r l i f e c y c l e i n f r e s h water and part i n s a l t water. Some components of the sockeye salmon l i f e c y c l e are r e l a t i v e l y w e l l understood w h i l e on others- there i s only sketchy information; f o r example, what happens to them i n the ocean and what f a c t o r s a f f e c t t h e i r s u r v i v a l there are almost completely unknown. N a t u r a l c o n d i t i o n s such as r i v e r flows, water tempera-t u r e s , sediment load vary from year to year and are very d i f f i c u l t to p r e d i c t . Then there are s o c i a l problems, etc. On top of t h i s the whole f i e l d i s so v a r i e d and complex i t i s not p o s s i b l e f o r one person to thoroughly understand a l l aspects of i t . Consequently, the a v a i l a b l e knowledge and e x p e r t i s e i s d i s t r i b u t e d among d i f f e r e n t experts who are expert on various components of the sockeye salmon l i f e c y c l e . Management dec i s i o n s f a l l i n t o two c a t e g o r i e s , those concerned w i t h day to day operations and those concerned w i t h long term e f f e c t s , planning d e c i s i o n s which might be c a l l e d enhancement d e c i s i o n s . The main operating d e c i s i o n i s the ta r g e t escapement, the number of sockeye salmon that should be allowed to escape f o r spawning purposes each year. In t h i s t h e s i s a procedure i s developed f o r making t h i s operating d e c i s i o n ; that i s , f o r d e c i d i n g on the optimal, escapement i n the l i g h t of a l l the a v a i l a b l e knowledge, us i n g the sockeye salmon run of the Babine R i v e r and Lake system as an example. The procedure i s based on the concepts of Bayesian d e c i s i o n theory, a set of concepts which a l l o w 2 u n c e r t a i n t y and informed o p i n i o n to be taken i n t o account i n a r r i v i n g at the optimal d e c i s i o n . The sockeye salmon l i f e c y c l e can be r e a d i l y d i v i d e d i n t o f i v e components or stages. In t h i s t h e s i s the r e l a t i o n s h i p between the numbers at the beginning and at the end of each stage are defined i n terms of p r o b a b i l i t y bands, the widths of the bands r e f l e c t i n g the degree of un-c e r t a i n t y . The o v e r a l l r e l a t i o n s h i p between escapement and the s i z e of the r e s u l t i n g r e t u r n run i s derived by converting the p r o b a b i l i t y bands i n t o p r o b a b i l i t y matrices and m u l t i p l y i n g the matrices together i n order to o b t a i n an o v e r a l l p r o b a b i l i t y matrix. In order to evaluate p o s s i b l e target escapements usi n g d e c i s i o n theory s e v e r a l chosen target escapements are s e l e c t e d and the t o t a l expected u t i l i t y i s c a l c u l a t e d f o r each s e l e c t i o n . The expected u t i l i t y i s the product of the p r o b a b i l i t i e s of the various p o s s i b l e outcomes and the r e l a t i v e d e s i r a b i l i t i e s of the outcomes expressed i n u t i l i t y u n i t s . The best d e c i s i o n i s that f o r which the t o t a l expected u t i l i t y i s a maximum. Enhancement d e c i s i o n s such as developing spawning channels, f i s h -ways, and in c u b a t i o n boxes could be evaluated i n terms of t h e i r e f f e c t on the r e l a t i o n s h i p that i s a f f e c t e d by the s p e c i f i c enhancement p r o j e c t and from t h i s the expected increase i n production could be computed, using e s s e n t i a l l y the same procedure. The steps i n t h i s procedure are explained. The Babine Lake and R i v e r System which provides the spawning grounds f o r 907o of the sockeye salmon of the Skeena R i v e r System i s described i n Chapter 2. In Chapter 3 Bayesian d e c i s i o n theory i s ex-p l a i n e d w h i l e the f i v e stages of the l i f e c y c l e of the sockeye salmon 3 are o u t l i n e d i n Chapter 4. U t i l i t y and the computation to determine the optimal d e c i s i o n are described i n Chapter 5 and a d i s c u s s i o n of the procedure and the r e s u l t s are presented i n Chapter 6. 4 CHAPTER 2 THE BABINE LAKE AND RIVER SYSTEM The Babine Lake and R i v e r System which i s l o c a t e d i n c e n t r a l B r i t i s h Columbia east of P r i n c e Rupert ( F i g . 2.1), includes t h i r t e e n t r i b u t a r y streams as w e l l as Babine Lake, N i l k i t k w a Lake, and s e v e r a l smaller lakes. The system produces 907o of the sockeye salmon i n the Skeena R i v e r and there are a l s o pink, chum, cohoe, and chinook salmon runs. Babine Lake drains by way of the Upper Babine R i v e r i n t o N i l k i t k w a Lake which i n t u r n i s drained by the Lower Babine R i v e r . A counting fence l o c a t e d on Lower Babine R i v e r has been operated s i n c e 1945. Counts of a d u l t s and smolts have been made each year s i n c e then, except f o r 1948 and 1964 when there were very high r i v e r f l o w s , ( F i g . 2.2). Johnson (1956-58, 1961, 1965) e s t a b l i s h e d that Babine Lake and N i l k i t k w a Lake were u n d e r u t i l i z e d as a nursery. Thus, the c o n s t r u c t i o n of the f i s h e r y channels was undertaken i n order to increase the production of young f r y . Spawning channels have been constructed at F u l t o n R i v e r and at Pinkut Creek as part of the 8 m i l l i o n d o l l a r Babine Development P r o j e c t (Jordan and Smith, 1972).,(Figs. 2.3 and 2.4). For t h i s study the a n a l y s i s of the Skeena R i v e r sockeye has been r e s t r i c t e d to the Babine Lake and R i v e r System. The counting fence i s considered the s t a r t of the system. Since the c o n s t r u c t i o n of the spawning channels has been completed r e c e n t l y , i t was decided to analyze two sets of data ( i e . before the spawning channels were introduced and upon completion of the spawning Fig,2.L SKEENA AND BABINE RIVER SYSTEM. 6 Fig.2.2 LOCATION OF THE BABINE R. COUNTING FENCE 7 LENGTH '4900 FEET Fig. 2.3 SKETCH OF FULTON SPAWNING CHANNEL NO. I. Fig 2.4 FULTON RIVER WITH IN SET OF BAB I N E LAKE. 00 9 channels). The r e s u l t s i n t h i s t h e s i s only p e r t a i n to the system before the spawning development was completed. The t o t a l sockeye salmon production from the escapements f o r the years 1949 through to 1967 v a r i e d from 2,228,000 (1967) to 194,000 (1951) Table 2.1. A s l i d e which blocked the r i v e r i n 1951 accounts f o r the low escapement f i g u r e i n that year. The t o t a l production f i g u r e f o r each escapement includes a l l the 3, 4, and 5 year o l d sockeye as o u t l i n e d i n Table 2.1. However, to s i m p l i f y the a n a l y s i s and p r e s e n t a t i o n of r e s u l t s i t has been assumed f o r the present study that a l l sockeye r e t u r n a f t e r 4 years. TABLE 2.1 Babine Lake Sockeye Production 1949 - 67 ( A l l numbers i n thousands) Year Spawning Escapement Adul t Returns Recommended A c t u a l 3's 4's , 5's T o t a l 1949 461 28 759 604 1,391 1950 364 28 430 171 629 1951 141 10 61 123 194 1952 349 31 421 216 668 1953 687 18 524 825 1,367 1954 494 50 654 671 1,375 1955 71 31 252 127 410 1956 355 32 307 233 572 1957 433 49 1,569 610 2,228 1958 812 28 418 357 803 1959 783 46 381 1,125 1,552 1960 263 173 426 348 947 1961 500 942 60 615 437 1,112 1962 548 64 497 801 1,362 1963 810 588 182 809 1,121 2,112 1964 630 828 29 179 437 645 1965 810 580 53 704 361 1,118 1966 650 389 154 809 665 1,628 1967 900 608 166 954 1,056 2,176 11 CHAPTER 3 USE OF DECISION THEORY In d e c i s i o n making under u n c e r t a i n t y i t i s necessary to consider both the p r o b a b i l i t i e s of the various p o s s i b l e outcomes and t h e i r r e l a t i v e d e s i r a b i l i t i e s . D e c i s i o n theory allows p r o b a b i l i t i e s and out-comes to be considered s e p a r a t e l y and provides a method f o r combining the two. Bayesian d e c i s i o n theory allows the use of s u b j e c t i v e proba-b i l i t y estimates and hence, i s most s u i t a b l e when expert o p i n i o n i s a v a i l a b l e . The concepts of d e c i s i o n theory are pr e s c r i b e d i n numerous text s and papers (de N e u f v i l l e and S t a f f o r d , 1972; H a l t e r and Dean, 1973; Hershman, 1974) and are not repeated here. I n order t o apply d e c i s i o n theory to sockeye salmon management of the Babine Lake and R i v e r System i t i s necessary to consider not only the current year's catch but a l s o future catches from the all o w a b l e escape-ment. The f o l l o w i n g s p e c i f i c steps are involved. 1) D e f i n i n g the p r o b a b i l i t i e s of the s i z e of runs of r e t u r n i n g a d u l t s that could r e s u l t from various a l l o w a b l e escapements i n the current year. 2) D e f i n i n g the r e l a t i o n s h i p between the catch of r e t u r n i n g a d u l t s i n the current year and i t s u t i l i t y . 3) Computing the discounted expected u t i l i t y of various a l l o w a b l e escapements i n the current year on the basis of numbers of ad u l t s r e t u r n -i n g i n the next c y c l e . The discounted expected u t i l i t y i s the r e t u r n of ad u l t sockeye salmon that i s r e a l i z e d four years i n t o the future from the present escapement. 4) D e f i n i n g the p r o b a b i l i t i e s of various numbers of r e t u r n i n g a d u l t s i n the current years. 5) Computing the escapement w i t h the maximum t o t a l expected u t i l i t y . The d e c i s i o n of recommending an escapement i s p r i m a r i l y made as a r e s u l t of assessing u n c e r t a i n t y adequately. For the purpose of a n a l y s i s , u n c e r t a i n t y i s defined as u n c e r t a i n t y r e l a t e d to the r e t u r n i n g sockeye salmon run, when a fo r e c a s t i s given and the r e t u r n of sockeye salmon four years l a t e r from a given recomm-ended escapement. In the f o l l o w i n g s e c t i o n the procedure used to express the r e l a t i o n s h i p between the escapement and the number of ad u l t s r e t u r n i n g i n the next c y c l e (step 1) i n terms of a p r o b a b i l i t y matrix i s o u t l i n e d . R e l a t i o n s h i p Between Escapement and Number of Adults Returning i n the Next Cycle-Fig. 3.1 The r e l a t i o n s h i p between the target escapement and the number of adu l t s r e t u r n i n g i n the next c y c l e i s derived by o b t a i n i n g i n f o r m a t i o n on various components of the salmon l i f e c y c l e and combining these i n t o an o v e r a l l r e l a t i o n s h i p . Steps i n the c y c l e were defined as; 1) Recommended escapement, the number of sockeye salmon that the Management Committee would l i k e to see enter the Babine System - the ba s i c d e c i s i o n to be made. 2) A c t u a l escapement, the number of spawning salmon that pass the counting fence. 3) Egg d e p o s i t i o n i n the system - i n channels, r i v e r s , and a l s o 4 0 0 0 200 4 0 0 600 8 0 0 1000 Recommended Escapement x |0; LEGEND ; D 6 5 Recommended Escapement in 1965 O 6 1 Actual Escapement in 1961 F I G . 3 . i RELATIONSHIP BETWEEN RECOMMENDED ESCAPEMENT AND NO. OF RETURNING ADULTS the eggs deposited by lake spawners. 4) Number of f r y , the young f i n g e r l i n g s that hatch and enter the Babine and N i l k i t k w a Lakes. 5) Number of smolts, the young salmon that pass the counting fence on t h e i r way to sea. 6) Number of r e t u r n i n g a d u l t s , the ad u l t s that r e t u r n at the end of the c y c l e . Some are caught and some r e t u r n to spawn. The development of the component r e l a t i o n s h i p s between the above steps which are defined as p r o b a b i l i t y bands, i s discussed i n Chapter 4. The other steps o u t l i n e d above are described i n subsequent chapters. TABLE 3.1 Babine System Sockeye Salmon Fi s h e r y , P r o b a b i l i t y R e l a t i o n s h i p Between Chosen Escapement and Number of Returning A d u l t s P r o b a b i l i t i e s Chosen Escapement i n thousands 400 450 500 550 600 650 700 750 800 850 900 950 Returning Adults i n thousands 150 0, ,070 0, ,027 0. 009 0.003 0.001 - - - -150 - 450 0. .082 0. ,038 0. 018 0.009 0.005 0. 003 0. ,002 0.001 0.001 0. 001 - -450 - 750 0. .336 0, .299 0. 229 0.160 0.106 0. 068 0. .044 0.029 0.021 0. 016 0.013 0.010 750 - 1050 0. .352 0, ,330 0. 274 0.214 0.163 0. 123 0. 095 0.075 0.063 0. 055 0.048 0.044 1050 - 1350 0. ,074 0, ,131 0. 184 0.218 0.231 0. 225 0. 209 0.192 0.177 0. 164 0.152 0.143 1350 - 1650 0. ,063 0. ,123 0. 183 0.'228 0.251 0. 256 0. 250 0.239 0.229 0. 219 0.210 0.202 1650 - 1950 0. ,018 0. ,039 0. 066 0.095 0.123 0. 146 0. 165 0.177 0.185 0. 189 0.193 0.194 1950 - 2250 0. ,002 0.009 0. 022 0.042 0.068 0. 095 0. 120 0.140 0.154 0. 164 0.172 0.178 2250 - 2850 0. ,001 0. ,004 0.010 0.021 0.036 0.052 0.069 0.084 0.094 0. 103 0.110 0.116 2850 - 3150 - 0. ,001 0. 003 0.006 0.012 0. 020 0. 028 0.037 0.044 0. 050 0.055 0.060 3150 - 3450 - - 0. 001 0.002 0.004 0. 007 0. 011 0.016 0.020 0. 024 0.027 0.031 3450 - 3750 - - - 0.001 0.001 0. 003 0. 005 0.007 0.009 0. 011 0.012 0.014 3750 - 4050 - - - - - 0. 001 0. 002 0.002 0.003 0. 004 0.004 0.005 4050 0.001 0.001 0. 001 0.001 0.002 16 CHAPTER 4 COMPONENT RELATIONSHIPS OF THE SOCKEYE SALMON LIFE CYCLE I n t r o d u c t i o n Component r e l a t i o n s h i p s between steps i n the c y c l e are described i n t h i s chapter together w i t h the f a c t o r s considered i n t h e i r d e r i v a t i o n . Each of the component r e l a t i o n s h i p s i s expressed i n the form of a p r o b a b i l i t y band ra t h e r than a unique curve, the width of the band r e f l e c -t i n g the extent of u n c e r t a i n t y and unknowns i n the r e l a t i o n s h i p . The de-r i v e d r e l a t i o n s h i p s were a l l reviewed by experts - personnel from the P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo (Smith, A l d e r d i c e , and W i t h l e r per-sonal communication), and they agreed that the curves appeared s a t i s f a c -t o r y i n l i g h t of t h e i r knowledge, experience, and judgment. R e l a t i o n s h i p Between the Chosen Escapement and the A c t u a l Escapement  F i g . 4.1 The a c t u a l escapement i s g e n e r a l l y not the same as the recommended escapement. There are s e v e r a l reasons f o r t h i s but the main one i s that c o n t r o l of the f i s h e r y i s r a t h e r tenuous since i t has to be conducted at "arms length". I f f i s h traps were b u i l t across the Skeena R i v e r , then i t would be a r e l a t i v e l y s t r a i g h t f o r w a r d procedure to ensure that the a c t u a l escapement was the same as that decided upon. However, as i t i s , c o n t r o l i s obtained by a d j u s t i n g . t h e a l l o w a b l e f i s h i n g times. There i s no d i r e c t r e l a t i o n s h i p between f i s h i n g times and escapement so the d e c i s i o n s have to be based on f o r e c a s t s , which them-selves might not be very accurate, and experience b u i l t up over the years. 17 400 600 800 1000 1200 Recommended Escapement x I0 3 RELATIONSHIP BETWEEN RECOMMENDED AND ACTUAL ESCAPEMENT.. FIG. 4.1 18 The effectiveness of the fishing fleet varies from year to year depending on factors such as the degree to which the fishing time coincides with the peak of the salmon run. There is also the Indian Fishery in which the catch also varies from year to year. In addition, there are subtle long term effects which are not fully understood, as is evidenced by the fact that the level of recent yields (1968-71) of the Skeena River fishery are about 45% as large as those of the system's best 4-year period, 1908-1911 (Ricker and Smith, 1975). The relationship between the chosen escapement and the actual escapement on the Babine Lake and River System is given in Fig. 4.1 in the form of a probability band. This was obtained from a comparison of the escapement objectives and an estimated actual escapement during a number of years from 1963 to 1974 (Skeena River Management Committee Annual Reports, 1963-74). Relationship Between the Actual Escapement and the Potential Egg  Deposition-Fig. 4.2 The potential egg deposition is defined as the number of eggs that enter the Babine Lake and River System. It is necessary to charac-terize the actual escapement in order to determine the number of eggs that w i l l enter Babine Lake and River System in terms of the sex ratio, the size and age of the females, and the mixture of the stocks. The number of eggs entering the system depends not only on the number of fish, but also on the sex ratio of the returning sockeye salmon. The sex ratio is important in considering the eventual survival of the eggs as well as the number of eggs that are brought into the system. If 19 200 400 600 800 1000 Actual Escapement x I0 3 RELATIONSHIP BETWEEN ACTUAL ESCAPEMENT AND POTENTIAL EGG DEPOSITION. FIG, 4.2 there i s a l a r g e female to male r a t i o , there may not be adequate space i n the t r i b u t a r i e s and spawning channels f o r the female sockeye salmon or e l s e there may not be enough males to f e r t i l i z e the eggs. The sockeye salmon e n t e r i n g the Babine Lake and R i v e r System are those that escape the combined Indian and commercial f i s h e r y . The f i s h e r y s e l e c t s f i s h from the r e t u r n i n g run on the basis of s i z e and, i n tu r n , on the basis of sex (Jordan and Smith, Fig? -Af '1972). Since the p o t e n t i a l reproductive c a p a c i t y , which i s based on the number of eggs c a r r i e d by the female sockeye salmon, i s a f u n c t i o n of s i z e and, i n t u r n , equivalent ocean age, the number of eggs deposited i n the g r a v e l i s g r e a t l y i n f l u -enced by the r a t i o of 4 and 5 years o l d females i n the escapement. The mean age of the sockeye salmon, f o r the t o t a l escapement has d e c l i n e d ( R i c k e r , 1972, 1975) w h i l e the sex r a t i o does not appear t o have v a r i e d s i g n i f i c a n t l y r e l a t i v e to other escapement years. This may account f o r the f a c t that the number of eggs which are c a r r i e d by the female sockeye salmon f o r the years 1967-1971 i s low r e l a t i v e to the number of eggs c a r r i e d by female sockeye salmon from other years. There are s e v e r a l p o s s i b l e reasons f o r the occurrence of a s h i f t i n the sockeye salmon mean age such as an inherent s h i f t i n the genetic makeup of the sockeye salmon stocks, the f i s h i n g gear used, and the approved f i s h i n g schedule. R i c k e r (1972) has shown that there has been a gradual increase i n the p o r t i o n of jacks r e l a t i v e to other age c l a s s e s of sockeye salmon stocks, where the jack p o r t i o n of a stock has been i n i t i a l l y considered moderate. Jack sockeye salmon are excluded from the escapement f i g u r e s ? u s e d i n the a n a l y s i s f o r the Babine-Nilkitkwa lakes system as they are considered immature sockeye. There are at l e a s t 10 stocks of sockeye salmon a s s o c i a t e d w i t h the "21 Babine Lake and R i v e r System (R i c k e r , 1972). Each stock d i f f e r s i n mean s i z e and mean age, thus the number of eggs c a r r i e d by the sockeye female of each stock v a r i e s and as a r e s u l t the mixture of the stocks which r e t u r n to the spawning channels and t r i b u t a r i e s i s a f a c t o r i n determin-ing the number of eggs that enter the system. The p r o b a b i l i t y band which defines the r e l a t i o n s h i p between the a c t u a l escapement and the p o t e n t i a l egg d e p o s i t i o n was a r r i v e d at by f i r s t , p l o t t i n g the t o t a l escapement of la r g e sockeye against the number of eggs ( p o t e n t i a l egg deposition) brought i n t o the system (Skeena R i v e r data, 1946-1971, su p p l i e d by the B i o l o g i c a l S t a t i o n , Nanaimo). The upper and lower l i m i t s of the data which formed the p r o b a b i l i t y band were extended to include v a r i a t i o n that might occur as a r e s u l t of e x t r a o r d i n a r y events such as a high male to female r a t i o . The R e l a t i o n s h i p Between the P o t e n t i a l Egg Deposition and the Number of  F r y - F i g . 4.3 Not a l l eggs that enter the Babine Lake and R i v e r System, the p o t e n t i a l egg d e p o s i t i o n , are deposited i n the g r a v e l . The number of eggs that are deposited i n the spawning channels and t r i b u t a r i e s depends on s o c i a l behaviour of the salmon i n the spawning channels and t r i b u t a r i e s , the number of spawning sockeye salmon i n the spawning channels and t r i b u -t a r i e s , and the time of a r r i v a l of the sockeye salmon at the spawning grounds. The e f f e c t of s o c i a l behaviour on the egg d e p o s i t i o n cannot be e n t i r e l y i s o l a t e d from the f a c t o r of density. A. Tautz (1974) has ob-served that i n high d e n s i t y s i t u a t i o n s i n the Ful t o n channels females are forced i n t o the pools where they wait f o r an opportunity to move i n t o the ! [ R E L A T I O N S H I P B E T W E E N P O T E N T I A U EGG DEPOSIT ION AND NO. O F FRY FIG. 23 g r a v e l beds. In some cases the females do not reach the g r a v e l beds. Thus, egg d e p o s i t i o n does not occur and the eggs that were r e t a i n e d i n t h e i r bodies decompose w i t h the f i s h t i s s u e . In a p r e l i m i n a r y study, Ginefez ( F i g . 12, 1972) has shown that i f spawning area a v a i l a b l e to each female i n F u l t o n channel No. 1 i s l e s s than 1.0 sq.yd;, but greater than 0.82 sq.yd., the percentage of unspawned females i s 3% to 47»; whereas, i n the F u l t o n channel No. 2, i f the area a v a i l a b l e per female i s l e s s than 1.0 sq.yd. but greater than 0.52 sq.yd. the percentage of unspawned females i s 5.5% to 6.57». Simultaneous studies were not conducted i n the r i v e r . Overcrowding i n the spawning channels i s not e n t i r e l y due to high density. Sockeye salmon spawn i n waves and as a r e s u l t , mechanical a c t i o n by spawners plays a r o l e i n the d i s r u p t i o n of eggs p r e v i o u s l y deposited (Ginetz, 1972). I f s e v e r a l waves of sockeye salmon spawn i n the channels some of the eggs w i l l be removed from the g r a v e l . A large number of eggs that enter the Babine Lake and R i v e r System are not deposited i n the g r a v e l due to the f a c t that many a d u l t sockeye salmon do not reach the spawning grounds. They may be l o s t as a food source to hawks, bears, and eagles, deprived of s u f f i c i e n t water s u p p l i e s , or confronted w i t h l o g and rock o b s t r u c t i o n s . Even i f the eggs are deposited i n the g r a v e l , they may not s u r v i v e . The s u r v i v a l of the eggs i n the g r a v e l of the spawning channels, r i v e r s , and streams depends on the r a t e of s i l t a t i o n , flow f l u c t u a t i o n s , predation, disease, water temperature, and the q u a l i t y of the water supply. S i l t a t i o n of the spawning grounds i s l i k e l y to lead to reduced gravel p e r m e a b i l i t y and subsequent embryonic m o r t a l i t y from i n s u f f i c i e n t oxygen. The s i l t a t i o n r a t e w i l l vary from year to year depending on the water r u n o f f and a c t i v i t i e s such as logging and mining which can dislodge 24 a great deal of sediment. F l u c t u a t i n g flows i n the streams and r i v e r s r e s u l t i n extensive movements of the r i v e r beds and can lead to a lack of water during the period when the eggs are developing i n t o a l e v i n s and i n tur n , f r y . Although an even flow i s d e s i r a b l e during the inc u b a t i o n p e r i o d , f l u c t u a -t i n g flows r e s u l t i n a n a t u r a l c l e a n i n g process. In studies conducted by Ginetz (1972) i n F u l t o n channels, preda-t i o n of the eggs by macroinvertebrates, such as s t o n e f l y nymph (Allopeda sp., Acroneuria p a c i f i c a ) was not considered to be a major source of embryonic m o r t a l i t y of sockeye eggs. I t i s a l s o p o s s i b l e that m o r t a l i t y of the eggs i s due to fungal and v i r a l i n f e c t i o n s . M o r t a l i t y of the eggs can be g r e a t l y i n f l u e n c e d by the high l e v e l s of s e v e r a l water q u a l i t y parameters such as NH^, NC^, NO-j, C O 2 , Temp, and O 2 that may i n t e r f e r e w i t h p e r m e a b i l i t y or e l s e reach t o x i c l e v e l s i n s i d e the eggs. Some of the m o r t a l i t y f a c t o r s seems to be accentuated i n the channels of the Babine Lake and R i v e r System. The Pinkut Creek channel system i s exposed to the f r e e z i n g winds i n the w i n t e r and as a r e s u l t anchor i c e forms. The g r a v e l i s scoured and a high w i n t e r m o r t a l i t y of a l e v i n s occurs. Wickett (1974) points out that the phenomena occur only under c l e a r s k i e s . I t has been suggested that the p l a n t i n g of Black Spruce would a l l e v i a t e the problem and a l s o reduce the i n f l u e n c e of the l i g h t during the summer. The p o t e n t i a l f o r a l g a l blooms i s present and i t i s p o s s i b l e that t o x i c biproducts produced by the algae w i l l a f f e c t the s u r v i v a l of a p o r t i o n of the a l e v i n s and the eggs p a r t i c u l a r l y i f the a l g a l blooms occur i n e a r l y May. Ginetz (1972) p r e d i c t s that m o r t a l i t y w i l l r i s e i f algae growth and s i l t a t i o n continue unchecked i n the F u l t o n channels. The p r o b a b i l i t y band which defines the r e l a t i o n s h i p between the p o t e n t i a l egg d e p o s i t i o n and the number of f r y was a r r i v e d a t by f i r s t , p l o t t i n g the p o t e n t i a l egg d e p o s i t i o n , the number of eggs brought i n t o the system, against the estimated number of f r y , f i n g e r l i n g s that enter the lakes system f o r the years 1955-1961 (Johnson, 1955-61). This i n f o r -mation s u p p l i e d by the P a c i f i c B i o l o g i c a l S t a t i o n acted as a basis f o r the c o n s t r u c t i o n of a p r o b a b i l i t y band. The Skeena R i v e r System has spawning channels at Pinkut Creek and F u l t o n R i v e r which were not present when the p o p u l a t i o n studies were undertaken. Subsequent studies lead to an approximate s u r v i v a l f i g u r e of 407» f o r the eggs i n the channels. For the purpose of a n a l y z i n g a second set of data, i t i s assumed that 20% of the eggs that enter the system enter the spawning grounds. R e l a t i o n s h i p Between the Number of Fry and the Number of Smolts-Fig. 4.4 The f r y emerge from the r i v e r s , streams, and spawning channels and enter Babine and N i l k i t k w a Lakes i n the s p r i n g . They remain i n the lakes f o r approximately one year before migrating as smolts to the sea by the Skeena R i v e r . Once i n the la k e s , the s u r v i v a l r a t e of the f r y depends on p h y s i c a l and b i o l o g i c a l f a c t o r s such as water temperature d i f f e r e n c e s , a v a i l a b i l i t y of food, and i n t e n s i t y of the pressure from predators such as Rainbow t r o u t , D o l l y Varden, and lake t r o u t . The f r y are exposed to a d i f f e r e n t thermal environment when they emerge from the t r i b u t a r i e s and spawning channels. I f there i s a l a r g e d i f f e r e n c e i n the temperature between the r i v e r s and the lake water, i t i s l i k e l y m o r t a l i t y w i l l be high. B r e t t (1952) demonstrated that the young sockeye (4.7 months of age) acclimated to 5°C could not t o l e r a t e long 2,6 FIG. 14,4 27 exposure (four days) to 0°C. His work o u t l i n e d the thermal tolerance of young sockeye salmon i n r e l a t i o n to d i f f e r e n t a c c l i m a t i o n temperatures ( B r e t t , F i g . 22, 1952). Babine Lake i s considered to have an abundant supply of food i n the form of zooplankton biomass. Johnson (1956, 1958, and 1961) measured the standing crop of zooplankton (mg dry weight/m ) i n the 0-5 m depth i n t e r v a l i n order to estimate food abundance. He found that the mean con c e n t r a t i o n of zooplankton v a r i e d from 8-100 mg/m^  from mid-June to mid-October f o r seven defined basins i n N i l k i t k w a and Babine Lakes. His studies i m p l i e d that the main b a s i n on Babine Lake (which accounts f o r 88% of the t o t a l surface area) was u n d e r u t i l i z e d as a lake nursery f o r sockeye. This info r m a t i o n provided one of the main reasons f o r c o n s t r u c t i o n of the spawning channels at F u l t o n R i v e r and Pinkut Creek. Although the abundance i n t o t a l q u a n t i t y may be more than adequate to meet the needs of the young sockeye, the standing crop of zooplankton w i l l vary w i t h the time of year. In the s p r i n g , before the lake warms up, p r o d u c t i v i t y w i l l be low so that when the f r y f i r s t enter the lake, food may be scarce and competition f o r i t intense. B i l t o n and Robins (1971) found from c o n t r o l l e d experiments that young sockeye salmon de-p r i v e d of food f o r a p e r i o d of 20 weeks d i d not s u f f e r a high r a t e of m o r t a l i t y (1 out of 79 f i s h ) . They a l s o found that the f i s h were capable of enduring a longer p e r i o d of s t a r v a t i o n (30.5 weeks) but w i t h an i n -creased m o r t a l i t y r a t e (8 out of 54 f i s h ) . However, the young sockeye salmon u t i l i z e energy due to the f a c t that they are c o n t i n u a l l y being subjected to s t r e s s e s such as attacks from predators, temperature f l u c t u a -t i o n s , and competition w i t h r i v a l s f o r food. The lack of food can con-t r i b u t e to m o r t a l i t y of the young sockeye by d e p r i v i n g them of energy 28 re q u i r e d to s u s t a i n l i f e i n the n a t u r a l environment. McCart (1966) found that seven species of f i s h were preying on the sockeye f r y : rainbow t r o u t , c u t t h r o a t t r o u t , cohoe salmon, D o l l y Varden, lake t r o u t , lake w h i t e f i s h , and burbot. The r a t e of m o r t a l i t y was high (6.7 f i s h per predator stomach) i n the Upper Babine R i v e r , a r i v e r which j o i n s N i l k i t k w a and Babine Lakes w h i l e the r a t e of m o r t a l i t y was low (0.4 f i s h per predator stomach) i n Babine Lake. The hi g h r a t e of predation appears to be due to the greater a v a i l a b i l i t y of f r y on the Upper Babine R i v e r . The s i z e of the sockeye f r y population i s not s t a b l e . One year a l a r g e number of f r y enter the lake and the next year a small number of f r y enter the lake; f o r example, i n 1958, 189 x 10 f r y entered the lake and i n 1959, 95 x 10 f r y emerged from the streams and spawning channels. The r e s u l t i s that there i s a c o n t i n u a l l y f l u c t u a t i n g popula-t i o n of predators and prey. In Babine and N i l k i t k w a Lakes f i s h are not the only predators of the sockeye f r y . The Bonaparte g u l l and the American merganser were seen on the Upper Babine R i v e r . Although an accurate assessment was not made, the b i r d s appeared to be feeding on the sockeye f r y ( A l l a n , 1953-54). There i s evidence which i n d i c a t e s that the predator pop u l a t i o n s i z e may vary r e l a t i v e to the f r y population s i z e although there i s a time l a g involved. Ward and L a r k i n (1964) found that the c o n d i t i o n of the rainbow t r o u t i n the western region of Shuswap Lake was r e l a t i v e l y poor when the j u v e n i l e sockeye were scarce. The substandard c o n d i t i o n of the t r o u t presumably would r e s u l t i n an increased m o r t a l i t y r a t e and a 2 9 r e d u c t i o n i n the number of rainbow t r o u t predators. The f o l l o w i n g year the young sockeye salmon would not be as s u s c e p t i b l e to attackes from the rainbow t r o u t so, i n that year, the number of sockeye w i l l be h i g h r e l a t i v e to the number of rainbow t r o u t . The few rainbow t r o u t that remained would have ample prey so that they would be expected to m u l t i p l y i n t o a l a r g e predator po p u l a t i o n which would r e s u l t i n a reduced number of juve-n i l e sockeye salmon, thus completing the c y c l e . Babine and N i l k i t k w a Lakes support a number of smaller land-locked sockeye known as kokanee. There i s no morphological c r i t e r i a that could be used to d i s t i n g u i s h sockeye progeny from andronomous parentage and sockeye f r y of kokanee parentage (Johnson, 1 9 5 8 ) . However, the eggs are smaller and the kokanee f r y were found to be smaller when they emerged i n the s p r i n g (Johnson, 1 9 5 8 ) . Estimates were e s t a b l i s h e d during the period August 2 1 - 2 5 , 1 9 5 7 , which i n d i c a t e d that 2 6 7 o or 2 2 . 3 m i l l i o n progeny of kokanee w h i l e 6 1 . 3 m i l l i o n or 7 4 7 , of the progeny were andronomous sockeye. I t i s assumed that some of the f r y of the non-andronomous f i s h may go to sea and so c o n t r i b u t e to andronomous r e t u r n of the a d u l t s (Johnson, 1 9 5 8 ) . I t i s a l s o p o s s i b l e that the kokanee were progeny of the andronomous sockeye. Thus, i t i s d i f f i c u l t to e s t a b l i s h an accurate f i g u r e f o r non-andronomous sockeye. The p r o b a b i l i t y band which defines the r e l a t i o n s h i p between the number of f r y ( f i n g e r l i n g ) and smolts was based on the estimated number of f i n g e r l i n g s i n the lake f o r the years 1 9 5 6 - 1 9 6 1 (data obtained from P a c i f i c B i o l o g i c a l S t a t i o n ) and the r e s u l t i n g number of smolts l e a v i n g the lake f o r those years. 30 R e l a t i o n s h i p Between the Numbers of Smolts and A d u l t s - F i g . 4 . 5 The young sockeye or smolts migrate from the Babine Lake and R i v e r System by way of the Skeena R i v e r to the sea. Once they emerge from the l a k e , the s u r v i v a l r a t e of the smolts depends on p h y s i c a l and b i o l o g i c a l f a c t o r s such as the s i z e of the smolts, the s i z e of the smolt population, the ocean nursery c o n d i t i o n s upon a r r i v a l , the prey d e n s i t y i n the Skeena R i v e r and i n the ocean (Ri c k e r , 1 9 6 8 ) , and the l o s s of a d u l t s due to the h a r v e s t i n g methods employed. A f t e r one or more years of ocean l i f e the sockeye r e t u r n as a d u l t s to e i t h e r spawn or be caught. The Skeena R i v e r sockeye u s u a l l y mature at e i t h e r 4 or 5 years of age, though the sockeye populations g e n e r a l l y i n c l u d e some 3 year olds or " j a c k s " . The jack sockeye salmon are predominantly males. For the pur-pose of a n a l y s i s , the smolts are not c l a s s e d as a d u l t s u n t i l they begin to migrate from the ocean to the spawning channels and t r i b u t a r i e s of the Babine and N i l k i t k w a Lakes. The s i z e of the smolts that leave Babine Lake and R i v e r System may be a f a c t o r that r e s u l t s i n e i t h e r increased or decreased m o r t a l i t y . R i c k e r ( 1 9 6 9 ) points out that predators or p a r a s i t e s may k i l l more of a group of small f i s h than of l a r g e , and as an example Parker ( 1 9 7 1 ) demonstrated that j u v e n i l e cohoe salmon i s a predator of j u v e n i l e pink salmon u n t i l the j u v e n i l e pink salmon reach a c e r t a i n s i z e . He found the growth r a t e of cohoe salmon to be . 7 % / d a y w h i l e the pink salmon had a growth r a t e of 1 . 4 7 o / d a y . Thus, the s u r v i v a l of the pink salmon increases as they "outgrow" t h e i r s u i t a b i l i t y as prey f o r the j u v e n i l e cohoe salmon. However, there i s a l s o a p o s s i b i l i t y that the l a r g e r smolts are the prey fo r l a r g e r predators that would ignore the smaller smolts. The s i z e of the smolt pop u l a t i o n that leave the lakes i s a f a c t o r 0 20 40 60 80 100 No.of Smolts x 10 6 RELATIONSHIP BETWEEN NO.OF SMOLTS AND NO.OF ADULTS FIG 4,5 i n determining the a d u l t p o p u l a t i o n r e t u r n . A high d e n s i t y of smolts at the mouth of the Skeena R i v e r , which i s l i k e l y to develop as a r e s u l t of the smolts l e a v i n g Babine and N i l k i t k w a Lakes at the same time, may a t t r a c t l a r g e numbers of predators such as the cohoe salmon. The d e n s i t y of smolts would not be high at the mouth of the Skeena R i v e r i f the smolts a r r i v e at i n t e r v a l s . However, the m o r t a l i t y r a t e could be s i m i l a r . This time the number of smolts would be supporting the r e s i d e n t p r e d a t i o n p o p u l a t i o n which may have the a b i l i t y to crop the prey p o p u l a t i o n at a constant r a t e . I t i s p o s s i b l e that smolts depend on a high d i s p e r s i o n r a t e i n order to avoid the predators at the mouth of the Skeena R i v e r . The s u r v i v a l of the young smolts i s thought to be dependent l a r g e l y on the distance that the smolts have to t r a v e l from the lakes to the feeding grounds which may be l o c a t e d s e v e r a l miles o f f the mouth of the r i v e r . A h i g h c o n c e n t r a t i o n of zooplankton (mg dry weight/m ) which i s the source of food f o r the young smolts i s a s s o c i a t e d w i t h a high l e v e l of primary p r o d u c t i v i t y . In the case of the Fraser R i v e r estuary, the maximum l e v e l of primary production i s l o c a t e d s e v e r a l miles o f f s h o r e and i s dependent on such f a c t o r s as the increased a v a i l a b i l i t y of l i g h t due to decreased sedimentation, mixing processes w i t h distance, and a time f a c t o r which allows the c e l l s of the phytoplankton to increase e x p o n e n t i a l l y as the water moves away from the r i v e r mouth (Parsons et al? ?\1969) . I f the smolts have to swim a long distance to the feed-ing grounds and they are a s u i t a b l e s i z e as prey f o r such predators as cohoe salmon, then they are s u s c e p t i b l e to increased attacks-and m o r t a l i t y w i l l increase. There are d i f f i c u l t i e s i n studying the subject of predator-prey r e l a t i o n s h i p s i n the ocean because of the i n t e r r e l a t i o n s that are l i k e l y to e x i s t between the predator populations and the prey populations. Predator d e n s i t y may or may not be r e l a t e d to the emergence of the smolt population. There may be c e r t a i n times of the year where other prey are i n short supply and thus, f o r c e r t a i n periods the smolts are the most a v a i l a b l e source of food for a host of predators. C e r t a i n species of f i s h , such as cohoe salmon, may act as predators f o r a c e r t a i n p eriod of the smolt l i f e c y c l e , but not a f t e r the smolts reach a c e r t a i n s i z e . These predators could reduce the smolt p o p u l a t i o n s u b s t a n t i a l l y at that stage i n the l i f e c y c l e of the sockeye salmon; however, they would not be a f a c t o r c o n t r i b u t i n g to m o r t a l i t y at a l a t e r stage i n the l i f e c y c l e of the sockeye salmon. There may be a high m o r t a l i t y f a c t o r attached to the h a r v e s t i n g method employed. Adult sockeye salmon that become entangled w i t h the f i s h i n g nets and drop out before the net i s taken i n are not counted as r e t u r n i n g a d u l t s i n the a n a l y s i s . These f i s h are part of the m o r t a l i t y f i g u r e , presumably they die prematurely as a r e s u l t of damage sustained. The i n f o r m a t i o n s u p p l i e d by the P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo, covered the years 1949 to 1972. The b a s i c r e l a t i o n s h i p between smolts and a d u l t returns i s presented i n the form of a p r o b a b i l i t y band which i s based on counts of the smolts and a d u l t r e t u r n s . Combining the Component R e l a t i o n s h i p s The component r e l a t i o n s h i p s were each transformed i n t o p r o b a b i l i t y matrices on the assumption that a "skew normal" p r o b a b i l i t y d i s t r i b u t i o n could be f i t t e d to the upper and lower p r o b a b i l i t y l i m i t s w i t h the l i m i t s being two standard d e v i a t i o n s from the mode. A "skew normal" d i s t r i b u -t i o n i s simply a composite of two halves of the two d i f f e r e n t normal d i s -t r i b u t i o n s adjusted to meet i n the center and maintain the area under the curve equal to 1.0. Another d i s t r i b u t i o n could have been used. Neverthe-l e s s , a skew normal had been used elsewhere (Hershman, 1974) and a com-puter program f o r the conversion was a v a i l a b l e . Once the component r e l a t i o n s h i p s had been converted to p r o b a b i l i t y matrices they were com-bined by m u l t i p l y i n g the matrices together to o b t a i n one o v e r a l l proba-b i l i t y m atrix (Table 3.1). This has been converted back to a p r o b a b i l i t y band, as shown i n F i g . 3.1, and records of a c t u a l escapements (Jordan and Smith, 1972) w i t h corresponding numbers of r e t u r n i n g adults have been p l o t t e d f o r comparison. 35 CHAPTER 5 UTILITY I n t r o d u c t i o n I t can be shown (de N e u f v i l l e and S t a f f o r d , 1972) that to be c o n s i s t e n t , a d e c i s i o n maker must choose the course of a c t i o n w i t h the maximum expected u t i l i t y . The expected u t i l i t y E(U) = P i ( U i ) where P^ = p r o b a b i l i t y of outcome i , and U^ = u t i l i t y ( r e l a t i v e d e s i r a b i l i t y ) of outcome i . The u t i l i t i e s of p a r t i c u l a r outcomes i n a s p e c i f i c s i t u a t i o n are obtained by f i r s t a s s i g n i n g a r b i t r a r y numbers to the best and worst out-comes under c o n s i d e r a t i o n ( g e n e r a l l y 100 and 0 or 1 and 0). Next, f o r an intermediate outcome the d e c i s i o n maker i s asked, "What chance of o b t a i n i n g the best outcome (with the complementary chance of o b t a i n i n g the worst) i s equivalent to o b t a i n i n g t h i s p a r t i c u l a r outcome f o r c e r t a i n ? " Chances are expressed as a percentage i f us i n g the s c a l e 0 to 100, or as a f r a c t i o n i f us i n g 0 to 1. The answer gives i t s u t i l i t y . U t i l i t y of the Current Year's Catch Developing a u t i l i t y curve f o r the Babine system sockeye salmon catch involves s u b j e c t i v e judgment on the part of the Skeena R i v e r Manage-ment Committee, the body r e s p o n s i b l e f o r management of the f i s h e r y . The Skeena R i v e r Management Committee would have to take i n t o account not only the economic advantage of a l a r g e sockeye catch, but a l s o the d i s -advantage of p o s s i b l y i n t e r f e r i n g w i t h the management of other species 36 such as chinook and steelhead, the needs of the Indian f i s h e r y , and the need to maintain the run. F i g . 5.1 shows the curve used i n the present study. I t i s b e l i e v e d to be =. reasonably r e p r e s e n t a t i v e and adequate f o r purposes of i l l u s t r a t i o n . The "worst" normal case was assumed to be a catch of 400,000 ( u t i l i t y value 0, F i g . 5 H ) . Below that a curve goes sharply negative r e f l e c t i n g the f a c t that at lower f i g u r e s there would be severe s o c i a l problems, i t could be d i f f i c u l t to c o n t r o l f i s h i n g and the whole run could be endangered. A catch of 3.5 m i l l i o n i s assumed to be the "best" ( u t i l i t y value of 100, F i g . 5.1). Returns are e x c e l l e n t and processing f a c i l i t i e s are not overloaded. Higher catches mean higher r e t u r n s , but a l s o more overloading of processing f a c i l i t i e s and the i n t e r f e r e n c e i n the management of other species. Above a catch of 3.5 m i l l i o n the u t i l i t y decreases to r e f l e c t the i n c r e a s i n g negative e f f e c t s of g r e a t e s t numbers. As an example of the meaning of u t i l i t y , a d e c i s i o n maker would be reasonably s a t i s f i e d w i t h a catch of 1.7 m i l l i o n (50 u t i l i t y points) and would consider t h i s as equivalent to a 50-50 chance of having a catch of 400,000 (0 u t i l i t y points which would be considered as h i g h l y u n s a t i s -factory) or a catch of 3.5 m i l l i o n (100 u t i l i t y points which would be considered to be e x c e l l e n t ) . The expected u t i l i t y of the current year's catch, E(C), at the time the d e c i s i o n i s being made i s : E(C) = f U ( R i - E ) P i where R^ = Number of r e t u r n i n g a d u l t s , E = Escapement, (R± - E) = Catch, R^ = P r o b a b i l i t y that there are R-^  r e t u r n i n g a d u l t s (obtained from f o r e c a s t ) , and 37 UTILITY CURVE FOR CATCH. FIG 5.1 38 V(R± - E) = U t i l i t y of catch (R± - E) (obtained from F i g . 5.1). Expected U t i l i t y of the Escapement The matrix r e l a t i n g escapement to numbers of r e t u r n i n g adults (Table 3.1) gives the p r o b a b i l i t i e s of v arious numbers of r e t u r n i n g adults i n the next c y c l e r e s u l t i n g from a recommended escapement i n the current year. The expected u t i l i t y of the escapement, thus, i s : E(e) = €.U(R i e - F ) - P i e where F = average escapement, R^e = number of r e t u r n i n g a d u l t s i n c y c l e year, (R-ie " F) = catch i n c y c l e year, and ^ i e = p r o b a b i l i t y that there w i l l be R^e r e t u r n i n g a d u l t s i f escapement i n current year i s e. In the above, the average escapement F i s used to s i m p l i f y the computations. In the study, F was taken as equal to 620,000, the average escapement during the p e r i o d from 1957 to 1967. The f u t u r e catch i s assumed to be r e a l i z e d i n 4 years time. Thus, i t seems proper to discount the future catch. For the present purposes the r a t e has been taken as 107° per year which probably errors °n the high s i d e . The T o t a l Expected U t i l i t y of the Current Year's Run The t o t a l expected u t i l i t y of the current year's run, i n c l u d i n g both the catch and the escapement, thus, i s : E(C) + E ^ e ) , , which i s equal to ( l . l ) 4 l U ( R i - E ) P i e + e r U ( R i e - F ) - P i e ( l . l ) 4 39 Computing the Recommended Escapement w i t h the Maximum T o t a l Expected  U t i l i t y A f o r e c a s t i s made of the number of r e t u r n i n g a d u l t s i n the current year and w i t h the u t i l i t y curve f o r the catch ( F i g . 5.1) and a matrix r e l a t i n g numbers of ad u l t s r e t u r n i n g i n the c y c l e year to the recommended escapement i n the current year, i t i s then p o s s i b l e to compute the t o t a l expected u t i l i t y f o r a range of p o s s i b l e escapements. A fo r e c a s t was simply assumed to be normally d i s t r i b u t e d w i t h a mean of 1,400,000 and a standard d e v i a t i o n of 500,000. This was derived from the a c t u a l numbers recorded during the pe r i o d from 1957 to 1967 and t h i s i s roughly what one would assume i f there were no for e c a s t s and had to r e l y on records. The r e l a t i o n s h i p between the expected u t i l i t y and the c a l c u l a t e d escapement i s shown i n F i g . 5.2. The optimal escapement i n t h i s case i s 720,000 but any value between 650,000 and 800,000 would be q u i t e acceptable. 40 30 r 400 500 600 700 800 Recommended Escapement x |Q 3 900 TOTAL EXPECTED UTILITY ASSOCIATED WITH ESCAPEMENT DECISION. FIG 5.2 41 CHAPTER 6 DISCUSSION The example given above i s intended to i l l u s t r a t e a procedure and approach r a t h e r than to document an a c t u a l working example. This approach could be used to make a d e c i s i o n provided a l l of the f a c t o r s i n the a n a l y s i s were examined c a r e f u l l y and agreed w i t h those r e s p o n s i b l e f o r the d e c i s i o n . For example, great care would be necessary i n estab-l i s h i n g the u t i l i t y curve; the f a c t that some sockeye r e t u r n a f t e r 3, 4, and 5 years would have to be taken i n t o account. The discount value of future returns would need to be examined as would the skew normal d i s t r i -b ution. These f a c t o r s could be d e a l t w i t h . The concepts have been used elsewhere (Caselton and R u s s e l l , 1976) and i t would be qui t e p o s s i b l e to extend the a n a l y s i s to f i n d the present value of a future salmon run. With the procedure o u t l i n e d f o r handling separate components of the salmon l i f e c y c l e , i t should be p o s s i b l e to compute an expected value f o r any proposed change a f f e c t i n g any of the component r e l a t i o n s h i p s (Brox, 1976). This could be a u s e f u l t o o l i n ev a l u a t i n g enhancement d e c i s i o n p o s s i b i l -i t i e s that otherwise are d i f f i c u l t to compare. For example, i n order to increase the a d u l t r e t u r n of sockeye salmon, should the d e c i s i o n maker cons t r u c t spawning channels or f e r t i l i z e the lake? I t has been suggested by Mr. Howard Smith of the P a c i f i c B i o l o g i -c a l S t a t i o n that the f i n a l p r o b a b i l i t y matrix developed could act as a for e c a s t t a b l e f o r the f i s h i n g i n d u s t r y . A long range f o r e c a s t would be p a r t i c u l a r l y u s e f u l f o r the f i s h processing plants that order cans and equipment w e l l i n advance of the f i s h i n g season. 42 The procedure brings an o b j e c t i v e approach to the area of resource management. The procedure does encourage d i r e c t debate on c o n t r o v e r s i a l points yet i t reduces the p o s s i b i l i t y of arguments at cross purposes. Thus, wiser d e c i s i o n s and a general increase i n understanding should p r e v a i l . 43 CHAPTER 7 FUTURE DEVELOPMENT This t h e s i s deals w i t h o p e r a t i o n a l decision-making, namely the escapement to aim f o r i n the current year. I t i s meant f o r use i n r e a l time u s i n g f o r e c a s t information about the current year's run and the u t i l i t y or value of the catch i n the current year. The technique could be used to evaluate p o s s i b l e enhancement p r o j e c t s . The b a s i c procedure of examining various stages of the salmon l i f e c y c l e tends i t s e l f to assess the e f f e c t s of changes i n one or more stages of the c y c l e on the t o t a l run. Information on the immediate e f f e c t s of changes such as i n c r e a s i n g spawning channels, would come from present a v a i l a b l e i n f o r m a t i o n and from past research and experience. Information need not be p r e c i s e to be usable, but the procedure permits the use of a l l a v a i l a b l e information. I t could be extended to assess the value of a d d i t i o n a l information and hence could be a va l u a b l e a i d i n a s s i g n i n g research p r i o r i t i e s . The technique could a l s o be used f o r assessing a l t e r n a t e manage-ment s t r a t e g i e s . For example, i t could be p o s s i b l e to evaluate d i f f e r e n t methods of h a r v e s t i n g such as the use of traps as opposed to u t i l i z i n g a f i s h i n g f l e e t , i n terms of p o t e n t i a l b e n e f i t s versus s o c i a l consequences. 44. BIBLIOGRAPHY A l l a n , V.I.F. 1953-54. Unpublished report at the P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo. B i l t o n , H.T. and G.L. Robins. Response of young sockeye salmon (Oncor-hynchus nerka) to prolonged periods of s t a r v a t i o n . J . F i s h e r i e s Res. Board of Can., 28(11), 1971. B r e t t , J.R. 1952. Temperature to l e r a n c e i n young P a c i f i c salmon genus Oncorhynchus. J . F i s h e r i e s Res. Board Can., j)(16). Brox, G.H. 1976. Water q u a l i t y i n the Lower Fraser R i v e r basin: A method to estimate the e f f e c t of p o l l u t i o n on the s i z e of the salmon run. Unpublished MASc. t h e s i s , Dept. of C i v i l Eng., U n i v e r s i t y of B.C., Vancouver. Caselton, W.F. and S.O. R u s s e l l . Long-term operation of storage hydro p r o j e c t s . J o u r n a l of Water Resources Planning and Management D i v i s i o n , American S o c i e t y of C i v i l Engineers, A p r i l 1976. de N e u f v i l l e , R. and J.H. S t a f f o r d . 1971. Systems A n a l y s i s f o r Engineeers and Managers. McGraw H i l l , New York. Ginetz, R.M. 1972. Sockeye egg to f r y m o r t a l i t y i n F u l t o n R i v e r spawn-ing channels. Dept. of the Environment, F i s h e r i e s S e r v i c e P a c i f i c Region Tech. Rep. 1972-10. H a l t e r , A. and G. Dean. 1972. D e c i s i o n Under Un c e r t a i n t y w i t h Research A p p l i c a t i o n , Southwestern P u b l i s h i n g Co., C i n c i n n a t t i , Ohio. Hershman, S.H. 1974. An a p p l i c a t i o n of D e c i s i o n Theory to water q u a l i t y management. Thesis, Dept. of C i v i l Eng., U n i v e r s i t y of B.C., Vancouver. Johnson, W.E. 1956. On the d i s t r i b u t i o n of young sockeye salmon (Oncorhynchus nerka) i n Babine and N i l k i t k w a Lakes, B.C. J . F i s h e r i e s Res. Board Can., 13:695-708. 1958. Density and d i s t r i b u t i o n of young sockeye salmon (Oncorhynchus nerka) throughout a m u l t i b a s i n lake system. J . F i s h e r i e s Res. Board Can., 15:961-982. 1961. Aspects of the ecology of a p e l a g i c , zooplankton-e a t i n g f i s h . Verh I n t . Verein. Limnol. 245:727-731. 1965. On mechanisms of s e l f - r e g u l a t i o n of population abund-dance i n Oncorhynchus nerka. M i l t . I n t . Verein. Limnol. 13: 66-87. 1955-1961. Data s u p p l i e d by P a c i f i c B i o l o g i c a l S t a t i o n used f o r the p o t e n t i a l egg d e p o s i t i o n vs f r y graph. Jordan, F.P. and H.D. Smith. 1972. Summary of salmon counts and observa-t i o n s from the Babine R i v e r counting fence 1967-1971. Res. Board Can. Tech. Rep. 331:1-63. McCart, P. 1966. Behaviour and ecology of sockeye salmon f r y i n the Babine R i v e r . J . F i s h e r i e s Res. Board Can., 24(2), 1967. Parker, R.R. 1971. S i z e s e l e c t i v e predation among j u v e n i l e salmonid f i s h e s i n a B r i t i s h Columbia i n l e t . J . F i s h e r i e s Res. Board Can., 28(10):1503-1510. Parsons, T.R. and Takahashi. 1973. B i o l o g i c a l Oceanographic Processes. Pergamon Press, Oxford. R i c k e r , W.E. 1968. Background information and theory r e l a t e d to management of the Skeena sockeye salmon. F i s h . Res. Bd. Can., M.S. Rep.(Biol) 961. 1969. E f f e c t s of s i z e - s e l e c t i v e m o r t a l i t y and sampling bias on estimates of growth, m o r t a l i t y , production, and y i e l d . J . F i s h e r i e s Res. Board Can., 26(3):479-534. 1972. He r e d i t a r y and environmental f a c t o r s a f f e c t i n g c e r t a i n salmonid populations, pp.27-160. In: R.C. Simon and P.A. L a r k i n . The stock concept i n P a c i f i c salmon. H.R. MacMillan l e c t u r e s i n f i s h e r i e s , U n i v e r s i t y of B.C., Vancouver. Skeena R i v e r Management Committee Annual Reports (1963-1974). Tautz, A. 1974. (Notes) from Workshop on Spawning Channels: P a r k s v i l l e , Vancouver I s l a n d , December 18, 1973. Ward, F.J. and P.A. L a r k i n . 1964. C y c l i c dominance i n Adams Ri v e r sockeye salmon. I n t . Pac. Salmon F i s h . Comm. Prog. Rep. 11: 116 p. Wickett, P. 1974. (Notes) from Workshop on Spawning Channels: P a r k s v i l l e , Vancouver I s l a n d , December 18, 1973. 

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