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Analysis of stock-recruitment dynamics of British Columbia salmon Wong, Fred Yuen Churk 1982

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ANALYSIS OF STOCK-RECRUITMENT DYNAMICS OF BRITISH COLUMBIA SALMON by FRED YUEN CHURK WONG B.Sc. i n F i s h e r i e s , U n i v e r s i t y of W a s h i n g t o n , 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES ( D e p a r t m e n t o f Z o o l o g y ) We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1982 © F r e d Yuen Churk Wong, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree 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 study. I f u r t h e r agree 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 copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or 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 allowed without my w r i t t e n p e r m i s s i o n . Department of Z* et° f r 7  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date ABSTRACT An o v e r v i e w o f s t o c k - r e c r u i t m e n t d y n a m i c s f o r m a j o r B.C. salmon ( , O n c o r h y n c h u s spp.) s t o c k s i s p r e s e n t e d . S t o c k -r e c r u i t m e n t p a t t e r n s r a n g e from l i n e a r r e l a t i o n s h i p s t o " R i c k e r " t y p e r e l a t i o n s h i p s t o no r e l a t i o n s h i p a t a l l . However, s t o c k s f o r w h i c h t h e r e a r e a c c u r a t e e s c a p e m e n t e s t i m a t e s g e n e r a l l y show p a t t e r n s e x p e c t e d from s t o c k - r e c r u i t m e n t t h e o r y . I t i s c o n c l u d e d t h a t e r r o r s i n s t o c k d e f i n i t o n , m i x e d c a t c h a l l o c a t i o n , and s p a w n i ng c o u n t s b i a s optimum escapement e s t i m a t e s downward so t h a t p o o r l y m o n i t o r e d s t o c k s may become s e v e r e l y o v e r e x p l o i t e d w i t h o u t b e i n g n o t i c e d . B e c a u s e o f p o o r e s c a p e m e n t c o u n t s a n d / o r d i f f i c u l t i e s i n s e p a r a t i n g m i x e d c a t c h e s , optimum e s c a p e m e n t s f o r many B.C. salmon s t o c k s , w h i c h a c c o u n t f o r a b o u t h a l f of t h e t o t a l - B.C. p r o d u c t i o n , c a n n o t be e s t i m a t e d . Most s t o c k s f o r w h i c h optimum escapement c a n be e s t i m a t e d a r e now b e i n g s e v e r e l y d e p l e t e d . R e s t o r a t i o n of t h e s e s t o c k s by i n c r e a s i n g escapement t o optimum l e v e l s w ould i n c r e a s e t h e t o t a l c a t c h by a t l e a s t 40% of t h e c u r r e n t y i e l d . F u r t h e r , e x p e r i m e n t a l management by i n c r e a s i n g escapement a p p e a r s t o be t h e b e s t p o l i c y f o r most o f t h e o t h e r s t o c k s . TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS i i L I S T OF TABLES v L I S T OF FIGURES . v i ACKNOWLEDGEMENTS v i INTRODUCTION " l ESTIMATION OF SPAWNING STOCK AND RECRUITMENT 8 2.1 S o u r c e s o f D a t a 8 2.2 S t o c k D e f i n i t i o n 9 2.3 E s t i m a t i o n o f Spawners.... 11 2.4 E s t i m a t i o n of R e c r u i t m e n t . . . 18 2.5 P o s s i b l e S o u r c e s o f E r r o r . . 39 ESTIMATION OF STOCK-RECRUITMENT RELATIONSHIPS 42 3.1 Model F i t t i n g P r o c e d u r e s 44 3.1.1 R i c k e r M o d e l 45 3.1.2 B e v e r t o n - H o l t M o d e l 46 3.1.3 Power M o d e l 47 3.2 C o r r e c t i o n s f o r Measurement E r r o r 49 3.2.1 C o r r e c t i o n s f o r Spawning Count E r r o r s 54 3.3 R e s u l t s . 56 3.3.1 S t o c k - R e c r u i t m e n t P a r a m e t e r E s t i m a t e s 56 3.3.2 S p a t i a l P a t t e r n s i n P r o d u c t i v i t y 70 3.3.3 C o r r e l a t i o n s Among S t o c k s 78 3.3.4 D e n s i t y Dependence and F e c u n d i t y 89 3.3.5 E f f e c t s of Measurement E r r o r s on The E s t i m a t e s . . 89 iv 4. OPTIMAL POLICIES 97 4.1 N o n - f e e d b a c k P o l i c i e s 98 4.2 F e e d b a c k P o l i c i e s 99 4.2.1 Random " E n v i r o n m e n t a l " E f f e c t s 100 4.2.2 Measurement E r r o r s 102 4.2.3 U n c e r t a i n t y i n P a r a m e t e r E s t i m a t e s and Mo d e l S t r u c t u r e 103 4.3 R e s u l t s 107 5. DISCUSSION AND CONCLUSION 130 R e f e r e n c e s 137 A p p e n d i x I . Age C o m p o s i t i o n o f C a t c h and Escapement 147 A p p e n d i x I I . S t o c k - R e c r u i t m e n t R e l a t i o n s h i p s f o r M a j o r S t o c k s 169 <2? V L I S T OF TABLES T a b l e 1. P r o d u c t i o n a r e a s and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s 14 T a b l e 2. P e r c e n t a g e o f F r a s e r R i v e r s o c k e y e a d u l t s t h a t r e t u r n e d v i a J o h n s t o n e S t r a i t 19 T a b l e 3. P e r c e n t a g e o f F r a s e r R i v e r p i n k a d u l t s t h a t r e t u r n e d v i a J o h n s t o n e S t r a i t 19 T a b l e 4. H a r v e s t a r e a s a n d c o r r e s p o n d i n g s t a t i s t i c a l a r e a s 21 T a b l e 5 - 1 0 . P e r c e n t a g e a l l o c a t i o n o f h a r v e s t t o p r o d u c t i o n a r e a s 22-24 T a b l e 11. R e s i d e n c e a r e a s a n d c o r r e s p o n d i n g s t a t i s t i c a l a r e a s 32 T a b l e 12-16. P r o p o r t i o n o f t o t a l s t o c k r e a r i n g i n e a c h r e s i d e n c e a r e a by p r o d u c t i o n a r e a 33-35 T a b l e 17. R i c k e r model p a r a m e t e r s 58 T a b l e 1 8 . Power model p a r a m e t e r s 59 T a b l e 19. B e v e r t o n - H o l t model p a r a m e t e r s 60 T a b l e 20. Rank t e s t o f R i c k e r model "o ( " p a r a m e t e r s . . . . . . . . 75 T a b l e 21. W i t h i n s p e c i e s c o r r e l a t i o n of p r o d u c t i o n a r e a , R i c k e r "cX" p a r a m e t e r , v a r i a n c e and a v e r a g e escapement . 77 T a b l e 22-27. Optimum e s c a p e m e n t , optimum y i e l d , optimum e x p l o i t a t i o n r a t e and maximum t o l e r a b l e e x p l o i t a t i o n r a t e e s t i m a t e d by R i c k e r and B e v e r t o n - H o l t m o d e l s 109-111 T a b l e 28-33. "Bayes e q u i v a l e n t " optimum escapement a t d i f f e r e n t l e v e l s o f 7\. 114-116 T a b l e 34-39. Optimum e x p l o i t a t i o n r a t e and maximum t o l e r a b l e e x p l o i t a t i o n r a t e a t d i f f e r e n t l e v e l s o f A 119-121 T a b l e 40-45. C u r r e n t e s c a p e m e n t , G.W.G. optimum escapement e s t i m a t e s and our optimum escapement e s t i m a t e s w i t h p r o b a b l e b o u n d s . 123-125 T a b l e 46. R a t i o o f c u r r e n t e s c a p e m e n t t o v a r i o u s optimum & escapement e s t i m a t e s 126 vi L I S T OF FIGURES F i g u r e 1. The h i s t o r y o f C a n a d i a n salmon c a t c h e s s i n c e 1870. 2 F i g u r e 2. " P r o d u c t i o n u n i t s " and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s 13 F i g u r e 3. " A c t u a l " and " o b s e r v e d " s t o c k - r e c r u i t m e n t d a t a p o i n t s u s i n g f i x e d a l l o c a t i o n method t o s e p a r a t e m i x e d c a t c h e s 27 F i g u r e 4. " A c t u a l " and " o b s e r v e d " s t o c k - r e c r u i t m e n t d a t a p o i n t s w i t h c o m p a r a b l e measurement e r r o r s i n t h e c a t c h a n d e s c a p e m e n t r e s p e c t i v e l y 53 F i g u r e 5a. C o m p a r i s o n o f <X and d"^ ( R i c k e r model) e s t i m a t e d by b a c k - c a l c u l a t i o n v e r s u s f i x e d a l l o c a t i o n o f m i x e d c a t c h e s 62 F i g u r e 5b. C o m p a r i s o n o f e q u i l i b r i u m s t o c k s i z e s e s t i m a t e d by b a c k - c a l c u l a t i o n v e r s u s f i x e d a l l o c a t i o n of m i x e d c a t c h e s .. 64 F i g u r e 6a. C o m p a r i s o n o f maximum r e c r u i t s p e r spawner and v a r i a n c e e s t i m a t e d by R i c k e r and B e v e r t o n - H o l t m o d e ls 67 F i g u r e 6b. C o m p a r i s o n o f e q u i l i b r i u m s t o c k s i z e s e s t i m a t e d by R i c k e r and B e v e r t o n - H o l t m o d e l s . . 69 F i g u r e 7. R i c k e r model "c<" p a r a m e t e r and 95% c o n f i d e n c e l i m i t s 72 F i g u r e 8. R i c k e r model v a r i a n c e s 74 F i g u r e 9. A v e r a g e e s c a p e m e n t v e r s u s R i c k e r model "o<" p a r a m e t e r 80 F i g u r e 10. A v e r a g e e s c a p e m e n t v e r s u s R i c k e r model v a r i a n c e . . . 82 F i g u r e 11. R i c k e r m odel "c<" p a r a m e t e r v e r s u s v a r i a n c e 84 F i g u r e 12. C o r r e l a t i o n o f d e v i a t i o n i n l o g r e c r u i t s p e r spawner f r o m R i c k e r model p r e d i c t i o n s by s p e c i e s and p r o d u c t i o n a r e a 86 F i g u r e 13. C o r r e l a t i o n o f d e v i a t i o n i n l o g r e c r u i t s p e r spawner f r o m R i c k e r model p r e d i c t i o n s v e r s u s c oho s t o c k s i z e 88 F i g u r e 14. 95% c o n f i d e n c e l i m i t s o f Power model " f l " e s t i m a t e s 91 ^ r vii F i g u r e 15. Index of d e n s i t y dependence (Power model "(3") v e r s u s cube r o o t of f e c u n d i t y 93 F i g u r e 16. Changes of R i c k e r model "o(" and "/S" parameters as i s i n c r e a s e d from 0.0 t o 2.0 96 F i g u r e 17. Optimum escapement e s t i m a t e s and p r o b a b l e bounds.. 129 } ACKNOWLEDGEMENTS v i 1 1 I am d e e p l y i n d e b t e d t o my s u p e r v i s o r , C . J . W a l t e r s , f o r h i s s u p p o r t and encoura g e m e n t d u r i n g t h e c o u r s e o f t h i s s t u d y , and t o R. H i l b o r n , D. Ludwig and M. S t a l e y f o r p r o v i d i n g i n s p i r a t i o n s n e e d e d f o r t h e a n a l y s i s . Many p e o p l e o f t h e D e p a r t m e n t o f F i s h e r i e s and Oceans were h e l p f u l and g e n e r o u s w i t h t h e i r t i m e i n d i r e c t i n g me t o e s s e n t i a l d a t a s o u r c e s . I wo u l d p a r t i c u l a r l y l i k e t o t h a n k D. A n d e r s o n , R. H a r r i s o n , R. K a d o w a k i , M. P e t e r s , B. R i d d e l l , P. S t a r r and E. Z y b l u t . I am g r a t e f u l t o I . Y e s a k i f o r p r e p a r i n g t h e f i g u r e s . F i n a l l y I wo u l d l i k e t o t h a n k my p a r e n t s f o r t h e i r e n c o u r a g e m e n t d u r i n g my s t u d e n t y e a r s . K_ INTRODUCTION The f i v e s p e c i e s o f P a c i f i c salmon ( O n c o r h y n c h u s spp.) i n d i g e n o u s t o B r i t i s h C o l u m b i a have been e x p l o i t e d c o m m e r c i a l l y s i n c e t h e l a t e 1800s. L a n d i n g s by C a n a d i a n f i s h e r m a n i n d i c a t e t h a t s o c k e y e ( O^ n e r k a ) and chum ( O^ k e t a ) were much more a b u n d a n t h i s t o r i c a l l y t h a n a t t h e p r e s e n t ( F i g . 1 ) . P i n k ( 0. q o r b u s c h a ) c a t c h e s have been h i g h l y v a r i a b l e due t o t h e two-y e a r c y c l e of t h i s s p e c i e s and due t o f l u c t u a t i o n s i n p o p u l a t i o n s i z e s . However no s i g n i f i c a n t t r e n d i s a p p a r e n t i n t h e l a n d i n g s s i n c e t h e e a r l y 1900s. Coho ( 0^ k i s u t c h ) and s p r i n g ( O. t s h a w y t s c h a ) p r o d u c t i o n i n c r e a s e d s t e a d i l y u n t i l t h e e a r l y 1970s. C a t c h e s o f b o t h s p e c i e s have d e c l i n e d r e c e n t l y . S o c k e y e p r o d u c t i o n d r o p p e d s i g n i f i c a n t l y a f t e r t h e H e l l ' s G a t e d i s a s t e r on t h e F r a s e r R i v e r i n 1913 and 1914. C o n t i n u e d h e a v y e x p l o i t a t i o n has p r e v e n t e d r e c o v e r y of t h e s e s t o c k s even t o t h i s d a t e . I t has o n l y r e c e n t l y been r e c o g n i z e d t h a t chum i s t h e l e a s t p r o d u c t i v e salmon s p e c i e s i n B.C. I t s p e r s i s t e n t d e c l i n e i s g e n e r a l l y b e l i e v e d t o be t h e r e s u l t of o v e r f i s h i n g t h r o u g h o u t most of t h i s c e n t u r y . I t i s d i f f i c u l t t o r e l a t e c oho and s p r i n g c a t c h e s t o l o c a l p r o d u c t i v i t y . T a g g i n g s t u d i e s i n t h e 1930s and 1960s ( P r i t c h a r d 1934, H o l l e t t 1970), and t h e more r e c e n t Coded W i r e T a g g i n g Program, show t h a t s i g n i f i c a n t p o r t i o n s of t h e s p r i n g and coho c a t c h e s i n B.C. a r e from s t o c k s o f U n i t e d S t a t e s o r i g i n . ( R i d d e l l p e r s . Comm). Be c a u s e of t h e anadromous n a t u r e o f P a c i f i c s a l m o n , c o n c e r n s have been v o i c e d s i n c e as e a r l y a s 1909 (Babcock 1909) t h a t a " s u f f i c i e n t " number of s p a w n ing a d u l t s must be a l l o w e d t o o U n d c . o y i e l d . « i n c 0 1 0 , 0 , . n d t h o t e r n d e c l i n e i n chum p r o d u c t i o n , (from Walters . 1 . . U 9 B 2 ) C A T C H (millions of pieces) 3 p a s s t h r o u g h t h e f i s h e r y . R e s t r i c t i o n s on f i s h i n g t i m e , l o c a t i o n a n d g e a r have been i n e f f e c t s i n c e t h e l a t e 1800s t o l i m i t c a t c h e s on m a j o r salmon p r o d u c i n g s t r e a m s i n B.C. However, what c o n s t i t u t e s " s u f f i c i e n t " escapement r e m a i n s r a t h e r u n c e r t a i n e v e n t o t h e p r e s e n t . B e f o r e t h e 1950s, t h e r e was g r e a t u n c e r t a i n t y a b o u t t h e p r o d u c t i o n p o t e n t i a l of t h e s t o c k s , and no c l e a r c o n c e n s u s a b o u t t h e i n f o r m a t i o n n e e d e d t o improve u n d e r s t a n d i n g . C a t c h , e s capement and o t h e r b i o l o g i c a l d a t a were c o l l e c t e d o n l y s p o r a d i c a l l y , and were s e l d o m a n a l y s e d s y s t e m a t i c a l l y . The e f f e c t and e x t e n t of h a b i t a t d e g r a d a t i o n on p r o d u c t i o n were l a r g e l y unknown. W i t h o u t q u a n t i t a t i v e m e a s u r e s of " s u f f i c i e n t " e s c a p e m e n t , management a c t i o n s were l a r g e l y c o m p r o m i s e s between f i s h e r m e n ' s demand f o r l a r g e r c a t c h e s on one hand and b i o l o g i s t s ' d e s i r e f o r l a r g e r e s c a p e m e n t s on t h e o t h e r . S i n c e t h e 1950s, more p r e c i s e q u a n t i t a t i v e m o d e ls have been u s e d e x t e n s i v e l y f o r salmon management. R i c k e r ( 1 9 5 4 ) p r o p o s e d t h e " s t o c k - r e c r u i t m e n t m o d e l " from w h i c h t h e l e v e l o f escapement t h a t w i l l p r o d u c e t h e maximum s u s t a i n e d y i e l d (MSY) c a n be c a l c u l a t e d . U n f o r t u n a t e l y , f i t t i n g t h e " R i c k e r c u r v e " t o d a t a i s n o t s t r a i g h t - f o r w a r d . T a n a k a (1962) s u g g e s t e d d i f f e r e n t ways t o f i t t h e c u r v e and a r g u e d a b o u t t h e p r o p e r d a t a t o i n c l u d e . R i c k e r and S m i t h (1975) s u g g e s t e d t h a t o l d d a t a may not be r e l e v a n t t o c u r r e n t management b e c a u s e c o n d i t i o n s may have c h a n g e d due t o e n v i r o n m e n t a l d e t e r i o r a t i o n , s e l e c t i o n by t h e f i s h e r y , and e x t i n c t i o n of s u b s t o c k s . C o n c e r n s have a l s o been r a i s e d a b o u t t h e p o s s i b i l i t y of i n t e r a c t i o n between d i f f e r e n t y e a r c l a s s e s (Ward and L a r k i n 1964, L a r k i n 1971, R i c k e r 1962), 4 and a b o u t p o s s i b l e m u l t i p l e e q u i l i b r i a (Neave 1954, P e r t e r m a n 1977) i n some salmon p o p u l a t i o n s . More r e c e n t l y , W a l t e r s and L u d w i g (1981) and L u d w i g and W a l t e r s (1981) c o n c l u d e d t h a t measurement e r r o r s commonly f o u n d i n e s capement e s t i m a t e s t e n d t o b i a s t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p so as t o p r o m o t e s e v e r e o v e r e x p l o i t a t i o n . A n o t h e r p r o b l e m i s t o d e t e r m i n e what c o n s t i t u t e s a u n i t s t o c k . I t i s w e l l r e c o g n i s e d t h a t salmon r u n s t o l a r g e r i v e r s y s t e m s ( e . g . F r a s e r , Skeena) a r e made up o f many s u b s t o c k s , w h i c h may have o v e r l a p p i n g r u n t i m i n g s and d i f f e r e n t s u s t a i n e d h a r v e s t r a t e s ( L a r k i n and M c D o n a l d 1 9 6 8 ) . But t h e s e s u b s t o c k s a r e o f t e n h a r v e s t e d j o i n t l y i n a common f i s h e r y and t h e m i x e d c a t c h e s c a n s e l d o m be s e p a r a t e d a c c u r a t e l y . R e c e n t l y t h e D e p a r t m e n t o f F i s h e r i e s and O c e a n s has been moving f i s h i n g a r e a s away f r o m r i v e r mouths t o a v o i d o v e r f i s h i n g o f some l o c a l s t o c k s by t h e i n c r e a s i n g l y e f f i c i e n t f l e e t ( A n d e r s o n 1980). S i m i l a r l y t h e t r o l l f l e e t , w h i c h o p e r a t e s where a l l N o r t h A m e r i c a n s t o c k s mix , has been e n c o u r a g e d t o t a k e a d v a n t a g e o f t h e A m e r i c a n enhancement p r o d u c t i o n o f c oho and s p r i n g . The r e s u l t i s t h a t i t i s now a l m o s t i m p o s s i b l e t o measure t h e c o n t r i b u t i o n of any s i n g l e s t o c k v e r y a c c u r a t e l y . R i c k e r (1973) warned t h a t i f s t o c k s o f u n e q u a l p r o d u c t i v i t y a r e h a r v e s t e d t o g e t h e r , t h e o p t i m a l e x p l o i t a t i o n r a t e c a n be e x c e e d e d w i t h o u t b e i n g n o t i c e d . F u r t h e r m o r e t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p o f t h e m i x t u r e b e h a v e s d i f f e r e n t l y d u r i n g t h e e x p a n s i o n p h a s e of t h e f i s h e r y t h a n when f i s h i n g p r e s s u r e i s r e l a x e d . R e h a b i l i t a t i o n of t h e s t o c k s t o optimum l e v e l s by i n c r e a s i n g o v e r a l l e scapement may t a k e s e v e r a l g e n e r a t i o n s . 5 S i n c e t h e a d v e n t o f c o m p u t e r s , more complex m o d e l s have been p r o p o s e d f o r f i s h e r i e s management ( P a u l i k and G r e e n o u g h 1966, S o u t h w a r d 1968, W a l t e r s 1969, P a r r i s h ( e d . ) 1973) ,and f o r e c o l o g i c a l o p t i m i z a t i o n i n g e n e r a l ( P a t t e n ( e d . ) 1971, H o l l i n g (ed.) 1980). U n f o r t u n a t e l y most o f t h e s e m o d e l s a r e u s e d t o p r e d i c t o p t i m a l p o l i c i e s a t e q u i l i b r i u m . A l l e n (1973) and W a l t e r s ( 1 9 7 5 ) a r g u e d t h a t by f o l l o w i n g s u c h p o l i c i e s , t h e f i s h e r y m i g h t be b r o u g h t t o an e q u i l i b r i u m t h a t i s n e i t h e r t r u l y optimum nor p r o d u c t i v e o f i n f o r m a t i o n n e c e s s a r y t o d e t e r m i n e t h e t r u e optimum. H a r v e s t s t r a t e g y c u r v e s or " c o n t r o l l a w s " have been d e v e l o p e d t o s p e c i f y optimum h a r v e s t r a t e s f o r n o n - e q u i l i b r i u m s i t u a t i o n s a s w e l l as d e a l i n g w i t h u n c e r t a i n t y a s s o c i a t e d w i t h v a r i o u s e s t i m a t e s (Huang e t . a l 1976, W a l t e r s and H i l b o r n 1976, S i l v e r t 1978, W a l t e r s 1981, Ludwig and W a l t e r s 1981). By t h e l a t e 1970s, q u a n t i t a t i v e t e c h n i q u e s f o r e s t i m a t i n g t h e " d e s i r e d " e s capement t h a t would p r o d u c e t h e maximum b i o l o g i c a l s u s t a i n e d y i e l d were w e l l e s t a b l i s h e d . However, G o r d o n ( 1 9 5 4 ) , C r u t c h f i e l d and P o n t e c o r r o (1969) and R o e d e l (ed.) (1975) n o t e d t h a t maximum s u s t a i n e d b i o l o g i c a l y i e l d i s r a r e l y t h e optimum p o l i c y f o r most f i s h e r i e s b e c a u s e o f s o c i a l and e c o n o m i c o b j e c t i v e s . U n f o r t u n a t e l y , v e r y l i t t l e e f f o r t has been s p e n t t o d e t e r m i n e what t h e a c t u a l g o a l s a r e f o r management. Keeney (1977) and H i l b o r n and W a l t e r s (1977) u s e d m u l t i a t t r i b u t e u t i l i t y a n a l y s i s t o i n v e s t i g a t e t h e d i f f e r i n g g o a l s o f salmon management, b u t t h e r e s u l t s a r e r a t h e r s u b j e c t i v e and depend g r e a t l y on i n d i v i d u a l p r e f e r e n c e s a n d / o r b i a s e s . Much t i m e and e f f o r t have been s p e n t i n t h e p a s t 30 y e a r s t o m o n i t o r B.C. salmon c a t c h and e s c a p e m e n t . Y e t few a t t e m p t s 6 have been made t o s y s t e m a t i c a l l y s t u d y t h e s t o c k - r e c r u i t m e n t p r o b l e m . B e c a u s e of t h e above p r o b l e m s and t h e p r e s e n c e o f l a r g e s a m p l i n g e r r o r s , most r e s e a r c h e r s and b i o l o g i s t s s hy away from u s i n g t h e d a t a t o e s t i m a t e "optimum" e s c a p e m e n t s . W i t h l i t t l e o r no h e l p f r o m r e s e a r c h e r s , some managers r e s o l v e t h i s d i f f i c u l t p r o b l e m by d e f i n i n g " d e s i r e d " o r "optimum" e s c a p e m e n t v e r y s i m p l i s t i c a l l y ( f o r example, t h e l a r g e s t escapement s i n c e 1950 t h a t h as p r o d u c e d an e q u a l o r h i g h e r s u b s e q u e n t e s c a p e m e n t ) . Some s e t t l e f o r t h e p r e s e r v a t i o n o f t h e s t a t u s quo w i t h o u t q u e s t i o n i n g what t h e c u r r e n t c o n d i t i o n of t h e s t o c k s i s . O t h e r s s i m p l y r e a c t t o wha t e v e r p o l i t i c a l p r e s s u r e i s on hand r e g a r d l e s s o f t h e c o n s e q u e n c e s t o t h e s t o c k s . The S a l m o n i d Enhancement P r o g r a m (MacLeod 1977) i s c r e a t i n g i n c r e a s e d f i s h i n g r a t e s on n a t u r a l s t o c k s , and t h e im p a c t o f enhancement f o r t h e c o a s t a s a whole has n o t been e x a m i n e d . I t i s q u i t e p r o b a b l e t h a t t h e enhancement p r o g r a m w i l l r e s u l t i n as much l o s s o f w i l d p r o d u c t i o n as i s added by enhancement a c t i v i t i e s . Thus t h e r e i s a c r i t i c a l n e ed t o examine n a t u r a l p r o d u c t i v i t y f o r t h e c o a s t a s w h o l e . A c c u m u l a t e d h i s t o r i c a l d a t a have n e v e r been p u l l e d t o g e t h e r t o p r o v i d e an o v e r v i e w o f p a t t e r n s a n d t r e n d s , o r a n a l y s e d c a r e f u l l y and c o n s i s t e n t l y f o r s t o c k - r e c r u i t m e n t p a t t e r n s . The p u r p o s e of t h i s t h e s i s i s t o p r o v i d e a g e n e r a l a c c o u n t of t h e n a t u r a l s t o c k - r e c r u i t m e n t d y n a m i c s f o r a l l major manageable s t o c k s of salmon a l o n g t h e B.C. c o a s t , and t o e s t i m a t e o p t i m a l p o l i c i e s t h a t w o u l d p r o d u c e maximum e x p e c t e d y i e l d s u n d e r d i f f e r e n t a s s u m p t i o n s a b o u t b i o l o g i c a l u n c e r t a i n i t i e s . Such p o l i c i e s may not n e c e s s a r i l y be t h e most 7 d e s i r a b l e nor a c h i e v a b l e i n p r a c t i c e , but should serve as a standard of comparison with other p o l i c i e s t h a t take i n t o account r i c h e r s e t s of o b j e c t i v e s and c o n s t r a i n t s . Chapter 2 o u t l i n e s methods f o r e s t i m a t i n g spawning stoc k s and catches a s s o c i a t e d with these s t o c k s from mixed f i s h e r i e s . Chapter 3 p r e s e n t s methods and r e s u l t s from s t o c k - r e c r u i t m e n t a n a l y s i s . Chapter 4 d e s c r i b e s methods and r e s u l t s of e s t i m a t i n g optimal p o l i c i e s under d i f f e r e n t assumptions of b i o l o g i c a l u n c e r t a i n t i e s . F i n a l l y chapter 5 d i s c u s s e s the major f i n d i n g s and c o n c l u s i o n s of t h i s study. 5/ 8 2. ESTIMATION OF SPAWNING STOCK AND RECRUITMENT D e s p i t e t h e f a c t t h a t P a c i f i c s a l m on ( O n c o r h y n c h u s spp.) i s one o f t h e most s t u d i e d g e n e r a o f f i s h i n t h e w o r l d , much u n c e r t a i n t y s t i l l s u r r o u n d s many i m p o r t a n t r e l a t i o n s h i p s e s s e n t i a l t o soun d management p r a c t i c e . Sound p o p u l a t i o n s t u d i e s r e q u i r e many y e a r s of d a t a c o l l e c t i o n , w h i c h i n v o l v e s t r e m endous manpower, e q u i p m e n t and f i n a n c i a l s u p p o r t . The Dep a r t m e n t o f F i s h e r i e s and Oceans has not been p r e p a r e d t o make s u c h i n v e s t m e n t s s y s t e m a t i c a l l y o v e r t h e v a s t g e o g r a p h i c a l a r e a c o v e r e d by t h i s s t u d y . C o n s e q u e n t l y , much o f t h e d a t a u s e d i n t h i s t h e s i s came from p u b l i s h e d and u n p u b l i s h e d b i t s a nd p i e c e s o f i n f o r m a t i o n r e c o r d e d d u r i n g t h e p a s t t w e n t y - f i v e y e a r s by many f i s h e r i e s o f f i c e r s , t e c h n i c i a n s , b i o l o g i s t s and r e s e a r c h e r s o f t h e D e p a r t m e n t of F i s h e r i e s and O c e a n s . F r e q u e n t c h a n g e s of p e r s o n n e l , e q uipment and methods u s e d u n d o u b e d l y r e n d e r t h e e r r o r s t r u c t u r e of t h e s e d a t a e x t r e m e l y d i f f i c u l t t o e s t i m a t e . Some p o s s i b l e s o u r c e s o f e r r o r a n d a t t e m p t s t o d e a l w i t h them w i l l be d i s c u s s e d i n t h i s c h a p t e r . 2. 1 S o u r c e s o f D a t a S i n c e 1951, r e l i a b l e r e c o r d s of c o m m e r c i a l c a t c h e s of t h e f i v e s p e c i e s o f P a c i f i c salmon n a t i v e t o B r i t i s h C o l u m b i a have been r e p o r t e d a n n u a l l y by t h e F i s h e r i e s and M a r i n e S e r v i c e (B.C. C a t c h S t a t i s t i c s , D e p a r t m e n t o f F i s h e r i e s and Oceans, P a c i f i c r e g i o n ) . F o r most s t r e a m s , e s c a p e m e n t s t o s p a w n i n g g r o u n d s have a l s o been e s t i m a t e d s i n c e 1948 by f i s h e r i e s o f f i c e r s and 9 r e p o r t e d on f o r m bc16 o f t h e D e p a r t m e n t of F i s h e r i e s and O c e a n s . T h e s e s p a w n i n g f i l e s a r e c u r r e n t l y b e i n g o r g a n i z e d and p u b l i s h e d as s p a w n i n g c a t a l o g u e s f o r e a c h s t a t i s t i c a l a r e a ( D e p a r t m e n t of F i s h e r i e s and Oceans D a t a R e p o r t s ) . Most of t h e e s c a p e m e n t e s t i m a t e s u s e d i n t h i s s t u d y were o b t a i n e d f r o m t h e s e s p a w n i n g c a t a l o g u e s where p u b l i s h e d , or by summing t h e f i s h e r i e s o f f i c e r s ' e s t i m a t e s o f i n d i v i d u a l s p a w n i n g s t r e a m s t o o b t a i n s t a t i s t i c a l a r e a t o t a l s . D a t a f o r F r a s e r r i v e r s o c k e y e and p i n k s t o c k s were o b t a i n e d from a n n u a l r e p o r t s of t h e I n t e r n a t i o n a l P a c i f i c Salmon F i s h e r i e s C o m m i s s i o n . Age c o m p o s i t i o n o f s o c k e y e , chum and s p r i n g salmon c a t c h e s from 1957 t o 1972 were from t h e s e r i e s o f p u b l i c a t i o n s by B i l t o n e t . a l . ( 1 9 6 5 - 1 9 7 3 ) , w h i l e e a r l i e r and l a t e r d a t a were o b t a i n e d from v a r i o u s d i s t r i c t management b i o l o g i s t s . Coho and s p r i n g s p o r t s c a t c h e s t i m a t e s were o b t a i n e d from t h e A n n u a l B.C. S p o r t s C a t c h S t a t i s t i c s R e p o r t s w i t h more r e c e n t e s t i m a t e s f r o m A r g u e e t . a l . ( 1 9 7 7 ) . C a t c h s t a t i s t i c s f o r W a s h i n g t o n s t a t e and C o l u m b i a r i v e r c o ho and s p r i n g were from I.N.P.F.C. S t a t i s t i c a l y e a r b o o k s ( 1 9 6 7 - 7 8 ) , and e s c a p e m e n t s were from K o r n 1977 and H o l l a n d 1977 w i t h u p d a t e d d a t a from R i d d e l l ( p e r s . Comm.). The methods, c o n s i d e r a t i o n s and a s s u m p t i o n s u s e d i n v a r i o u s e s t i m a t e s ( e . g . s t o c k d e f i n i t i o n ) a r e d i s c u s s e d i n more d e t a i l i n t h e f o l l o w i n g s e c t i o n s . 2 . 2 S t o c k D e f i n i t i o n ? One of t h e most f u n d a m e n t a l r e q u i r e m e n t s f o r t h e s u c c e s s f u l management o f a f i s h e r y r e s o u r c e i s t o d e f i n e what c o n s t i t u t e s a 10 u n i t s t o c k . I d e a l l y , a u n i t s t o c k c a n be d e f i n e d a s "a s i n g l e , i n t e r b r e e d i n g p o p u l a t i o n " . In n a t u r e , however, i t i s u s u a l l y t h e e x c e p t i o n r a t h e r t h a n t h e r u l e t h a t s u c h an i d e a l e x i s t s . F o r P a c i f i c s a l m o n , a u n i t s t o c k i s u s u a l l y r e f e r r e d t o as a s p e c i e s of salmon i n h a b i t i n g a p a r t i c u l a r s t r e a m ( L a r k i n 1970). But b e c a u s e o f t h e i r s t r o n g homing t e n d e n c y , a s p e c i e s o f s almon u t i l i z i n g a s t r e a m may be d i v i d e d i n t o numerous s e m i -d i s c r e t e " s u b - s t o c k s " w h i c h , t o a l a r g e e x t e n t , do n o t p a r t i c i p a t e i n a common gene p o o l ( e . g . v a r i o u s F r a s e r r i v e r s o c k e y e s t o c k s ) . A l s o s t r a y i n g among s t r e a m s i s common ( M e r r e l l 1962, Simon 1972, and r e c e n t r e i n v a s i o n o f p i n k a b o v e H e l l s g a t e i n t h e F r a s e r ) . Thus t h e d e f i n i t i o n of a u n i t s t o c k becomes r a t h e r a r b i t r a r y even i n a s t r i c t l y b i o l o g i c a l s e n s e . In p r a c t i c e b o t h b i o l o g i c a l , p o l i t i c a l a n d e conomic c o n s i d e r a t i o n s have t o be t a k e n i n t o a c c o u n t f o r d e l i m i t i n g c e r t a i n g r o u p s o f salmon as management u n i t s o r m anageable s t o c k s . W i t h i n t h e p o l i t i c a l b o u n d a r i e s of t h e B r i t i s h C o l u m b i a c o a s t , d i f f e r e n t s p e c i e s o f salmon from d i f f e r e n t o r i g i n s a r e h a r v e s t e d j o i n t l y i n many p l a c e s ( e . g . J o h n s t o n e S t r a i t ) . B e c a u s e o f t h e h i g h m o b i l i t y of t h e f l e e t and t h e y e a r t o y e a r f l u c t u a t i o n s i n t h e a bundance of f i s h _and t h e i r r o u t e s of m i g r a t i o n ,the p r o b l e m o f a l l o c a t i n g t h e s e c a t c h e s c o r r e c t l y t o t h e i r s t r e a m s o f o r i g i n i s v e r y d i f f i c u l t . U n l e s s t h e m i x e d c a t c h e s c a n be s e p a r a t e d w i t h some c o n f i d e n c e , a l l t h e s t r e a m s c o n t r i b u t i n g a s i g n i f i c a n t p o r t i o n o f t h e i r p r o d u c t i o n t o t h e s e f i s h e r i e s s h o u l d be t r e a t e d as a s i n g l e u n i t f o r a s s e s s m e n t p u r p o s e s ( G u l l a n d 1969). Any c l a i m f o r a more d e t a i l e d breakdown i n t o s u b s t o c k u n i t s would s i m p l y be m i s l e a d i n g . W i t h t h e above c o n s i d e r a t i o n s i n mind, and a f t e r c o n s i d e r a b l e d i s c u s s i o n w i t h salmon management b i o l o g i s t s o f t h e D e p a r t m e n t of F i s h e r i e s and O c e a n s (D. A n d e r s o n , A.W. A r g u e , F. F r a s e r , K. P e t r i e , D. S c h u t z , E. Z y b l u t ) , t w e l v e " p r o d u c t i o n a r e a s " were d e l i m i t e d a l o n g t h e B r i t i s h C o l u m b i a c o a s t ( f i g . 2 ) . T a b l e 1 l i s t s t h e s e " p r o d u c t i o n a r e a s " and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s u s e d f o r r e p o r t i n g by t h e D e p a r t m e n t o f F i s h e r i e s and O c e a n s . W i t h i n e a c h p r o d u c t i o n a r e a , s o c k e y e , c o h o , chum, c h i n o o k , odd y e a r p i n k and even y e a r p i n k salmon were c o n s i d e r e d as s e p a r a t e p r o d u c t i o n s t o c k s . O b v i o u s l y , as knowledge o f v a r i o u s a s p e c t s o f salmon b i o l o g y i m p r o v e s , f u t u r e d e f i n i t i o n s o f p r o d u c t i o n u n i t s may be s u b s t a n t i a l l y more r e f i n e d . 2.3 E s t i m a t i o n o f Spawners As i n o t h e r p o p u l a t i o n s , many f a c t o r s have t o be t a k e n i n t o a c c o u n t i n d e s i g n i n g methods t o c e n s u s a s p a w n ing p o p u l a t i o n o f s a l m o n . B e c a u s e of t h e i m p o r t a n c e o f e r r o r s i n s p a w n ing e s t i m a t e s f o r t h e f i n a l s t o c k - r e c r u i t m e n t a n a l y s i s t o be d e t a i l e d i n t h e n e x t c h a p t e r , s e v e r a l methods commonly u s e d t o enumerate s p a w n i n g p o p u l a t i o n s of salmon s t o c k s i n B r i t i s h C o l u m b i a a r e r e v i e w e d below so as t o p r o v i d e a f e e l i n g f o r t h e l i k e l y m a g n i t u d e o f e r r o r s i n v o l v e d . A common method i s t o make s e v e r a l v i s u a l a p p r a i s a l s o f a s pawning p o p u l a t i o n from a i r p l a n e s , c o u n t i n g t o w e r s o r on f o o t . E s t i m a t e s may be o b t a i n e d by c o u n t i n g t h e numbers o f l i v e o r d e ad salmon p r e s e n t t h e n e x t r a p o l a t i n g t o t h e t o t a l p o p u l a t i o n 12 F i g . 2. " P r o d u c t i o n u n i t s " and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s . \ PRODUCTION AREA ST A T I S T I C A L AREA 1. Queen C h a r l o t t e 1 ... (Q.C.1) 2. Queen C h a r l o t t e 2 ... (Q.C.2) 3. N a s s (Nass) 4. S k e e n a ( S k e e n a ) 5. C e n t r a l C o a s t (C.C.) 6. R i v e r s - S m i t h (R-S) 7. J o h n s t o n e S t r a i t .... ( J . S . ) 8. G e o r g i a S t r a i t (G.S.) 9. F r a s e r R i v e r ( F r a s e r ) 10. J u a n de F u c a S t r a i t . ( J . F . S . ) 11. S.W. V a n c o u v e r I s l a n d (SWVI) 12. N.W. V a n c o u v e r I s l a n d (NWVI) 1 2 3 4 5,6,7,8 9,10 11,12,13 14,15,16,17, 18,28 29 19,20 21,22,23,24 25,26,27 T a b l e 1 : P r o d u c t i o n a r e a s and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s . 1 5 f r o m t h e s e s a m p l e s . The e x t r a p o l a t i o n i s u s u a l l y n o t done s y s t e m a t i c a l l y ; j u s t an i n d e x i s p r o v i d e d by t h e o b s e r v e r , g i v i n g h i s o v e r a l l i m p r e s s i o n o f a b u n d a n c e . T h e s e e s t i m a t e s ( o r i n d e x e s ) d e p e n d g r e a t l y on t h e o b s e r v e r ' s s u b j e c t i v e judgement and e x p e r i e n c e . U n d o u b t e d l y s u c h e s t i m a t e s a r e a f f e c t e d by f l u c t u a t i o n s o f t h e p h y s i c a l c h a r a c t e r i s t i c s o f t h e s t r e a m s , t h e i n t e r v a l s o f i n s p e c t i o n , e x p e r i e n c e o f t h e o b s e r v e r , t h e r u n t i m i n g and s t r e a m l i f e of t h e f i s h , and many o t h e r u n d e t e r m i n e d f a c t o r s . In a r a r e c a s e when t h e a c c u r a c y of f o o t s u r v e y was p u t t o a d i r e c t t e s t , the d i s c r e p a n c y was f o u n d t o be a r o u n d 50% t h e e s t i m a t e s from f o o t s u r v e y were o n l y h a l f o f t h e a c t u a l t o t a l ( B r e t t 1952)'. V a r i a t i o n s of +- 50% were a l s o f o u n d i n a e r i a l s u r v e y s , and d i f f e r e n t o b s e r v e r s made i n c o n s i s t e n t c o u n t s among d i f f e r e n t s t r e a m s (Bevan 1961). D i s c u s s i o n s w i t h f i s h e r y o f f i c e r s and b i o l o g i s t s d u r i n g r e c e n t workshops f o r t h e P e a r s e C o m m i s s i o n on P a c i f i c F i s h e r i e s P o l i c y ( W a l t e r s , p e r s . Comm.) have r e v e a l e d some even more d r a m a t i c e x a m p l e s , where v i s u a l s u r v e y e s t i m a t e s have d i f f e r e d by up t o an o r d e r of m a g n i t u d e f r o m e s t i m a t e s b a s e d on more s y s t e m a t i c p r o c e d u r e s s u c h as f e n c e c o u n t s and m a r k - r e c a p t u r e t r i a l s . W h i l e v i s u a l c o u n t s g e n e r a l l y u n d e r e s t i m a t e s p a w n i n g p o p u l a t i o n s , t a g g i n g and r e c o v e r y p r o c e d u r e s t e n d t o o v e r e s t i m a t e ( B r e t t 1961 ,Vernon e t a l 1964). F o r H a r r i s o n r i v e r s o c k e y e , f a i r l y p r e c i s e e s t i m a t e s c o u l d be o b t a i n e d o n l y by t a g g i n g v e r y c l o s e t o t h e s p a w n i n g g r o u n d s . As t h e d i s t a n c e between t a g g i n g t o r e c o v e r y i n c r e a s e d , t h e c a l c u l a t e d p o p u l a t i o n a l s o i n c r e a s e d . And a t some d i s t a n c e , t h e e r r o r became so l a r g e t h a t t h e e s t i m a t e s were u s e l e s s by any c r i t e r i o n ( S c h a e f f e r 16 1951). The t h e o r y , a s s u m p t i o n s , a d v a n t a g e s and d r a w b a c k s o f e n u m e r a t i n g a p o p u l a t i o n by mark and r e c a p t u r e methods have been w e l l s t u d i e d and can be o b t a i n e d f r o m H o w a r d ( 1 9 4 8 ) , V e r n o n e t a l ( 1 9 6 4 ) , S c h a e f f e r ( 1 9 5 1 ) and R i c k e r ( 1 9 7 5 ) . T e s t f i s h i n g c o n d u c t e d j u s t u p s t r e a m o f c o m m e r c i a l f i s h e r i e s s u p p l i e s r a p i d i n f o r m a t i o n on escapement s t r e n g t h i n a few s y s t e m s . A s m a l l , b u t unknown, p e r c e n t a g e o f e s c a p e m e n t i s i n t e r c e p t e d and c a t c h p e r s t a n d a r d i z e d e f f o r t p r o v i d e s an i n d e x o f a b u n d a n c e . T h e s e i n d e x e s have been u s e d t o e s t i m a t e t o t a l e s c a p e m e n t s but f r e q u e n t l y s u f f e r f r o m l a c k of c o n s i s t e n c y f r o m y e a r t o y e a r . R e l a t i v e l y good e s t i m a t e s , w i t h i n 15% o f t h e a c t u a l e s c a p e m e n t , were o b t a i n e d t h i s way f o r t h e S k e e n a r i v e r s o c k e y e f r o m 1956 t o 1963. But t h e s e e s t i m a t e s became more e r r a t i c and e r r o r s of +- 40% have o c c u r r e d i n some y e a r s s i n c e 1964 (Vroom 1971). Many f a c t o r s c o u l d have c a u s e d t h e i n c o n s i s t e n c y , and no mechanism has y e t been i d e n t i f i e d t o c o r r e c t some o f t h e e x i s t i n g e r r o r ( K a d o w a k i , pers.comm.). G a t t o and R i n a l d i (1979) p r e s e n t e d a p r o c e d u r e t o e s t i m a t e t h e a n n u a l r u n and e s c a p e m e n t o f a p o p u l a t i o n of s a l m o n . T h i s method r e q u i r e s t h a t t h e p o p u l a t i o n be s a m p l e d a t two d i f f e n t p a r t s of i t s m i g r a t i o n r o u t e e v e r y day by some form of t e s t f i s h i n g . The r e l i a b i l i t y o f t h i s method has y e t t o be t e s t e d v i g o r o u s l y under f i e l d c o n d i t i o n s . E c ho s o u n d i n g i s one of t h e newer t e c h n i q u e s f o r f i s h s t o c k a s s e s s m e n t and i t s p o t e n t i a l i s q u i t e p r o m i s i n g ( Anon. 1980, Drew 1980). As w i t h o t h e r newer methods ( e l e c t r o n i c c o u n t e r s , a e r i a l p h o t o g r a p h y e t c . ) i t w i l l t a k e many y e a r s o f f i e l d t r i a l s f o r i t s c r e d i b i l i t y t o be e s t a b l i s h e d . Some d e s c r i p t i o n s of 17 u s i n g s o n a r e q uipment t o e n u m e rate s p a w n i n g p o p u l a t i o n s o f s a l m on a r e d i s c u s s e d by Wood and Mason (1971) and Vroom ( 1 9 7 1 ) . In r a r e c i r c u m s t a n c e s when t h e e x p l o i t a t i o n r a t e o f a salmon s t o c k can be e s t i m a t e d w i t h c o n f i d e n c e , t h e e s c a p e m e n t c a n be c a l c u l a t e d i f t h e c a t c h i s known. The a v e r a g e i n s t a n t a n o u s r a t e of f i s h i n g p e r b o a t i s computed f r o m d e t a i l e d r e c e n t d a t a . A s s u m i n g t h a t f i s h i n g r e g u l a t i o n s and c a t c h i n g power o f t h e f l e e t have n o t c h a n g e d , e x p l o i t a t i o n r a t e s f o r p a s t y e a r s c a n be e s t i m a t e d i f p a s t f i s h i n g e f f o r t s a r e r e c o r d e d ( e . g . S h e p a r d and W i t h l e r 1958). E s c a p e m e n t s f o r e a r l y y e a r s c a n be c a l c u l a t e d s i m p l y a s c a t c h * ( ( 1 / e x p l o i t a t i o n r a t e ) - l ) . However, w i t h t h e r a p i d improvement o f f i s h i n g ' t e c h n o l o g y i n t h e p a s t 20 y e a r s , t h i s method c a n n o t be w i d e l y e m p l o y e d t o d a y . F i n a l l y t h e most a c c u r a t e method i s t o e r e c t a b a r r i e r below t h e s p a w n i n g a r e a and c o u n t t h e spawners as t h e y p a s s t h r o u g h a g a t e i n t h e f e n c e . However , i n most s i t u a t i o n s , t h e a c c u r a c y g a i n e d t h i s way c a n s e l d o m j u s t i f y t h e c o s t o f c o n s t r u c t i o n and m a i n t e n a n c e o f t h e c o u n t i n g f e n c e , even i f c o n f l i c t s w i t h o t h e r u s e r g r o u p s c a n be kept t o a minimum. T h e r e f o r e u s u a l l y p a r t s ( s a m p l e s ) o f t h e p o p u l a t i o n c a n be c o u n t e d o r m a n i p u l a t e d t o p r o v i d e e s t i m a t e s o f t h e t o t a l numbers p r e s e n t . W h i l e p r o c e d u r e s have been d e v e l o p e d t o c a l c u l a t e c o n f i d e n c e l i m i t s f o r t h e s e e s t i m a t e s , (Chapman 1948, C o c h r a n 1963), t h e d e g r e e t o w h i c h t h e i r a s s u m p t i o n s have been v i o l a t e d i s v e r y d i f f i c u l t t o e v a l u a t e . 18 2.4 E s t i m a t i o n o f R e c r u i t m e n t In most f i s h e r i e s l i t e r a t u r e , r e c r u i t m e n t i s d e f i n e d as t h e number o f f i s h r e p r o d u c e d by a b r e e d i n g p o p u l a t i o n , and s u r v i v i n g t o become v u l n e r a b l e t o t h e f i s h i n g g e a r s i n u s e . F o r P a c i f i c salmon ( e x c e p t c o h o and s p r i n g ) , r e c r u i t m e n t o c c u r s j u s t p r i o r t o s p a w n i n g . Thus t h e r e c r u i t m e n t f r o m a g i v e n b r o o d s t o c k c a n be e s t i m a t e d i f t h e age s t r u c t u r e ,escapement and c o r r e s p o n d i n g c a t c h e s a r e known. B e c a u s e most salmon f i s h e r i e s i n B.C. a r e c o n d u c t e d i n a r e a s where many s t o c k s mix, one o f t h e major p r o b l e m s o f r e c r u i t m e n t e s t i m a t i o n i s t h e c o r r e c t a l l o c a t i o n of t h e s e m i x e d c a t c h e s t o t h e i r p r o d u c t i o n a r e a s . B e s i d e s t h e p r o b l e m s a s s o c i a t e d w i t h t h e b a s i c c a t c h s t a t i s t i c s ( C a m p b e l l , u n p u b l i s h e d r e p o r t ) , t h e a c t u a l numbers o f f i s h c a u g h t i n an a r e a do n o t n e c e s s a r i l y i n d i c a t e t h e r e l a t i v e a b undance o f r e c r u i t s p r o d u c e d f r o m t h a t a r e a . The m i g r a t i o n r o u t e s o f v a r i o u s s t o c k s change f r o m y e a r t o y e a r . F o r example, t a b l e 2 shows t h a t t h e p e r c e n t a g e of F r a s e r r i v e r s o c k e y e m i g r a t i n g t h r o u g h J o h n s t o n e S t r a i t has v a r i e d f r o m 3 p e r c e n t t o 57 p e r c e n t s i n c e 1954. Even when t h e m i g r a t i o n r o u t e s u s e d a r e f a i r l y c o n s i s t e n t ( e . g . T a b l e 3 ) , t h e r u n t i m i n g , g e a r d i s t r i b u t i o n a n d o p e n i n g p a t t e r n s v a r y f r o m y e a r t o y e a r . S i n c e t h e c u r r e n t management scheme a l l o w s and s o metimes even p r o m o t e s c a p t u r i n g f i s h d e s t i n e d t o a n o t h e r a r e a , ( e . g . J o h n s t o n e S t r a i t f i s h e r y t o t a k e F r a s e r p i n k and s o c k e y e ) , t h e p r o b l e m of a l l o c a t i n g t h e c a t c h e s back t o t h e i r s t r e a m s ( o r a r e a s ) of o r i g i n i s d i f f i c u l t / i n d e e d . T h r e e methods a r e commonly u s e d t o e s t i m a t e h i s t o r i c a l YEAR PERCENTAGE YEAR PERCENTAGE 1 954 2.5 1967 " 25.0 1 955 9.0 1968 18.0 1 956 9.5 1969 16.0 1 957 19.0 1 970 24.0 1 958 35.0 1 971 11.0 1 959 14.0 1 972 34.0 1 960 18.0 1973 10.0 1 961 16.5 1974 • 21 .0 1 962 11.0 1 975 10.0 1 963 10.5 1976 19.0 1 964 10.0 1 977 12.0 1965 10.0 1978 57.0 1 966 24.5 1979 30.0 T a b l e 2 : P e r c e n t a g e o f F r a s e r R i v e r s o c k e y e a d u l t s t h a t r e t u r n e d v i a J o h n s t o n e S t r a i t ( I . P . S . F . C . pers.comm.) YEAR PERCENTAGE 1 957 26.0 1 959 33.0 1 961 25.0 1 963 32.0 1 965 28.0 1 967 25.0 1 969 39.0 1 971 22.0 1 973 29.0 1 975 25.0 1 977 23.0 1 979 23.0 T a b l e 3 : P e r c e n t a g e o f F r a s e r R i v e r p i n k a d u l t s t h a t r e t u r n e d v i a J o h n s t o n e S t r a i t ( I . P . S . F . C . pers.comm.) 20 s t o c k c o n t r i b u t i o n s t o m i x e d c a t c h e s . The f i r s t method i s t o a l l o c a t e f i x e d p r o p o r t i o n s ( o v e r t i m e ) o f t h e mixed c a t c h t o t h e c o n t r i b u t i n g p r o d u c t i o n a r e a s . C a t c h a l l o c a t i o n t a b l e s h a v e been g e n e r a t e d f o r t h i s p u r p o s e from p r e l i m i n a r y c o d e d w i r e t a g g i n g s t u d i e s a n d t h e e x p e r i e n c e s o f s i x members o f t h e D e p a r t m e n t o f F i s h e r i e s and Oceans - D . A n d e r s o n , A.W.Argue, M . F a r w e l l , K . P e t r i e , D . S h u t z and E . Z y b l u t ( S t a l e y , pers.comm.). F o r e a c h o f t h e p r o d u c t i o n a r e a s ( a s d e f i n e d i n t a b l e 1 ) , t h e b i o l o g i s t s were a s k e d t o e s t i m a t e t h e p e r c e n t a g e o f f i s h p r o d u c e d i n t h a t a r e a b u t c a u g h t i n a n o t h e r c a t c h a r e a ( a s d e f i n e d i n t a b l e 4 ) f o r e a c h s p e c i e s a l o n g t h e c o a s t . T a b l e s 5 t o 10 show t h e e s t i m a t e d p r o p o r t i o n of f i s h c a u g h t i n a h a r v e s t a r e a w h i c h a r e p r o d u c e d f r o m t h e a p p r o p i a t e p r o d u c t i o n a r e a ( f o r example, row 1 of c o l u m n 4 o f t a b l e 5 r e a d s 79.7 w h i c h means o f t h e s o c k e y e c a t c h e s i n t h e n o r t h c o a s t , 79.7% a r e p r o d u c e d from t h e S k e e n a ) . U n f o r t u n a t e l y , t h i s a l l o c a t i o n method i g n o r e s t h e f a c t t h a t p r o d u c t i o n f r o m d i f f e r e n t s t o c k s f l u c t u a t e s from y e a r t o y e a r . Under most c i r c u m s t a n c e s , s e p a r a t i n g m i x e d c a t c h e s by f i x e d p r o p o r t i o n a l l o c a t i o n t e n d s t o b i a s t h e p a r a m e t e r s o f t h e f i n a l s t o c k - r e c r u i t m e n t a n a l y s i s , a s d e m o n s t r a t e d by t h e f o l l o w i n g s i m p l e s i m u l a t i o n m o d e l . " A c t u a l " s t o c k - r e c r u i t m e n t d a t a f o r two s e v e r e l y o v e r e x p l o i t e d s t o c k s , e a c h h a v i n g i n d e p e n d e n t e n v i r o n m e n t a l e f f e c t s and d i f f e r e n t p r o d u c t i v i t i e s were g e n e r a t e d f r o m t h e e q u a t i o n R, = S. e ' where i s t h e s p a w n i n g s t o c k a t g e n e r a t i o n t , Rt+, i s t h e HARVEST AREA A l a s k a (AL) N o r t h C o a s t (NC) C e n t r a l C o a s t (CC) J o h n s t o n e S t r a i t ( J S ) G e o r g i a S t r a i t (GS) F r a s e r R i v e r (FR) J u a n de Fu c a S t r a i t .. ( J F S ) S.W. V a n c o u v e r I s l a n d (SWVI) N.W. V a n c o u v e r I s l a n d (NWVI) S T A T I S T I C A L AREA S.W. A l a s k a I, 2,3,4,5 6,7,8,9,10 I I , 12,13 14,15,16,17, 18,28 29 19,20 21,22,23,24 25,26,27 T a b l e 4 : H a r v e s t a r e a s and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s . PRODUCTION AREA H Q.C 1 Q.C.2 NASS SK CC RS JS GS FR JFS SWVI NWVI A R AL 0. 0 0.0 68 . 2 30.0 1 .8 0. 0 0.0 0. 0 0.0 0. 0 0.0 0.0 V NC 0. 4 0.3 16 .6 79.7 3.0 0. .0 0.0 0. 0 0.0 0. 0 0.0 O.O E CC 0. 0 0.0 0.0 0.0 21.0 79. ,0 0.0 0. .0 0.0 0. 0 0.0 0.0 S JS 0. 0 0.0 0.0 0.0 0.0 0. .0 12.0 1 . 0 87 .0 0. 0 0.0 0.0 T GS 0. 0 0.0 0.0 0.0 0.0 0. .0 0.0 0. ,0 100.0 0. 0 ' 0.0 0.0 FR 0. 0 0.0 0.0 0.0 0.0 0. .0 0.0 0, ,0 100.0 0. 0 0.0 0.0 A JFS 0. 0 0.0 0.0 0.0 0.0 0. .0 0.0 0. o 100.0 0. 0 0.0 0.0 R SWVI 0. 0 0.0 0.0 0.0 0.0 0 .0 0.0 0. .0 53 .0 0. 0 47 .0 0.0 E A NWVI 0. 0 0.0 0.0 0.0 0.0 17 . 5 0.0 0. .0 82.5 0. 0 0.0 0.0 T a b l e 5 Percentage a l l o c a t i o n of h a r v e s t t o p r o d u c t fon a r e a s ( s o c k e y e ) . PRODUCTION I AREA H Q.C. 1 Q.C.2 NASS SK CC RS JS GS FR JFS SWVI NWVI A R AL 4 . ,0 10.0 70.0 15.0 1 .0 0 .0 0.0 0 .0 O.O 0 .0 0.0 0.0 V NC 6 . G 48 .0 27 .7 9 . 7 8.0 0 .0 0.0 0 .0 0.0 0 .0 0.0 0.0 E CC 0. .0 0.0 0.0 0.0 93.7 6 . 3 0.0 0 .0 0.0 0 .0 0.0 O.O S JS 0, ,0 0.0 0.0 0.0 0.0 0 .0 21.8 48 .9 29.3 0 .0 0.0 0.0 T GS 0. .0 0.0 0.0 0.0 0.0 0 .0 0.0 100 .0 0.0 0 .0 0.0 O.O FR 0. .0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .O 100.0 0 .0 0.0 0.0 A JFS 0 .0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0 .0 0.0 0.0 R SWVI 0 .0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0 .0 100.0 O.O E A NWVI 0 .0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0 .0 0.0 100.0 Tabl e G Percentage a l l o c a t i o n of h a r v e s t to p r o d u c t Ion a r e a s (chum). ro ro PRODUCTION AREA H O.C. 1 O.C . 2 NASS SK cc RS JS GS FR JFS SWVI NWVI A R ' AL 18 . 5 10.8 23 .0 25.7 21.8 0. .2 0.0 0. 0 0.0 0. 0 0.0 0.0 V NC 18 . 3 15.0 18.2 20.4 23.7 0. .6 0.3 1 . 2 0.0 0. 0 1 .0 1 .3 E CC 0. 0 4.7 0.0 0.0 49.7 2 . ,6 9.0 21 . 5 1 .0 0. 0 6.5 5.0 S JS 0. 0 0.0 0.0 0.0 7.7 1 . . 3 43 . 7 45 . 5 1 .8 0. 0 0.0 0.0 T GS 0. 0 0.0 0.0 0.0 0.0 0. .0 1 .6 85 . 6 12.8 0. 0 0.0 0.0 FR 0. 0 0.0 0.0 0.0 0.0 0. .0 0.0 0. 0 100.0 0. O 0.0 0.0 A JFS 0. 0 0.0 0.0 0.0 0.0 0, ,0 0.0 67 . 0 17.0 16 . 0 0.0 0.0 R SWVI 0. 0 0.0 0.0 0.0 0.0 0. . 3 2 . 1 18 . 6 3.7 13 . 5 55 .9 5.9 LU < NWVI o. 0 O.O 0.0 0.0 3 . 2 0. ,9 10.8 17 . 8 1 .4 6. 3 35.8 23.8 T a b l e 7 Percentage a l l o c a t i o n of h a r v e s t to p r o d u c t i on a r e a s ( c o h o ) . PRODUCTION AREA H O.C. 1 O.C.2 NASS SK cc RS JS GS FR JFS SWVI NWVI A R AL 0. 0 0.0 12.3 15.6 7.4 2 . 8 4 . 3 4 . 9 23.6 0. .0 20.4 7.9 V NC 0. .0 0.0 17.5 22 . 2 9 . 7 3 .8 4 . 1 5. . 2 25.6 0 .0 8.4 3.5 E cc 0. 0 0.0 0.0 0.0 10.8 6 .5 15 . 1 7 . 4 41.2 0 .0 13.7 5. 1 S JS 0. 0 0.0 0.0 0.0 0.0 0 .0 18 . 2 21 .5 58.0 0 .0 0.0 3 . 2 T GS 0. .0 0.0 0.0 0.0 0.0 0 .0 0.0 21 .6 78.6 0 .0 0.0 0.0 FR 0. 0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 100.0 0 .0 0.0 0.0 A JFS 0. 0 0.0 O.O 0.0 0.0 0 .0 0.0 0 .0 100.0 0 .0 0.0 0.0 R SWVI 0. ,0 0.0 0.0 0.0 0.0 0 .0 6.2 0 .0 57.6 0 .0 35.4 0.8 E A NWVI 0. ,0 0.0 0.0 0.0 0.0 2 . 1 27 .0 5 . 2 26 . 3 0 .0 26.5 12. 1 T a b l e 8 Percentage a l l o c a t i o n of h a r v e s t to p r o d u c t i o n a r e a s ( s p r i n g ) . ro O J PRODUCTION AREA H O.C.I O.C. 2 NASS SK CC RS JS GS FR JFS SWVI NWVI A R AL 0.0 0.0 100.0 0.0 0.0 0. 0 0.0 0. 0 0.0 0.0 0.0 0.0 V NC 0.7 0.0 20.8 68.3 10. 2 0. 0 0.0 0. 0 0.0 0.0 0.0 0.0 E CC 0.0 0.0 0.0 0.0 91 .0 9. 0 0.0 0. 0 0.0 0.0 0.0 0.0 S JS 0.0 0.0 0.0 0.0 0.0 0. .0 32 .0 0. 0 68.0 0.0 0.0 0.0 T GS 0.0 0.0 0.0 0.0 0.0 0. .0 6.0 0. 0 94 .0 0.0 0.0 0.0 FR 0.0 0.0 0.0 0.0 0.0 0. .0 0.0 0. 0 100.0 0.0 0.0 0.0 A JFS 0.0 0.0 0.0 0.0 0.0 0. ,0 2.0 0. 0 98 .0 0.0 0.0 0.0 R SWVI 0.0 0.0 0.0 0.0 0.0 0. .0 3.0 0. 0 97 .0 0.0 0.0 0.0 E A NWVI 0.0 0.0 0 0 0.0 0.0 0 .0 4.2 0. 0 95.8 0.0 0.0 0.0 T a b l e 9 : Percentage a l l o c a t i o n of h a r v e s t to p r o duct1on a r e a s (odd y e a r p1nk ) . PRODUCTION AREA H O.C. 1 O.C .2 NASS SK CC RS JS GS FR JFS SWVI NWVI A R AL 0.0 0.0 100.0 0.0 1 .0 0 .0 0.0 0 .0 0.0 0.0 0.0 0.0 V NC 3.2 25.3 19. 1 36.4 16.0 0 .0 0.0 0 .0 0.0 0.0 0.0 0.0 E CC 0.0 0.0 0.0 0.0 89 . 7 10 . 3 0.0 0 .0 0.0 0.0 0.0 0.0 S JS 0.0 0.0 0.0 0.0 0.0 0 .0 100.0 0 .0 0.0 0.0 0.0 0.0 T GS 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 100 .0 0.0 0.0 0.0 0.0 FR 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0.0 0.0 0.0 A JFS 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0.0 0.0 0.0 R SWVI 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0.0 100.0 0.0 E A NWVI 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0 .0 0.0 0.0 0.0 100.0 T a b l e 10 : Percentage a l l o c a t i o n of h a r v e s t to p roduct 1 on ar e a s (even year 1 p i n k ) . ro 25 r e s u l t i n g r e c r u i t s f r o m St , °< i s a p r o d u c t i o n p a r a m e t e r and i s a random e n v i r o n m e n t a l f a c t o r , n o r m a l l y d i s t r i b u t e d w i t h mean 0.0 and v a r i a n c e 6^ . R e c r u i t m e n t s f o r b o t h s t o c k s were s u b j e c t t o t h e same e x p l o i t a t i o n r a t e by a common f i s h e r y . The s p a w n i n g p o p u l a t i o n s were f u r t h e r r e g u l a t e d by t e r m i n a l f i s h e r i e s t o v a r y a r o u n d f i x e d e s capement g o a l s w h i c h were l i a b l e t o "management e r r o r s " o f a b o u t +-45%. F i x e d p r o p o r t i o n s of t h e m i x e d c a t c h were t h e n a l l o c a t e d t o e a c h s t o c k a c c o r d i n g t o t h e i r r e l a t i v e s t o c k s i z e s a t t h e b e g i n n i n g o f a s i m u l a t i o n r u n . " O b s e r v e d " r e c r u i t m e n t , , f o r s t o c k i a t y e a r t would be t h e sum o f t h e a l l o c a t e d c a t c h , t e r m i n a l c a t c h and spawning p o p u l a t i o n of t h a t s t o c k a t y e a r t . W i t h t h e e n v i r o n m e n t a l f a c t o r ( S\ ) f i x e d a t 0.1, many s i m u l a t i o n c a s e s were examined by v a r y i n g e a c h o f t h e p a r a m e t e r s : i n i t i a l s t o c k s i z e s , p r o d u c t i v i t i e s , and t o t a l e x p l o i t a t i o n r a t e . By v a r y i n g t h e i n i t i a l s t o c k s i z e s a l o n e , s i g n i f i c a n t c u r v a t u r e of t h e " o b s e r v e d " s t o c k - r e c r u i t m e n t d a t a became a p p a r e n t when one s t o c k was a b o u t t h r e e t i m e s o r b i g g e r t h a n t h e o t h e r s t o c k . O n l y t h e s m a l l e r s t o c k s were a f f e c t e d i n most c a s e s as shown f o r a t y p i c a l c a s e i n f i g u r e 3. S t o c k B was f i v e t i m e s as b i g a s s t o c k A. B o t h s t o c k s have t h e same p r o d u c t i v i t y (o< =1) and were e x p l o i t e d a t 50% by t h e common f i s h e r y . I t was more d i f f i c u l t t o f i n d v i s u a l d i s t o r t i o n a s t h e o t h e r p a r a m e t e r s were a l s o v a r i e d . The g e n e r a l c o n c l u s i o n i s t h a t s m a l l e r s t o c k s a r e a f f e c t e d s i g n i f i c a n t l y more t h a n l a r g e r s t o c k s as l o n g a s t h e t o t a l e x p l o i t a t i o n r a t e s a r e l e s s t h a n or e q u a l t o t h e maximum e q u i l i b r i u m e x p l o i t a t i o n r a t e , 1-exp ( - o < ) , o f t h e l e s s p r o d u c t i v e s t o c k . O t h e r w i s e b o t h t h e s m a l l e r s t o c k 26 F i g . 3 . " A c t u a l " and " o b s e r v e d " s t o c k - r e c r u i t m e n t d a t a p o i n t s u s i n g f i x e d a l l o c a t i o n method t o s e p a r a t e m i x e d c a t c h e s . 27 S T O C K A S T O C K B • • • •• • OBSERVED A C T U A L " 28 and t h e l e s s p r o d u c t i v e s t o c k ( c a n be e i t h e r s t o c k ) w i l l be a f f e c t e d . T h i s c a n be e x p l a i n e d by t h e f a c t t h a t t h e l e s s p r o d u c t i v e s t o c k i s b e i n g s y s t e m a t i c a l l y e x p l o i t e d t o w a r d s e x t i n c t i o n b u t i s t r e a t e d a s t h o u g h i t c o n t r i b u t e s t h e same p r o p o r t i o n t o t h e common f i s h e r y a s i t d i d a t t h e b e g i n n i n g o f t h e f i s h e r y . An i n t u i t i v e e x p l a n a t i o n o f t h e above outcome i s t h a t i n d e p e n d e n t random s e r i e s t e n d t o show a c o r r e l a t i o n c o e f f i c i e n t o f -.707 ( E b e r h a r d t 1970) w h i c h , i n t h i s ' c a s e , s u g g e s t s t h a t " s m a l l e r t h a n a v e r a g e " s p a w n i n g p o p u l a t i o n s i n one s t o c k a r e more l i k e l y t o be a c c o m p a n i e d by " l a r g e r t h a n a v e r a g e " s p a w ning p o p u l a t i o n s f r o m t h e o t h e r s t o c k and v i c e v e r s a . The e f f e c t o f t h i s i s more a p p a r e n t when many s t o c k s a r e m i x e d t o g e t h e r . D e s p i t e v a r y i n g c o n t r i b u t i o n s f r o m e a c h i n d i v i d u a l s t o c k , t h e t o t a l r e c r u i t m e n t o f a l l s t o c k s c a n r e m a i n f a i r l y c o n s t a n t f r o m y e a r t o y e a r due t o s i m p l e " a v e r a g i n g " . T h e r e f o r e t ro a l l o c a t e a f i x e d p o r t i o n o f t h e t o t a l r e c r u i t m e n t ( i n m i x e d c a t c h e s ) t o a s t o c k t e n d s t o b i a s t h e e s t i m a t e d r e c r u i t m e n t upwards when t h e s p a w n i n g p o p u l a t i o n i s low, b u t b i a s i t downwards when t h e sp a w n i n g p o p u l a t i o n i s h i g h . F u r t h e r m o r e , s m a l l e r s t o c k s a r e more s e n s i t i v e t o t h i s f o r m o f b i a s b e c a u s e s t o c k - r e c r u i t m e n t d a t a a r e e x p r e s s e d i n a b s o l u t e numbers r a t h e r t h a n p r o p o r t i o n s . To c o r r e c t f o r p o s s i b l e b i a s e s of t h i s k i n d , a s e c o n d method i s t o use a back c a l c u l a t i o n t e c h n i q u e t o s e p a r a t e m i x e d c a t h e s . I f we assume e v e r y s t o c k t h a t m i g r a t e s t h r o u g h a mixed a r e a - i s e q u a l l y v u l n e r a b l e t o t h e f i s h i n g g e a r s , and t h a t t h e sp a w n i n g e s t i m a t e s among t h e s t o c k s a r e c o n s i s t e n t , we can e s t i m a t e t h e p r o p o r t i o n of c a t c h a r i s i n g f r o m e a c h p a r t i c u l a r 29 s t o c k by t h e method f i r s t a r t i c u l a t e d c l e a r l y by J o h n s o n ( 1 9 7 5 ) . E q u a l v u l n e r a b i l i t y i m p l i e s t h a t a l l s t o c k s a r e s u b j e c t t o t h e same o v e r a l l e x p l o i t a t i o n r a t e i n f i s h e r y j , w h i c h i s ^. tota( <rrt.Cc A ^ J tot&( CatcA + total **se*f>*'"*rit where t o t a l escapement i n c l u d e s c a t c h e s t a k e n i n l a t e r f i s h e r i e s ( h e n c e t h e need f o r back c a l c u l a t i o n f r o m t h e l a s t f i s h e r y t o w h i c h a s t o c k i s s u b j e c t e d ) . S i n c e t h e c a t c h o f s t o c k i i s U: t i m e s t h e r e c r u i t m e n t ( c a t c h p l u s e s c a p e m e n t ) of s t o c k i t o \J f i s h e r y j , so E-; = (1-U;)(C-,; + E:: ), we c a n s o l v e f o r c a t c h o f J J \J J s t o c k i g i v e n escapement E-- as J Cr. - JL - Er. = ^ E ; ; The c a l c u l a t i o n becomes somewhat more c o m p l i c a t e d f o r s o u t h c o a s t s t o c k s w i t h s p l i t m i g r a t i o n r o u t e s . The method i s most e a s i l y u n d e r s t o o d by example, as f o r s o u t h c o a s t ( F r a s e r r i v e r , G e o r g i a S t r a i t , J o h n s t o n e S t r a i t ) chums. The p r o p o r t i o n o f F r a s e r r i v e r chum salmon c a u g h t i n G e o r g i a S t r a i t i n a g i v e n y e a r w o u l d be: where S, i s t h e number o f F r a s e r chum s p a w n e r s , i s t h e number of G e o r g i a S t r a i t chum s p a w n e r s , <TM i s t h e number of chums c a u g h t i n t h e F r a s e r e s t u a r y , fj, t h e p r o p o r t i o n of F r a s e r chum t h a t m i g r a t e d t h r o u g h t h e n o r t h e r n r o u t e i n t h a t y e a r , and r°, r t h e p r o p o r t i o n of chum c a u g h t i n G e o r g i a S t r a i t t h a t b e l o n g 3 0 t o t h e F r a s e r . Then t h e p r o p o r t i o n o f F r a s e r chum c a u g h t ( e a r l i e r ) i n J o h n s t o n e S t r a i t w o u l d be: r, 12 " cvc,,^ ,-* <v<WVS 3 CJ'*'<0 where !>, , Sz , Cn , V, and Pn a r e t h e same as b e f o r e , S>j i s t h e number o f J o h n s t o n e S t r a i t chum s p a w n e r s , C / 2 i s t h e number o f F r a s e r chum c a u g h t i n G e o r g i a S t r a i t , C2l i s t h e G e o r g i a S t r a i t chum c a t c h i n G e o r g i a S t r a i t , i s t h e p r o p o r t i o n of G e o r g i a S t r a i t chum m i g r a t i n g t h r o u g h t h e n o r t h e r n r o u t e , and P/z i s t h e p r o p o r t i o n of chum c a u g h t i n J o h n s t o n e S t r a i t t h a t came f r o m t h e F r a s e r . The m i x e d c a t c h e s i n G e o r g i a S t r a i t c a n be s e p a r a t e d s i m p l y by : where TcC^ i s t h e t o t a l c a t c h o f chum i n G e o r g i a S t r a i t . The m i x e d c a t c h e s i n J o h n s t o n e S t r a i t c a n t h e n be s e p a r a t e d a c c o r d i n g l y . T h e s e c a l c u l a t i o n s a r e v e r y s t r a i g h t - f o r w a r d i f t h e p r o p o r t i o n o f a s t o c k m i g r a t i n g t h r o u g h e a c h r o u t e r e m a i n s f a i r l y c o n s i s t e n t from y e a r t o y e a r . O t h e r w i s e , e s t i m a t e s o f t h e p r o p o r t i o n t h a t went t h r o u g h a g i v e n a r e a have t o be o b t a i n e d a n n u a l l y . M i x e d c a t c h e s o f chum i n G e o r g i a S t r a i t a nd J o h n s t o n e S t r a i t a r e s e p a r a t e d by a s s u m i n g 100% o f t h e m a t u r i n g f i s h m i g r a t e t h r o u g h J o h n s t o n e S t r a i t . S o c k e y e and p i n k c a t c h e s i n t h e same a r e a s a r e s e p a r a t e d s i m i l a r y by u s i n g t h e p e r c e n t a g e of 3 I n o r t h e r n a p p r o a c h o f F r a s e r f i s h e s t i m a t e d by I.P.S.F.C. ( t a b l e 2 & 3 ) . A l l s o c k e y e and p i n k c a t c h e s i n J u a n de F u c a S t r a i t ( C a n a d i a n s i d e ) and t r o l l c a u g h t s o c k e y e i n t h e west c o a s t of V a n c o u v e r I s l a n d a r e assumed t o be F r a s e r f i s h . I.P.S.F.C. e s t i m a t e s o f F r a s e r s o c k e y e and p i n k c a u g h t i n U.S.A. a r e a l s o i n c l u d e d . W i t h t h e e x c e p t i o n o f c o h o and s p r i n g , o t h e r s t o c k s have n e g l i g i b l e ( o r unknown) mixed f i s h i n g and t h e c a t c h s t a t i s t i c s r e p o r t e d by t h e D e p a r t m e n t o f F i s h e r i e s f o r e a c h s t o c k a r e assumed t o be p r o d u c e d by t h a t s t o c k r e s p e c t i v e l y . T a g g i n g s t u d i e s i n t h e e a r l y 1960s and t h e more r e c e n t Coded W i r e T a g g i n g Program r e v e a l e d t h a t a l l t h e s t o c k s of c h i n o o k and c oho a r e e x p l o i t e d e x t e n s i v e l y by m i x e d f i s h e r i e s ( m a i n l y by t r o l l i n g g e a r ) a l l o v e r t h e c o a s t . S i n c e t h e v a r i a t i o n s o f t h e i r m i g r a t i o n r o u t e s o r t h e e x t e n t t o w h i c h d i f f e r e n t s t o c k s mix a r e v a g u e l y known, t h e above method c a n n o t be a p p l i e d f o r s e p a r a t i n g t h e s e mixed c a t c h e s . However i t i s g e n e r a l l y b e l i e v e d t h a t t h e s e two s p e c i e s a r e e x p l o i t e d by t r o l l i n g g e a r m a i n l y a t t h e i r r e a r i n g a r e a s , w h i l e n e t f i s h e r i e s g e n e r a l l y c a t c h m a t u r i n g f i s h c l o s e t o t h e i r s p a w n i n g a r e a s . I f we assume t h a t f a i r l y c o n s i s t e n t p r o p o r t i o n s o f d i f f e r e n t s t o c k s r e a r i n t h e same r e s i d e n c e a r e a s e v e r y y e a r , t h a t a l l r e s i d e n t f i s h a r e e q u a l l y v u l n e r a b l e t o f i s h i n g , and t h a t a l l s t o c k s a r e s u b j e c t t o s i m i l a r o v e r a l l e x p l o i t a t i o n r a t e s , t h e n a m o d i f i e d v e r s i o n o f t h e back c a l c u l a t i o n method c a n be u s e d t o s e p a r a t e t h e mixed c a t c h e s by t r o l l i n g g e a r . T a b l e s 12 t o 16 show t h e p r o p o r t i o n o f d i f f e r e n t age g r o u p s o f coho and s p r i n g r e a r i n g i n d i f f e r e n t r e s i d e n c e a r e a s ( t a b l e 11) ( S t a l e y , p e r s . Comm. ). F o r e i t h e r s p e c i e s , t h e m i x e d t r o l l c a t c h a t d i f f e r e n t a g e s from a RESIDENCE AREA S T A T I S T I C A L AREA A l a s k a N o r t h C o a s t G e o r g i a S t r a i t W. V a n c o u v e r I s l a n d W a s h i n g t o n S.W. A l a s k a I- 10 I I - 20,28,29 21-27 W a s h i n g t o n C o a s t T a b l e 11 : R e s i d e n c e a r e a s and c o r r e s p o n d i n g s t a t i s t i c a l a r e a s . RESIDENCE AREA T~) AL NC GS WVI WASH c R AL . 9 5 . 0 5 0 0 0 0 Q.C. 1 . 8 5 . 1 5 0 0 0 D Q.C.2 - - - - -U Nass . 7 0 . 3 0 0 0 0 C Skeena . 6 0 . 4 0 0 0 0 T C.C. . 4 0 . 6 0 0 0 0 I R-S . 2 0 . 8 0 0 0 0 0 J . S . . 1 0 . 4 0 . 4 . 1 0 0 N G.S. 0 . 2 0 . 8 0 0 F r a s e r 0 . 1 0 . 7 . 1 5 . 0 5 J . F . S . - - - - -A S.W.V.I. . 0 5 . 4 0 . 0 5 . 5 0 0 R N.W.V.I. . 1 0 . 4 5 . 0 5 . 4 0 0 E Puget S. 0 . 0 5 . 2 0 . 1 5 . 6 0 A W/0 C o a s t 0 . 1 0 0 . 4 0 . 5 0 T a b l e 12 : P r o p o r t i o n o f t o t a l s t o c k r e a r i n g i n e a c h r e s i d e n c e a r e a by p r o d u c t i o n a r e a ( s p r i n g age 2 ) . RESIDENCE AREA AL NC GS WVI WASH C R AL . 9 5 . 0 5 0 0 0 0 Q.C. 1 . 9 0 . 1 0 0 0 0 D Q.C.2 - - - - -U Nass . 7 5 . 2 5 0 0 0 c Skeena . 7 0 . 3 0 0 0 0 T C.C. . 5 0 . 5 0 0 0 0 I R-S . 3 0 . 7 0 0 0 0 0 J . S . . 2 0 . 5 5 . 2 0 . 0 5 0 N G.S. . 0 5 . 2 5 . 6 5 . 0 5 0 F r a s e r . 0 5 . 2 0 . 6 0 . 1 0 . 0 5 J . F . S . - - - - -A S.W.V.I. . 1 5 . 4 5 0 . 4 0 0 R N.W.V.I. . 2 0 . 5 0 0 . 3 0 0 > E Puget S. . 0 5 . 0 5 . 3 0 . 2 0 . 4 0 A W/O C o a s t . 1 5 . 1 5 0 . 3 5 . 3 5 T a b l e 13 : P r o p o r t i o n o f t o t a l s t o c k r e a r i n g i n e a c h r e s i d e n c e a r e a by p r o d u c t i o n a r e a ( s p r i n g age 3 ) . 34 RESIDENCE AREA AL NC GS WVI WASH tr R AL 1 .00 0 0 0 0 0 Q.C.1 1 .00 0 0 0 0 D Q.C2 - - - - -U Nass .90 .10 0 0 0 C Skeena .90 .10 0 0 0 T C.C. .70 .30 0 0 0 I R-S .50 .50 0 0 0 0 J.S. .35 .55 .10 0 0 N G.S. .15 .50 .30 .05 0 F r a s e r .15 .35 .40 .10 0 J.F.S. - - - - -A S.W.V.I. .35 .35 0 .30 0 R N.W.V.I. .40 .40 0 .20 0 E Puget S. .10 .20 .35 . 1 5 .20 A W/0 Coast .20 .35 0 .30 .15 T a b l e 14 : P r o p o r t i o n of t o t a l s t o c k r e a r i n g i n each r e s i d e n c e a r e a by p r o d u c t i o n a r e a ( s p r i n g age 4 & 5 ) . RESIDENCE AREA AL NC GS WVI WASH tr R AL 1 .00 0 0 0 0 0 Q.C.1 .20 . 8 0 0 0 0 D Q . C 2 .20 . 8 0 0 0 0 U Nass . 20 . 8 0 0 0 0 C Skeena . 20 . 8 0 0 0 0 T C.C. . 0 5 . 9 0 x 0 . 0 5 0 I R-S 0 . 9 0 0 . 1 0 0 0 J.S . 0 . 2 0 . 70 . 10 0 N G.S. 0 . 0 5 . 7 5 . 20 0 F r a s e r 0 0 .60 . 30 . 10 J . F . S . 0 0 .60 .30 .10 A S.W.V.I. 0 . 0 5 0 . 8 5 . 10 R N.W.V.I. 0 . 1 0 0 . 8 5 . 0 5 E Puget S. 0 0 .10 . 3 0 . 60 A W/0 C o a s t 0 0 0 . 1 5 . 8 5 T a b l e 15 : P r o p o r t i o n o f t o t a l s t o c k r e a r i n g i n e a c h r e s i d e n c e a r e a by p r o d u c t i o n a r e a (coho age 2 ) . RESIDENCE AREA T") AL NC GS WVI WASH r R AL . 90 . 1 0 0 0 0 0 Q.C.1 .40 . 6 0 0 0 0 D Q . C 2 .40 . 6 0 0 0 0 U Nass . 50 . 5 0 0 0 0 c Skeena . 50 . 5 0 0 0 0 T C.C. . 1 0 . 8 0 0 .10 0 I R-S 0 . 9 0 0 .10 0 0 J.S . 0 . 3 0 .70 . 20 0 N G.S. 0 . 1 5 . 7 5 . 2 5 . 10 F r a s e r 0 . 0 5 .60 . 30 . 2 5 J . F . S . 0 . 0 5 .60 . 3 0 . 2 5 A S.W.V.I. 0 . 1 0 0 . 7 5 . 1 5 R N.W.V.I. 0 . 1 5 0 . 7 5 .10 E Puget S. 0 , 0 .10 . 4 5 .50 A W/0 C o a s t 0 0 0 .20 .80 T a b l e 16 : P r o p o r t i o n o f t o t a l s t o c k r e a r i n g i n e a c h r e s i d e n c e a r e a by p r o d u c t i o n a r e a (coho age 3 ) . 36 r e s i d e n c e a r e a i n any y e a r c a n be s e p a r a t e d a s : C ; ; --wiere C1J i s t h e c a t c h b e l o n g i n g t o s t o c k i f r o m r e s i d e n c e a r e a j * S i i s t h e spawning p o p u l a t i o n o f s t o c k i t h a t y e a r , / V / i s t i e n e t c a t c h o f s t o c k i , P;j i s t h e p r o p o r t i o n o f s t o c k i r e a r i n g i n r e s i d e n c e a r e a j , TCj i s t h e t o t a l t r o l l c a t c h i n r e s i d e n c e a r e a j , and n i s t h e number o f s t o c k s i n r e s i d e n c e . T i e t o t a l t r o l l c a t c h b e l o n g i n g t o s t o c k i would s i m p l y be t h e sm of a l l t h e s e p a r a t e d c a t c h e s a t d i f f e r e n t a g e s f r o m a l l r e s i d e n c e a r e a s : ^ £ M where m i s t h e number o f r e s i d e n c e aneas f o r s t o c k i , a and b a r e t h e y o u n g e s t and o l d e s t f i s h r e c r u i t e d r e s p e c t i v e l y . The t h i r d method r e l i e s on v a r i o u s s t o c k i d e n t i f i c a t i o n t e c h n i q u e s ( e . g . s c a l e a n a l y s i s , s e r o l o g i c a l and b i o c h e m i c a l s t u d i e s , head t a g g i n g and r e c o v e r y p r o g r a m , e t c . ) t o e s t i m a t e t i e c o n t r i b u t i o n of e a c h s t o c k i n a m i x e d f i s h e r y . B e c a u s e of p r e s e n t t e c h n i c a l and e c o n o m i c p r o b l e m s , l o n g t e r m d a t a o b t a i n e d t l d s way e i t h e r do not e x i s t o r were n o t a v a i l a b l e ( e . g . F r a s e r sockeye) f o r t h i s s t u d y . T h e r e f o r e o n l y t h e f i r s t two methods were u s e d t o s e p a r a t e t h e m i x e d c a t c h e s and t h e s t o c k -rase r u i t m e n t a n a l y s e s from t h e s e e s t i m a t e s a r e compared i n t h e next c h a p t e r . When t h e age s t r u c t u r e , c a t c h and e s capement d a t a f o r a p a r t i c u l a r s t o c k have been e s t i m a t e d , r e c r u i t m e n t from any spawning p o p u l a t i o n would s i m p l y be: r.. = i cxcr{ + 1 SiSP: • ci-H-l) 0 »s* 37 where Rj i s t h e r e c r u i t m e n t f r o m s p a w n i n g p o p u l a t i o n a t g e n e r a t i o n C\ i s t h e t o t a l c a t c h i y e a r s a f t e r s p a w n i n g , Si i s t h e t o t a l escapement i y e a r s f r o m s p a w n i n g , CP- i s t h e p r o p o r t i o n o f age i f i s h i n t h e c a t c h , SP,- i s t h e p r o p o r t i o n o f age i f i s h i n t h e es c a p e m e n t , a i s t h e y o u n g e s t age o f f i s h r e t u r n i n g , a n d b i s t h e o l d e s t age o f f i s h r e t u r n i n g . U n f o r t u n a t e l y t h e age s t r u c t u r e of t h e c a t c h e s i n most a r e a s was s a m p l e d o n l y from 1957 t o 1972, and t h e escapement age s t r u c t u r e h as been samp l e d o n l y s p o r a d i c a l l y . A p p e n d i x I a l i s t s t h e raw d a t a o b t a i n e d f r o m v a r i o u s s o u r c e s f r o m 1951 t o 1979. B e c a u s e o f t h e p r e s e n c e of many gaps i n t h e d a t a , I d e c i d e d t o combine t h e age s t r u c t u r e of c a t c h and escapement by w e i g h t i n g them w i t h t h e sample s i z e s t o o b t a i n an a v e r a g e age s t r u c t u r e f o r e a c h y e a r ( a p p e n d i x l b ) . T h i s w e i g h t e d a v e r a g e i s assumed t o be r e p r e s e n t a t i v e of t h e age s t r u c t u r e f o r b o t h t h e c a t c h and es c a p e m e n t f o r t h a t y e a r . When age s t r u c t u r e d a t a i s a b s e n t i n a p a r t i c u l a r y e a r , t h e o v e r a l l a v e r a g e ( f o r a l l y e a r s ) i n t h a t a r e a i s u s e d ( a p p e n d i x I c ) . Coho and p i n k a r e assumed t o r e c r u i t e x c l u s i v e l y a t age 3 and 2 r e s p e c t i v e l y . W i t h o u t a c c u r a t e age s t r u c t u r e d a t a , i t i s a p p a r e n t t h a t s t r o n g y e a r c l a s s e s may be a s s i g n e d i n c o r r e c t l y t o s e v e r a l b r o o d y e a r s , e s p e c i a l l y f o r c h i n o o k . To examine t h i s p r o b l e m , t h e a u t o c o r r e l a t i o n p a t t e r n s i n r e s i d u a l s f r o m t h e s t o c k - r e c r u i t m e n t r e g r e s s i o n ( R i c k e r model) were p l o t t e d ( A p p e n d i x I I ) . S i g n i f i c a n t c o r r e l a t i o n s a t any l a g i n d i c a t e s t h e p r e s e n c e o f a g i n g e r r o r s , o r b i o l o g i c a l p r o c e s s e s ( e . g . c y c l e s ) t h a t may i n v a l i d a t e t h e s t a t i o n a r i t y a s s u m p t i o n of s t o c k - r e c r u i t m e n t a n a l y s i s u s e d i n t h i s s t u d y . 38 A s t o c h a s t i c p r o c e s s i s s a i d t o d i s p l a y s t a t i o n a r i t y when i t s p r o p e r t i e s a r e not a f f e c t e d by a c h a n g e of t i m e o r o r i g i n so t h a t t h e j o i n t p r o b a b i l i t y d i s t r i b u t i o n o f any s e t o f o b s e r v a t i o n s , H.. 2 . , i s u n a f f e c t e d by s h i f t i n g t h e t i m e o f o b s e r v a t i o n f o r w a r d o r b a c k w a r d by any amount o f t i m e , k. The n a t u r e o f t h i s j o i n t d i s t r i b u t i o n c a n be i n f e r r e d by t h e a u t o c o r r e l a t i o n c o e f f i c i e n t , , a t l a g k (Box a n d J e n k i n s 1970 p. 2 7 ) : A s t r o n g e r d e f i n i t i o n o f s t a t i o n a r i t y c a n be a p p l i e d i n a n a l y s i n g r e s i d u a l s f r o m model p r e d i c t i o n s . E s t i m a t e s o f a u t o c o r r e l a t i o n c o e f f i c i e n t s f o r r e s i d u a l s f r o m a s t o c k -r e c r u i t m e n t r e g r e s s i o n , (J^ , a t any l a g k c a n be c a l c u l a t e d as ( f r o m J e k i n s and Watts 1969, p . 1 8 2 ) : Where u, , Oz a r e means of t h e f i r s t a nd l a s t n-k o b s e r v a t i o n s r e s p e c t i v e l y . I f t h e form o f t h e model i s c o r r e c t and t h e t r u e model p a r a m e t e r s a r e known, t h e n t h e U's s h o u l d be u n c o r r e l a t e d and t h e ^ f " ) a u t o c o r r e l a t i o n s s h o u l d be d i s t r i b u t e d a p p r o x i m a t e l y n o r m a l l y a b o u t z e r o w i t h v a r i a n c e n . The s t a t i s t i c a l s i g n i f i c a n c e of a p p a r e n t d e p a r t u r e o f t h e s e a u t o c o r r e l a t i o n s from z e r o c a n be a s s e s s e d a p p r o x i m a t e l y by u s i n g n 2 as t h e s t a n d a r d e r r o r f o r r ^ ( u ) , but t h i s method t e n d s 3 9 t o u n d e r e s t i m a t e t h e s t a t i s t i c a l s i g n i f i c a n c e a t low l a g s (Box and J e n k i n s 1970, p . 2 9 0 ) . 2.5 P o s s i b l e S o u r c e s o f E r r o r B e f o r e p r e s e n t i n g f u r t h e r a n a l y s i s , i t i s a p p r o p i a t e t o d i s c u s s some o f t h e m a j o r s o u r c e s o f e r r o r t h a t c o u l d have a r i s e f r o m t h e above d a t a and a n a l y s i s methods. A l l forms o f measurement a r e more o r l e s s s u b j e c t t o e r r o r and t h e s e e r r o r s a r e sometimes v e r y l a r g e , e s p e c i a l l y i n c o m m e r c i a l f i s h e r i e s . F r e q u e n t l y t h e s e e r r o r s a r e r e c o g n i z e d b u t a r e s e l d o m e x p l i c i t l y s t a t e d , and t h e e f f e c t s o f them on t h e f i n a l r e s u l t s of a n a l y s i s a r e s e l d o m m e n t i o n e d . T h r e e major s o u r c e s o f e r r o r a r e f o u n d i n t h i s s t u d y : d e f i n i t o n o f s t o c k u n i t s , a l l o c a t i o n of m i x e d c a t c h e s t o p r o d u c t i o n a r e a s , and s p a w n i n g s t o c k e s t i m a t e s . L u d w i g and W a l t e r s (1981) u s e d f o r m a l methods t o d e a l w i t h measurement e r r o r s c a u s e d by poor e s c a p e m e n t c o u n t s . H o p e f u l l y more e f f o r t w i l l be s p e n t on d e a l i n g w i t h t h e o t h e r t y p e s o f e r r o r d i s c u s s e d below. An o b v i o u s and immediate p r o b l e m i s t h a t t h e management u n i t s we a d o p t e d may n o t be a p p r o p r i a t e u n i t s f o r r e p r e s e n t i n g t h e r e p r o d u c t i v e d y n a m i c s o f t h e p o p u l a t i o n s c o n c e r n e d . To t r e a t o r g a n i s m s t h a t b r e e d and r e a r i n numerous d i f f e r e n t r i v e r s , s t r e a m s , t r i b u t a r i e s and l a k e s as a homogenous mass would make most e c o l o g i s t s u n c o m f o r t a b l e . However, so l o n g as t h e . f i s h a r e b e i n g c a u g h t i n a common g r o u n d , c o m p r o m i s e s have t o be made i n d e c i d i n g what c o n s t i t u t e s an " a p p r o p i a t e " r e p r o d u c t i v e u n i t . By l u m p i n g " t o o l a r g e " an a r e a as a u n i t , t h e d y n a m i c s of s m a l l e r 4 0 p r o d u c t i o n a r e a s w i t h i n t.he u n i t a r e o f t e n masked by t h a t o f t h e l a r g e r o n e s . On t h e o t h e r hand, b i a s e d e s t i m a t e s a r e o b t a i n e d when u s i n g " t o o s m a l l " an a r e a a s a u n i t due t o t h e i n c r e a s i n g c h a n c e o f e r r o r i n s e p a r a t i n g t h e m i x e d c a t c h e s i n t o s m a l l e r u n i t s . U n d o u b t e d l y , some o f o u r d e f i n e d " s t o c k s " may r e a s o n a b l y be b r o k e n down i n t o f i n e r u n i t s w h i l e some " s t o c k s " s h o u l d have been lumped i n t o a s i n g l e a s s e s s m e n t u n i t b e c a u s e o f t h e i r p e c u l a r i t i e s of m i g r a t i o n , r u n t i m i n g o r e x p l o i t a t i o n p a t t e r n s . I t i s a c c e p t a b l e t o v i e w any l a r g e u n i t a s h a v i n g some s t a t i s t i c a l d y n a m i c s a c r o s s t h e v a r i a b l e r e p r o d u c t i v e s u b u n i t s c o m p r i s i n g i t , and t o h y p o t h e s i z e t h a t t h i s s t a t i s t i c a l b e h a v i o r w i l l r e s e m b l e t h e d y n a m i c s o f a s i n g l e u n i t s t o c k . However, a s R i c k e r (1973) n o t e d , we s h o u l d a t l e a s t e x p e c t l o n g t e r m c h a n g e s i n t h e s t a t i s t i c a l p a r a m e t e r s , due t o p e r s i s t e n t c h a n g e s i n t h e s t o c k c o m p o s i t i o n ( l o s s o f weak s t o c k s ) . However, f o r B.C. s t o c k s , s u c h p a r a m e t e r c h a n g e s may have t a k e n p l a c e m o s t l y b e f o r e 1950, t h e e a r l i e s t y e a r u s e d i n t h i s s t u d y . B e c a u s e of t h e l a c k o f u n d e r s t a n d i n g of t h e m i g r a t i o n r o u t e s , r u n t i m i n g s and e x p l o i t a t i o n p a t t e r n s o f most s t o c k s , two methods a r e u s e d t o a l l o c a t e m i x e d c a t c h e s back t o t h e i r p r o d u c t i o n u n i t s . The u n d e r l y i n g a s s u m p t i o n s o f t h e s e methods were d i s c u s s e d a b o v e . To some e x t e n t , t h e s e a s s u m p t i o n s must have been v i o l a t e d i n most a r e a s a t l e a s t d u r i n g some o f t h e t i m e p e r i o d c o v e r e d by t h i s a n a l y s i s . E ven i f t h e methods of a l l o c a t i n g mixed c a t c h e s c o u l d be made more p r e c i s e , t h e c o m m e r c i a l c a t c h f i g u r e s do not n e c e s s a r i l y r e p r e s e n t t h e r e a l c a t c h e s from a g i v e n a r e a . Modern v e s s e l t e c h n o l o g y has l e d t o r a p i d movement of t h e f i s h i n g 41 f l e e t , and i m p r o v e d c o l d s t o r a g e has l e n g t h e n e d t h e t i m e o f s t a y a t s e a . H i g h l y m o b i l e f i s h i n g g e a r s h a v e t h e c a p a b i l i t y o f f i s h i n g i n many of t h e d e f i n e d management u n i t s i n a s i n g l e o u t i n g , w h i l e r e p o r t i n g l a n d i n g s o n l y a t a s i n g l e l o c a t i o n . Most i m p o r t a n t i s t h e s y s t e m a t i c b i a s o r t r e n d i n t r o d u c e d t h i s way by r a p i d improvement o f f i s h i n g t e c h n o l o g y i n t h e p a s t d e c a d e . I t i s w e l l r e c o g n i z e d t h a t e r r o r s o f d i f f e r e n t f o r m s and s i z e s accompany most spawning s t o c k a s s e s s m e n t d a t a ( s p a w n i n g c o u n t s , age s t r u c t u r e s , e t c . ) . D e p e n d i n g on t h e met^qds u s e d , .ft It". •% t h e r e p o r t i n g s y s t e m and t h e manpower i n v o l v e d , these* e r r o r s a r e s o m etimes v e r y l a r g e and o f t e n t h e y c a n n o t be e v a l u a t e d due t o p o o r r e p o r t i n g o f t h e methods u s e d . F o r example, t h e f i s h e r y o f f i c e r s ' r e c o r d i n g p r o c e d u r e a l o n e (by wide abundance c l a s s e s ) w o u l d i n t r o d u c e +- 30% e r r o r i n s p a w n ing c o u n t s . S y s t e m a t i c b i a s of t h e s e e s t i m a t e s o v e r t i m e due t o t e c h n o l o g i c a l improvement a n d / o r i n c r e a s e d i n v o l v e m e n t may have had s e r i o u s c o n s e q u e n c e s , and t h e r e has been l i t t l e i n s t r u c t i o n f o r f i e l d s t a f f t o r e c o g n i z e o r c o r r e c t f o r t h e s e c h a n g e s . More i m p o r t a n t , t h e p r e s e n c e o f one o r more o f t h e above e r r o r s does n o t s i m p l y make the s t o c k - r e c r u i t m e n t r e l a t i o n s h i p n o i s e r and h a r d e r t o d e f i n e ; r a t h e r i t b i a s e s t h e a p p a r e n t r e l a t i o n s h i p , l e a d i n g t o more l i b e r a l r e g u l a t i o n s when i n f a c t v e r y s t r i n g e n t m e a s u r e s of c o n s e r v a t i o n s h o u l d h a v e been i n e f f e c t ( a s shown i n t h e n e x t c h a p t e r ) . B e c a u s e of t h e d i v e r s i t y of p o s s i b l e s o u r c e s of e r r o r i n t h e d a t a f o r d i f f e r e n t s t o c k s , a p p e n d i x II l i s t s t h e s e major s o u r c e s on a s t o c k by s t o c k b a s i s , t o g e t h e r w i t h o t h e r i m p o r t a n t s t a t i s t i c s r e l a t e d t o t h e s t o c k -r e c r u i t m e n t d y n a m i c s . 42 3_;_ ESTIMATION OF STOCK-RECRUITMENT RELATIONSHIPS The i m p o r t a n c e of s t o c k - r e c r u i t m e n t r e l a t i o n s h i p s i n c o n n e c t i o n w i t h t h e s u c c e s s f u l management o f salmon r e s o u r c e s has been w i d e l y d i s c u s s e d . L a r k i n (1973) d e s c r i b e d s e v e r a l t y p e s o f m o d e l s t h a t c a n be u s e d f o r i n t e r p r e t i n g t h e s e r e l a t i o n s h i p s . D e p e n d i n g on t h e a s s u m p t i o n s u s e d , many p o s s i b l e s t o c k -r e c r u i t m e n t m o d e l s can c e r t a i n l y be d e v e l o p e d ( s e e P a r r i s h (ed.) 1973). F r e q u e n t l y , i d e n t i c a l m o d e l s c a n be d e r i v e d w i t h d i f f e r e n t a s s u m p t i o n s , and t h e a d d i t i o n of s i m p l e p l a u s i b l e b i o l o g i c a l a s s u m p t i o n s can d r a m a t i c a l l y i n c r e a s e t h e c o m p l e x i t y o f m o d e l s and hence the d a t a r e q u i r e m e n t s . The a v a i l a b l e r e c o r d s f o r most B.C. s t o c k s h a r d l y s a t i s f y t h e d a t a demands f o r any. but t h e s i m p l e s t models, but e v e n t h e s e s h o u l d be h e l p f u l i n t h e i n t e r p r e t a t i o n of h i s t o r i c a l s t o c k - r e c r u i t m e n t d y n a m i c s . O b v i o u s l y as more i n f o r m a t i o n becomes a v a i l a b l e , more complex m o d e l s s h o u l d be used t o p r o v i d e a b e t t e r u n d e r s t a n d i n g o f t h e p o p u l a t i o n d y n a m i c s of t h e s t o c k s c o n c e r n e d . B e c a u s e o f t h e i n h e r e n t v a r i a b i l i t y o f salmon p o p u l a t i o n s and i n a c c u r a t e s t o c k a s s e s s m e n t m e t h o d s , i t o f t e n happens t h a t a s e t of s t o c k - r e c r u i t m e n t d a t a i s c o n s i s t e n t w i t h more t h a n one m o d e l . T h i s c a n l e a d t o s e r i o u s p r o b l e m s i f t h e d i f f e r e n t m o d e ls i m p l y s i g n i f i c a n t l y d i f f e r e n t management a c t i o n s . S c i e n t i s t s c a n o n l y f i n d and d e s c r i b e t h e s e m o d e l s , and management a c t i o n s s h o u l d be b a s e d on b a l a n c i n g p o s s i b l e outcomes w i t h o u t p r e t e n d i n g t h a t any s i n g l e model i s t h e b e s t c h o i c e . The manager s h o u l d examine p o s s i b l e s t r a t e g i e s i n l i g h t o f v a r i o u s p l a u s i b l e m o d e l s r a t h e r t h a n s e l e c t i n g o n l y one and u s i n g i t as a b a s i s 4 3 f o r management ( W a l t e r s 1977, W a l t e r s 1981). F o r t h i s s t u d y o n l y two s i m p l e , two p a r a m e t e r s t o c k -r e c r u i t m e n t m o d e l s were u s e d f o r most a n a l y s e s . The f i r s t , a R i c k e r m o d e l , assumes a dome-shaped r e l a t i o n s h i p between s t o c k and r e c r u i t m e n t , so i t a d m i t s t h a t l a r g e s p a w n i n g s t o c k s may r e s u l t i n p o o r r e t u r n s . The s e c o n d , a B e v e r t o n - H o l t m o d el, assumes t h a t r e c r u i t m e n t i n c r e a s e s t o a maximum b i o l o g i c a l l i m i t a s s p a w n i n g s t o c k i n c r e a s e s , b u t d o e s n o t c o l l a p s e i f v e r y l a r g e s p a w n i n g s t o c k s a r e a l l o w e d . A t h i r d , t h r e e p a r a m e t e r model d e v e l o p e d by L u d w i g ( p e r s . Comm.) was a l s o f i t t e d t o some d a t a s e t s . The L u d w i g model a l l o w s f o r t h e p o s s i b i l i t y o f r e d u c e d p r o d u c t i v i t y a t low s t o c k s i z e s due t o d e p e n s a t o r y m o r t a l i t y a g e n t s . However, i t g e n e r a l l y gave r e s u l t s e q u i v a l e n t t o t h e R i c k e r model ( i n s i g n i f i c a n t d e p e n s a t i o n ) , so r e s u l t s f o r i t w i l l n o t be p r e s e n t e d b e l o w . D e s i g n i n g f i s h e r y s t r a t e g i e s f r o m t h e s e m o d e l s would be v e r y m i s l e a d i n g i f measurement e r r o r s a n d t h e ra n g e of o b s e r v a t i o n s a r e n o t t a k e n i n t o a c c o u n t i n t h e a n a l y s i s . W a l t e r s and L u d w i g (1980) showed t h a t m o d e r a t e e r r o r i n escapement measurements c a n make r e c r u i t m e n t s a p p e a r t o be i n d e p e n d e n t o f s p a w n i n g s t o c k s , w h i c h p r o m o t e s o v e r e x p l o i t a t i o n r a t h e r t h a n s i m p l y s a y i n g t h a t t h e r e l a t i o n s h i p d o e s n o t e x i s t . F u r t h e r , t h e o b s e r v e d e x p l o i t a t i o n h i s t o r y a l s o c a n have p r o f o u n d e f f e c t s on t h e p e r f o r m a n c e o f any s t a t i s t i c a l p r o c e d u r e . H i l b o r n (1979) showed t h a t e s t i m a t i o n p e r f o r m a n c e i s g e n e r a l l y much p o o r e r when d a t a a r e a v a i l a b l e o n l y a f t e r t h e s t o c k becomes h e a v i l y e x p l o i t e d , t h a n when d a t a a r e a l s o a v a i l a b l e f r o m t h e e a r l y d e v e l o p m e n t o f t h e f i s h e r y . D r a m a t i c d e c r e a s e i n l o n g - t e r m 44 c a t c h e s c a n r e s u l t w i t h c e r t a i n c o m b i n a t i o n s o f t h e s e two f a c t o r s ( s e e s i m u l a t i o n s t u d y i n W a l t e r s and Ludwig,1980) T h i s c h a p t e r f i r s t f o c u s s e s on t r a d i t i o n a l m o d e l - f i t t i n g and p a r a m e t e r e s t i m a t i o n , t h e n t u r n s t o t h e e x a m i n a t i o n o f v a r i o u s measurement e r r o r s and t h e i r e f f e c t s on t h e p e r f o r m a n c e o f e s t i m a t i o n p r o c e d u r e s . I t c o n c l u d e s w i t h an e x a m i n a t i o n o f a p p a r e n t p a t t e r n s i n s t o c k - r e c r u i t m e n t p a r a m e t e r s among s p e c i e s and g e o g r a p h i c a r e a s . 3.1 Model F i t t i n g P r o c e d u r e s Many m o d e l s can be f i t t e d u s i n g m u l t i p l e l i n e a r r e g r e s s i o n a n a l y s i s a f t e r t h e y a r e t r a n s f o r m e d i n t o l i n e a r f o r m s . T h e s e methods a r e d e s c r i b e d i n many s t a t i s t i c s b o oks and a r e n o t r e p e a t e d h e r e . However, when no t r a n s f o r m a t i o n w i l l c o n v e r t an e q u a t i o n i n t o a form t h a t c a n be h a n d l e d t h i s way, i t e r a t i v e methods a r e commonly u s e d t o e s t i m a t e t h e p a r a m e t e r s . S i n c e t h e a r r i v a l o f c o m p u t e r s , many i t e r a t i v e methods o f p a r a m e t e r e s t i m a t i o n have been d e v e l o p e d ( s e e B a r d 1974). In p r i n c i p l e , t h e s e a r e t r i a l - a n d - e r r o r methods so t h a t t h e p r e d i c t i o n r e s i d u a l s l e f t a f t e r e a c h i t e r a t i o n show us how t o imp r o v e t h e n e x t t r y . A s i m p l e method d e s c r i b e d by Watt (1968) i s : l e t be t h e model t o be f i t t e d t o d a t a , where X j a r e i n d e p e n d e n t 4 5 v a r i a b l e s and (2 s a r e p a r a m e t e r s t o be e s t i m a t e d . Suppose we c a n o b t a i n e s t i m a t e s , b , f o r t h e t r u e p a r a m e t e r s , ^3 . Then we c a n c o r r e c t t h e b i t e r a t i v e l y by i n c r e m e n t a l a m o u n t s , ^ , u n t i l no s i g n i f i c a n t improvement c a n be made. T h a t i s = b + s t h e v e c t o r S. a t i t e r a t i o n X c a n be o b t a i n e d by where (nit) S>j: 5 '(fe-/'>3iI - * T l V ' V . > ] 3.1.1 R i c k e r Model The most commonly u s e d model i n salmon r e s e a r c h and management i s t h a t d e v e l o p e d by R i c k e r ( 1 9 5 4 ) , w h i c h c an be w r i t t e n i n v a r i o u s ways. The f o l l o w i n g f o r m i s u s e d i n t h i s a n a l y s i s : t+i t (2-1 •<*•). where i s spawners a t g e n e r a t i o n t , i s r e c r u i t s r e s u l t i n g from , °< i s a p r o d u c t i v i t y p a r a m e t e r , ^ i s an e q u i l i b r i u m s t o c k p a r a m e t e r and i s a random e n v i r o n m e n t a l f a c t o r , n o r m a l l y d i s t r i b u t e d w i t h mean 0.0 and v a r i a n c e 6\ . T h i s model can be t r a n s f o r m e d i n t o a s i m p l e l i n e a r r e g r e s s i o n form ( D a h l b e r g 1973, R i c k e r 1975) a s : 46 W i t h y - Jn (^/S) and x=5 , s t a n d a r d r e g r e s s i o n a n a l y s i s c a n be P u s e d t o e s t i m a t e d , & and 6\ 3.1.2 B e v e r t o n and H o l t M odel An a l t e r n a t i v e model t o R i c k e r 1 s i s t h a t d e v e l o p e d by B e v e r t o n and H o l t (1957) : where r ? ^ + ( , £ and ( a r e t h e same a s i n ( 3 . 1 . 5 ) , a and b a r e new p a r a m e t e r s w i t h a/b m e a s u r i n g p r o d u c t i v i t y and a, m e a s u r i n g t h e e q u i l i b r i u m s t o c k s i z e . The m u l t i p l i c a t i v e , l o g - n o r m a l n o i s e t e r m , e x p ( U ^ + ( ) , has been j u s t i f i e d by A l l e n ( 1 9 7 3 ) , W a l t e r s and H i l b o r n ( 1 9 7 6 ) , and Peterman ( 1 9 7 8 ) . S i n c e no t r a n s f o r m a t i o n c a n c o n v e r t (3.1.6) i n t o a l i n e a r form, i t e r a t i v e methods (3.1.2 t o 3.1.3) a r e u s e d t o e s t i m a t e t h e p a r a m e t e r s . The p r o c e d u r e i s as f o l l o w s . From ( 3 . 1 . 6 ) , we have L e t a ' = l n a, t h e n 4 7 The s p e c i f i c f o r m of (3.1.1) i n t h i s c a s e i s : 3' fi, - Xrs ((5; + X,-) The v e c t o r o f t r i a l p a r a m e t e r v a l u e s , b, i s o b t a i n e d f r o m a l i n e a r t r a n s f o r m a t i o n of ( 3 . 1 . 6 ) , i g n o r i n g z i f ' : a t + / R e g r e s s i o n o f y=1/R on X=1/S y i e l d s t h e t r i a l p a r a m e t e r v e c t o r , b . The c o r r e c t i o n v e c t o r , £ , a t i t e r a t i o n X is- computed f r o m ( 3 . 1 . 3 ) , u s i n g : X liL 9 b; 5 T = X 3.1.3 Power model When a s t o c k i s h e a v i l y f i s h e d , a n d i f d a t a a r e c o l l e c t e d w i t h l i t t l e e r r o r s i n c e t h e b e g i n n i n g of t h e f i s h e r y , t h e r e c r u i t m e n t p o i n t s w i l l o b v i o u s l y be d i s t r i b u t e d o v e r a wide r a n g e of s p a w n i n g p o p u l a t i o n s . Then, t h e maximum l i k e l i h o o d c u r v e t h a t f i t s t h r o u g h t h e d a t a p o i n t s c an be r e g a r d e d a s r e p r e s e n t a t i v e of t h e s t o c k - r e c r u i t m e n t d y n a m i c s o f t h e 4 8" p o p u l a t i o n . Most B r i t i s h C o l u m b i a s almon s t o c k s have been e x p l o i t e d h e a v i l y s i n c e t h e b e g i n n i n g o f t h i s c e n t u r y (MacLeod 1977). U n f o r t u n a t e l y , q u a n t i t a t i v e d a t a were c o l l e c t e d ( w i t h c o n s i d e r a b l e e r r o r ) o n l y s i n c e 1948. T h e r e f o r e , i t seems l i k e l y t h a t none o f t h e d a t a s e t s u s e d i n t h i s a n a l y s i s r e p r e s e n t t h e f u l l r a n g e o f a s t o c k - r e c r u i t m e n t c u r v e . R a t h e r , a l i m i t e d p o r t i o n , e s p e c i a l l y t h e l e f t - h a n d l i m b o f t h e c u r v e i s e x h i b i t e d . In t h i s c a s e , a s i m p l e Power model may d e s c r i b e t h e d a t a b e t t e r t h a n t h e R i c k e r or B e v e r t o n - H o l t m o d e l s . The Power model i s * i t l = s t f (*./.„) where /^ + | , S£ , oi and Uj.tl a r e t h e same a s i n t h e R i c k e r model ( 3 . 1 . 4 ) , w h i l e {Z i s an i n d e x o f d e n s i t y d e pendence ( C u s h i n g 1971). E q u a t i o n (3.2.1) c a n n o t be u s e d t o f i t a f u l l y dome s h a p e d c u r v e , b u t can be u s e d t o f i t a l e f t - h a n d l i m b o r a r i g h t - h a n d l i m b . A l s o , a l i g h t l y c o n v e x c u r v e c a n be r e a s o n a b l y f i t t e d . A n o t h e r a d v a n t a g e of t h e Power model i s t h a t i t s p p a r a m e t e r v a r i e s p r e d i c t a b l y (downward) w i t h i n c r e a s i n g e r r o r s i n s p a w n i n g s t o c k measurement. The p r o c e d u r e d e v e l o p e d by L u d w i g and W a l t e r s ( s e e below) c a n be e a s i l y u s e d t o e s t i m a t e t h e p a r a m e t e r v a l u e s o f t h i s m o d e l . By a s s u m i n g e v e r y s t o c k has e x p e r i e n c e d c o m p a r a b l e d e g r e e s o f e x p l o i t a t i o n , t h e i n d e x o f d e n s i t y d e p e n d e n c e , ,3 , can be compared w i t h i n s p e c i e s and among s p e c i e s f o r v a r i o u s a s s u m p t i o n s a b o u t t h e m a g n i t u d e of t h e spawn measurement e r r o r s . 4 9 3.2 C o r r e c t i o n s f o r Measurement E r r o r s Measurement e r r o r s e n t e r t h e R i c k e r model (3.1.4) i n t h e f o l l o w i n g way. F i r s t , i t i s r e a s o n a b l e t o assume t h a t measurement e r r o r s a r e p r o p o r t i o n a l r a t h e r t h a n a d d i t i v e . L e t f~t and st be t h e o b s e r v e d v a l u e s , t h e n a s i m p l e r e p r e s e n t a t i o n o f p r o p o r t i o n a l e r r o r i s where £ t and £ a r e i n d e p e n d e n t random v a r i a b l e s , w h i c h L u d w i g and W a l t e r s (1981) assume a r e n o r m a l l y d i s t r i b u t e d w i t h mean 0.0 and v a r i a n c e 6\ and 6\ r e s p e c t i v e l y . E q u a t i o n s (3.1.4) and (3.2.1) i m p l y t h a t C'3-3-2; o r a ( 2 ; ' ) = * * ^ t * f 2 + - - ^ where u> = U^ + £j . I f t h e s p a w n i n g c o u n t e r r o r , ^ , i s s m a l l , t h e n s t a n d a r d r e g r e s s i o n s t a t i s t i c s s t i l l a p p l y . E q u a t i o n (3.2.2) s u g g e s t s t h a t random measurement e r r o r s i n t h e r e c r u i t s , /?, L , i n c r e a s e t h e v a r i a n c e of t h e model w h i l e s a m p l i n g e r r o r s i n t h e s p a w n e r s , St , b i a s t h e p a r a m e t e r s . S i n c e t h e s p a w n i n g p o p u l a t i o n a t g e n e r a t i o n j i s a l s o p a r t o f t h e r e c r u i t s p r o d u c e d from g e n e r a t i o n j - 1 , measurement e r r o r s i n t h e s p a w n i n g c o u n t s not o n l y b i a s t h e p a r a m e t e r s , but a l s o i n c r e a s e t h e v a r i a n c e o f t h e m o d e l . 5 0 To i l l u s t r a t e t h e s e e f f e c t s , W a l t e r s and Lud w i g (1981) u s e d a s i m u l a t i o n model t o g e n e r a t e " a c t u a l " d a t a f r o m t h e e q u a t i o n where -Sj. i s t h e s p a w n i n g s t o c k a t g e n e r a t i o n t, i s t h e r e s u l t i n g r e c r u i t s f r o m , °< i s t h e p r o d u c t i o n p a r a m e t e r and U f t - i i s t h e random e n v i r o n m e n t f a c t o r , n o r m a l l y d i s t r i b u t e d w i t h mean 0.0 and v a r i a n c e S\ . T h i s model p o p u l a t i o n was a l w a y s o v e r - e x p l o i t e d , t h a t i s , e a c h a d d i t i o n a l f i s h a l l o w e d t o spawn w o u l d p r o d u c e , on a v e r a g e , a t l e a s t a s many r e c r u i t s as e a c h spawner a l r e a d y a l l o w e d . The p o p u l a t i o n s i z e was r e g u l a t e d by f i s h i n g t o a c h i e v e a f i x e d e s capement g o a l w h i c h was s u b j e c t e d t o a random d e v i a t i o n o f a b o u t 45%. W a l t e r s and Ludwig (1981) " s a m p l e d " f r o m t h e s e model d y n a m i c s u s i n g e q u a t i o n ( 3 . 3 . 1 ) , and showed t h a t t h e a p p a r e n t r e c r u i t m e n t r e l a t i o n s h i p c an _be s a t u r a t i n g o r dome s h a p e d . To see t h e c o m p a r a t i v e e f f e c t s o f s p a w n i n g c o u n t e r r o r s and c a t c h s t a t i s t i c s e r r o r s on t h e f i n a l a p p e a r a n c e of t h e s t o c k -r e c r u i t m e n t d a t a , I u s e d t h e same m o d e l , b ut g e n e r a t e two s e t s of " o b s e r v e d " d a t a . In t h e f i r s t c a s e , measurement e r r o r s o c c u r e d i n t h e c a t c h o n l y a s : where ^ i s t h e o b s e r v e d r e c r u i t m e n t , St i s t h e a c t u a l e s c a p e m e n t , R^ i s t h e a c t u a l r e c r u i t m e n t , h i s t h e h a r v e s t r a t e and v^ i s a n o r m a l l y d i s t r i b u t e d random v a r i a b l e w i t h mean 0.0 and v a r i a n c e <5y . The s e c o n d s e t of " o b s e r v e d " d a t a was g e n e r a t e d f r o m t h e i d e n t i c a l s e t of " a c t u a l " d a t a but w i t h t h e 5 I m u l t i p l i c a t i v e e r r o r t e r m , Jl* , o c c u r r i n g i n t h e s p a w n i n g c o u n t o n l y : where S t i s t h e o b s e r v e d s p a w n e r s , S t i s t h e a c t u a l spawners and i s t h e same a s i n ( 3 . 2 . 4 ) . O b s e r v e d r e c r u i t m e n t was t h e n c a l c u l a t e d a s : F i g u r e 4 shows " a c t u a l " and " o b s e r v e d " s t o c k - r e c r u i t m e n t d a t a f o r a s i m u l a t i o n c a s e w i t h 6XV = 0.1 and 6"2U =0.1 . Random measurement e r r o r o c c u r i n g i n t h e c a t c h o n l y d i d n o t have much e f f e c t on t h e f u n c t i o n a l f o r m o f t h e r e l a t i o n s h i p b u t t h e same r e l a t i v e e r r o r s i n t h e s p a w n i n g c o u n t made r e c r u i t m e n t a p p e a r t o be i n d e p e n d e n t of s p a w n e r s . More s i m u l a t i o n c a s e s were e x a m i n e d w i t h $ \ r a n g i n g from 0.01 t o 0.5 . In g e n e r a l , random measurement e r r o r s i n t h e spawning s t o c k seemed t o have b i g g e r i m p a c t s on t h e s t o c k -r e c r u i t m e n t d a t a t h a n c o m p a r a b l e e r r o r s i n t h e c a t c h . V i s u a l d i s t o r t i o n o f t h e " a c t u a l " d a t a o c c u r e d when s p a w n i n g c o u n t e r r o r s e x c e e d e d a b o u t +-45% ( 6^ = .0b). Whereas, s i g n i f i c a n t d i s t o r t i o n d i d n o t o c c u r u n t i l measurement e r r o r s i n t h e c a t c h e x c e e d e d ° v =.4 (95% l i m i t s a r e .29C" t and 3 . 4 5 0 ^ ) . H a s t i l y , one m i g h t c o n c l u d e t h a t e r r o r s i n t h e c a t c h s e l d o m have any s i g n i f i c a n t e f f e c t on t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p b e c a u s e e r r o r s o f t h e s e m a g n i t u d e s ( o f f by a f a c t o r of 2 t o 3.5) seldom o c c u r i n r e a l c a t c h s t a t i s t i c s . However, r e l a t i v e l y s m a l l nonrandom ( b i a s e d ) e r r o r s i n t h e a l l o c a t i o n of m i x e d c a t c h e s do 52 F i g . 4. " A c u t a l " and " o b s e r v e d " s t o c k - r e c r u i t m e n t d a t a p o i n t s w i t h c o m p a r a b l e measurement e r r o r s i n t h e c a t c h and escapement r e s p e c t i v e l y . ERRORS IN CATCH ONLY ERRORS IN SPAWNING COUNT ONLY OBSERVED ACTUAL 5 4 have s i g n i f i c a n t i m p a c t s on t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p , a s shown i n t h e p r e v i o u s c h a p t e r . 3.2.1 C o r r e c t i o n f o r Spawning Count E r r o r s I t h as been shown t h a t t h e t y p i c a l s a m p l i n g e r r o r s i n spawning c o u n t s ( +-50% o r more) o b l i t e r a t e t h e s t o c k -r e c r u i t m e n t r e l a t i o n s h i p . W a l t e r s and L u d w i g (1981) c o n c l u d e d t h a t most spawner and r e c r u i t m e n t e s t i m a t e s a r e o f l i t t l e v a l u e u n l e s s t h e a c c u r a c y o f t h e e s t i m a t e s i s a l s o a s s e s s e d . I f we assume t h a t a c t u a l r e c r u i t m e n t , R^ , and a c t u a l s p a w n e r s , S t , a r e s u b j e c t t o t h e same r e l a t i v e e r r o r , exp( V ), ( ) becomes: where i ^ . and S^ . a r e t h e o b s e r v e d v a l u e s and V t a r e n o r m a l l y d i s t r i b u t e d i n d e p e n d e n t random v a r i a b l e s w i t h mean 0.0 and v a r i a n c e &\ . Then t h e R i c k e r model (3.1.4) becomes or t + i * t •* where w t = U t + V t and * j t - Jn ( r t / , ) I f t h e v a r i a n c e of o b s e r v a t i o n e r r o r s , <fy , i s known t h e n c o n s i s t e n t e s t i m a t e s o f a and b e a n be o b t a i n e d ( f r o m W a l t e r s and Ludwig 1981 ) : 55 where a* i s a c o n s i s t e n t e s t i m a t e o f , i* i s a c o n s i s t e n t e s t i m a t e o f jZ , B i s a b i a s c o r r e c t i o n f a c t o r e q u a l t o e x p ( 2 6y ), i s t h e c o r r e c t e d sum o f p r o d u c t s and i s t h e c o r r e c t e d sum o f s q u a r e s o f S's However t h e e s t i m a t i o n o f 6\ r e q u i r e s l a r g e i n d e p e n d e n t d a t a s e t s w h i c h u s u a l l y do not e x i s t . A n o t h e r a p p r o a c h i s t o b a s e a l l t h e s t a t i s t i c a l i n f e r e n c e upon t h e l i k e l i h o o d o f t h e g i v e n o b s e r v a t i o n s , as a f u n c t i o n o f t h e p a r a m e t e r s t o be e s t i m a t e d . The l o g a r i t h m o f t h e l i k e l i h o o d of t h e o b s e r v a t i o n s i s g i v e n by ( L u d w i g and W a l t e r s 1980): where A must be p r e s c r i b e d as A = 6v/6\ and K-,, a r e d e t e r m i n e d f r o m (3.3.8) where A l l t h e p a r a m e t e r s , e x c e p t 6^ , can be e s t i m a t e d by m a x i m i z i n g L and 6u. can be e s t i m a t e d f r o m t h e r e s i d u a l sum o f s q u a r e s a s i f 2 * z ' < A 2 A f where ^ . , and V- a r e t h e e s t i m a t e d v a l u e s w h i c h m a x i m i z e L. A computer p r o g r a m ( L u d w i g , per.comm.) w h i c h f o l l o w s t h e e s t i m a t i o n p r e c e d u r e p r e s e n t e d by L u d w i g and W a l t e r s was u s e d t o 5 6 e s t i m a t e t h e p a r a m e t e r v a l u e s o f t h e R i c k e r and Power m o d e l . S i n c e t h e e r r o r r a t i o , A / was n o t known, a r a n g e o f v a l u e s between 0 ^ ^ - 2 were p r e s c r i b e d t o e a c h s t o c k and t h e c o r r e s p o n d i n g p a r a m e t e r s were e s t i m a t e d . 3.3 RESULTS 3.3.1 S t o c k R e c r u i t m e n t P a r a m e t e r E s t i m a t e s T a b l e s 17 t o 19 show p a r a m e t e r e s t i m a t e s f o r t h e R i c k e r , B e v e r t o n - H o l t and Power models r e s p e c t i v e l y w i t h o u t c o n s i d e r i n g measurement e r r o r s . The raw s t o c k - r e c r u i t m e n t d a t a a r e p r e s e n t e d g r a p h i c a l l y i n a p p e n d i x I I , a l o n g w i t h summary a s s e s s m e n t s b a s e d on v i s u a l i n s p e c t i o n o f t h e d a t a . In t h e a n a l y s i s , e v e r y d a t a p o i n t - i s g i v e n e q u a l w e i g h t r e g a r d l e s s of i t s c r e d i b i l i t y . O b v i o u s l y a more t h o r o u g h a n a l y s i s w o u l d i n c l u d e a w e i g h t i n g f a c t o r f o r e a c h d a t a p o i n t t o r e f l e c t i t s r e l a t i v e a c c u r a c y ( i . e . f o r example, i n 1958 one m i l l i o n s o c k e y e spawners were e x c l u d e d from t h e Adams r i v e r w i t h a t e m p o r a r y f e n c e , and t h e r e f o r e t h i s d a t a p o i n t s h o u l d be g i v e n l e s s w e i g h t i n t h e s t o c k - r e c r u i t m e n t a n a l y s i s ) . U n f o r t u n a t e l y , e s t i m a t i o n o f w e i g h t s w o u l d i n v o l v e t r e m e n d o u s amounts of e f f o r t t o r e v i e w e v e r y p i e c e o f h i s t o r i c a l i n f o r m a t i o n , and was b e y o n d t h e t i m e and manpower c o n s t r a i n t s o f t h i s s t u d y . Back c a l c u l a t i o n and a l l o c a t i o n t a b l e methods were u s e d t o s e p a r a t e m i x e d c a t c h e s back t o t h e i r p r o d u c t i o n u n i t s . F i g u r e s 5a and 5b compare t h e R i c k e r model c< , e n v i r o n m e n t a l v a r i a n c e and e q u i l i b r i u m s t o c k p a r a m e t e r s o b t a i n e d by t h e s e two methods. 5 7 T a b l e s 17-19. R i c k e r , Power and B e v e r t o n - H o l t model, p a r a m e t e r s , e s t i m a t e d by maximum l i k e l i h o o d w h i l e i g n o r i n g s p a w n i n g c o u n t e r r o r s . * = e s t i m a t i o n p r o c e d u r e f a i l e d - = i n s u f f i c i e n t i n f o r m a t i o n o r n e g l i g i b l e s t o c k SIG2 = 6\ V TABLE 17. RICKER MODEL PARAMETERS ( ALLOCATION TABLE BACK CALCULATION AREA A B SIG2 N A B SIG2 N 1 2 3 1 608 -4 82E-06 0 172 1 1 1 590 -3 62E-06 0 269 1 1 4 1 163 -7 00E-07 0 260 27 1 012 -5 90E-07 0 292 27 5 1 248 -2 23E-06 0 128 27 1 381 -2 77E-06 0 108 27 6 1 998 - 1 93E-06 0 4 10 27 1 895 -1 85E-06 0 508 27 7 1 463 - 1 45E-05 0 447 2 1 1 922 - 1 31E-05 0 432 21 n 9 2 098 -4 40E-07 0 160 2 1 2 035 -4 30E-07 0 163 21 10 - - - - - - - -S " 0 808 -2 38E-06 0 433 21 0 978 - 1 .65E-06 0 542 2 1 j 12 - - - - -Lunu ALLOCATION TABLE BACK CALCU LATION AREA A B SIG2 N A B SIG2 N T " 2 269 -2 47E-05 6 160 20 2 259 -2 21E-05 O. 3U4 19 2 1 516 - 1 03E-05 0 226 20 1 258 -8 37E-06 0. 122 19 3 2 235 -3 3 IE-05 0 507 20 2 499 -3 48E-05 0 292 19 4 1 277 -9 05E-06 0 293 20 1 892 - 1 18E-05 0 248 19 5 1 968 -4 04E-06 0 277 20 2 432 -5 78E-06 0 250 19 6 2 624 - 1 23E-04 0 435 20 3 979 -8 74E-05 0 469 19 7 1 869 -5 65E-06 0 389 20 2 664 -8 17E-06 0 133 19 8 2 637 -3 73E-06 0 257 2© 2 011 -3 68E-06 0 134 19 9 2 734 -9 55E-06 0 324 20 2 930 - 1 57E-05 0 1 18 19 10 11 1 .595 -6 81E-06 0 220 20 1 .406 -5 73E-06 0 161 19 12 1 965 -2 32E-05 0 239 20 2 146 -2 28E-05 0 337 19 SPRING ALLOCATION TABLE BACK CALCULATION rA'REA, A I B SIG2 N A B 5IG2 N • i 1 1 3 6 -2 04E-05 0 336 21 1 623 -1 95E-05 0 485 26 2 1 294 -2 24E-06 0 238 27 1 238 -2 18E-06 0 348 27 3 2 353 -2 16E-05 0 327 27 2 434 -2 13E-05 0 433 27 4 5 1 205 - / 60E-07 0 244 27 1 178 -7 70E-07 . 0 252 27 6 7 0 872 -2 77E-06 0 461 15 1 088 -2 76E-06 0 570 15 I a 1 016 -9 70E-07 0 305 15 0 985 -1 03E-06 0 297 15 j 9 • 0 579 + 4 10E-07 0 230 15 0 566 + 3 50E-06 0 226 15 |10 |1 1 0 66 1 - 1 04E-06 0 358 27 0 661 1 04E-06 0 358 27 ,!!2 1 388 -5 50E-06 0 323 27 1 388 -5 50E-0G 0 323 27 AREA 1 2 3 4 5 6 7 8 9 10 1 1 12 ALLOCATION TABLE 1.614 1 . 130 0.884 2. 145 1 .651 1 .443 3 .089 2 . 200 1 . 182 B -8.11E-05 -3.18E-05 - 1.65E-05 -2.51E-04 -3.85E-05 -2 . 22E-05 -9.26E-06 -7.15E-05 -6.65E-05 SIG2 198 024 038 042 ,054 .036 .015 0.080 0.036 12 12 12 12 12 12 12 12 12 BACK CALCULATION 2 .05 1 1 .251 1 .65 1 3 .086 2 . 179 1 .686 2.516 2.475 1 . 370 B -8.4 1E-05 -2 . 33E-05 -2 06E-05 -2.25E-04 -4 . 15E-05 - 1.97E-05 -5.03E-06 -9.00E-05 -6.98E-05 SIG2 O. 145 0.048 0.032 0.097 0.077 0.034 0.014 0. 126 0.084 ODD PINK u u u r ALLOCATION TABLE BACK CALC ULATION •'AREA A B SIG2 Kl A B SIG2 hi \ 2 3 2 . 648 - 1 06E -05 0.352 15 2 902 -1 02E-05 0.554 15 4 1 . 573 -8 40E -07 0. 179 15 1 488 -8 70E-07 0. 233 15 5 1 . 120 -2 20E -07 O. 294 15 1 058 -1 50E-07 0. 370 15 6 7 1 . 159 - 1 34E -06 0.680 1 1 1 599 -1 30E-06 0.700 1 1 3 0 204 - 1 20E -06 0.490 1 1 1 443 -1 76E-06 0.461 1 1 I 9 2 613 -6 50E -07 0. 366 1 1 2 359 -5 80E-07 0.428 1 1 IT <!2 - -_ - - - -CWCW PtWK ALLOCATION TABLE BACK CALCU LATI ON 11 AREA A B SIG2 N A B SIG2 N . j 1 2 3 4 5 6 7 8 9 10 1 1 12 0.578 1 . 494 2 .079 1 .724 1 .632 3 .093 1 .437 1 .349 1 . 393 -8.70E-07 - 1.20E-06 -4.46E-06 - 1.08E-06, - 1.50E-07 -7.61E-06 -4.90E-07 -2. 18E-05 -4.36E-06 0. 372 0.235 0.558 0. 298 0. 384 1 . 237 0. 484 0.964 0.7 14 15 15 15 15 15 15 15 13 15 0. 986 1 . 37 1 1 .877 1 . 505 1 . 580 2.311 1 .437 1 . 349 1 . 393 -9.50E-07 - 1.01E-06 -2 ..60E-06 - 1.03E-06 - 1.40E-07 -5.38E-06 -4.90E-07 -2.18E-05 -4.36E-06 0.692 0.448 0.936 0. 329 0.401 1.219 0.484 0.964 0.714 14 15 15 15 15 15 15 13 15 CJ1 0 0 TABLE 18. POWER MODEL PARAMETERS SOCKEYE ALLOCATION TABLE BACK CALC ULATION AREA A B SlG2 N A B SIG2 N 1 2 3 10.3 14 0 2042 0 165 11 8.297 0. 3883 0. 262 1 1 4 4 . 163 0 7406 0 270 27 3 . 353 0.7958 0.300 27 5 6 . 955 0 4927 0 1 15 27 7 .833 0.4226 0.097 27 6 10.957 0 2343 0 389 27 10.573 0.2589 0.484 27 7 16 .04 8 -0 4024 0 432 21 15.446 -0.2963 0.403 21 8 9 9 . 539 o 4245 0 175 2 1 9 . 223 0.4440 0. 177 21 10 - - - - - - - -1 1 6.734 o 4658 0 399 21 6 .089 0. 5437 0.511 2 1 ' 2 - - - - - -ALLOCATION TABLE BACK CALC ULATION AREA A B SIG2 N A B SIG2 N ' 1 11.456 0 0027" 0 202 20 8. 668 0 2931 0 300 19 2 7.672 0 3777 0 223 20 5. 934 0 5238 0 127 19 3 10.806 0 0487 0 393 20 10. 601 0 0898 0 283 19 4 7.635 0 3667 0 286 20:, 10. 920 0 1082 0 213 19 5' 10.628 0 2195 0 263 20 13 688 -0 0228 0 254 19 6 8.997 0 1495 0 231 20 a 848 0 3553 0 305 19 7 8.223 0 3936 0 373 20 10 968 0 2003 0 129 19 8 9.703 0 3565 0 260 20 9 278 0 3406 0 132 19 9 9.563 0 3233 0 330 20 15 646 -0 2467 0 095 19 10 1 1 7.278 0 4440 0 224 20 6 4B4 o 5069 0 160 19 12 1 1 . 190 O 0303 0 206 20 1 1 423 1 0 0280 O 304 19 r'-1 ' - " " I ALLOCATION TABLE BACK CALCULATION 1 AREA A n SIG2 N A B SIG2 N 1 TT rT65~ — t r 0077 0 283 27 10. 495 0. 13546 0 444 26 2 10 . 546 0 2004 O 203 27 9. 485 0. 2816 0 364 27 3 12 . 779 -0 0772 0 326 27 12. 704 -0 06 13 0 433 27 4 5 6 . 400 0 5727 0 242 27 6. 381 0 57 18 0 250 27 6 7 9 . 503 0 2403 0 405 15 9. 716 0 2408 0 514 15 8 6 .873 0 5119 0 297 15 7. 198 0 4822 0 289 15 9 - 1 .28 1 1 1584 0 230 15 -1 010 1 1343 0 226 15 10 i 1 ' 4 .060 0 7023 0 351 27 4 060 o 7023 0 351 27 I ' 12 12 . i>ii 1 -o 0207 0 346 27 12 681 I -o 0207 0 346 27 .SPRING AREA ~ r 2 3 4 5 6 7 8 9 10 1 1 12 ALLOCATION TABLE 9.262 8.979 7.842 9.511 12.092 9.397 8.375 12.038 8.824 B 0.0576 0. 1448 0.2774 -0.0379 -0.1313 0. 1604 0.4677 -0.1369 0 .09 14 SIG2 0. 236 0.027 0.034 0.020 0.031 0.039 0.014 0.016 0.033 12 12 12 12 12 12 12 12 12 BACK CALCULATION 1 1 .057 6.855 10.363 9.848 13.208 9.468 5.384 14.788 9 . 767 B -0. 0 0 0 -0 0 0 0865 3878 0957 0503 1978 1876 71 13 -0.4239 0.0068 SIG2 176 .050 .02 1 .037 .055 0.039 0.014 0. 0. 0. 0. 0. 0. 125 0.07 1 nrn> PINK EVEN PINK ALLOCATION TABLE \!<EA | 1 2 3 -1 5 G 7 8 9 10 1 1 1 2 A B SIG2 N A B SIG2 N 13.299 -0 04 51 0. 248 15 12.893 0 0178 0. 486 15 11.039 0 2467 0. 144 15 11.247 0 2231 0. 197 15 4 .425 O 748 1 0 . 294 15 3 . 453 0 8139 0. 368 15 9 0 2938 0. 627 1 1 9.879 0 3025 0.600 1 1 3 . 820 0 6730 0.590 1 1 7 .400 0 4673 0.621 1 1 17 . 947 -0 1484 0.349 1 1 16. 115 -0 0300 0.413 1 1 _ -1 --, 1 BACK CALCULATION 2 3 4 5 6 7 8 9 10 1 1 12 ALLOCATION TABLE B 1 1 .297 11.219 .391 .405 .656 .045 .082 9  1 1 4  1 1 . 6 . 3 . 322 7.753 0. 128 0. 2083 0.321 1 0.2109 O. 7668 0. 2026 0.6251 O. 7437 0.3887 3TG1T "309" 2 12 532 349 426 884 481 0.900 0.669 ~N~ T5~ 15 15 15 15 15 15 13 15 A 7 .633 10.005 6 .092 10.997 4 . 287 8.648 6.082 3 . 322 7.753 B 0.4474 BACK CALCULATION -SIG2" C7S5T 0.4 18 O. 928 0. 360 0. 439 0.909 0.481 3006 6084 228 1 7904 371 1 6251 O. 7437 0. 3887 0.900 0.669 15 15 15 15 15 15 13 151 CO TABLE 19. BEVERTON-HOLT MODEL PARAMETERS SOCKEYE ALLOCATION TABLE BACK CALCULATION A R E A A B SIG2 N A B SIG2 N 1 2 3 4 . 24E+05 3 30E+04 0 150 1 1 6 72E+05 9 . 14E+04 0. 239 1 1 4 3 . 47E+06 1 09E+06 0 254 27 3 87E+06 1 . 43E+06 0. 283 27 5 7 . 72E+05 1 56E+05 0 1 17 27 6 91E+05 1 . 12E+05 0 .097 27 6 1 . 46E+06 8 51E+04 0 371 27 1 40E+06 9 . 53E+04 0.464 27 7 * * * 2 1 * * • 2 1 8 - - - - - - - -9 9 . 46E+07 8 70E+05 O 163 21 9 42E+06 9 49E+05 0. 165 2 1 10 1 1 3 53E+05 9 25E+04 0 394 21 5 92E+05 1 53E+05 0. 504 21 i ! 2 - •• - - - - - ** COHO ALLOCATION TABLE BACK CALCUL ATI ON AREA A B SIG2 N A B SIG2 N i 1 04E+05 1 39E+03 0 188 20 1 63E+05 9. 08E+03 0 28 1 19 2 2 09E+05 2 90E+04 0 2 10 20 2 36E+05 5 . 40E+04 O 1 15 19 3 8 31E+04 5 76E+02 0 372 20 1 11E+05 2. 1 1E+03 0 259 19 4 1 86E+05 3 30E+04 0 273 20 1 92E+05 2. 81E+03 0 203 19 , 5 7 10E+05 3 56E+04 0 252 20 • * - * 19 ' 6 3 16E+04 2 97E+02 0 233 20 2 09E+05 1 . 60E+03 O 329 19 7 5 43E+05 5 21E+04 0 36 1 20 7 13E+05 2 . 04E+04 O 120 19 8 * * * 20 9 84E+05 8 . 42E+04 0 125 19 9 • * * 20 * . * • 19 10 1 1 3 96E+05 6 24E+04 0 210 20 4 05E+05 8 03E+04 0 151 19 12 * * * 20 * * * 19 CHUM ALLOCATION TABLE BACK CALCUL ATION A R E A A B SIG2 N A B SIG2 N 1 8 27E+04 1 88E+03 0 263 27 7 20E+04 2. 99E+03 0. 408 26 2 5 69E+05 4 58E+04 0 193 27 6 16E+05 8. 43E+04 0 340 27 3 * * * 27 • * * 27 4 5 2 66E+06 6 76E+05 0 233 27 2 57E+06 6. 72E+05 0 241 27 6 7 3 18E+05 4 46E+04 0 382 15 3 95E+05 4 42E+04 0 483 15 8 1 63E+06 4 88E+05 0 283 15 1 42E+06 4 23E+05 0 275 15 9 * * * 22 • • » 10 - - - - - - ~ 27 1 1 1 30E*06 6 28E+05 0 344 27 1 30E+06 6 28E+05 0 344 12 2 .64E+05 9 92E+03 0 331 27 2 64E+05 9 92E+03 0 331 27 ALLOCATION TABLE BACK CALCUL ATI ON AREA A B SIG2 N A B SIG2 N 1 2 3 2 03E+04 1 27E+03 0 205 12 2 84E+04 3 . 62E+02 0 160 1 1 4 4 20E+04 5 49E+03 0 024 12 8 30E+04 1 . 79E+04 0 044 1 1 5 6 64E+04 1 45E+04 0 032 12 9 39E+04 2 . 76E+03 0 020 1 1 6 * * * 12 2 90E+04 6 . 00E+01 0 036 1 1 7 * * * 12 « * * 1 1 8 7 88E+04 7 34E+03 0 034 12 1 20E+05 1 02E+04 0 034 1 1 9 1 35E+06 4 85E+04 0 013 12 1 80E+06 1 37E+05 0 013 1 1 10 11 * * * 12 + * * 1 1 12 1 .79E+04 1 . 28E+03 0 030 12 * * • 1 1 OOD P!k!K 1 ALLOCATION TABLE BACK CALCULATION | A R E A 1 i 2 i 3 A B SIG2 N A B SIG2 N * * * 15 5 13E+05 3 09E+03 0.448 15 I I 4 2 28E+06 1 92E+05 0 139 15 1 96E+06 1 60E+05 0. 189 15 ! 5 I _ 1 07E+07 3 03E+06 0 272 15 1 45E+07 4 B9E+06 0. 343 15 j 6 j 7 8 46E+05 1 20E+05 0 559 1 1 1 36E+06 1 22E+05 0.536 1 1 ! 8 7 15E+05 5 86E+05 0 489 1 1 1 24E+06 2 63E+05 0.515 1 1 I 9 ' * * 1 1 * * * 1 1 10 ! ' 1 12 _ - - - - • - -even r i iNr\ ALLOCATION TABLE BACK CALCUL ATI ON AREA A B SIG2 N A B S1G2 N 1 2 3 4 5 6 7 8 9 10 1 1 12 5.49E+05 1 .43E+06 7.66E+05 2.07E+06 * 6.02E+05 5.32E+06 9.60E+04 3.37E+05 1.00E+05 1.09E+05 5.32E+04 2.04E+05 * 1 . 10E+03 1.12E+06 2.27E+04 4.89E+04 0. 363 0. 201 0.502 0. 3.1 1 * 0. 886 0. 448 0 . 874 0.624 15 15 15 15 15 15 15 13 15 1 . 2 1E+06 1.62E+06 1.56E+06 1.74E+06 * 4.89E+05 5.32E+06 9.60E+04 3.37E+05 2.97E+05 1.93E+05 2.11E+05 2.08E+05 * 1.62E+04 1.12E+06 2.27E+04 4 .89E+04 0.621 0.395 0. 866 0.326 * 0.988 0.448 0 . 874 0.624 15 15 15 15 15 15 15 13 15 CD O 6 I F i g . 5a. C o m p a r i s o n o f c< and e s t i m a t e s ( R i c k e r m odel) o b t a i n e d by b a c k - c a l c u l a t i o n v e r s u s f i x e d a l l o c a t i o n o f m i x e d c a t c h e s . o -o -o f i x e d a l l o c a t i o n ....... back c a l c u l a t i o n 62 <0 0.6 0.4 0.2 0 12 SOCKEYE °0C1 0 C 2 NASS SKEENA CC RS £ GS FRASER JFS SWVI NWVI 0.6 0.4 h 0.2 ° Q C 1 QC2 NASS SKEENA CC RS JS . GS FRASER JFS SWVI NWVI 1.2 04 0 24 16 ODD PINK I, , , , , , , ~V i i • • I °QCI 0C2 NASS SKEENA CC RS JS GS FRASER J F S SWVI NWVI 0C1 0C2 NASS SKEENA CC RS J S GS FRASER JFS SWVI NWVI PRODUCTION AREA 6 3 F i g . 5b. C o m p a r i s o n of e q u i l i b r i u m s t o c k s i z e s e s t i m a t e d b a c k - c a l c u l a t i o n v e r s u s f i x e d a l l o c a t i o n o f m i x e d c a t c h e s . o-o—a f i x e d a l l o c a t i o n •—•-•••back c a l c u l a t i o n 64 6 5 I n g e n e r a l , t h e two d a t a s e t r e s u l t i n s i m i l a r p a r a m e t e r e s t i m a t e s . F o r s o c k e y e , s p r i n g and odd y e a r p i n k , no d i f f e r e n c e i s d e t e c t e d i n t h e v a r i a n c e . The b a c k - c a l c u l a t e d d a t a t e n d t o have h i g h e r v a r i a n c e s f o r chum and e v e n y e a r p i n k , but l o w e r v a r i a n c e s f o r c o h o . The b a c k - c a l c u l a t e d d a t a a l s o e s t i m a t e d h i g h e r e q u i l i b r i u m s t o c k s f o r s p r i n g and odd y e a r p i n k . However, s i n c e s i m u l a t i o n s t u d i e s i n t h e p r e v i o u s c h a p t e r showed t h e a l l o c a t i o n t a b l e method t e n d s t o b i a s t h e p a r a m e t e r s , o n l y d a t a s e t s b a s e d on back c a l c u l a t i o n were u s e d f o r t h e f o l l o w i n g c o m p a r i s o n s . When a s e t o f s t o c k - r e c r u i t m e n t d a t a i s c o n s i s t e n t w i t h more t h a n one model, and d i f f e r e n t m o d e ls have s i g n i f i c a n t l y d i f f e r e n t management i m p l i c a t i o n s , t h e manager i s f a c e d w i t h a d i f f i c u l t d e c i s i o n p r o b l e m . T h i s p r o b l e m i s r e v e a l e d i n f i g u r e s 6a and 6b w h i c h compares " e n v i r o n m e n t a l " v a r i a n c e s , maximum r e c r u i t s p e r spawner, and e q u i l i b r i u m s t o c k s i z e s e s t i m a t e d by t h e R i c k e r and B e v e r t o n - H o l t models f o r i d e n t i c a l s e t s of s t o c k -r e c r u i t m e n t d a t a . S t a t i s t i c a l l y , t h e B e v e r t o n - H o l t model f i t s t h e d a t a s e t s b e t t e r , i n t h e s e n s e t h a t v a r i a n c e s a r o u n d i t a r e c o n s i s t e n t l y l o w e r t h a n f o r t h e R i c k e r m o d e l . I t a l s o c o n s i s t e n t l y e s t i m a t e s h i g h e r maximum r e c r u i t s p e r spawner and h i g h e r e q u i l i b r i u m s t o c k s i z e s t h a n t h e R i c k e r m o d e l . However, many of t h e p a r a m e t e r v a l u e s e s t i m a t e d by t h e B e v e r t o n - H o l t model a r e b e y o n d t h o s e c o n s i d e r e d c r e d i b l e by most salmon b i o l o g i s t s ( e . g . r e c r u i t s / s p a w n e r o v e r 50 f o r some coho and s p r i n g s t o c k s ) . H e r e , we a r e f a c e d w i t h a dilemma of p o o r e r s t a t i s t i c a l f i t on one hand and i n c o n s i s t e n c y w i t h p o p u l a r b e l i e f on t h e o t h e r . In most c a s e s , t h e two models s u g g e s t 66 F i g . 6a. C o m p a r i s o n o f maximum r e c r u i t s p e r spawner and v a r i a n c e e s t i m a t e d by R i c k e r and B e v e r t o n - H o l t m o d e l s . R i c k e r model °—*-o B e v e r t o n - H o l t model ? e s t i m a t i o n p r o c e d u r e f a i l e d f o r B e v e r t o n - H o l t model MAXIMUM •• 3) O O c o H O z > > MAXIMUM O O p ro O o cn / . i / -jr 1 / « o /* / / / Jt I 1 \ \ \ \ 1 \! • i \x >\ b . - o \ / \ \ i ll r. - V-o S o o ro O O cn : rj—i 1 1 — / ^^^^ / ' ° x ' t x • r > / ' / / / ' j t Y 11 r\ ^ \ i \ \ \ J \ \ s • i \ \ \ I \ \ V } y / -''* if i • /'. it \ -\ i \ t \ I . cn 68 F i g . 6b. C o m p a r i s o n o f e q u i l i b r i u m s t o c k s i z e s e s t i m a t e d R i c k e r and B e v e r t o n - H o l t m o d e l s . R i c k e r model ° ° B e v e r t o n - H o l t model ? e s t i m a t i o n p r o c e d u r e f a i l e d f o r B e v e r t o n - H o l t model 69 u S3 CC u o oe CQ 3 UJ VO 10 8 r 6 4 2 ODD PINK 10 u 5 5 _ i 1 u 1 2 3 4 5~ 6 7 8 9 10 11 12 EVEN PINK T P R O D U C T I O N A R E A 70 d r a s t i c a l l y d i f f e r e n t management a c t i o n s . B e c a u s e t h e R i c k e r model i s commonly u s e d t o s t u d y s a l mon p o p u l a t i o n s , t h e f o l l o w i n g c o m p a r a t i v e s t u d y a t t e m p t s t o d i s c e r n i n t e r e s t i n g p a t t e r n s i n t h e p a r a m e t e r s e s t i m a t e d f o r i t . The more d i f f i c u l t p r o b l e m o f c h o o s i n g a b a s i s f o r management, g i v e n a l t e r n a t i v e m o d e l s , w i l l be d i s c u s s e d i n t h e n e x t c h a p t e r . 3.3.2 S p a t i a l P a t t e r n s i n P r o d u c t i v i t y A l t h o u g h t h o u s a n d s o f salmon s t o c k s have been i d e n t i f i e d on b o t h s i d e s o f t h e P a c i f i c ( A t k i n s o n e t . A l . 1967, A r o and S h e p a r d 1967), v e r y few a t t e m p t s have been made t o compare t h e p r o d u c t i v i t y o r v a r i a b i l i t y o f some o f t h e s e s t o c k s . Most s t u d i e s m e r e l y r e p o r t f l u c t u a t i o n s i n t h e c o m m e r c i a l c a t c h e s o f d i f f e r e n t s p e c i e s by a r e a o r compare t h e s u r v i v a l o f d i f f e r e n t c o h o r t s o f s a l m o n . F i g u r e s 7 and 8 show t h e R i c k e r model V " p a r a m e t e r s and t h e v a r i a n c e s , (5^ , o f d i f f e r e n t s a l m on s p e c i e s i n B.C. ( s i n c e "ft " i s r e l a t e d t o t h e e q u i l i b r i u m s t o c k s i z e w h i c h w i l l o b v i o u s l y v a r y f r o m p l a c e t o p l a c e , i t i s n o t c o n s i d e r e d h e r e ) . A rank t e s t o f t h e R i c k e r model "o<" p a r a m e t e r s ( t a b l e 20) shows t h a t a t low s p a w n i n g p o p u l a t i o n s , coho a r e s i g n i f i c a n t l y more p r o d u c t i v e t h a n chum, e v e n y e a r p i n k , a n d s o c k e y e . L i k e w i s e s p r i n g a r e more p r o d u c t i v e t h a n chum and even y e a r p i n k . I t i s p l a u s i b l e t h a t coho and s p r i n g a r e n a t u r a l l y more p r o d u c t i v e t h a n chum, even y e a r p i n k and s o c k e y e , e s p e c i a l l y c o n s i d e r i n g t h a t t r o l l and s p o r t c a t c h e s t a k e many coho and s p r i n g t h a t would have d i e d n a t u r a l l y i f t h e s e s p e c i e s were t a k e n o n l y i n t e r m i n a l f i s h e r i e s . However, i t i s a l s o known t h a t c oho and s p r i n g s p a w n i n g p o p u l a t i o n s a r e more d i f f i c u l t t o F i g . 7. R i c k e r model "<x" p a r a m e t e r and 95% c o n f i d e n c e l i m i t s (number i n g r a p h r e p r e s e n t s p r o d u c t i o n a r e a ) . 4.0 r 6 3.0 2.0 12 | 7 3 1.0 12 0 12 ? 5 12 8 II COHO SPRING SOCKEYE ODD PINK EVENPINK CHUM ro 73 F i g . 8. R i c k e r model v a r i a n c e s (number i n g r a p h r e p r e s e n t s p r o d u c t i o n a r e a ) . SOCKEYE CHUM SOCKEYE 0.00 CHUM 1 . 48 0 .00 COHO -1.99* -3 . 4 2 " SPRING -1 .27 -2 .30* O.PINK -0.71 -1 .65 E.PINK 0.74 -1 .24 COHO SPRING O.PINK E.PINK 0.00 1.22 0.00 1.21 0.82 0.00 2.89** 2. 12* 1.06 0.00 ** 0.01 * p < 0.05 T a b l e 20 : Rank t e s t o f R i c k e r model vc< " p a r a m e t e r s of d i f f e r e n t s almon s p e c i e s i n B.C. 76 enumerate t h a n o t h e r salmon s p e c i e s . A l s o , t h e e x p l o i t a t i o n p a t t e r n of t h e s e two s p e c i e s r e n d e r s t h e c a t c h a l l o c a t i o n p r o c e d u r e u s e d i n t h i s s t u d y more p r o n e t o e r r o r . C o n s e q u e n t l y , t h e e s t i m a t e d V p a r a m e t e r s f o r c o h o and s p r i n g s t o c k s a r e e x p e c t e d t o be b i a s e d upward. F u r t h e r m o r e , i t i s q u i t e p o s s i b l e t h a t n a t u r a l p r o d u c t i o n o f t h e s e s p e c i e s has d e c l i n e d d r a s t i c a l l y s i n c e 1960 from a l l B.C. r i v e r s , w i t h t h e t r e n d s b e i n g masked by more i n t e n s i v e e f f o r t s t o c o u n t escapement and by i n c r e a s e s i n t h e c a t c h e s due t o A m e r i c a n enhancement p r o d u c t i o n . S i n c e t h e above h y p o t h e s e s have s i g n i f i c a n t l y d i f f e r e n t management i m p l i c a t i o n s , more r e s e a r c h i s needed t o c l a r i f y t h i s p r o b l e m b e f o r e any l o n g t e r m p o l i c i e s c a n be d e v i s e d f o r t h e management of coho a n d s p r i n g s t o c k s i n B.C. The r e l a t i o n s h i p s of p r o d u c t i v i t y , v a r i a b i l i t y , and s t o c k s i z e t o g e o g r a p h i c a l d i s t r i b u t i o n o f d i f f e r e n t s t o c k s a r e o f t e n o f i n t e r e s t t o b i o l o g i s t s , f i s h e r i e s managers and f i s h e r m e n a l i k e . T a b l e 21 shows t h e w i t h i n s p e c i e s c o r r e l a t i o n s of p r o d u c t i o n a r e a ( f r o m n o r t h t o s o u t h ) , R i c k e r model "o<" p a r a m e t e r , v a r i c a n c e and s t o c k s i z e ( r e p r e s e n t e d by a v e r a g e e s c a p e m e n t ) . G e o g r a p h i c a l l y , o n l y chum salmon show a s i g n i f i c a n t t r e n d of d e c r e a s i n g p r o d u c t i v i t y f r o m n o r t h t o s o u t h . A l s o , t h e s t o c k s i z e o f chum g e t s s i g n i f i c a n t l y l a r g e r f r o m n o r t h t o s o u t h , w h i c h l o g i c a l l y l e a d s t o a s i g n i f i c a n t n e g a t i v e c o r r e l a t i o n between s t o c k s i z e and p r o d u c t i v i t y s i n c e s p a w n ing s t o c k s do n o t show s i m i l a r t r e n d s . S i g n i f i c a n t n e g a t i v e c o r r e l a t i o n between s t o c k s i z e and v a r i a b i l i t y i s a l s o f o u n d i n chum, coho, s p r i n g and odd p i n k . Coho a l s o show a s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n between p r o d u c t i v i t y and v a r i a b i l i t y ( F i g s . SOCKEYE AREA oc 6X ESC. AREA 1 .00 of 0.32 1 .00 <5l 0.23 -0.11 1 .00 ESC. 0.37 0.24 -0.3& 1 .00 COHO AREA ol 5* ESC. AREA 1 .00 o< 0.07 1 .00. <fl 0.43 0.58 1 .00 ESC. 0.39 -0.32 -0.56* 1 .00 ODD PINK AREA ESC. AREA 1 .00 -0.15 1 .00 0.21 0.35 1 .00 ESC. 0.44 '0.01 -0.34 1 .00 P< 0.01 » p < 0.05 CHUM AREA 6X ESC. AE.:A Cs. ESC. -0.88 -0.39 0.64* 1 .00 0.43 -0.73 1 .00 -0.62* 1 .00 SPRING AREA oi ESC. AREA ESC. 1 .00 0.32 -0.36 0.44 1 .00 0.30 0.01 1.00 - o . n 1 .00 EVEN PINK AREA ot ESC. AREA «* 6X ESC. 1 .00 -0.07 0.22 -0.15 1 .00 0.55 -0.04 1 .00 -0.66* 1 .00 T a b l e 21 : W i t h i n s p e c i e s c o r r e l a t i o n of p r o d u c t i o n a r e a , R i c k e r "o( " p a r a m e t e r , v a r i a n c e and a v e r a g e e s c a p e m e n t . 78 9 - 1 1 ) . A g a i n , t h e s e c o r r e l a t i o n s may r e p r e s e n t n a t u r a l r e l a t i o n s h i p s , but t h e y may a l s o be a r t i f a c t s due t o p o o r d a t a a n d / o r b i a s e d a s s e s s m e n t m e t h o d s : chum salmon p r o d u c e d f r o m t h e s o u t h may be c a u g h t much f u r t h e r n o r t h t h a n we have t h o u g h t , a s s e s s m e n t of l a r g e r s t o c k s may be g i v e n more a t t e n t i o n and e f f o r t , s m a l l e r s t o c k s a r e more s e n s i t i v e t o t h e m i x e d c a t c h s e p a r a t i o n p r o b l e m , and so f o r t h . F u r t h e r i n v e s t i g a t i o n s a r e n e e d e d t o r e s o l v e t h e s e h y p o t h e s e s . 3.3.3 C o r r e l a t i o n s Among S t o c k s F i g . 12 shows c o r r e l a t i o n s among s t o c k s and s p e c i e s o f d e v i a t i o n s i n l o g r e c r u i t s p e r spawner f r o m R i c k e r model p r e d i c t i o n s , by s p e c i e s and p r o d u c t i o n a r e a . S i g n i f i c a n t c o r r e l a t i o n s ( p < . 0 0 l ) a r e m o s t l y p o s i t i v e , w h i c h s u g g e s t s t h a t f l u c t u a t i o n s i n p r o d u c t i v i t y may be a f f e c t e d by some common f a c t o r s f o r many s t o c k s ( e . g . f a v o u r a b l e i n c u b a t i o n c o n d i t i o n s ) . However s i g n i f i c a n t c o r r e l a t i o n w i t h i n s p e c i e s ( e s p e c i a l l y coho and s p r i n g ) may a l s o r e f l e c t p o s s i b l e e r r o r s i n t h e a l l o c a t i o n of m i x e d c a t c h e s . B e c a u s e of t h e p r e d a c e o u s n a t u r e of c o h o , c o n c e r n s have been r a i s e d a b o u t t h e p o s s i b l e n e g a t i v e i m p a c t of coho enhancement on o t h e r salmon s p e c i e s . F i g . 13 shows (by s p e c i e s and p r o d u c t i o n a r e a ) c o r r e l a t i o n s o f d e v i a t i o n s i n l o g r e c r u i t s p e r spawner from R i c k e r model p r e d i c t i o n s v e r s u s c o h o abundance ( c a t c h + e scapement) a t d i f f e r e n t l a g s . I t i s a p p a r e n t t h a t most s i g n i f i c a n t c o r r e l a t i o n s o c c u r i n p i n k s t o c k s , and a t l a g t-1 n e g a t i v e c o r r e l a t i o n s o c c u r more f r e q u e n t l y t h a n p o s i t i v e c o r r e l a t i o n s . One i n t e r p r e t a t i o n i s t h a t coho abundance a t t-1 7 9 F i g . 9.. A v e r a g e e s c a p e m e n t v e r s u s R i c k e r model "oi" p a r a m e t e r (number i n c i r c l e r e p r e s e n t s p r o d u c t i o n a r e a ) . 80 S O C K E Y E 4 O r C H U M 3.0 t - Z.Oh ® « . 2 . 0 t 1.01-© © ® ® © 2 . 0 V 1 0 h © ® ® ® 4 0 0 , 0 0 0 8 0 0 , 0 0 0 1 , 2 0 0 , 0 0 0 1 5 0 , 0 0 0 3 0 0 , 0 0 0 4 5 0 , 0 0 0 6 0 0 , 0 0 0 4 0 r 3.0 y C O H O ® ® CT. 2.0 r 1.Ot-lS ® ® 4 . 0 r 3 0 2 . 0 1.0 S P R I N G ® ® ® © 5 0 , 0 0 0 1 0 0 , 0 0 0 ' 1 5 0 , 0 0 0 2 0 0 , 0 0 0 0 2 0 , 0 0 0 4 0 , 0 0 0 6 0 , 0 0 0 8 0 , 0 0 0 4.0 r 3.0 h O D D P I N K ® l . O h ® © ® 1 , 0 0 0 , 0 0 0 3.0 2 0 1.0 E V E N P I N K @ ® © ) ® ® 2 , 0 0 0 , 0 0 0 0 1 , 0 0 0 , 0 0 0 A V E R A G E E S C A P E M E N T ( 1 9 7 0 - 7 9 ) 2 , 0 0 0 , 0 0 0 3 , 0 0 0 , 0 0 0 8 I F i g . 10. A v e r a g e escapement v e r s u s R i c k e r model v a r i a n c e (number i n c i r c l e r e p r e s e n t s p r o d u c t i o n a r e a ) . 82 0 6 r 03h 0.4t> 0.1 S O C K E Y E ® ® ® © 0 6 0.5 0 4 0 3 0 2 0 1 C H U M ® ® . ® ® ® ® ® 400 ,000 800 ,000 1,200,000 150,000 300 ,000 4 5 0 , 0 0 0 600 ,000 0 6 r 0.5r-C O H O c r 2 0.31-0.2h 01 @ ® ' ® © ® ® ® ® ® 5 0 , 0 0 0 100,000 150,000 2 0 0 0 0 0 0.6 0.5 0.4 0.3t> 0 2 01 S P R I N G ® ® ® ® ® 20,000 40 ,000 60 ,000 80,000 0.6r 0 .5r 0.4 H 0 . 2 t 0 .4 0 67 O D D PINK ^ © 1,000.000 1.2r 0.8 0 6 0.4 0 2 E V E N P I N K ® © 2,000,000 0 1,000,000 A V E R A G E E S C A P E M E N T (1970-79) 2,000,000 ® 3,000,000 F i g . 11. R i c k e r model "o<" p a r a m e t e r v e r s u s v a r i a n c e ( 6 A ) ( n u m b e r i n c i r c l e r e p r e s e n t s p r o d u c t i o n a r e a ) . 84 4.0, 3 0 a 2 . 0 1.0 SOCKE YE ® © ® © ® 40 3.0 20 10 0 O l 0 2 0 3 0 4 O S ~ 0 . 6 u 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 6 CHUM ® ® 4 . 0 r 3 0 COHO D a 20r 1.0 ® ® 3) © (D 40 3 0 2 . 0 1 0 „.l L SPRING © © ® ® © @ 0 0 .1 6.2 0 . 3 0 . 4 " 0 . 5 0 6 0 0 1 0 2 0 . 3 0 4 0 5 0 6 4 . 0 r ODD PINK 3 . 0 a 2 . 0 1.0 © !0) '3> ® 4 0 3 0 2.0 1.0 EVEN PINK '•V 0 0 1 0 . 2 0 . 3 0 . 4 <r2 0 5 0 . 6 0 0 2 0 4 0.6 0 8 L o i: 85 F i g . 12. C o r r e l a t i o n o f d e v i a t i o n s i n l o g r e c r u i t s p e r spawner f r o m R i c k e r model p r e d i c t i o n s by s p e c i e s and p r o d u c t i o n a r e a ( e a c h p r o d u c t i o n a r e a i s r e p r e s e n t e d by one s q u a r e w i t h i n a s p e c i e s ) . + p o s i t i v e c o r r e l a t i o n ( p - £ . 0 0 l ) n e g a t i v e c o r r e l a t i o n ( p < . 0 0 l ) 8 7 F i g . 13. C o r r e l a t i o n o f d e v i a t i o n s i n l o g r e c r u i t s p e r spawner from R i c k e r model p r e d i c t i o n s v e r s u s c o h o s t o c k s i z e ( a t d i f f e r e n t l a g s ) . + p o s i t i v e c o r r e l a t i o n ( p 4 . 0 0 l ) n e g a t i v e c o r r e l a t i o n ( p < .001) 83 i s p o s i t i v e l y r e l a t e d t o s p a w n i n g s t o c k s a t t-1 and s u b s e q u e n t s m o l t o u t p u t a t t+1 when coho p r e d a t i o n on p i n k f r y i s most l i k e l y t o o c c u r . 3.3.4 D e n s i t y Dependence and F e c u n d i t y C u s h i n g (1971) a t t e m p t e d t o e s t a b l i s h d i f f e r e n c e s i n t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p s between g r o u p s o f f i s h : t u n a , c o d , f l a t f i s h , salmon and h e r r i n g . T h a t a t t e m p t f a i l e d b e c a u s e t h e v a r i a t i o n i n p a r a m e t e r s w i t h i n a g r o u p o f f i s h i s a s g r e a t as between g r o u p s . However, he f o u n d t h a t t h e i n d e x o f d e n s i t y d e p e n d e n c e ("j£" i n Power model) i s i n v e r s e l y c o r r e l a t e d w i t h t h e cube r o o t o f f e c u n d i t y . The same a n a l y s i s was a p p l i e d t o B.C. .salmon s t o c k s . No d i f f e r e n c e was f o u n d i n t h e i n d e x of d e n s i t y d e p e n d e n c e among s p e c i e s ( F i g . 14), and no c o r r e l a t i o n was f o u n d between t h e i n d e x o f d e n s i t y d e p e n d e n c e and t h e c u be r o o t o f f e c u n d i t y ( F i g . 15). S i n c e t h e i n d e x o f d e n s i t y d e p e n d e n c e , /5 , i s h i g h l y s e n s i t i v e t o p a s t e x p l o i t a t i o n p a t t e r n and t o e r r o r s i n t h e measurement of s p a w n i n g p o p u l a t i o n , c a t c h a l l o c a t i o n and age s t r u c t u r e , f u r t h e r a n a l y s i s o f p i s not w a r r a n t e d . 3.3.5 E f f e c t s o f Measurement E r r o r s on The E s t i m a t e s R e s u l t s from t h e L u d w i g and W a l t e r s (1981) p r o c e d u r e f o r e s t i m a t i n g s t o c k - r e c r u i t m e n t p a r a m e t e r s i n t h e p r e s e n c e of measurement e r r o r s a r e shown i n F i g . 16. S i n c e t h e r e q u i r e d e r r o r r a t i o , ;N , i s n o t known, a range of v a l u e s between 90 F i g . 14. 95% c o n f i d e n c e l i m i t s o f Power model "yS" e s t i m a t e s , COHO SPRING SOCKEYE CHUM ODD PINK EVEN PINK -2 9 2 F i g . 15. Index o f d e n s i t y d e p e n d e n c e (Power model ) v e r s u s cube r o o t o f f e c u n d i t y . 9 3 • • t» • • • ^ 5 x ? x o LU >- CD * — o or o o-a. o o co co • x ^ o • I CD O O CCD O X X X XX XXX ro CM CVJ 94 O f A ^1 was p r e s c r i b e d t o e a c h s t o c k i n o r d e r t o examine t h e s e n s i t i v i t y o f p a r a m e t e r e s t i m a t e s t o d i f f e r e n t l e v e l s o f measurement e r r o r . F i g u r e IG shows t h e c h a n g e s o f R i c k e r model V and "j3" p a r a m e t e r s a s A i s i n c r e a s e d f r o m 0.0 t o 2.0 f o r e a c h s t o c k . T h r e e g e n e r a l p a t t e r n s o f c hange a r e a p p a r e n t : 1. The "o4 n p a r a m e t e r i n c r e a s e s i n v a l u e w h i l e d e c r e a s e s , f o r most c o h o , s p r i n g and chum s t o c k s . 2. "oi" d e c r e a s e s i n v a l u e but r e m a i n s p o s i t i v e w h i l e i n c r e a s e s i n v a l u e and may become p o s i t i v e , f o r most even y e a r p i n k s t o c k s and some s o c k e y e and odd y e a r p i n k s t o c k s . 3. V d e c r e a s e s i n v a l u e and becomes n e g a t i v e n e g a t i v e w h i l e "/3" i n c r e a s e s t o become p o s i t i v e , for. two s o c k e y e , one chum, and one odd y e a r p i n k s t o c k . T h e s e t h r e e p a t t e r n s of c hange s u g g e s t d i f f e r e n t c o u r s e s o f a c t i o n when f a c e d w i t h i n c r e a s i n g l e v e l s of u n c e r t a i n i t y i n measurement e r r o r s . P a t t e r n 1 s u g g e s t s l o w e r i n g t h e e s c a p e m e n t t o t e s t t h e p r o d u c t i v i t y o f t h e s t o c k . P a t t e r n 2 f a v o u r s i n c r e a s i n g e scapement m o d e r a t e l y t o t e s t t h e c a r r y i n g c a p a c i t y of t h e s y s t e m . P a t t e r n 3 s u g g e s t s a v o i d i n g low e s c a p e m e n t s a t a l l c o s t s and o p t f o r t h e h i g h e s t e s c a p e m e n t l e v e l s one c a n p o s s i b l y g e t , a l t h o u g h t h e optimum e s c a p e m e n t i s h i g h l y u n c e r t a i n a t t h i s p o i n t i n t i m e . T h e s e a r e i m p o r t a n t c o n s i d e r a t i o n s i n e s t i m a t i n g optimum p o l i c i e s w h i c h w i l l be d i s c u s s e d i n t h e n e x t c h a p t e r . 95 F i g . 16. Changes, of R i c k e r model V " and "^3" p a r a m e t e r s as A i s i n c r e a s e d f r o m 0.0 t o 2.0 ( l e f t t o r i g h t ) . 96 4.0 2.0 -2.0 - 4 0 SOCKEYE -i 1 1 1 i i i i i i \ i QCl 0C2 NASS SKEENA CC RS JS GS FRASER JPS SWVI NWVI -4.0 -2.0 -2 .0 -4.0 " COHO r 1 \ I 1 1 1 1 • 1 QCl QC2 NASS SKEEMA CC RS JS GS FRASER JFS SWVI NWVI 4.0 2.0 -2 .0 •4.0 ODD PINK _J . i i i t —I 1 L_ QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI 4.0 2.0 -2.0 -4.0 " CHUM * * ^ ««. ITT H i i 1 1 1 1 QCl QC2 NASS SKEENA OC RS JS GS FRASER JFS SWVI NWVI 4.0 2.0 -2 .0 -4.0 ' SPRING • ooooo °"^xio $0000 1 1 1 1 1 1 1 1 • QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI 4 0 2.0 -2 .0 -4 .0 EVEN PINK ^ - ^ v- V . r r — ^ f 6 030t» _J I * ' L_ 0C1 0C2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI PRODUCTION AREA 9 7 4^ OPTIMAL POLICIES The d e f i n i t i o n o f o p t i m a l i t y b a s i c a l l y d e p ends on i n d i v i d u a l p r e f e r e n c e s among p e r f o r m a n c e m e a s u r e s . I t c a n , but need n o t be b a s e d on t h e m a x i m i z a t i o n o f q u a n t i f i a b l e o b j e c t i v e s . I f f i s h e r i e s were managed s o l e l y i n t e r m s o f a c h i e v i n g a s i m p l e c o n s i s t e n t g o a l ( e . g . maximum s u s t a i n e d y i e l d o r maximum economic v a l u e ) , management would i n d e e d be a s i m p l e r t a s k . However, management a g e n c i e s have l o n g r e c o g n i z e d t h a t d i f f e r e n t segments of s o c i e t y a r e a f f e c t e d by d i f f e r e n t management a c t i o n s . To f a v o u r one s i d e o f t e n e n t a i l s f o r e g o i n g b e n e f i t s f o r t h e o t h e r s ,and f a r t o o o f t e n , d e c i s i o n s t h a t f a v o u r s p e c i a l segments o f s o c i e t y may n o t be i n t h e b e s t i n t e r e s t o f t h e s o c i e t y as a whole. S i n c l a i r ( 1 9 7 8 ) e m p h a s i z e d t h a t t h e r e s p o n s i b i l i t y of a government f i s h e r y a g e n c y i s t o manage a f i s h e r y r e s o u r c e i n t h e b e s t i n t e r e s t of t h e owners o f t h e r e s o u r c e , i . e . t h e t a x - p a y e r s of t h e n a t i o n . I t i s i m p o r t a n t f o r government a g e n c i e s t o r e c o g n i z e t h a t c o n c e r n s f o r t h e p r i m a r y u s e r s s h o u l d n o t be u s e d a s j u s t i f i c a t i o n f o r e s t a b l i s h i n g p r o g r a m s t h a t may n o t be i n t h e b e s t i n t e r e s t of t h e p u b l i c . U n f o r t u n a t e l y t o i d e n t i f y a common s e t of o b j e c t i v e s f o r management i n t h i s c o n t e x t i s v e r y d i f f i c u l t , e s p e c i a l l y when p e o p l e ' s p r e f e r e n c e s and i n t e r e s t s c h a n g e o v e r t i m e . A t t e m p t s t o s o l i c i t p u b l i c o p i n i o n by government o f f i c i a l s o f t e n g a t h e r o n l y t h e o p i n i o n s o f v e s t e d -i n t e r e s t g r o u p s . A l t h o u g h r e c e n t a d v a n c e s i n m u l t i - a t t r i b u t e u t i l i t y a n a l y s i s c an be u s e d t o i n v e s t i g a t e c o n f l i c t i n g o b j e c t i v e s ( H i l b o r n and W a l t e r s 1977, Keeney 1977), u n c e r t a i n t y 98 a b o u t f u t u r e o b j e c t i v e s , w h i c h i s e s s e n t i a l i n e v a l u a t i n g c o n t r o l s t r a t e g i e s , i s n o t a d d r e s s e d . More i m p o r t a n t , t h e s e o b j e c t i v e s may change o v e r t i m e w i t h d i f f e r e n t i a l r a t e s a t t h e n a t i o n a l , p r o v i n c i a l a n d l o c a l l e v e l , making d e t a i l e d a n a l y s i s more ambiguous and u n c e r t a i n . In v i e w o f t h e above c o m p l e x i t i e s , i t w o u l d be n a i v e and p r e s u m p t e o u s t o s u g g e s t t h a t t h e s e p r o b l e m s a r e s o l u b l e t h r o u g h some f o r m of b i o l o g i c a l a n a l y s i s a l o n e . O n l y an i n t e r d i s c i p l i n a r y p r o g r a m i n c o r p o r a t i n g t h e e x p e r t i s e f r o m v a r i o u s s o c i a l , p o l i t i c a l and economic s c i e n c e s may c o n t r i b u t e t o w a r d s t h e i r r e s o l u t i o n . Due t o my i g n o r a n c e i n t h e s o c i a l , p o l i t i c a l and e c o n o m i c a l f i e l d s , t h e f o l l o w i n g s e c t i o n s c o n s i d e r o n l y t h e o p t i m a l p o l i c i e s t h a t would p r o d u c e maximum e x p e c t e d y i e l d s , f o r d i f f e r e n t a s s u m p t i o n s o f b i o l o g i c a l u n c e r t a i n t i e s . S u c h p o l i c i e s would n o t n e c e s s a r i l y be most d e s i r a b l e nor a c h i e v a b l e i n p r a c t i c e , b u t s e r v e as a s t a n d a r d o f c o m p a r i s o n w i t h o t h e r p o l i c i e s t h a t t a k e i n t o a c c o u n t r i c h e r s e t s of o b j e c t i v e s and c o n s t r a i n t s . , 4.1 N o n - f e e d b a c k P o l i c i e s W a l t e r s and H i l b o r n ( 1 9 7 8 ) c l a s s i f i e d " e q u i l i b r i u m " and " t i m e - d e p e n d e n t " c o n t r o l r u l e s as n o n - f e e d b a c k p o l i c i e s . H e r e , t h e d y n a m i c s o f t h e s y s t e m b e i n g managed a r e assumed t o be c o m p l e t e l y d e t e r m i n i s t i c . Examples o f s u c h s o l u t i o n s a r e e q u i l i b r i u m h a r v e s t r a t e s , f i x e d q u o t a s and e q u i l i b r i u m e f f o r t . T i m e - d e p e n d e n t p o l i c y a n a l y s i s does not assume t h e s y s t e m t o be a t or n e a r e q u i l i b r i u m , b u t i n s t e a d p r e s c r i b e s an o p t i m a l c o u r s e 99 o f a c t i o n t h a t i s d e p e n d e n t on t i m e a l o n e . Some examples a r e : a l i s t o f f u t u r e h a r v e s t r a t e s , f u t u r e q u o t a s o r a t e n y e a r d e v e l o p m e n t p l a n . I t i s w e l l r e c o g n i z e d t h a t u n c e r t a i n t i e s and u n p r e d i c t a b l e f l u c t u a t i o n s a r e e n c o u n t e r e d i n most f i s h e r i e s . T h e r e f o r e non-f e e d b a c k p o l i c i e s ( w h i c h do n o t r e q u i r e m o n i t o r i n g ) a r e c o n s i d e r e d t o be d e c e p t i v e and a r e n o t d i s c u s s e d f u r t h e r i n t h i s a n a l y s i s . 4 . 2 F e e d b a c k P o l i c i e s I m p l i c i t i n t h e d e s i g n of f e e d b a c k p o l i c i e s i s t h e a s s u m p t i o n t h a t u n c e r t a i n t i e s e x i s t i n t h e d y n a m i c s of t h e s y s t e m s b e i n g managed, and t h a t a c t i o n s s h o u l d be m o d i f i e d as new d a t a become a v a i l a b l e o v e r t i m e . T h e s e p o l i c i e s d i f f e r f r o m n o n - f e e d b a c k p o l i c i e s i n t h a t t h e o p t i m a l c o n t r o l s a t any t i m e depend on t h e s t a t e of t h e s y s t e m a t t h a t t i m e , r a t h e r t h a n on t i m e a l o n e . F e e d b a c k p o l i c i e s may d e p e n d on t i m e as w e l l as t h e f u t u r e s t a t e o f t h e s y s t e m , but when t h e o p t i m a l p o l i c i e s t u r n o u t t o be t i m e - i n d e p e n d e n t , t h e y a r e c a l l e d s t a t i o n a r y f e e d b a c k p o l i c i e s ( W a l t e r s and H i l b o r n 1978). D e p e n d i n g on t h e a s s u m p t i o n s made a b o u t t h e u n c e r t a i n t i e s o f t h e s t o c k b e i n g managed, v a r i o u s o p t i m i z a t i o n t e c h n i q u e s c a n be u s e d t o d e t e r m i n e t h e o p t i m a l p o l i c y . T h r e e t y p e s of u n c e r t a i n t i e s a r e g e n e r a l l y e n c o u n t e r e d i n e s t a b l i s h i n g f i s h e r i e s p o l i c i e s : 1. random " e n v i r o n m e n t a l " e f f e c t s , 2. measurement e r r o r s , and 3. u n c e r t a i n t y i n p a r a m e t e r e s t i m a t e s and model s t r u c t u r e . I 00 A l l t h e s e u n c e r t a i n t i e s e x i s t f o r most salmon s t o c k s a l o n g t h e B.C. c o a s t , and a t l e a s t t h e l a t t e r two c a n n o t be p r e c i s e l y q u a n t i f i e d w i t h e x i s t i n g d a t a . T h e r e f o r e , s e v e r a l o p t i m i z a t i o n t e c h n i q u e s a r e e xamined below, w i t h t h e hope t h a t t h e i r s o l u t i o n s c a n be compared w i t h e x i s t i n g management p r a c t i c e s a n d w i t h e a c h o t h e r t o p o i n t t o w a r d s ways o f i m p r o v i n g p r e s e n t p r a c t i c e s . I f t h e management o b j e c t i v e i s s i m p l y t o m a x i m i z e t h e sum o f e x p e c t e d c a t c h e s o v e r t i m e r e g a r d l e s s o f t h e v a r i a b i l i t y o f h a r v e s t , t h e o p t i m a l p o l i c y i s t o a l l o w a f i x e d escapement e v e r y y e a r . T h a t i s , i f i i s t h e o p t i m a l e s c a p e m e n t , t h e n h a r v e s t R-S o f t h e r e c r u i t s i f R>S , o t h e r w i s e do n o t h a r v e s t ( C l a r k 1 9 76). W h i l e a f e e d b a c k p o l i c y o f t h i s f o r m w i l l be o p t i m a l no m a t t e r what u n c e r t a i n t i e s '(of t h e above t y p e s ) a r e a d m i t t e d t o t h e a n a l y s i s , t h e optimum v a l u e of S d o e s depend on t h e s e u n c e r t a i n t i e s . In t h i s s e c t i o n , e s t i m a t e s of S a r e d e v e l o p e d f o r a r a n g e o f i n c r e a s i n g l y r e a l i s t i c a s s u m p t i o n s a b o u t u n c e r t a i n t i e s . 4.2.1 Random " E n v i r o n m e n t a l " E f f e c t s The s i m p l e s t a s s u m p t i o n , a b o u t u n c e r t a i n t y i s t h a t t h e r e c r u i t m e n t c u r v e i s known, and o n l y e n v i r o n m e n t a l e f f e c t s a r e u n p r e d i c t a b l e . We m i g h t f u r t h e r assume t h e n t h a t s t a t i s t i c a l e x p e c t a t i o n s a r e r e p r e s e n t a t i v e o f t h e f u t u r e s t a t e s of t h e s y s t e m , so f u t u r e r e t u r n s c a n be c a l c u l a t e d from t h e s e e x p e c t a t i o n s a l o n e . N u m e r i c a l m o d els w h i c h s u p e r i m p o s e r a n d o m l y g e n e r a t e d d e v i a t i o n s on d e t e r m i n i s t i c m o d e ls have been u s e d t o 1 0 1 s t u d y t h e e f f e c t of d i f f e r e n t l e v e l s o f v a r i a b i l i t y on f u t u r e y i e l d s ( R i c k e r 1958, L a r k i n and R i c k e r 1964) a n d t o compare t h e e c o n o m i c r e t u r n s of d i f f e r e n t h a r v e s t s t r a t e g i e s ( A l l e n 1973). In t h e s e s t u d i e s , t h e o p t i m a l e s c a p e m e n t s ( w h i c h p r o v i d e maximum e x p e c t e d c a t c h e s ) were f o u n d t o be v e r y s i m i l a r t o t h e o p t i m a l e s c a p e m e n t s e s t i m a t e d by a s s u m i n g t h e s y s t e m s were c o m p l e t e l y d e t e r m i n i s t i c . I n s t e a d o f b a s i n g e s t i m a t e s o n l y on t h e e x p e c t e d v a l u e s o f f u t u r e s t a t e s , a s e c o n d method r e c o g n i z e s t h a t many d i f f e r e n t s t a t e s may a r i s e , so t h a t a s e r i e s o f d e c i s i o n s must be made i n s e q u e n c e . E a c h d e c i s i o n a f f e c t s t h e s u b s e q u e n t s t a t e of t h e s y s t e m w h i c h i n t u r n a f f e c t s f u t u r e d e c i s i o n s . Dynamic programming can be u s e d t o f i n d t h e d e c i s i o n s w h i c h w i l l m a x i m i z e t h e e x p e c t e d c a t c h e s a c r o s s t h e s e s t a t e s ( W a l t e r s 1975, Reed 1975, W a l t e r s and H i l b o r n 1976). T h i s method t e n d s t o e s t i m a t e l o w e r o p t i m a l h a r v e s t r a t e s t h a n t h e p r e v i o u s one, but t h e r e l a t i v e m e r i t s o f d i f f e r e n t p o l i c i e s r e m a i n u n c h a n g e d . I n v i e w o f t h e above o p t i m i z a t i o n r e s u l t s , i t i s g e n e r a l l y c o n c l u d e d t h a t o p t i m a l p o l i c i e s f o r s t o c h a s t i c s y s t e m s a r e v e r y s i m i l a r t o t h e o p t i m a l p o l i c i e s e s t i m a t e d by a s s u m i n g d e t e r m i n i s t i c d y n a m i c s . T h e r e f o r e we c a n r e a s o n a b l y e s t i m a t e t h e o p t i m a l escapement by a s s u m i n g t h e s y s t e m i s c o m p l e t e l y d e t e r m i n i s t i c when f a c e d w i t h o n l y u n c e r t a i n t y a b o u t random " e n v i r o n m e n t a l " e f f e c t s . More c o n s e r v a t i v e p o l i c i e s a r e f a v o u r e d o n l y when t h e o b j e c t i v e f u n c t i o n i n v o l v e s s t r o n g e l e m e n t s o f r i s k a v e r s i o n o r d e s i r e t o a v o i d extreme low c a t c h e s . I n s t e a d of c a r r y i n g o u t t h e l e n g t h y n u m e r i c a l a n a l y s i s o r t h e t e d i o u s dynamic programming as m e n t i o n e d a b o v e , o p t i m a l 102 e s c a p e m e n t s f o r B.C. salmon s t o c k s were e s t i m a t e d by s o l v i n g t h e d e t e r m i n i s t i c v e r s i o n s o f t h e m o d e l s t o m a x i m i z e t h e s u s t a i n e d c a t c h e s . I f t h e d e t e r m i n i s t i c s t o c k - r e c r u i t m e n t model i s e x p r e s s e d i n g e n e r a l t e r m s a s : 4 Then, t h e o p t i m a l e s c a p e m e n t , 5 > c a n D e o b t a i n e d by c h o o s i n g 4 S as t h e s o l u t i o n o f t h e e q u a t i o n S p e c i f i c a l l y t h e o p t i m a l e s c a p e m e n t , S , i s o b t a i n e d by s o l v i n g for <S i n f o r t h e R i c k e r model ( 3 . 1 . 4 ) , and = faT - b (4-2-4-) f o r t h e B e v e l t o n - H o l t model ( 3 . 1 . 6 ) . 4.2.2 Measurement E r r o r s As m e n t i o n e d b e f o r e , measurement e r r o r s i n t h e spawning c o u n t s o b l i t e r a t e t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p , so r e g r e s s i o n p r e c e d u r e s n o r m a l l y u s e d t o e s t i m a t e model p a r a m e t e r s become i n v a l i d . O t h e r e s t i m a t i o n p r o c e d u r e s c a n be d e v e l o p e d i f e i t h e r 6 v o r 6\ or > = ^ y ^ i s known. At p r e s e n t , s i n c e none of t h e s e p a r a m e t e r s ( A , / * 6\r ) i s known f o r any of t h e s t o c k s I 0 3 c o n c e r n e d , s e v e r a l T \ v a l u e s ( f r o m low t o h i g h ) were p r e s c r i b e d t o e a c h s t o c k and t h e c o r r e s p o n d i n g p a r a m e t e r v a l u e s f o r t h e R i c k e r model and Power model were e s t i m a t e d . B e c a u s e o f t h e non-l i n e a r i t i e s i n t h e p a r a m e t e r s o f t h e B e v e r t o n - H o l t m o d e l , t h e l i k e l i h o o d e s t i m a t i o n p r o c e d u r e becomes e x t r e m e l y c o m p l e x . P o s s i b l e s o l u t i o n s a r e under i n v e s t i g a t i o n ( L u d w i g , p e r s . comm.). I f u n c e r t a i n t i e s i n t h e p a r a m e t e r s and model s t r u c t u r e a r e i g n o r e d , t h e r e s u l t s of t h e p r e c e e d i n g s e c t i o n s t i l l a p p l y . T h a t i s , t h e o p t i m a l escapement f o r a s t o c k a t d i f f e r e n t v a l u e s c a n be e s t i m a t e d by. (4.2.3) f o r t h e R i c k e r m o d e l . The e x i s t e n c e of ( o r l a c k o f ) d i f f e r e n c e s among t h e o p t i m a l p o l i c y e s t i m a t e s s h o u l d t h e n g i v e a g e n e r a l i d e a o f how i m p o r t a n t ( o r u n i m p o r t a n t ) i t i s t o measure A more a c c u r a t e l y f o r f u t u r e a s s e s s m e n t s . A s i d e f r o m t h e l a c k o f knowledge o f A v a l u e s , t h e p a r a m e t e r c o r r e c t i o n p r o c e d u r e d o e s n o t a l w a y s g i v e r e l i a b l e o r c o n s i s t e n t e s t i m a t e s of t h e t r u e model - p a r a m e t e r s , e s p e c i a l l y when d a t a s e t s a r e s m a l l (n<50) and t h e r a n g e o f o b s e r v a t i o n n a r r o w . Even i f d a t a s e t s were l a r g e and x v a l u e s known, t h e r e i s s t i l l c o n s i d e r a b l e d a n g e r o f m a k i n g v e r y p o o r p o l i c y c h o i c e s , a s i n d i c a t e d i n t h e f o l l o w i n g s e c t i o n . 4.2.3 U n c e r t a i n t y i n P a r a m e t e r E s t i m a t e s and M odel S t r u c t u r e So f a r we have o n l y d i s c u s s e d t h e e f f e c t s of random e r r o r s on t h e d e s i g n of f i s h i n g p o l i c i e s . The r e a s o n i s n o t t h a t t h e s e k i n d s of e r r o r a r e more i m p o r t a n t , but t h a t t h e y a r e e a s i e r t o 1 0 4 d e a l w i t h i n a s t a t i s t i c a l manner. Non-random e r r o r s , i n t r o d u c e d v i a s y s t e m a t i c b i a s e s i n s p a w n i n g c o u n t s , c a t c h a l l o c a t i o n s o r age s t r u c t u r e e f f e c t s a r e i n t r i n s i c a l l y i n s e p a r a b l e f r o m t h e e s t i m a t e d model p a r a m e t e r s . B e s i d e s , t h e model p a r a m e t e r s may have c h a n g e d due t o p e r s i s t e n t s h i f t s i n t h e e n v i r o n m e n t o r s e l e c t i o n by t h e f i s h e r y . W i t h o u t t i m e s p e c i f i c , i n d e p e n d e n t e s t i m a t e s o f t h e s e p a r a m e t e r c h a n g e s and measurement b i a s e s , one s h o u l d a l w a y s pay more a t t e n t i o n t o t h e q u e s t i o n o f how f i s h e r y p o l i c i e s s h o u l d be m o d i f i e d t o t a k e a c c o u n t o f u n c e r t a i n t i e s i n p a r a m e t e r e s t i m a t e s and model s t r u c t u r e . W a l t e r s (1981) d i s c u s s e d t h r e e k i n d s of a p p r o a c h e s t h a t can be t a k e n when f a c e d w i t h t h e s e u n c e r t a i n t i e s . F i r s t , one may i g n o r e t h e a n a l y t i c a l r e s u l t s and r e l y on i n t u i t i o n t o make h a r v e s t i n g d e c i s i o n s . T h i s a p p r o a c h c a n be j u s t i f i e d o n l y i f t h e q u a l i t y o f d a t a c o l l e c t e d i-s e x t r e m e l y poor and w i l l l i k e l y r e m a i n so i n t h e n e a r f u t u r e ; u n d e r t h i s e x t r e m e of u n c e r t a i n t y , t h e r e • may n o t be an o p t i m a l p o l i c y a t a l l . In t h i s c a s e , i n t u i t i o n i s t h e o n l y b a s i s f o r making d e c i s i o n s . F o r salmon management, t h i s u s u a l l y means j u s t t r y i n g t o m a i n t a i n t h e same escapement as i n t h e r e c e n t y e a r s . However, g i v e n t h e c u r r e n t amount o f government i n v o l v e m e n t i n t h e B.C. s a l m o n f i s h e r y , t h e r e i s a t l e a s t some b a s i s . a n d r e s p o n s i b i l i t y f o r f o l l o w i n g a more s o p h i s t i c a t e d a p p r o a c h . The s e c o n d a p p r o a c h i s t o l a u n c h r e s e a r c h p r o j e c t s t o s t u d y t h e s t o c k - r e c r u i t m e n t d y n a m i c s o f "model" s t o c k s , but m a i n t a i n t h e s t a t u s quo o f a l l o t h e r s t o c k s w h i l e w a i t i n g f o r t h e r e s u l t s . The p r o b l e m w i t h t h i s a p p r o a c h i s t h a t t h e r e c o m m e n d a t i o n s t h u s o b t a i n e d c a n o n l y be v a l i d a t e d by a c t u a l I 0 5 m a n i p u l a t i o n o f e s capement o f t h e o t h e r s t o c k s . T h e r e f o r e t h e r e s e a r c h e s s e n t i a l l y j u s t d e l a y s t h e h a r d d e c i s i o n s w h i c h w o u l d have t o be made anyway. The t h i r d a p p r o a c h i s t o d e v e l o p some f o r m o f a d a p t i v e p o l i c y w h i c h e m p h a s i z e s t h e need o f l e a r n i n g by d o i n g . Here t h e f i s h e r y i s m o n i t o r e d t o p r o d u c e more r e l i a b l e e s t i m a t e s o f s t a t e i n d i c a t o r s ( s p a w n i n g s t o c k s i z e , c a t c h e s , age s t r u c t u r e , e t c . ) . W i t h t h i s i n f o r m a t i o n , one o r more m o d e l s can be u s e d t o p r o d u c e i m p r o v e d e s t i m a t e s of t h e s y s t e m s t a t e and p a r a m e t e r s . T h e s e e s t i m a t e s p r o v i d e t h e b a s i s f o r c h o o s i n g t h e n e x t s e t o f c o n t r o l s , and t h e whole e x e r c i s e i s r e p e a t e d y e a r a f t e r y e a r . D e p e n d i n g on whether f u t u r e u n c e r t a i n t y i s v i e w e d as a component of t h e management s y s t e m , t h r e e k i n d s o f a d a p t i v e c o n t r o l s c a n be d e v i s e d : A. O p e r a t e as t h o u g h t h e most l i k e l y . model i s r i g h t and p r e t e n d t h e p a r a m e t e r e s t i m a t e s a r e a c t u a l l y c o r r e c t ( i . e . i g n o r e p a r a m e t e r u n c e r t a i n t y ) . T h i s a p r o a c h i s c a l l e d " p a s s i v e " a d a p t i v e c o n t r o l by W a l t e r s and H i l b o r n ( 1 9 7 8 ) , meaning t h a t t h e u n c e r t a i n t y i n model s t r u c t u r e o r p a r a m e t e r e s t i m a t e s w i l l e v e n t u a l l y be r e s o l v e d by t h e v a r y i n g i n p u t s ( e s c a p e m e n t l e v e l s ) t o t h e s y s t e m due t o u n c o n t r o l l a b l e n a t u r a l o r human f a c t o r s . However, s i n c e u n c e r t a i n t y i s n o t e x p l i c i t l y c o n s i d e r e d i n t h e management p l a n , t h e s y s t e m c o u l d be l o c k e d i n t o a s u b o p t i m a l s t a t e f o r a l o n g t i m e w i t h o u t i n f o r m a t i v e v a r i a t i o n o c c u r r i n g . B. I n c l u d e u n c e r t a i n t i e s i n t h e f o r m u l a t i o n of c o n t r o l s e a c h y e a r , but do not c o n s i d e r t h e e f f e c t o f t h e c h o i c e o f c o n t r o l s now on u n c e r t a i n t i e s i n t h e f u t u r e . H e r e , t h e a n a l y s i s I 0 6 a d m i t s a l l p o s s i b l e m o d e l s ( o r p a r a m e t e r s ) by w e i g h t i n g t h e p o s s i b l e outcomes a c c o r d i n g t o p r i o r odds p l a c e d on e a c h model ( o r p a r a m e t e r ) . M e n d e l s s o h n (1980) and W a l t e r s (1981 ) c a l l e d t h i s t h e "Bayes e q u i v a l e n t " p o l i c y . "Bayes e q u i v a l e n t " p o l i c i e s f o r B.C. salmon s t o c k s a t d i f f e r e n t measurement e r r o r l e v e l s ( > » ) , c a n be e s t i m a t e d by t h e c o m p u t a t i o n p r o c e d u r e s d e s c r i b e d by L u d w i g and W a l t e r s (1981) (computer p r o g r a m d e v e l o p e d by L u d w i g , p e r s . comm.). C. D e v e l o p an " a c t i v e " a d a p t i v e p o l i c y w h i c h t a k e s i n t o a c c o u n t t h e e f f e c t of a c t i o n s now on t h e p o s s i b l e l o n g - t e r m b e n e f i t s o f i m p r o v e d k n o w ledge. T h i s a p p r o a c h s e e k s t o o p t i m a l l y b a l a n c e t h e t r a d e - o f f s between s h o r t - t e r m y i e l d a n d l e a r n i n g a b o u t t h e s y s t e m so as t o i m prove y i e l d s i n t h e f u t u r e . T h i s o p t i m i z a t i o n p r o b l e m i s known as t h e d u a l c o n t r o l p r o b l e m , and i t h as n o t been f u l l y r e s o l v e d even f o r v e r y s i m p l e s y s t e m s . B e s i d e s t h e m a t h e m a t i c a l c o m p l e x i t i e s , t h e t i m e h o r i z o n f o r management and t h e d i s c o u n t r a t e c a n s e l d o m be d e t e r m i n e d o b j e c t i v e l y , a l t h o u g h t h e y a r e c r i t i c a l l y i m p o r t a n t t o t h e s e s t i m a t e s o b t a i n e d . I n t u i t i v e l y , i f t h e d i s c o u n t r a t e i s low and t h e t i m e h o r i z o n i n f i n i t e , we would p u t more e m p h a s i s on g e t t i n g b e t t e r i n f o r m a t i o n f o r t h e f u t u r e . Whereas, i f t h e d i s c o u n t r a t e were h i g h and t h e t i m e h o r i z o n s h o r t , we would p u t more e m p h a s i s on h a r v e s t i n g now but pay l e s s a t t e n t i o n t o g a i n i n g o f knowledge f o r t h e f u t u r e . B e c a u s e o f t h e above p r o b l e m s , " a c t i v e " a d a p t i v e p o l i c i e s a r e not computed f o r t h e s t o c k s c o n c e r n e d i n t h i s s t u d y . S e v e r a l a p p r o x i m a t e s o l u t i o n s of t h i s p r o b l e m f o r f i s h e r i e s s y s t e m s have been d i s c u s s e d by W a l t e r s and H i l b o r n ( 1 9 7 8 ) , S i l v e r t ( 1 9 7 8 ) , S m i t h (1978) and W a l t e r s .(1981) . 107 As an a i d t o f u t u r e d e s i g n o f a c t i v e l y a d a p t i v e p o l i c i e s , we have c h o s e n t o p r e s e n t t a b u l a r e s t i m a t e s o f and bounds f o r optimum e s c a p e m e n t s b a s e d on our ( W a l t e r s , H i l b o r n , S t a l e y and m y s e l f ) i n f o r m e d judgement and i n t u i t i o n r e g a r d i n g e a c h s t o c k . The b l i n d s t a t i s t i c a l f i t t i n g d i s c u s s e d e a r l i e r i s p a r t i c u l a r l y s e n s i t i v e t o e x t r e m e o b s e r v a t i o n s i n v o l v i n g spawning s t o c k s ; i n some c a s e s we know t h a t t h e ext r e m e e v e n t s e i t h e r d i d n o t a c t u a l l y o c c u r ( f o r example, h i g h F r a s e r s o c k e y e s p a wning i n 1958), o r a r e l i k e l y t o be t h e r e s u l t o f p o o r spawning c o u n t s a n d / o r m i s a l l o c a t i o n of c a t c h t o a s t o c k . In t h e s e i n s t a n c e s , our t a b u l a r a s s e s s m e n t o f o p t i m a l e s c a p e m e n t i s b a s e d on d i s c a r d i n g t h e o u t l i e r s , t h o u g h we a d m i t them as b i o l o g i c a l p o s s i b i l i t i e s i n s e t t i n g c r u d e bounds on o p t i m a l e s c a p e m e n t . 4.3 R e s u l t s T a b l e s 22 t o 27 show t h e optimum e s c a p e m e n t , optimum y i e l d , optimum e x p l o i t a t i o n r a t e and maximum t o l e r a b l e e x p l o i t a t i o n r a t e f o r e a c h s t o c k e s t i m a t e d by t h e R i c k e r and B e v e r t o n - H o l t m o d e l s w i t h o u t c o r r e c t i o n s f o r measurement e r r o r and w i t h o u t c o n s i d e r a t i o n f o r p a r a m e t e r u n c e r t a i n t y . In g e n e r a l , t h e R i c k e r model s u g g e s t s more c o n s e r v a t i v e p o l i c i e s t h a n t h e B e v e r t o n - H o l t m o d e l . F o r most s t o c k s , t h e R i c k e r model e s t i m a t e s much h i g h e r optimum e s c a p e m e n t l e v e l s w i t h c o r r e s p o n d i n g l y h i g h e r optimum y i e l d s and l o w e r optmum e x p l o i t a t i o n r a t e s t h a n does t h e B e v e r t o n - H o l t m o d e l . The R i c k e r model a l s o e s t i m a t e s l o w e r maximum t o l e r a b l e r a t e s of e x p l o i t a t i o n t h a n t h e B e v e r t o n - H o l t model f o r a l l s t o c k s . A c r o s s s p e c i e s c o m p a r i s o n o f optimum e x p l o i t a t i o n r a t e s 1 0 8 / T a b l e s 22-27. Optimum e s c a p e m e n t , optimum y i e l d , optimum e x p l o i t a t i o n r a t e and maximum t o l e r a b l e e x p l o i t a t i o n r a t e e s t i m a t e d by R i c k e r and B e v e r t o n - H o l t m o d e l s . M1 = R i c k e r model M2 = B e v e r t o n - H o l t model S o p t . = optimum escapement Yopt = optimum y i e l d Uopt = optimum e x p l o i t a t i o n r a t e Umax = maximum e x p l o i t a t i o n r a t e ? = e s t i m a t i o n p r o c e d u r e f a i l e d = i n s u f f i c i e n t i n f o r m a t i o n o r N n e g l i g i b l e s t o c k 109 SOCKEYE AREA S o p t . Y o p t . Uopt. Umax. Ml M2 M1 M2 M1 M2 M1 M2 Q.C. 1 - - - - — — — -Q.C.2 - - — — .86 Nass 172000 156000 281000 268000 .62 .63 .80 Skeena 743000 924000 577000 600000 .44 .39 .64 .63 C.C. 202000 166000 257000 246000 .56 .60 .75 .84 R-S 377000 270000 872000 765000 .70 .74 .85 .93 J . S . 54000 7 129000 ? .70 .85 7 G.S. F r a s e r 1713000 2040000 4610000 4388000 .73 .68 .87 .90 J . F . S . - - - — — - — SWVI 258000 148000 191000 143000 .43 .49 .62 .74 NWVI - — - — T a b l e 22 : CHUM AREA So p t . Y o p t . Uopt. Um ax. M1 M2 M1 M2 M1 M2 Ml M2 Q.C. 1 32000 12000 55000 46000 .63 .80 .80 .96 Q.C.2 236000 144000 250000 245000 .52 .63 .71 .86 Nass 38000 7 155000 7 .80 7 .91 7 Skeena - - • - — — - — — C.C. 646000 642000 633000 613000 .50 .49 .69 .74 R-S J. S . 168000 88000 146000 175000 .46 .67 .66 .89 G.S. 414000 353000 309000 295000 .43 .46 .63 .70 F r a s e r 7 7 7 7 7 7 7 7 J . F . S . - - — — -— SWVI 291000 275000 126000 120000 .30 .30 .48 .52 NWVI 102000 41 000 131000 172000 .56 .81 .75 .96 T a b l e 23 : no COHO S o p t . Y o p t . U o p t . Umax. AREA M1 M2 Ml M2 Ml M2 M1 M2 Q.C.I 35000 2900C 1 20000 95000 .77 .76 .90 .94 Q.C.2 62000 59000 68000 64000 .52 .52 .72 .77 Nass 23000 13000 103000 83000 .82 .86 .92 .98 Skeena 59000 20000 136000 149000 .70 .88 .85 .98 C.C. 139000 7 570000 ? .80 7 .91 7 R-S 1 1 000 17000 214000 174000 .95 .91 .98 .99 J . S . 103000 100000 534000 492000 .84 .83 .93 .97 G.S. 197000 204000 51 6000 492000 .72 .71 .87 .91 F r a s e r 56000 ? 380000 7 .87 7 .95 7 J . F . S . - - — — — — — — SWVI 99000 100000 130000 125000 .57 .56 .76 .80 NWVI 33000 7 100000 ? .75 7 .88 7 T a b l e 24 : SPRING AREA ' S o p t . Y o p t . U o p t . Umax. M1 M2 M1 M2 Ml M2 M1 M2 Q.C. 1 - — — — — — — : -Q.C.2 - - — — — — — • — Nass 9000 3000 24000 22000 .73 .89 .87 .99 Skeena 22000 21 000 24000 24000" .52 .54 .71 .78 C.C. 31 000 13000 54000 64000 .64 .83 .81 .97 R-S 4000 1 300 32000 26000 .89 .96 .95 .99 J . S . 18000 7 57000 7 .76 7 .89 7 G.S. 33000 25000 60000 60000 .65 . 71 .82 .91 F r a s e r 163000 360000 726000 945000 .82 .72 .92 .92 J . F . S . - - - - - — — — SWVI 9000 7 39000 7 .81 7 .92 7 NWVI 8000 7 10000 7 .56 7 .75 7 T a b l e 25 : ODD PINK S o p t . Y o p t . U o p t . Umax. AREA M1 M2 Ml M2 M1 M2 M1 M2 Q.C. 1 - - — - — — — Q.C.2 - - — -Nass 86000 37000 568000 436000 .87 .92 .95 .99 Skeena 683000 400000 991000 1000000 .59. .71 .77 .92 C.C. 3011000 3543000 2500000 2568000 .45 .42 .65 .66 R-S - - - — — — — -J . S . 481000 285000 795000 665000 .62 .71 .80 .91 G.S. 329000 308000 451000 361000 .58 .54 .76 .79 F r a s e r 1370000 ? 5198000 .79 - .91 7 J . F . S . - - — — — SWVI - - — — — NWVI — — T a b l e 26 : EVEN PINK AREA Sopt.. Y o p t . U o p t . Umax. M1 M2 M1 M2 ~ Ml M2 M1 M2 Q.C. 1 451000 303000 337000 309000 .43 .51 .63 .76 Q.C.2 553000 367000 695000 698000 .56 .67 .75 .88 Nass 267000 363000 605000 623000 .69 .63 .85 .87 Skeena 582000 394000 861000 745000 .60 .65 .78 .88 C.C. 4482000 7 7245000 7 .62 7 .79 7 R-S 145000 73000 525000 327000 .78 .82 .90 .97 J . S . 1179000 1322000 1607000 1563000 .58 .54 .76 .79 b . b . F r a s e r - - - - - - - -J . F . S . - - - — — - — — SWVI 25000 24000 31 000 25000 .55 .51 .74 .76 NWVI 129000 80000 167000 129000 .56 .62 .75 .86 T a b l e 27 112 e s t i m a t e d by t h e R i c k e r model shows t h a t s p r i n g s have t h e h i g h e s t optimum e x p l o i t a t i o n r a t e a t .745 ( a v e r a g e w e i g h t e d by optimum e s c a p e m e n t ) , f o l l o w i n g by c o h o (.734), s o c k e y e (.626), e v e n p i n k (.600), odd p i n k (.585) a n d chum (.463). The maximum t o l e r a b l e r a t e o f e x p l o i t a t i o n f o l l o w s t h e same o r d e r , w i t h s p r i n g s a v e r a g i n g .875 ( a v e r a g e w e i g h t e d by optimum e s c a p e m e n t ) , f o l l o w i n g by coho (.866), s o c k e y e (.789), even p i n k (.778), odd p i n k (.747) and chum (.655). However, s i n c e t h e e r r o r s t r u c t u r e s among s p e c i e s may not be c o m p a r a b l e , t h e s e t e n t a t i v e r e s u l t s s h o u l d be v e r i f i e d by i n d e p e n d e n t s t u d i e s i n t h e f u t u r e . When b o t h measurement e r r o r a n d p a r a m e t e r u n c e r t a i n t y a r e i n c l u d e d i n t h e e s t i m a t i o n p r o c e d u r e , d i f f e r e n t optimum e s c a p e m e n t s a r e g e n e r a l l y s u g g e s t e d . T a b l e s 28 t o 33 show t h e "Bayes e q u i v a l e n t " optimum e s c a p e m e n t f o r e a c h s t o c k e s t i m a t e d by t h e R i c k e r model f o r d i f f e r e n t l e v e l s o f A (measurement e r r o r / e n v i r o n m e n t a l e r r o r ) . Even when 7\ = 0 (no measurement e r r o r ) , t h e "Bayes e q u i v a l e n t " optimum e s c a p e m e n t s a r e u s u a l l y much h i g h e r t h a n t h e optimum e s c a p e m e n t s e s t i m a t e d by t h e d e t e r m i n i s t i c v e r s i o n o f t h e model ( T a b l e s 22 - 2 7 ) . F o r some s t o c k s ( e . g . F r a s e r chum, C.C. odd p i n k ) , t h e "Bayes e q u i v a l e n t " optimum e s c a p e m e n t s c a n n o t be d e t e r m i n e d due t o t h e h i g h u n c e r t a i n t i e s i n t h e s t o c k - r e c r u i t m e n t p a r a m e t e r s . Under t h e s e - c i r c u m s t a n c e s , escapement l e v e l s much h i g h e r t h a n t h e p r e s e n t l e v e l s a r e recommended ( W a l t e r s 1981). As 7\ i s i n c r e a s e d , f o u r g e n e r a l p a t t e r n s o f change i n t h e "Bayes e q u i v a l e n t " optimum e s c a p e m e n t a r e a p p a r e n t : 1) t h e optimum escapement may r e m a i n f a i r l y s t a b l e , a s shown by most s p r i n g and some coho s t o c k s ; 2) t h e optimum escapement may 1 I 3 T a b l e s 28-33. "Bayes e q u i v a l e n t " optimum e s c a p e m e n t a t d i f f e r e n t l e v e l s o f A . L = e s t i m a t i o n p r o c e d u r e f a i l e d , optimum e s c a p e m e n t i s p r o b a b l y much h i g h e r t h a n t h e c u r r e n t e s capement = i n s u f f i c i e n t i n f o r m a t i o n o r n e g l i b i b l e s t o c k 114 SOCKEYE AREA A = 0.0 *=0.5 A=1 .0 A=1 .5 x = 2.0 Q.C. 1 - - - - -Q.C.2 - - - - -Nass 181000 159000 135000 125000 125000 Skeena 868000 L L L L C.C. 199000 193000 181000 168000 159000 R-S 405000 475000 508000 506000 504000 J . S . 54000 38000 37000 38000 36000 G.S. - - - - -F r a s e r 1670000 1650000 1590000 1530000 1500000 J . F . S . - - - - -SWVI L L L L L NWVI . — - — - -T a b l e 28 : CHUM AREA ^=0.0 K = 0 .5 A=1 .0 A = 1 .5 A=2.0 Q.C. 1 35000 30000 28000 28000 27000 Q.C.2 254000 211000 186000 182000 182000 Nass , 38000 33000 34000 35000 35000 Skeena - - - - -C.C. 684000 600000 514000 493000 481000 R-S - - - - -J . S . 187000 222000 L L L G.S, 432000 437000 426000 383000 317000 F r a s e r L L L L L J . F . S . - - - - -SWVI 372000 L L L L NWVI 104000 98000 98000 98000 98000 T a b l e 29 : 1 1 5 COHO AREA X =0.0 X =0.5 X = 1 .0 X =1 . 5 x =2.0 Q.C. 1 34000 35000 35000 34000 33000 Q.C.2 64000 65000 63000 62000 61000 Nass 22000 21 000 22000 22000 23000 Skeena 59000 56000 51000 50000 49000 C.C. 1 35000 119000 61000 60000 58000 R-S 1 1000 6500 6000 6000 6000 J . S . 100000 101000 105000 108000 1 10000 G.S. 201000 194000 184000 172000 158000 F r a s e r 54000 50000 40000 34000 33000 J . F . S . - ' - - - -SWVI 102000 121000 131000 132000 132000 NWVI 33000 22000 20000 20000 20000 T a b l e 30 : SPRING AREA x=0.0 x = 0.5 x = 1 . 0 x = 1 . 5 x =2.0 Q.C.1 - -Q . C 2 - - . - - -Nass 8000 8000 8000 8000 8000 Skeena 22000 22000 21000 21000 21000 C.C. •30000 29000 28000 280CK) • 27000 R-S 4000 4000 3000 3000 3000 J . S . 18000 15000 1 4000 1 4000 14000 G.S. 32000 31000 30000 30000 30000 F r a s e r 205000 L L L L J . F . S . - - - - -SWVI 9000 8000 8000 8000 8000 NWVI 8000 8000 7000 7000 7000 T a b l e 31 : ODD PINK AREA A = 0.0 x. = 0.5 A =1 . 0 x = i .5 A =2.0 Q.C.1 - - - - -Q.C.2 Na s s 87000 70000 71 000 73000 77000 Skeena 700000 615000 594000 584000 579000 C.C. L L L L L R-S J . S . 497000 370000 312000 282000 272000 G.S. 362000 365000 L L L F r a s e r 1270000 L L - L L J . F . S . - - - — — SWVI - - — — — NWVI — — — - — T a b l e 32 : EVEN PINK AREA A=0.0 x = 0.5 A =1 .0 A = 1 .5 A =2.0 Q.C. 1 508000 486000 483000 480000 478000 Q.C.2 576000 L L L L N a s s L L L L L S k e e n a 597000 564000 570000 586000 598000 C.C. 5160000 L L L L R-S 155000 224000 268000 229000 242000 J . S . 1860000 L L L L G.S. - - - — -F r a s e r - - — — — J . F . S . - - - - — SWVI L L L L L NWVI 140000 151000 154000 155000 155000 T a b l e 33 : 1 17 i n c r e a s e o r d e c r e a s e more o r l e s s s t e a d i l y , a s shown i n many s o c k e y e , chum and coho s t o c k s ; 3) t h e optimum escapement may change r a p i d l y a t low A v a l u e s b u t become more s t a b l e a s A i n c r e a s e s , a s shown i n J . S . s o c k e y e , NWVI chum and some coho s t o c k s ; 4) t h e optimum e s c a p e m e n t may become h i g h l y u n c e r t a i n and t h e e s t i m a t i o n p r o c e d u r e f a i l a s A i n c r e a s e s , a s shown i n many p i n k , some chum, one s o c k e y e a nd one s p r i n g s t o c k s ( T a b l e s 28 - 3 3 ) . The optimum e x p l o i t a t i o n r a t e a nd maximum e x p l o i t a t i o n r a t e show s i m i l a r c h a n g e s a s A i n c r e a s e s ( T a b l e s 2 4 - - 3*7 ) . S t a t i s t i c a l e s t i m a t e s o f optimums a r e v e r y s e n s i t i v e t o extre m e o b s e r v a t i o n s i n v o l v i n g s p a w n i n g s t o c k s a n d / o r r e c r u i t m e n t . In some c a s e s , we know t h e extre m e e v e n t s e i t h e r d i d n o t o c c u r o r a r e l i k e l y t o be t h e r e s u l t o f poor spawning c o u n t s a n d / o r m i s a l l o c a t i o n o f c a t c h t o a s t o c k . T h e r e f o r e , t a b l u l a r e s t i m a t e s o f optimum e s c a p e m e n t s and t h e i r p r o b a b l e bounds a r e p r e s e n t e d i n t a b l e s 40 t o 45, F i g . 15, and A p p e n d i x I I . T h e s e e s t i m a t e s a r e b a s e d on t h e above s t a t i s t i c a l e s t i m a t e s , p l u s o ur i n f o r m e d judgement and i n t u i t i o n r e g a r d i n g e a c h s t o c k . Optimum e s c a p e m e n t s e s t i m a t e d by t h e G e o g r a p h i c W o r k i n g G r o u p of t h e SEP p r o g r a m and t h e a v e r a g e escapement from 1975-1979 a r e a l s o i n c l u d e d f o r c o m p a r i s o n . T a b l e 46 shows t h a t on a- c o a s t w i d e b a s i s , r e c e n t e s c a p e m e n t s (1975-79) o f s o c k e y e a n d even p i n k were o n l y h a l f of th e G.W.G. optimums, w h i l e chum, c o h o , s p r i n g and odd p i n k e s c a p e m e n t s were o n l y a r o u n d 40% o f t h e G.W.G. Optimums. L i k e w i s e , o ur e s t i m a t e s ( A p p e n d i x I I ) i n d i c a t e t h a t r e c e n t e s c a p e m e n t s f o r a l l s p e c i e s were b a r e l y w i t h i n t h e lo w e r bounds of o u r e s t i m a t e s , and were o n l y a b o u t 25% t o 45% of t h e upper I I 8 T a b l e s . . 34-39. Optimum e x p l o i t a t i o n r a t e and maximum t o l e r a b l e e x p l o i t a t i o n r a t e a t d i f f e r e n t l e v e l s of A . ? = e s t i m a t i o n p r o c e d u r e f a i l e d = i n s u f f i c i e n t i n f o r m a t i o n o r n e g l i g i b l e s t o c k SOCKEYE AREA \=0.0 S = 0.5 A = 1.0 A = 1 . E A = 2.0 Uopt Umax Uopt Umax Uopt Umax Uopt Umax Uopt Umax Q.C. 1 - - - - - — - - - -Q.C.2 - - - - - - - - - -Nass .66 .80 .67 .82 .70 .84 .72 .85 .72 .85 S k e e n a .48 .64 7 7 7 ? 7 7 7 7 C.C. .59 .75 .59 .76 .60 .77 .62 .79 .64 .79 R-S .75 .85 .71 .83 .69 .82 .69 .82 .69 .82-J . S . .77 .85 .90 .95 .90 .95 .90 .95 .90 .95 G.S. - - - - - - - - - -F r a s e r .76 .87 .76 .88 .76 .88 .77 .89 .77 .89 J . F . S . - - - - - - - - - -SWVI ? 7 7 7 7 7 7 7 7 7 NWVI - - • - - - - - - - -T a b l e 34 : CHUM AREA A = D.O x = 0.5 x = 1 .0 x = 1 .5 A = 2.0 U o p t Umax Uopt Umax Uopt Umax Uopt Umax Uopt Umax Q.C.1 .69 .80 .70 .82 .72 .84 .72 .84 .72 .85 Q.C.2 .58 .71 .62 .75 .68 .80 .69 .81 .69 .82 Nass .84 .92 .76 .93 .86 .93 .86 .93 .86 .93 S k e e n a - - • - - - - - - - -C.C. O — c .54 .69 .56 .72 .60 .76 .61 .77 .62 .78 K b J . S . .58 .66 .48 .58 7 7 7 7 7 7 G.S. .50 .63 .48 .63 .49 .64 .52 .67 .58 .73 F r a s e r 7 7 7 7 7 7 7 7 7 7 J . F . S . - - - - - - - - - -SWVI .37 .48 7 7 7 7 7 7 7 7 NWVI . 63 .75 .66 .80 .66 .81 .66 .81 .66 .81 T a b l e 35 : 120 COHO AREA 3.0 >\ = 0.5 A = 1 .0 A = 1 .5 A = 2.0 U o p t Umax Uopt Umax UODt Umax Uopt Umax Uopt Umax Q.C. 1 .81 .90 .80 .90 .80 .90 .80 .90 .80 .90 Q.C.2 .55 .72 .63 .71 .53 .71 .53 .72 .54 .72 Nass .85 .95 .84 .93 .84 ^ .92 .83 .92 .83 .92 Skeena .73 .85 .73 .85 .75 .86 .75 .87 .75 .87 C.C. .83 . 9 1 .85 .92 .96 .99 .97 .99 .97 .99 R-S .96 .98 .97 .99 .98 .99 .97 .99 .97 .99 J . S . .85 .93 .85 .93 .84 .93 .84 .92 .83 .92 G.S. .74 .87 .74 .87 .75 .88 .76 .88 .78 .89 F r a s e r .88 .95. .90 .96 '.92 .96 .94 .97 .94 .98 J . F . S . - - - - - - - - - -SWVI .60 .76 .56 .76 .54 .73 .54 .73 .54 .74 NWVI .79 .88 .86 .93 .87 .94 .87 .94 .87 .94 T a b l e 36 : SPRING AREA A = 0.0 A = 0.5 x = 1 .0 A = 1 .5 A = 2.0 Uopt Umax Uopt Umax Uopt Umax Uopt Umax Uopt Umax Q.C. 1 - - - - - - - - -Q.C.2 - - - - - • - - - - -Nass .76 .87 .79 .90 .79 .90 .79 .90 .79 .90 Skeena .54 .71 .54 .71 .54 .72 .55 .73 .56 .73 C.C. .65 .81 .67 .82 .68 .83 .69 .84 .69 .84 R-S .89 .95 .90 .96 .90 .96 .90 .96 .90 .96 J . S . .77 .89 .82 .91 .84 .93 .85 .93 .85 .93 G.S. .66 .82 .67 .82 .68 ..83 .68 .83 .68 .83 F r a s e r .79 .92 ? 7 7 7 7 7 7 7 J . F . S . - - - - - - - - - -SWVI .84 .92 .86 .93 .85 .93 .85 .93 .85 .93 NWVI .58 .75 .60 .77 .61 .77 .61 .78 .62 .78 T a b l e 37 : 121 ODD PINK AREA X -0.0 A = 0.5 X = 1.0 X = 1 .5 x = 2.0 U o p t Umax Uopt Umax Uopt Umax Uopt Umax Uopt Umax Q.C. 1 - - - - - - - - - -Q.C.2 - - - - - - - - - - -Nass .90 • .95 .91 .95 .90 .95 .89 .95 .89 .95 Skeena .64 .77 .65 .79 .66 .80 .66 .80 .66 .81 C.C. r> — C ? 7 7 7 7 7 7 7 7 7 H o J . S . .73 .80 .73 .82 .75- .84 .76 .85 .77 .86 G.S. .65 .76 .60 .74 7 7 7 7 7 7 F r a s e r .85 .91 7 7 7 7 7 7 7 7 J . F . S . - - - - - - , - - - -SWVI - - - - - - - - - -NWVI — — — — - — — — — -T a b l e 38 : • EVEN PINK AREA _ > = 0 .0 ' x=0 .5 X = 1 .0 x = 1 .5 > = 2 .0 U o p t Umax Uopt Umax Uopt Umax Uopt Umax Uopt Umax Q.C. 1 .57 .63 .50 .59 .47 .57 .45 .57 • .44 .57 Q.C.2 .64 .75 7 7 7 7 ? 7 7 7 Nass 7 7 7 7 7 ? 7 7 7 7 Skeena .66 .78 .62 .76 .60. .75 .58 .73 .56 .72 C.C. .66 .79 7 7 7 7 7 7 7 7 R-S .88 .90 .79 .89 .75 .89 .76 .89 .75 .89 J . S . .57 .76 7 7 7 7 7 7 7 7 G.S. - — - — - - : — - — -F r a s e r - - - - - - - - - -J . F . S . - - - - - - - - - -SWVI 7 7 7 7 7 7 7 7 7 7 NWVI .68 .75 .60 .73 .57 .72 .56 .71 .55 .71 T a b l e 39 1 2 2 T a b l e s 40-45. C u r r e n t e s c a p e m e n t , G.W.G. Optimum escapement e s t i m a t e s , and our optimum e s c a p e m e n t e s t i m a t e s w i t h p r o b a b l e b o unds. ? = no e s t i m a t e = i n s u f f i c i e n t i n f o r m a t i o n o r n e g l i g i b l e s t o c k SOCKEYE CURRENT G.W.G. AREA ESC. OPT. OPT. LOWER UPPER Q.C. 1 25000 55000 ? 7 7 Q.C.2 1 3000 40000 7 7 7 Nass 195000 250000 181000 120000 360000 Skeena 820000 880000 868000 600000 1500000 C.C. 100000 325000 200000 100000 400000 R-S 390000 1200000 500000 400000 2000000 J.S. 37000 132000 7 7 7 G.S. - - - - -F r a s e r 1370000 7 4000000 2000000 8000000 J.F.S. - - - - -SWVI 260000 300000 300000 100000 1000000 NWVI 10000 ? 7 7 7 T a b l e 40 : CHUM CURRENT G.W.G. AREA ESC. OPT. OPT. LOWER UPPER Q.C. 1 78000 85000 7 7 7 Q.C.2 155000 450000 600000 206000 1000000 Nass 53000 90000 7 7 7 Skeena 10000 50000 7 7 7 C.C. 380000 1300000 684000 400000 1000000 R-S 34000 115000 7 7 7 J.S. 242000 430000 210000 150000 350000 G.S. 472000 1460000 415000 300000 500000 F r a s e r 435000 700000 1000000 600000 3000000 J.F.S. 18000 75000 7 7 7 SWVI 471000 362000 372000 300000 500000 NWVI 1 17000 280000 150000 100000 200000 T a b l e 41 COHO CURRENT G.W.G. AREA ESC. OPT. OPT. LOWER UPPER Q.C. 1 70000 150000 35000 1 5000 75000 Q.C.2 48000 7 80000 50000 140000 N a s s 26000 45000 30000 10000 60000 Skee n a 35000 148000 54000 10000 120000 C.C. 137000 369000 135000 80000 250000 R-S 5000 45000 10000 4000 7 J . S . 52000 122000 100000 • 40000 180000 G.S. 155000 410000 20100'0 100000 400000 F r a s e r 61 000 175000 54000 20000 100000 J . F . S . - - - - — SWVI 48000 ? 100000 50000 200000 NWVI 27000 ? 35000 20000 50000 T a b l e 42 : SPRING CURRENT G.W.G. AREA ESC. OPT. OPT. LOWER UPPER Q.C. 1 1000 5000 7 7 7 Q.C.2 - - - — — N a s s 7000 30000 80000 6000 10000 Skee n a 22000 80000 22000 20000 50000 C.C. 29000 82000 30000 1 6000 50000 R-S 3000 10000 4000 3000 8000 J . S . 1 7000 50000 18000 10000 30000 G.S. 19000 148000 32000 20000 50000 F r a s e r 68000 155000 200000 100000 400000 J . F . S . - - - — — SWVI 15000 23000 7 7 7 NWVI 5000 7 7 7 7 T a b l e 43 : ODD PINK CURRENT G.W.G. AREA ESC. OPT. x OPT. LOWER UPPER Q.C. 1 1 3000 10000 7 7 7 Q.C.2 - - - - -Nass 130000 300000 7 7 7 Skeena 1 1 20000 1600000 701000 500000 900000 C.C. 1020000 3500000 3280000 2000000 7 R-S 58000 800000 7 7 7 J . S . 600000 1400000 600000 400000 1000000 G.S. 86000 7 362000 250000 2000000 F r a s e r 2440000 2000000 1500000 6000000 J . F . S . - - - - -SWVI - - - - -NWVI — - - - -T a b l e 44 : EVEN PINK CURRENT G.W.G. AREA ESC. OPT. OPT. LOWER UPPER Q.C. 1 251000 1000000 750000 600000 2500000 Q.C.2 692000 1600000 576000 400000 1000000 Nass 278000 300000 7 600000 7 Skeena 700000 1400000 600000 500000 1000000 C.C. 3300000 5345000 5160000 3000000 7 R-S 193000 275000 155000 100000 7 J . S . 1350000 1523000 7 1000000 7 G.S. 8000 426000 7 ? 7 F r a s e r - • - - - -J . F . S . - - - - -SWVI 7000 7 7 25000 7 NWVI 131000 255000 7 150000 7 T a b l e 45 G.W.G. OPT. LOWER UPPER SOCKEYE .58 .52 .94 .24 CHUM .46 .66 1.11 .35 COHO .37 .80 1 .66 .42 SPRING .31 .53 .94 .28 0. PINK .39 .76 1.13 .43 E. PINK .57 .71 1 .08 T a b l e 46 : R a t i o of c u r r e n t escapement t o v a r i o u s optimum escapement e s t i m a t e s . ? = no e s t i m a t e 127 b o unds. F i g u r e 17 shows g r a p h i c a l l y o u r optimum escapement e s t i m a t e s and t h e i r p r o b a b l e bounds, w i t h a r r o w s p o i n t i n g t o t h e a v e r a g e e s c a p e m e n t s from 1975-1979. I t i s a p p a r e n t t h a t most s t o c k s a r e now b e i n g o v e r e x p l o i t e d , w i t h many l a r g e r ones b e i n g s e v e r e l y d e p l e t e d ( F r a s e r s o c k e y e , F r a s e r chum, C.C. chum, Q.C. 2 chum, J . S . c o h o , SWVI coh o , F r a s e r s p r i n g , G.S. odd p i n k , C.C. odd p i n k , Q.C.1 even p i n k and C.C. even p i n k ) . 17. Optimum escapement e s t i m a t e s and p r o b a b l e b ounds. a v e r a g e escapement from 1975-1979 no e s t i m a t e 1 2 9 4E6 3E6^ 2E6^ 2E6 lESr-CHUM QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI H Z UJ 2 Id a. < o co u i 2 5 H -0. o 4E5 3E5 2E5 1E5 2E5 1E5 QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI QCl QC2 NASS SKEENA CC RS JS GS FRASER JFS SWVI NWVI PRODUCTION AREA I 3 0 5. DISCUSSION AND CONCLUSION Much t i m e and e f f o r t have been s p e n t i n t h e p a s t 30 y e a r s t o m o n i t o r B.C. salmon c a t c h e s and e s c a p e m e n t s . Y e t few a t t e m p t s have been made t o s y s t e m a t i c a l l y s t u d y t h e s t o c k -r e c r u i t m e n t p r o b l e m . B e c a u s e o f d i f f i c u l t i e s i n s e p a r a t i n g m i x e d c a t c h e s and t h e p r e s e n c e o f l a r g e s a m p l i n g e r r o r i n spawning c o u n t s , most r e s e a r c h e r s and b i o l o g i s t s shy away from u s i n g t h e d a t a t o e s t i m a t e "optimum" e s c a p e m e n t s . W i t h l i t t l e o r no h e l p f r o m r e s e a r c h e r s , some managers a t t e m p t t o r e s o l v e t h i s d i f f i c u l t p r o b l e m by d e f i n i n g " d e s i r e d " o r "optimum" escapement v e r y s i m p l i s t i c a l l y ( f o r example, t h e l a r g e s t e s c a p e m e n t s i n c e 1950 t h a t has p r o d u c e d an e q u a l o r h i g h e r s u b s e q u e n t e s c a p e m e n t ) . Some s e t t l e f o r t h e p r e s e r v a t i o n of t h e s t a t u s quo w i t h o u t q u e s t i o n i n g whether t h e c u r r e n t c o n d i t i o n i s even n e a r optimum. And some s i m p l y r e a c t t o w h a t e v e r p o l i t i c a l p r e s s u r e i s on hand r e g a r d l e s s of t h e c o n s e q u e n c e s t o t h e s t o c k s t h a t may be a f f e c t e d . U n t i l r e c e n t l y , i t was g e n e r a l l y b e l i e v e d t h a t " a d e q u a t e s e e d i n g " has been m a i n t a i n e d i n most r i v e r s b e c a u s e r e c r u i t m e n t s have a p p e a r e d t o be i n d e p e n d e n t o f s p a w n i n g s t o c k s . However W a l t e r s and L u d w i g ( 1 9 8 1 ) , L u d w i g an d W a l t e r s (1981) and t h e p r e v i o u s c h a p t e r s have d e m o n s t r a t e d t h a t e r r o r s i n spawning c o u n t s a n d / o r p o o r c a t c h s e p a r a t i o n t e c h n i q u e s c a n l e a d t o t h e a p p e a r a n c e t h a t r e c r u i t m e n t i s i n d e p e n d e n t o f spawners even f o r b a d l y o v e r e x p l o i t e d s t o c k s . D e s p i t e s u c h o b v i o u s b i a s e s , t h e d a t a u s e d i n t h i s s t u d y c l e a r l y show t h a t many B.C. salmon s t o c k s a r e now s e v e r e l y d e p l e t e d (namely, F r a s e r s o c k e y e , F r a s e r 1 3 1 chum, C.C. chum, J . S . c o h o , SWVI c o h o , F r a s e r s p r i n g , G.S. odd p i n k , C.C. odd p i n k , Q.C.1 even p i n k and C.C. even p i n k ) . R e s t o r a t i o n o f t h e s e s t o c k s by i n c r e a s i n g e s capement t o t h e optimum l e v e l s , a c c o r d i n g t o o u r e s t i m a t e s i n A p p e n d i x I I , wo u l d i n c r e a s e t h e a n n u a l s u s t a i n a b l e y i e l d o f s o c k e y e by 3.5 m i l l i o n p i e c e s ( a r o u n d 50% of c u r r e n t y i e l d ) , chum by 1.3 m i l l i o n ( 8 3 % ) , s p r i n g by .2 m i l l i o n ( 2 3 % ) , odd p i n k by 2.8 m i l l i o n ( 2 5 % ) , and even p i n k by 6.8 m i l l i o n ( 6 5 % ) . We p r e d i c t t h e t o t a l i n c r e a s e i n c a t c h w o u l d be 14.7 m i l l i o n p i e c e s ( 4 3 % of c u r r e n t y i e l d ) . C o n c l u s i v e e s t i m a t e s c a n n o t be made f o r most o f t h e o t h e r s t o c k s ( w h i c h a c c o u n t f o r a b o u t h a l f o f t h e t o t a l B.C. p r o d u c t i o n ) b e c a u s e of poor e s c a p e m e n t c o u n t s a n d / o r d i f f i c u l t i e s i n s e p a r a t i n g mixed c a t c h e s ( e s p e c i a l l y c o ho and s p r i n g s t o c k s ) . F u r t h e r , e x p e r i m e n t a l management (by i n c r e a s e d e s c a p e m e n t ) a p p e a r s t o be t h e b e s t p o l i c y f o r a few s t o c k s ( e . g . R-S s o c k e y e , G.S. coho, Skeena s p r i n g , F r a s e r odd p i n k , Nass even p i n k and J . S . even p i n k ) . T h r e e o p t i o n s have been s u g g e s t e d ( W a l t e r s e t . a l . 1982) f o r i n c r e a s i n g B.C. salmon p r o d u c t i o n . One o p t i o n ( " b i t e t h e b u l l e t " ) i s t o s t o p f i s h i n g F r a s e r s o c k e y e , most chum and p i n k s t o c k s and a few s p r i n g s t o c k s f o r some y e a r s , and t h e n e x p l o i t t h e r e s u l t i n g l a r g e r s t o c k s a t a l o w e r r a t e i n t o t h e f u t u r e . S u ch d r a s t i c a c t i o n i s o b v i o u s l y u n a c c a p t a b l e b o t h s o c i a l l y and p o l i t i c a l l y . A s e c o n d o p t i o n ("the A m e r i c a n p l a n " ) i s t o c o n t i n u e i n c r e a s i n g t h e p r o d u c t i v i t y of some s t o c k s by enhancement t e c h n o l o g y ( h a t c h e r i e s , spawning c h a n n e l s e t c . ) t o s u s t a i n t h e c u r r e n t l a r g e f l e e t a nd h i g h e f f o r t . The h i g h e r e x p l o i t a t i o n r a t e s r e q u i r e d t o h a r v e s t t h i s e n h a n c e d p r o d u c t i o n 132 w o u l d i n e v i t a b l y c a u s e a s h a r p d e c l i n e i n w i l d s t o c k s ( t r a d i t i o n a l . f i s h i n g methods a r e i n c a p a b l e o f h a r v e s t i n g e n h a n c e d s t o c k s s e p a r a t e l y ) . T h i s a p p r o a c h would b e s t s e r v e t h e i m m e d i a t e demands of t o d a y ' s c o m m e r c i a l and s p o r t i n d u s t r y . The t h i r d o p t i o n ( " H i l b o r n p l a n " ) i s t o c o - o r d i n a t e t h e c u r r e n t SEP enhancement p r o j e c t s w i t h management e f f o r t s t o " b u f f e r " t h e n a t u r a l s t o c k s w i t h enhancement p r o d u c t i o n . Under t h i s o p t i o n , m i x e d a r e a c a t c h e s would be l i m i t e d t o c u r r e n t o r l o w e r l e v e l s , w i t h much enhancement p r o d u c t i o n t a k e n a t ( o r n e a r ) enhancement f a c i l i t i e s . By l i m i t i n g t h e c a t c h e s i n t h e mixed a r e a s , i n c r e a s e d s t o c k s i z e s due t o enhancement would r e s u l t i n l o w e r e x p l o i t a t i o n r a t e s on w i l d s t o c k s and t h e s e s h o u l d b e g i n a g r a d u a l r e c o v e r y t o optimum l e v e l s . One drawback i n t h i s a p p r o a c h i s t h e p o t e n t i a l e c o n o m i c l o s s and m a r k e t i n g p r o b l e m a s s o c i a t e d w i t h t e r m i n a l h a r v e s t o f l o w e r q u a l i t y e n h a n c e d f i s h , a n d t h e l e s s d e s i r e a b l e s t y l e o f f i s h i n g imposed on f i s h e r m e n t o h a r v e s t t h e e n h a n c e d s t o c k s n e a r enhancement f a c i l i t i e s . A s e c o n d drawback w i t h t h e " H i l b o r n P l a n " i s t h e e n v i r o n m e n t • f o r management c r e a t e d by t h e f i s h e r m e n s e e i n g i n c r e a s i n g a b u n d a n c e , and c a t c h p e r e f f o r t c o m b i n e d w i t h r e d u c e d f i s h i n g t i m e ( l e s s e f f o r t t o t a k e t h e same q u o t a ) ; i t m i g h t p r o v e p o l i t i c a l l y i m p o s s i b l e t o h o l d t h e l i n e w i t h f i x e d q u o t a s . R e g a r d l e s s of t h e f u t u r e a p p r o a c h t o enhancement, i m p r o v e d m o n i t o r i n g of c a t c h e s , e s c a p e m e n t s , age s t r u c t u r e , m i g r a t i o n r o u t e s , and f i s h i n g e f f o r t s h o u l d be g i v e n t h e h i g h e s t p r i o r i t y among d e p a r t m e n t a l p r o g r a m s . I t has been c l e a r l y d e m o n s t r a t e d i n t h i s s t u d y t h a t o c c a s i o n a l t a g g i n g s t u d i e s and i n t u i t i v e e s c a p e m e n t e v a l u a t i o n s a r e n o t a d e q u a t e t o p r o v i d e a sound b a s i s 1 3 3 f o r salmon management. I t i s i m p e r a t i v e t h a t a l o n g t e r m p r o g r a m , p r o v i d e d w i t h a d e q u a t e r e s o u r c e s and w e l l t r a i n e d s t a f f , be e s t a b l i s h e d w i t h i n t h e D e p a r t m e n t o f F i s h e r i e s and O c e a n s t o c o n d u c t p r o p e r s a m p l i n g and e n s u r e t h e e f f i c i e n t d i s t r i b u t i o n o f e s s e n t i a l d a t a . W i t h o u t s u c h a program, c u r r e n t management p o l i c i e s can n e v e r be e v a l u a t e d , and t h e l i k e l y c o n s e q u e n c e s o f new p o l i c i e s c a n n o t be p e r c e i v e d . As l o n g as salmon f i s h i n g i s c o n d u c t e d on m a t u r i n g f i s h i n c o a s t a l w a t e r s , t h e most c r u c i a l n eed i n management w i l l c o n t i n u e t o be u n d e r s t a n d i n g o f t h e r e l a t i o n s h i p between spawning s t o c k and s u b s e q u e n t r e c r u i t m e n t . To measure t h e q u a n t i t a t i v e e f f e c t of d i f f e r e n t spawning l e v e l s on s u b s e q u e n t r e c r u i t m e n t , t h i s s t u d y has t a k e n as an i n i t i a l w o r k i n g h y p o t h e s i s t h a t f o r e a c h s t o c k t h e r e e x i s t s a s t a t i o n a r y ( t i m e i n d e p e n d e n t ) p r o b a b i l i t y d i s t r i b u t i o n of r e c r u i t s f o r e a c h p o s s i b l e l e v e l o f s p a w n ing p o p u l a t i o n , w i t h t h e means o f t h e s e d i s t r i b u t i o n s v a r y i n g s m o o t h l y a c c o r d i n g t o some s t o c k - r e c r u i t m e n t c u r v e . By f i t t i n g s t o c k - r e c r u i t m e n t c u r v e s t h r o u g h h i s t o r i c a l d a t a , d e v i a t i o n s f r o m t h e c u r v e s c a n be u s e d as a c r u d e t e s t o f t h e s t a t i o n a r i t y h y p o t h e s i s . No c l e a r t r e n d s i n t h e s e d e v i a t i o n s were e v i d e n t f o r most s t o c k s ( A p p e n d i x I I ) . However, b e c a u s e o f d i f f i c u l t i e s i n s e p a r a t i n g mixed c a t c h e s , many " s t o c k s " from l a r g e g e o g r a p h i c a l a r e a s were a g g r e g a t e d as " p r o d u c t i o n a r e a s " t o f o r m t h e b a s i c u n i t s o f t h i s a n a l y s i s . Under t h e s e c i r c u m s t a n c e s , t h e s t a t i o n a r i t y h y p o t h e s i s i s v a l i d o n l y i f t h e component " s t o c k s " w i t h i n t h e a g g r e g a t e d u n i t have s t a b l e r e l a t i v e v u l n e r a b i l i t i e s t o f i s h i n g and a r e s u b j e c t t o t h e same or c o r r e l a t e d e n v i r o n m e n t a l i n f l u e n c e s . O t h e r w i s e th e s t o c k - r e c r u i t m e n t 134 r e l a t i o n s h i p f o r t h e a g g r e g a t e d u n i t s h o u l d c h a n g e o v e r t i m e , and t h e optimum r a t e of e x p l o i t a t i o n becomes v e r y d i f f i c u l t t o d e f i n e ( R i c k e r 1973). I t i s more d i f f i c u l t t o d e t e c t o v e r e x p l o i t a t i o n i n a g g r e g a t e d u n i t s b e f o r e c o n s i d e r a b l e damage has been done, and r e h a b i l i t a t i o n e f f o r t s (by i n c r e a s i n g o v e r a l l e s c a p e m e n t ) may r e q u i r e much l o n g e r t h a n would be p r e d i c t e d by a s s u m i n g s t a t i o n a r i t y o f h i s t o r i c a l p a t t e r n s . One o f t h e b i g g e s t u n c e r t a i n t i e s e n c o u n t e r e d i n t h i s a n a l y s i s i s t h e e s t i m a t i o n o f t h e c o n t r i b u t i o n o f s t o c k s t o m i x e d f i s h e r i e s . The p a s t d e c a d e w i t n e s s e d a d r a m a t i c i n c r e a s e i n . t h e e f f i c i e n c y o f f i s h i n g g e a r s , e s p e c i a l l y p u r s e s e i n e s , u s e d i n t h e B.C. salmon f i s h e r y . To p r e v e n t o v e r f i s h i n g o f some l o c a l s t o c k s , t h e D e p a r t m e n t of F i s h e r i e s has been moving f i s h i n g a r e a s away from r i v e r mouths i n t o a r e a s where s t o c k s a r e m i x e d ( A n d e r s o n 1980). I n t e r n a t i o n a l c o n f l i c t s p r o m p t e d t h e d e v e l o p m e n t of t h e J o h n s t o n e S t r a i t m i x e d f i s h e r y t o t a k e F r a s e r p i n k and s o c k e y e b e f o r e t h e y r e a c h t h e I.P.S.F.C. c o n v e n t i o n a l w a t e r s where t h e y a r e s p l i t 50:50 w i t h t h e A m e r i c a n s . S i m i l a r l y t h e t r o l l f l e e t , w h ich o p e r a t e s where a l l N o r t h A m e r i c a n s t o c k s a r e m i x e d , has been e n c o u r a g e d t o t a k e a d v a n t a g e of t h e A m e r i c a n enhancement p r o d u c t i o n of- c oho and s p r i n g . The r e s u l t o f a l l t h i s i s t h a t i t i s now a l m o s t i m p o s s i b l e t o measure t h e c o n t r i b u t i o n o f any s i n g l e s t o c k v e r y a c c u r a t e l y . H o p e f u l l y , t h e r e c e n t i n c r e a s e i n f u e l c o s t s , t h e i n t e r i m a g r e e m e n t w i t h t h e U n i t e d S t a t e s and t h e p o s s i b i l i t y o f a r e a l i c e n c i n g w i l l p r o v i d e t h e r a t i o n a l e f o r moving t h e f i s h e r i e s back i n t o more t e r m i n a l a r e a s . And by i n c r e a s i n g t h e use of s t o c k i d e n t i f i c a t i o n t e c h n i q u e s ( e . g . s c a l e a n a l y s i s , c o d e d w i r e t a g s , p a r a s i t e 135 c o m p o s i t i o n , e t c . ) , t h e c o n t r i b u t i o n o f s t o c k s t o m i x e d f i s h e r i e s c a n be e s t i m a t e d more a c c u r a t e l y i n t h e f u t u r e . E q u a l l y u n c e r t a i n i s t h e e s t i m a t i o n o f spawning p o p u l a t i o n s f o r most s t o c k s . A p a r t f r o m t h e few r i v e r s e q u i p p e d w i t h c o u n t i n g f e n c e s , t h e r e a r e no s t a n d a r d i z e d s a m p l i n g p r o c e d u r e s o r p r e s c r i b e d o b s e r v a t i o n s i t e s t o e n s u r e c o n s i s t e n c y i n s p a w n i n g e s t i m a t e s made by f i s h e r i e s o f f i c e r s . D i s c r e p a n c i e s by an o r d e r o f m a g n i t u d e have been f o u n d between o f f i c e r e s t i m a t e s and i n d e p e n d e n t c h e c k s t h r o u g h mark r e c o v e r y , d i v i n g or f e n c e c o u n t s . A p p r a i s a l s by d i f f e r e n t o f f i c e r s a l s o show l a r g e and i n c o n s i s t e n t d i s c r e p a n c i e s among d i f f e r e n t s t r e a m s . F u r t h e r m o r e , t h e r e c o r d i n g p r o c e d u r e a l o n e (by wide abundance c l a s s e s ) would i n t r o d u c e e r r o r s o f +- 30%. O b v i o u s l y more r i g o r o u s and c o n s i s t e n t p r o c e d u r e s a r e needed f o r t h e e n u m e r a t i o n o f s p a w n i n g p o p u l a t i o n s . However, t o a c c u r a t e l y e n u m e rate more t h a n 1200 s t r e a m s , e a c h w i t h 1 t o 5 s p e c i e s o f salmon spawning a t d i f f e r e n t t i m e s of t h e y e a r , w o u l d r e q u i r e s u b s t a n t i a l l y more r e s o u r c e s and manpower. G i v e n t h e l i m i t e d r e s o u r c e s a v a i l a b l e t o d a y , a b e t t e r a p p r o a c h t o t h i s p r o b l e m may be t o r i g o r o u s l y a s s e s s a few r e p r e s e n t a t i v e s t o c k s i n e a c h p r o d u c t i o n a r e a , r a t h e r t h a n t r y i n g t o o b t a i n d o u b t f u l i n f o r m a t i o n f o r a l l s t o c k s . B e c a u s e o f t h e g e n e r a l l y p o o r q u a l i t y of t h e d a t a base and l a c k o f u n d e r s t a n d i n g of i t s e r r o r s t r u c t u r e , c o n c l u s i v e r e m a r k s c a n n o t be made ab o u t t h e s t o c k - r e c r u i t m e n t d y n a m i c s of more t h a n h a l f of t h e B.C. salmon s t o c k s . However, s e v e r a l f i n d i n g s a r e w o r t h f u r t h e r i n v e s t i g a t i o n . P e r h a p s t h e l a r g e s t u n c e r t a i n t y a b o u t f u t u r e salmon p r o d u c t i o n c o n c e r n s coho and s p r i n g . T h i s 136 s t u d y i n d i c a t e s t h a t t h e y a r e s i g n i f i c a n t l y more p r o d u c t i v e t h a n t h e o t h e r s p e c i e s . But i t i s a l s o known t h a t c oho and s p r i n g s p a w n i n g s t o c k s a r e g e n e r a l l y t h e most d i f f i c u l t t o e n u m e r a t e . B e s i d e s , t h e e x p l o i t a t i o n p a t t e r n o f t h e s e two s p e c i e s ( m o s t l y by t r o l l i n g i n a r e a s where many s t o c k s mix) r e n d e r s t h e c a t c h a l l o c a t i o n p r o c e d u r e s more p r o n e t o e r r o r . C o n s e q u e n t l y t h e e s t i m a t e d V p a r a m e t e r s ( R i c k e r model) f o r c o h o and s p r i n g s t o c k s a r e most l i k e l y t o be b i a s e d upward. F u r t h e r m o r e , i t i s q u i t e p o s s i b l e t h a t n a t u r a l p r o d u c t i o n o f t h e s e s p e c i e s has d e c l i n e d d r a s t i c a l l y s i n c e 1960 f r o m a l l B.C. r i v e r s , w i t h t h e t r e n d b e i n g masked by more i n t e n s i v e e f f o r t s t o c o u n t e s c a p e m e n t s and by i n c r e a s e s i n t h e c a t c h e s due t o A m e r i c a n enhancement p r o d u c t i o n . Chum salmon s t o c k s show a s i g n i f i c a n t t r e n d o f d e c r e a s i n g p r o d u c t i v i t y f r o m n o r t h t o s o u t h . However, t h e p o p u l a t i o n s i z e s o f chum s t o c k s i n t h e s o u t h a r e s i g n i f i c a n t l y l a r g e r t h a n t h o s e i n t h e n o r t h . Hence a s i g n i f i c a n t n e g a t i v e c o r r e l a t i o n i s f o u n d between s t o c k s i z e and p r o d u c t i v i t y . A s i g n i f i c a n t n e g a t i v e c o r r e l a t i o n i s a l s o f o u n d between s t o c k s i z e and v a r i a b i l i t y i n chum salmon s t o c k s . T h e s e o b s e r v a t i o n s may r e p r e s e n t n a t u r a l r e l a t i o n s h i p s o r t h e y may be due t o p o o r d a t a a n d / o r a s s e s s m e n t m ethods. F o r example, chum salmon p r o d u c e d from t h e s o u t h m i g h t be c a u g h t much f u r t h e r n o r t h t h a n we have t h o u g h ; a s s e s s m e n t o f l a r g e r s t o c k s m i g h t have been g i v e n more a t t e n t i o n and e f f o r t ; and s m a l l e r s t o c k s a r e more s e n s i t i v e t o t h e m i x e d c a t c h a l l o c a t i o n p r o b l e m . In any c a s e , f u r t h e r i n v e s t i g a t i o n i s recommended. 137 REFERENCES A l l e n , K.R.1973. The i n f l u e n c e o f random f l u c t u a t i o n s i n t h e s t o c k - r e c r u i t m e n t r e l a t i o n s h i p on t h e e c o n o m i c r e t u r n from salmon f i s h e r i e s . C o n s. I n t . E x p l o r . Mer. Rapp. 164:351-359. A n d e r s o n , A.D. (ed.) 1980. G e o g r a p h i c a l W o r k i n g Group m a n a g e a b i l i t y / e n h a n c e m e n t r e p o r t . D e p t . F i s h . O c e a n s , u n p u b l i s h e d r e p o r t . Anon. 1980. 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Age c o m p o s i t i o n o f c a t c h ( f r o m B i l t o n e t . A l . ) a r e a = s t a t i s t i c a l a r e a 3/2 = 3 :. t h r e e y e a r s o l d , l e f t f r e s h w a t e r a t age 2 # = number sample d %F = p e r c e n t f e m a l e ? = no d a t a t S O C K E Y E AREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 It %F AREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 M %F 3 51 0 4 10 90 0 0 310 130 ? ? 4 70 1 606 302 0 0 50 39 572 591 3 52 0 280 190 0 0 460 40 ? ? 4 71 2 568 385 0 0 30 13 660 589 3 53 0 230 220 0 0 460 90 7 ? 4 72 16 207 724 0 2 34 16 752 621 3 54 0 350 200 0 0 400 50 ? ? 4 73 0 544 367 O 0 66 3 ? 7 3 55 0 120 150 0 o 700 20 ? 7 4 74 0 325 637 0 0 28 10 ? ? 3 56 O 270 90 0 0 500 140 ? ? 4 75 0 702 27 1 0 0 23 3 ? ? 3 57 2 135 120 0 1 704 35 996 583 4 76 O 387 602 0 0 8 3 ? ? 3 58 1 254 275 0 0 425 40 1916 544 4 77 0 441 530 0 0 27 2 ? ? 3 59 1 56 258 0 5 635 38 1264 551 4 78 3 60 2 523 101 0 0 270 85 771 378 4 79 3 61 2 515 131 1 1 301 8 1883 505 5 57 3 62 1 180 503 1 1 270 41 1759 583 5 58 3 63 1 523 109 0 1 314 51 493 507 5 59 10 289 403 0 3 234 58 1 137 517 3 64 16 127 372 0 2 460 14 1241 583 5 60 14 487 267 4 3 109 1 12 565 501 3 65 9 508 161 1 3 222 91 914 517 5 61 19 573 276 0 12 80 33 738 548 3 66 59 367 326 0 0 212 31 1413 548 5 62 40 465 272 0 15 181 24 750 498 3 67 1 432 495 0 1 46 19 2452 521 5 63 27 475 137 0 1 1 297 43 614 534 3 68 3 12 1 646 3 0 194 31 429 586 5 64 15 2 19 526 0 6 180 49 632 551 3 69 5 287 309 0 2 353 43 781 53 1 5 65 8 523 309 0 1 92 58 643 550 3 70 7 308 296 0 3 313 73 308 574 5 66 75 31 1 475 0 28 76 24 453 527 3 7 1 0 420 199 0 0 324 54 203 502 5 67 7 56 1 2 1 1 0 3 172 30 267 492 3 72 29 216 365 0 5 307 76 817 558 5 68 2 305 529 2 0 1 18 40 331 559 . 3 73 5 69 4 366 369 0 O 235 24 276 496 3 74 5 70 3 75 5 71 12 473 340 O 18 97 50 276 551 3 76 5 72 59 287 461 1 26 1 19 44 6 14 559 3 77 5 73 3 78 5 74 3 79 5 75 4 51 0 330 610 0 0 40 10 7 ? 5 76 4 52 0 660 260 0 0 30 50 ? ? 5 77 4 53 0 480 430 0 0 60 30 ? ? 5 78 4 54 0 330 540 0 0 100 20 ? ? 5 79 4 55 0 150 590 0 0 140 1 10 ? ? 6 57 4 56 0 840 140 0 0 10 10 ? ? 6 58 4 57 6 677 268 0 0 41 8 1022 488 6 59 1 233 427 0 3 236 100 361 520 4 58 2 338 630 0 1 25 3 3033 585 6 60 1 1 445 309 1 6 1 16 1 12 1002 512 4 59 1 139 654 0 1 181 24 943 587 6 61 39 487 282 0 18 96 42 729 498 4 60 4 492 373 0 1 53 74 1099 473 6 62 24 387 431 2 5 1 19 2 1 1400 543 4 61 1 783 177 0 1 23 14 2240 557 6 63 95 575 1 19 0 39 1 13 32 694 392 4 62 1 319 630 1 0 33 14 1931 610 6 64 5 187 601 0 7 144 42 538 598 4 63 3 619 252 0 1 102 20 1794 488 6 65 30 5 18 269 5 17 109 30 658 517 4 64 1 225 706 0 0 54 1 1 3324 602 6 66 130 385 395 3 16 50 1 1 602 462 4 65 0 432 487 1 0 47 32 853 588 6 67 17 504 394 0 2 42 13 228 428 4 66 8 449 456 0 1 62 24 2258 547 6 68 8 240 550 0 7 131 43 405 564 4 67 0 442 510 0 0 19 28 1499 522 6 69 48 290 428 0 0 205 19 240 537 4 68 1 1 1 1 829 0 0 34 25 677 654 6 70 96 356 127 0 19 144 23 1 104 47 1 4 69 2 484 424 0 0 64 25 914 557 6 7 1 0 627 240 0 0 120 13 75 560 RE A YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 ¥ %F 6 72 37 35 1 385 4 17 129 50 757 574 6 73 6 74 6 75 6 76 6 77 6 78 6 79 7 57 7 58 7 59 7 60 21 596 84 2 19 232 : 45 507 522 7 6 1 99 643 121 0 76 55 3 378 446 7 62 19 563 248 0 4 144 14 863 534 7 63 27 793 30 0 18 132 0 535 545 7 64 25 446 242 0 28 247 12 611 537 7 65 28 572 201 0 4 145 40 254 568 7 66 1 802 146 0 0 39 4 868 533 7 67 15 7 14 97 0 21 134 8 795 530 7 68 8 390 312 0 27 2 14 6 409 551 7 69 55 295 308 0 0 342 0 57 561 7 70 62 547 13 1 1 1 24 81 1 19 434 449 7 7 1 7 72 7 73 7 74 7 75 7 76 7 77 7 78 7 79 8 57 8 58 8 59 9 537 262 0 1 164 20 496 597 8 60 16 704 167 2 1 93 1 1 1528 538 8 61 13 64 1 147 0 6 183 2 606 521 8 62 33 631 187 1 8 129 2 1787 583 8 63 2 1 755 97 0 5 107 " 1 965 560 8 64 12 391 4 13 0 4 150 17 1865 612 8 65 182 588 76 3 8 106 6 743 466 8 66 7 649 244 0 1 75 3 1117 578 8 67 7 722 59 0 4 179 8 2147 552 8 68 1 1 231 564 0 8 149 10 756 640 8 69 0 465 143 0 0 32 1 0 28 607 8 70 130 572 1 15 2 17 7 1 26 469 559 8 7 1 O 794 87 0 0 106 0 277 563 8 72 8 73 iREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 H %F 8 74 8 75 8 76 8 77 8 78 8 79 9 51 0 380 600 0 0 10 10 ? ? 9 52 0 410 580 0 0 10 6 ? ? 9 53 0 730 260 0 0 10 0 ? ? 9 54. 0 600 390 0 0 10 0 ? ? 9 55 0 450 540 0 0 0 10 762 ? 9 56 0 100 900 0 0 0 0 ? 7 9 57 i 645 336 3 0 9 4 1000 455 9 58 2 280 701 1 0 10 2 1545 472 9 59 2 187 764 4 0 28 12 1289 524 9 60 2 38 1 552 3 0 20 40 2079 525 9 61 1 • 486 460 . 0 1 30 20 1299 545 9 62 3 904 55 1 1 27 4 1657 428 9 63 2 37 1 581 0 1 22 18 1636 514 9 64 1 127 776 1 0 16 74 1678 593 9 65 8 690 250 2 0 21 5 836 483 9 66 1 336 637 0 1 17 3 1 182 560 9 67 1 782 14 1 0 1 57 8 2777 368 9 68 1 69 894 1 1 5 26 1282 639 9 69 1 350 592 JO 1 17 20 1070 460 9 70 6 425 433 9 0 40 40 223 646 9 71 1 753 159 0 1 65 1 1 427 492 9 72 0 442 474 0 0 18 37 283 392 9 73 O 82 916 0 0 0 0 827 7 9 74 0 42 1 567 12 0 0 0 323 ? 9 75 11 735 250 4 • 0 0 0 616 ? 9 76 9 77 9 78 9 79 10 51 0 220 770 0 • 0 0 0 ? ? 10 52 0 80 910 0 0 0 0 ? ? 10 53 0 890 100 0 0 0 10 7 ? 10 54 10 6 10 380 0 0 0 0 7 ? 10 55 0 420 580 0 0 0 0 7 ? 10 56 0 40 960 0 0 0 O 7 ? 10 57 0 584 410 1 0 2 3 661 478 10 58 0 257 724 0 0 19 0 3 10 577 10 59 1 159 782 1 1 37 9 593 47 1 10 60 1 226 7 12 2 0 20 35 2038 535 10 61 0 446 514 1 0 26 9 1287 546 10 62 1 859 65 0 0 65 6 1332 436 10 63 0 314 653 0 0 23 6 705 525 VREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 H %F 10 64 0 135 773 0 4 34 36 819 539 10 65 0 646 296 4 0 4 1 2 1 124 460 10 66 0 56 920 0 0 6 6 177 594 10 67 0 708 178 0 0 58 13 1 165 330 10 68 1 18 1 783 0 0 6 2 777 572 10 69 0 2 1 1 767 1 1 0 0 0 97 515 10 70 • 12 290 575 0 4 23 62 304 566 10 7 1 0 604 370 2 0 16 0 205 55 1 10 72 10 73 10 74 10 75 10 76 10 77 10 78 10 79 12 57 12 58 1 976 10 0 0 13 0 1082 544 12 59 5 869 66 1 1 53 5 1214 58 1 12 60 5 892 75 1 1 22 4 2227 547 12 61 27 848 97 0 2 21 1 1783 519 12 62 9 847 74 0 6 62 2 1 120 524 12 63 6 843 84 0 1 59 5 1522 551 12 64 9 336 512 0 1 1 12 19 1637 571 12 65 56 775 97 0 5 59 1 953 480 12 66 31 901 49 0 1 12 2 1766 524 12 67 1 917 34 0 1 42 1 4151 550 12 68 8 543 325 0 0 106 16 4 16 600 12 69 16 792 146 0 0 42 2 1324 493 12 70 18 899 59 0 1 19 1 822 490 12 •11 4 892 67 0 0 32 0 846 . 510 12 72 1 814 120 0 0 53 1 1 290 559 13 57 13 58 6 974 1 1 0 0 7 0 920 578 13 59 9 843 84 0 1 59 4 657 549 13 60 3 950 31 0 2 13 1 867 494 13 6 1 55 877 55 1 3 6 2 1650 477 13 62 0 978 0 0 15 7 0 107 701 13 63 22 908 19 0 1 47 0 329 545 13 64 44 783 90 0 5 66 10 304 591 13 65 226 676 75 0 4 19 0 332 480 13 66 13 67 3 945 20 0 1 28 0 817 602 13 68 0 845 99 0 0 53 2 129 527 13 69 39 792 1 1 1 0 0 32 26 307 54 1 13 70 0 974 0 0 0 0 0 38 737 13 7 1 1 933 45 0 0 21 0 527 512 13 72 0 798 174 0 0 2 1 0 128 500 AREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 H %F 16 57 16 58 16 59 16 60 16 61 23 920 33 0 2 2 1 O 274 550 16 62 6 927 4 1 0 0 26 0 227 620 16 63 O 919 23 0 12 46 0 86 558 16 64 0 845 95 0 0 60 0 84 464 16 65 16 66 16 67 16 68 16 69 16 70 16 7 1 16 72 0 780 147 0 0 73 0 4 1 527 20 57 20 58 20 59 20 60 20 61 20 62 20 63 29 '836 16 0 0 1 10 0 1 15 606 20 64 20 65 126 748 43 0 7 63 2 806 477 20 66 19 924 25 0 1 22 5 562 517 20 67 2 956 22 0 1 16 1 1878 562 20 68 6 922 40 0 0 31 0 402 592 20 69 21 815 103 0 1 33 19 602 535 20 70 15 941 15 0 0 27 1 453 556 20 71 3 923 37 0 0 3 1 0 804 474 20 72 7 921 22 0 1 20 17 635 527 23 57 23 58 23 59 23 60 0 738 1 18 0 0 134 10 660 515 23 61 0 810 147 0 3 17 21 467 528 23 62 0 748 135 0 0 1 1 1 3 1 154 506 23 63 0 743 101 0 0 143 10 219 508 23 64 ' 0 621 150 0 0 136 7 678 469 23 65 23 66 23 67 0 635 122 0 0 156 70 1 15 391 23 68 23 69 0 761 159 0 0 80 0 1 13 487 23 70 0 408 487 0 0 65 26 76 447 23 71 0 741 153 10 ! 0 87 9 104 4 13 23 72 0 749 87 0 0 156 6 241 512 AREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 H %F 23 73 23 74 23 75 23 76 23 77 23 78 23 79 24 57 24 58 24 59 24 60 0 633 354 0 0 1 1 2 315 474 24 61 46 681 22 1 0 5 16 1 331 507 24 62 0 953 26 0 0 21 0 568 450 24 63 24 64 5 579 386 0 0 30 0 424 513 24 65 24 66 24 67 0 795 190 0 0 10 0 283 473 24 68 0 394 578 0 0 18 8 187 532 24 69 1 442 512 1 1 40 3 155 506 24 70 24 7 1 24 72 27 57 27 58 27 59 27 60 27 6 1 27 62 27 63 27 64 27 65 27 66 27 67 0 738 1 15 3 0 1 19 10 466 352 27 68 0 46 8 14 0 0 46 »94 43 488 27 69 0 815 148 0 o 37 0 27 370 27 70 27 7 1 0 812 1 28 0 0 50 O 179 475 27 72 29 57 29 58 29 59 29 60 29 61 29 62 1 938 27 0 1 30 1 2412 527 29 63 2 932 4 0 5 53 2 1627 518 29 64 9 828 101 0 1 47 1 1 1868 499 29 65 5 91 1 42 0 0 39 2 2562 539 AREA YEAR 3/2 4/2 5/2 6/2 4/3 5/3 6/3 H %F 29 66 13 880 75 0 0 28 2 1772 51 1 29 67 3 956 28 0 1 9 1 3223 560 29 68 1 878 57 0 4 54 0 914 517 29 69 1 877 82 0 0 36 4 1 163 538 29 70 6 944 18 0 1 2 1 1 684 542 29 71 1 934 4 1 0 16 3 0 1207 526 29 72 0 874 7 1 0 0 46 2 677 558 29 73 29 74 29 75 29 76 29 77 29 78 29 79 CHUM YEAR 2/1 3/1 4/1 5/1 6/1 H %F AREA YEAR 2/1 3/1 4/1 5/1 6/1 t> %F 3 57 0 108 776 1 16 0 1 176 458 5 59 0 329 528 143 0 333 400 3 58 0 125 734 141 0 1627 4 18 5 60 0 602 392 6 0 353 510 3 59 0 169 622 209 0 805 468 5 61 0 1 13 864 23 0 773 521 3 60 0 183 803 14 0 1237 482 5 62 2 256 596 146 O 975 506 3 6 1 0 45 917 38 0 1665 52 1 5 63 0 482 484 32 2 701 465 3 62 0 377 33 1 292 0 1 1 16 405 5 64 0 209 772 19 0 1233 531 3 63 0 215 768 14 3 373 495 5 65 0 142 795 63 0 123 543 3 64 0 56 917 27 0 923 518 5 66 0 SO 900 20 0 582 555 3 65 1 68 723 208 0 286 242 5 67 0 308 549 143 0 91 4 18 3 66 0 58 893 49 0 190 511 5 68 0 31 950 19 0 4 12 5 16 3 67 0 219 580 201 0 767 575 5 69 0 130 217 653 0 23 521 3 68 0 18 909 68 5 512 585 5 70 0 58 922 13 0 126 476 3 69 0 150 559 291 0 264 466 5 71 0 392 469 139 0 66 469 3 70 0 28 96 1 1 1 0 199 472 5 72 0 28 900 72 0 37 1 483 3 7 1 0 173 433 394 0 84 464 5 73 3 72 0 17 945 36 2 58 1 520 5 74 3 73 5 75 3 74 5 76 3 75 5 , 77 3 76 5 78 3 77 5 79 3 78 6 57 3 79 6 58 0 28 944 28 0 201 447 4 57 0 39 926 35 0 744 353 6 59 0 554 246 200 0 235 527 4 58 0 68 829 103 0 1000 399 6 60 0 640 355 4 1 1275 482 4 59 6 61 0 328 657 14 1 795 574 4 60 0 186 79 1 23 0 355 456 6 62 0 226 745 29 0 2612 480 4 61 0 89 873 38 0 1230 433 6 63 0 658 31 1 31 O 967 508 4 62 0 274 510 2 16 0 1 123 434 6 64 0 189 801 10 0 544 540 4 63 0 286 690 24 0 825 413 6 65 0 127 792 81 0 322 443 4 64 0 95 852 53 0 379 373 6 66 0 105 866 29 0 1236 603 4 65 0 0 1000 0 0 8 625 6 67 o 250 510 240 0 150 324 4 66 o 20 980 0 0 50 680 6 68 0 2 1 975 4 ,0 587 590 4 67 0 285 402 313 0 133 505 6 69 0 235 550 215 0 149 3 16 4 68 0 17 952 25 6 262 44 1 6 70 0 61 '937 2 0 843 47 1 4 69 0 264 491 245 0 130 308 6 7 1 4 70 0 0 867 133 0 14 643 6 72 0 73 902 23 2 958 5 15 4 7 1 0 153 553 294 0 36 500 6 73 4 72 0 9 935 56 0 622 485 6 74 4 73 6 75 4 74 0 0 809 191 0 .? ? 6 76 4 75 0 0 875 125 0 ? ? 6 77 4 76 0 0 1000 0 0 ? ? 6 78 4 77 0 0 929 7 1 0 ? 7 6 79 4 78 . 7 57 4 79 7 58 0 9 1 884 25 0 1768 493 5 57 0 177 734 89 0 192 364 7 59 0 349 524 127 0 394 460 5 58 0 54 907 39 0 301 5 14 7 60 0 598 391 1 1 0 3376 498 CP ro i i YEAR 2/1 3/1 4/1 5/1 6/1 H %F 7 61 0 533 456 1 1 0 17 15 467 7 62 0 398 592 10 0 1008 48 1 7 63 0 546 434 20 0 1 164 501 7 64 0 97 875 28 0 1655 535 7 65 0 257 637 106 0 496 488 7 66 o 15 1 837 12 0 1428 52 1 7 67 0 343 523 134 0 895 458 7 68 1 172 814 12 1 753 48 1 7 69 0 599 347 49 5 330 400 7 70 0 1 17 883 0 0 707 554 7 7 1 7 72 0 204 740 56 0 303 514 7 73 7 74 7 75 7 76 7 77 7 78 7 79 8 57 8 58 0 101 856 43 0 2695 488 8 59 0 269 67 1 60 0 492 570 8 60 0 585 405 10 0 3817 489 8 6 1 2 366 6 15 17 0 1395 454 8 62 0 484 493 23 0 2838 46 1 8 63 1 480 506 13 0 1959 489 8 64 1 34 94 1 24 0 2021 477 8 65 0 142 544 314 0 392 46 1 3 66 0 184 802 14 0 2670 509 8 67 0 304 533 162 1 1252 464 8 68 0 36 939 25 0 1 102 501 8 69 0 69 1 229 80 0 304 326 8 70 0 52 948 0 0 458 443 8 7 1 0 160 753 87 0 243 280 3 72 0 0 1000 0 0 49 449 8 73 8 74 8 75 8 76 8 77 8 78 8 79 9 57 9 58 0 1 14 869 17 0 34 1 443 9 59 9 60 0 745 249 6 0 1099 572 9 61 0 320 659 21 0 739 478 9 62 0 257 723 20 0 531 397 iRE A YEAR 2/1 3/1 4/1 5/1 6/1 H %F 9 63 0 586 399 15 0 619 53 1 9 64 0 58 920 22 0 9 1 381 9 65 • 0 185 720 95 0 2 12 4 15 9 66 0 163 8 15 22 0 497 504 9 67 0 375 459 166 0 800 532 9 68 O 34 956 9 1 532 468 9 69 0 772 137 90 1 556 343 9 70 0 83 915 2 0 329 486 9 7 1 9 72 9 73 9 74 9 75 9 76 9 77 9 78 9 79 10 57 10 58 10 59 0 398 530 72 0 194 456 10 60 0 7 13 275 12 0 812 ' 536 10 61 0 433 560 7 0 149 552 10 62 0 161 8 16 23 0 270 466 10 63 0 693 297 10 0 178 535 10 64 0 142 850 8 O 278 520 10 65 0 137 645 218 0 209 345 10 66 0 190 760 50 0 79 316 10 67 0 395 546 59 0 1283 517 10 68 0 62 931 5 2 445 499 10 69 0 303 5 18 179 0 75 253 10 70 0 175 825 0 0 163 528 10 7 1 10 72 10 73 10 74 10 75 10 76 10 77 10 78 10 79 12 57 12 58 0 8 1 907 12 0 549 425 12 59 0 3 17 660 23 0 1230 487 12 60 0 4 16 57 1 12 1 2602 488 12 61 1 100 88 1 .18 0 1790 554 12 62 0 6 17 355 28 0 766 51 1 12 63 0 386 606 8 0 18 12 547 12 64 1 133 854 12 o 2014 538 AREA YEAR 2/1 3/1 4/1 5/1 6/1 tt 12 65 3 84 839 74 0 519 12 66 1 261 686 52 0 637 12 67 0 384 533 83 0 1226 12 68 0 155 837 7 1 4 13 12 69 1 385 558 56 0 1678 12 70 0 50 942 8 0 709 12 71 0 326 545 129 0 322 12 72 0 78 895 27 0 842 12 73 12 74 12 75 12 76 12 77 12 78 1 2 79 13 57 13 58 o 428 57 1 1 0 322 13 59 0 355 627 18 0 124 1 13 60 0 4 17 576 7 0 1626 13 6 1 0 125 842 33 0 1 120 13 62 0 833 142 25 0 51 1 13 63 0 347 652 1 0 748 13 64 0 125 750 125 0 1 10 13 65 0 191 68 1 128 0 47 13 66 13 67 0 594 384 22 0 471 13 68 0 228 769 3 0 425 13 69 0 450 503 47 0 577 1 3 70 0 70 925 5 o 362 1 3 7 1 0 382 383 235 0 1 15 13 72 0 64 922 1 1 3 651 1 3 73 13 74 13 75 13 76 13 77 13 78 13 79 14 57 14 58 14 59 14 60 0 429 564 7 0 227 1 4 6 1 0 92 903 5 0 1 10 14 62 0 767 206 27 0 2 19 14 63 14 64 14 65 14 66 AREA 426 14 470 14 398 14 523 14 423 14 479 14 435 16 568 16 16 16 . 16 16 16 16 16 16 42 1 16 506 16 464 16 552 16 394 16 554 16 386 18 553 18 18 435 18 533 18 478 18 497 18 330 18 534 18 18 18 18 18 18 18 18 20 20 20 427 20 752 20 429 20 20 20 20 20 YEAR 2/1 3/1 4/1 5/1 6/1 %F 67 68 69 70 71 72 57 58 59 0 345 645 10 0 474 553 60 0 460 539 1 0 279 420 61 0 176 820 4 0 274 547 62 0 788 184 28 0 261 487 63 64 65 66 67 68 69 70 7 1 72 57 58 59 60 0 596 388 16 0 3 1 2 526 61 0 235 763 2 0 455 533 62 0 846 148 6 0 182 5 16 63 0 281 7 19 0 0 423 643 64 0 652 348 0 0 89 7 19 65 66 67 68 69 70 71 72 0 40 960 0 0 101 545 57 \ 58 2 7 16 264 18 0 352 465 59 4 297 695 4 0 828 487 60 0 674 320 6 0 958 494 61 0 266 725 9 0 390 539 62 0 840 148 12 0 44 1 536 63 2 490 503 5 0 515 542 64 2 7 16 272 1 0 1392 524 65 0 1 14 882 4 0 735 488 66 2 45 1 500 47 0 753 457 I'" AREA YEAR 2/1 3/1 4/1 5/1 6/1 H %F AREA YEAR 2/1 3/1 4/1 5/1 6/1 20 67 0 598 389 13 0 1 156 494 23 67 20 68 1 186 800 13 0 574 500 23 68 20 69 1 167 802 3 0 613 506 23 69 0 160 840 0 0 7 ? 20 70 0 262 724 14 0 398 487 23 70 0 392 584 24 0 209 ? 20 71 0 508 447 45 0 87 368 23 7 1 0 301 676 23 0 216 ? 20 72 0 20 973 7 0 422 637 23 72 0 102 866 32 0 385 ? 20 73 23 73 0 149 770 81 0 87 ? 20 74 23 74 20 75 23 75 0 222 754 25 0 394 7 20 76 23 76 0 54 901 45 0 ? ? 20 77 23 77 0 450 500 50 0 478 7 20 78 23 78 0 200 777 3 0 ? ? 20 79 23 79 20 80 23 80 22 57 24 57 22 58 24 58 22 59 24 59 22 60 0 424 575 1 0 44 1 464 24 60 0 407 585 8 0 232 394 22 61 24 61 0 423 554 23 0 267 506 22 62 24 62 22 63 24 63 0 504 496 0 0 224 371 22 64 24 ' 64 22 65 24 65 22 66 24 66 22 67 • 24 67 22 68 24 68 22 69 24 69 0 400 600 0 0 7 ? 22 70 24 70 22 7 1 0 957 14 29 0 70 ? 24 7 1 0 437 523 40 0 197 ? 22 72 0 16 984 0 0 540 525 24 72 22 73 0 9 523 468 0 643 ? 24 73 22 74 0 394 129 477 0 155 ? 24 74 0 176 583 221 0 240 7 22 75 24 75 0 399 593 8 0 391 7 22 76 0 206 765 29 0 7 ? 24 76 0 138 846 14 0 282 7 22 77 0 84 897 19 0 107 7 24 77 0 430 500 7 0 634 ? 22 78 0 300 600 100 0 ? ? 24 78 22 79 24 79 22 80 24 80 23 57 25 57 23 58 25 58 23 59 0 4 14 564 22 0 276 436 25 59 0 598 396 6 0 394 353 23 60 0 467 520 13 0 566 472 25 60 0 800 200 0 0 4 1 1 513 23 6 1 0 518 459 17 0 446 501 25 61 0 259 730 10 0 1 189 500 23 62 0 575 417 4 0 273 538 25 62 0 430 554 12 0 905 537 23 63 25 63 0 7 1 1 278 1 1 0 270 44 1 23 64 25 64 0 327 673 0 0 6 17 584 23 65 25 65 23 66 25 66 25 25 25 25 25 25 25 25 25 25 25 25 25 25 2G 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 27 67 68 69 70 7 1 72 73 74 75 76 77 78 79 80 57 58 59 26. 60 26 61 62 63 64 65 66 67 68 69 70 7 1 72 73 74 75 76 77 78 79 80 57 58 59 60 61 62 63 64 65 66 2/1 3/1 4/1 5/1 6/1 %F 0 583 4 17 0 0 ? ? 0 319 68 1 0 0 91 7 0 349 580 71 0 612 ? 0 94 885 21 0 192 7 0 143 675 181 0 154 7 0 261 595 144 0 383 7 0 137 806 57 0 124 7 0 266 649 35 0 ? 7 0 561 413 26 0 726 7 0 569 408 21 0 363 493 0 634 359 7 0 472 424 0 142 848 10 0 906 558 0 504 482 1 1 0 759 526 0 469 520 1 1 0 179 447 0 o 0 165 90 644 833 20 0 102 ? 694 141 0 ? ? 840 64 0 7 ? 339 17 0 492 ? 917 83 305 450 AREA YEAR 2/1 3/1 4/1 5/1 6/1 %F 27 67 27 68 27 69 27 70 27 71 27 72 27 73 0 66 778 156 0 486 7 27 74 27 75 27 76 27 77 0 61 1 377 12 O 424 7 27 78 27 79 27 80 . 29 57 0 259 697 '44 0 329 427 29 58 0 571 424 .5 0 452 446 29 59 0 408 587 5 0 1576 48 1 29 60 0 346 643 1 1 0 1660 427 29 61 0 75 907 18 0 14 17 600 29 . 62 0 772 206 22 0 1 15 - 7 454 29 63 0 289 707 4 0 745 547 29 64 0 147 832 21 0 954 487 29 65 O 2 1 970 9 0 168 452 29 66 0 70 908 22 0 231 515 29 67 0 549 423 28 0 733 523 29 68 0 203 791 6 0 790 495 29 6 1 O 375 601 24 0 525 368 29 70 0 90 906 4 o 332 494 29 7 1 29 72 0 2 1 976 3 0 32 1 574 29 73 29 74 29 75 29 76 29 77 29 78 29 79 29 80 CD 157 Age c o m p o s i t i o n of escapement ( f r o m d i s t r i c t management b i o l o g i s t s ) S O C K E Y E RE A YEAR 3 / 2 4 / 2 5 / 2 6 / 2 4 / 3 5 / 3 6 / 3 * %F 3 6 4 0 4 8 1 2 0 0 0 8 1 0 1 1 ? ? 3 6 5 0 5 9 1 1 5 0 0 3 1 1 4 6 7 ? 3 6 6 0 6 4 2 4 7 0 0 6 6 4 1 5 7 ? 3 6 7 0 5 9 4 1 0 2 0 0 2 3 3 5 5 ? ? 3 6 8 0 1 1 9 1 7 2 0 0 5 5 5 2 2 7 ? 3 6 9 0 4 6 4 9 6 0 0 3 6 6 5 5 7 ? 3 7 0 0 2 3 7 1 2 2 0 0 5 8 0 4 8 1 2 3 9 7 3 7 1 0 3 0 1 1 0 5 0 0 5 5 1 2 8 2 0 2 2 6 0 5 3 7 2 0 1 8 3 1 5 8 0 0 4 6 3 1 5 4 9 9 9 5 3 0 3 7 3 0 4 2 7 6 6 0 0 4 6 1 2 6 2 3 3 0 5 4 8 3 7 4 0 7 3 3 17 0 0 4 8 4 1 2 5 1 5 6 6 4 7 1 3 7 5 0 2 2 2 7 7 0 0 6 3 1 4 6 9 9 0 5 12 3 7 6 0 2 5 1 ' 9 0 O 0 5 9 2 3 7 1 2 9 0 5 4 1 3 7 7 O 2 8 6 1 9 4 0 0 4 4 8 4 6 2 0 9 3 5 3 1 3 7 8 0 7 4 2 2 4 0 0 5 7 8 1 19 ? ? 3 7 9 0 2 3 6 6 2 0 0 6 1 8 3 6 1 3 12 5 8 3 3 8 0 0 1 5 7 6 2 0 0 6 3 8 4 8 9 1 5 ? 4 5 7 * 4 5 8 * 4 5 9 * 4 6 0 * 4 6 1 • 4 6 2 4 6 3 * 4 6 4 0 2 9 4 6 5 5 1 0 4 1 8 1 3 8 6 4 8 0 4 6 5 0 5 9 3 3 12 0 0 4 9 4 6 1 0 5 9 5 2 0 4 6 6 0 4 6 9 4 0 6 0 0 7 4 5 0 1 1 1 4 4 9 0 4 6 7 0 6 3 9 3 1 3 0 0 2 5 2 2 1 6 3 1 4 4 6 4 6 8 • 0 1 4 2 8 0 8 0 0 2 3 2 7 1 0 8 4 5 3 6 4 6 9 3 5 5 9 5 3 3 8 0 1 2 0 1 0 1 4 5 5 4 7 8 4 7 0 0 6 3 4 3 0 1 0 0 3 3 13 ? ? 4 7 1 0 5 6 1 3 7 9 0 0 2 6 3 7 ? ? 4 7 2 0 2 9 5 6 7 5 0 0 9 2 0 ? ? 4 7 3 0 4 8 1 5 0 2 0 0 1 1 7 7 7 4 7 4 0 4 0 7 5 7 8 0 0 8 7 ? ? 4 7 5 0 7 6 0 2 2 6 0 0 1 1 3 ? ? 4 7 6 0 4 17 5 5 5 0 0 1 5 1 3 7 7 4 7 7 0 4 7 0 5 0 3 0 0 2 4 3 ? ? 4 7 8 0 2 2 8 7 2 3 0 0 15 3 2 ? 7 4 7 9 0 7 9 2 135 0 0 5 3 1 9 1 1 0 6 ? 4 8 0 o 2 18 7 2 7 0 0 14 4 1 1 3 4 6 7 9 6 9 2 6 5 9 0 3 7 2 12 0 0 0 2 9 4 ? 9 7 0 6 6 3 13 5 3 6 8 5 0 0 0 8 1 6 ? 9 7 t 0 6 6 2 3 2 6 12 0 0 0 3 5 1 ? 9 7 2 6 1 6 8 0 2 2 2 3 7 0 O 0 5 5 0 7 9 7 3 0 8 2 9 1 7 0 0 0 0 8 2 7 ? 9 7 4 2 1 2 5 0 7 2 1 1 0 0 O 4 6 9 ? 9 7 5 0 5 6 4 4 3 2 0 0 0 0 2 12 1 7 9 7 6 0 5 8 0 4 2 0 0 0 0 0 ? ? 9 7 7 0 4 0 0 6 0 0 0 0 0 0 ? 7 9 7 8 0 G O 9 4 0 0 0 0 O ? 7 9 7 9 0 6 4 0 3 6 0 0 0 0 0 ? ? iRE A YEAR 3 / 2 4 / 2 5 / 2 6 / 2 4 / 3 5 / 3 6 / 3 H %l 1 2 5 8 O 9 5 2 4 8 0 0 0 o ? ? 1 2 5 9 0 8 9 5 1 0 0 5 0 0 o ? ? 1 2 6 0 O 7 8 3 2 1 7 0 0 0 0 ? ? 1 2 6 1 O 8 8 0 1 1 9 1 0 0 0 ? ? 12 6 2 O 7 8 5 2 1 0 5 0 0 0 ? ? 1 2 6 3 O 7 1 3 2 7 4 1 3 0 0 o ? ? 12 6 4 0 7 4 1 2 3 7 2 2 0 0 0 ? 7 12 6 5 1 2 8 0 8 1 7 7 3 0 0 0 ? ? 12 6 6 5 8 6 1 1 3 1 3 0 0 0 ? ? 1 2 6 7 2 8 3 4 1 6 2 2 0 0 0 ? 7 1 2 6 8 O 8 3 8 7 1 4 6 0 0 0 ? ? 1 2 6 9 1 1 7 9 5 1 9 3 1 0 0 0 ? ? 1 2 7 0 4 4 7 2 1 2 3 3 2 0 0 0 7 ? 12 7 1 4 8 9 8 9 8 0 0 0 0 7 ? 1 2 7 2 O 6 6 0 3 3 5 5 0 0 0 ? ? 1 2 7 3 O 5 0 0 4 7 9 2 1 0 o o ? ? 1 2 7 4 O 4 2 8 5 7 1 . 1 0 0 0 ? ? 1 2 7 5 0 3 1 9 6 6 7 1 4 o 0 0 ? ? 00 CHUM AREA YEAR 2/1 3/1 4/1 5/1 6/1 » %\ 2 6 1 0 330 680 20 0 748 ? 2 64 O 2 20 780 0 0 1449 7 2 65 0 50 920 30 0 233 ? 2 7 1 0 90 870 40 • 0 1200 ? 2 72 0 160 750 80 10 1079 7 2 73 O 100 750 150 0 465 7 2 74 0 1 10 750 140 0 1302 ? 2 75 0 220 740 40 0 685 7 2 76 0 0 940 60 0 53 ? 2 79 0 563 332 105 0 325 ? 2 80 O 535 465 0 0 86 ? 4 74 0 0 809 19 1 0 ? ? 4 75 0 O 875 125 0 ? ? 4 76 0 0 1000 0 0 ? ? 4 77 0 0 929 71 0 ? ? 4 78 0 13 827 160 0 75 ? 4 79 0 527 404 69 0 146 ? 4 80 0 7 965 28 0 142 ? 29 60 0 27 1 629 0 0 529 ? 29 6 1 0 1 10 884 6 0 1 167 ? 29 62 0 766 227 7 0 972 ? 29 63 0 359 639 2 0 999 ? 29 64 o 236 758 6 0 1892 ? 29 65 0 3 17 660 23 0 1245 ? 29 66 0 1 12 876 12 0 1 183 ? 29 67 0 565 408 27 0 2 175 ? 29 68 0 160 837 3 0 1975 ? 29 69 0 405 573 22 0 2309 7 29 70 0 78 9 15 7 0 ? ? 29 7 1 0 354 545 101 0 ? ? 29 72 0 35 936 29 • 0 ? ? 29 73 0 33 804 163 0 ? ? 29 74 0 192 568 240 0 ? 7 29 75 0 537 444 19 0 ? 7 29 76 0 172 823 5 0 7 ? 29 77 0 237 742 2 1 0 ? ? 29 78 0 132 85 1 17 0 ? ? 29 79 0 258 606 136 0 7 7 O l CO 1 6 0 A p p e n d i x l b . A v e r a g e age c o m p o s i t i o n of c a t c h and escapement (age a t m a t u r i t y ) a r e a = " p r o d u c t i o n a r e a " ( s e e t a b l e 1) SOCKEYE AREA YEAR 4 5 6 3 . 51 . 0 . 4 10 0 . 400 0 . 130 3 . 52 . 0 . 280 0 . 650 0 .040 3 . 53 . 0 . 230 0 . 680 0 .090 3 . 54 . 0 . 350 0 . 600 0 .050 3 . 55 . 0 . 120 0 . 850 0 .020 3 . 56 . 0 . 270 0 . 590 0 . 140 3 . 57 . 0 . 136 0 .824 0 .035 3 . 58 . 0 . 254 O . 700 0 .040 3 . 59 . 0 .06 1 O . 893 0 .038 3 . 60. o . 523 0 . 37 1 0 .085 3 . 6 1 . o .5 16 o .432 0 . 009 3 . 62 . 0 . 18 1 0 . 773 0 .042 3 . 63 . o . 524 o .423 0 . 05 1 3 . 64 . o . 129 0 . 832 0 .014 3 . 65 . 0 .511 0 . 383 0 .092 3 . 66 . 0 . 367 0 . 538 0 .03 1 3 . 67 . 0 . 433 0. . 54 1 0 .019 3 . 68 . 0 .12 1 o . 840 o . 034 3 . 69 . 0. . 289 0. . 662 0 .04 3 3 . 70. 0. 311 0. 609 0 073 3 . 7 1 . 0. 420 0. 523 0 .054 3 . 72 . 0. 22 1 o. 672 o . 076 3 .- 73 . 0. 427 0. 527 0. 026 3 . 74 . 0. 073 0. 801 0. 125 3 . 75 . 0. 222 0. 708 0. 046 3 . 76 . 0. 25 1 o. 682 0. 037 3 . 77 . o. 286 o. 642 o. 046 3 . 78 . 0. 074 0. 802 0. 1 19 3 . 79 . 0. 236 o. 680 0. 036 4 . 5 1 . 0. 330 0. 650 0. 0 10 4 . 52 . 0. 660 0. 290 0. O50 4 . 53 . 0. 480 0. 490 0. 030 4 . 54 . 0. 330 0. 640 0. 020 4 . 55 . 0. 150 0. 730 0. 1 10 4 . 56 . 0. 840 0. 150 0. 010 4 . 57 . 0. 677 0. 309 0. 008 4 . 58 . 0. 339 0. 655 0. 003 4 . 59 . 0. 140 0. 835 0. 024 4 . 60. o. 493 0. 426 0. 074 4 . 6 1 . 0. 784 0. 200 0. 014 4 . 62 . 0. 3 19 0. 663 0. 015 4 . 63 . 0. 620 0. 354 0. 020 4 . 64 . 0. 225 0. 760 0. 01 1 4 . 65 . 0. 432 0. 534 0. 033 4 . 66 . 0. 450 0. 5 18 0. 024 4 . 67 . o. 442 o. 529 0. 028 4 . 68 . 0. 1 1 1 0. 863 0. 025 4 . 69 . 0. 484 0. 488 0. 025 4 . 70. o. 606 0. 352 0. 039 4 . 7 1 . 0. 568 0. 4 15 0. 013 4 . 72 . o. 209 o. 758 0. 016 4 . 73 . 0. 544 0. 433 0. 003 AREA YEAR 4 5 6 4 . 74 . 0 . 325 0 665 0 .010 4 . 75 . 0 . 702 0 . 294 0 .003 4 . 76 . 0 . 387 0 . 6 10 0 . 003 4 . 77 . 0 . 44 1 0 . 557 0 .002 4 . 78 . 0 . 228 0 .738 0 .032 4 . 79 . 0 . 792 0 . 188 0 .019 5 . 57 . 5 . 58 . 5 . 59 . 0 . 343 0 . 589 0 .056 5 . 60. 0 . 588 0 . 332 0 .062 5 . 6 1 . 0 . 597 0 . 328 0 .02 3 5 . 62 . 0 . 529 0 .4 19 0 .014 5 . 63. 0 . 674 0 . 253 0 .018 5 . 64 . 0 . 349 0 .602 0 .025 5 . 65. 0 . 556 o .3 18 0 .034 5 . 66 . 0 . 598 0 . 340 0 . 009 5 . 67 . 0 . 701 0 . 26 1 0 .010 5 . 68 . 0 . 290 0 ,654 0 .022 5 . 69 . 0 . 334 0 .613 0 .019 5 . 70. 0 . 559 0 .206 0 .093 5 . 7 1 . 0 . 64 1 0 . 320 0 .024 5 . 72 . 0. . 343 0 . 544 0 .050 5 . 73. 5 . 74 . 5 . 75. 5 . 76 . 5 . 77 . 5. 78 . 5 . 79. 6 . 51 . 0. 300 0. 690 0. 005 6 . 52 : 0. 245 0. 750 0. 0 6 . 53 . 0. 810 0. 185 0. 005 6 . 54. 0. 605 0. 390 0. 0 6 . 55 . 0. 435 0. 560 Q. 005 • 6 . 56 . 0. 070 0. 930 0. 0 6. 57 . 0. 62 1 0. 372 0. O06 6. 58 . 0. 276 0. 7 16 0. 002 6 . 59. 0. 178 0. 801 0. 014 6 . 60. 0. 304 0. 651 0. 040 6 . 61 . 0. 467 0. 5 15 0. 015 6 . 62 . 0. 885 0. 103 0. 005 6 . 63 . 0. 355 0. 625 0. 014 6. 64 . 0. 13 1 0. 797 0. 062 6 . 65. 0. 665 0. 309 0. 006 6 . 66 . 0. 300 0. 689 0. 003 6 . 67 . 0. 761 0. 209 0. 009 6 . 68 . 0. 1 12 0. 857 0. 018 6 . 69. 0. 339 0. 622 0. 028 6 . 70. 0. 349 0. 545 0. 056 6 . 7 1 . 0. 705 0. 277 0. 008 6 . 72 . 0. 442 0. 492 0. 037 6 . 73 . 0. 082 0. 915 0. 0 AREA YEAR 4 5 6 6. 74 . O . 420 0 . 565 0 .012 6. 75. 0 . 734 0 . 250 0 .004 6. 76 . O . 580 0 . 420 0 .0 6. 77,. 0 . 400 0 .600 0 .0 6. 78. 0 .060 0 .940 0 .0 6. 79. O .640 0 . 360 0 .0 7 . 57 . 7 . 58 . 0 .952 0 .04 8 0 .0 7 . 59. 0 .895 0 . 100 0 .005 7 . 60. 0 . 783 0 .217 0 .000 7 . 61 . 0 .880 0 .119 0 .001 7 . 62 . 0 . 785 0 . 2 10 0 .005 7 . 63 . 0 .7 13 0 . 274 0 .013 7 . 64 . 0 . 74 1 0 . 237 0 .022 7 . 65 . 0 .808 0 . 177 0 .003 7 . 66 . 0 . 86 1 0 .13 1 0 .003 7 . 67 . 0 . 834 0 . 162 0 .002 7 . 68 . 0 .083 0. . 87 1 0. .046 7 . 69. 0. . 795 0. . 193 0. .001 7 . 70. O . 72 1 0. 233 0. 002 7 . 7 1 . 0. 898 0. 098 0. 0 7 . 72 . 0. 660 0. 335 0. 005 7 . 73 : 0. 500 0. 479 0. 02 1 7 . 74 . 0. 428 0. 57 1 0. 001 7 . 75 . 0. 319 0. 667 0. 014 7 . 76 . 7 . 77 . 7 . 78 . 7 . 79 . 8 . 57 . 8 . 58 . 8 . 59 . 8 . 60. 8 . 6 1 . 0. 922 0. 054 0. 0 8 . 62 . 0. 927 0. 067 0. 0 . 8 . 63 . 0 . 93 1 0. 069 0. 0 8 . 64 . 0. 845 0. 155 0. 0 8 . 65 . 8 . 66 . 8 . 67 . 8 . 68 . 8 . 69 . 8 . 70. 8 . 7 1 . 8 . 72 . 0. 780 0. 220 0. 0 9 . 57. 9 . 58 . 9 . 59 . 9 . 60. 9 . 61 . 9 . 62 . 0. 939 0. 057 0. 001 9 . 63 . 0. 937 0. 057 0. 002 AREA YEAR 4 5 6 AREA YEAR 4 5 6 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . 9 . ? . 9 . 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 10. 1 1 1 1 1 1 1 1 ' 1 ' 1 1 1 1 1 1 1 1 1 1 1 64 . 65 . 66 . 67 . 68 . 69 . 70. 7 1 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 57 . 58 . 59 . 60. 61 . 62 . 63 . 64 . 65. 66. 67 . 68 . 69 . 70. 7 1 . 72 . 57 . 58 . 59 . 60. 6 1 . 62 . 63 . 64 . 65 . 66 . 67 . 68. 69 . 70. 7 1 . 72 . 73 . 74 . 75 . 76 . 829 9 1 1 880 957 882 877 945 950 874 148 08 1 103 037 1 1 1 1 18 039 04 4 1 17 0.011 0.002 0.002 001 0 004 OOI O 002 0.836 O.126 0.0 755 925 957 922 8 16 94 1 923 .922 106 047 038 07 1 136 04 2 068 04 2 .002 .005 .001 .O .019 .001 .0 .017 O. 704 0. 760 0.816 0.740 0.605 0.289 0.007 0. 194 0.013 O.180 0.002 0.243 0.010 O.336 0.004 749 0.223 392 0 593 0 577 403 734 746 420 0. 545 0. 238 0. 242 020 008 002 .026 .019 . 006 11. 77 . 11. 78 . 11. 79 . 12 . 57 . 12 . 58 . 12 . 59 . 12 . 60. 12 . 6 1 . 12 . 62 . 12 . 63 . 12 . 64 . 12 . ' 65 . 12 . 66 . 12 . 67 . 0 12 . 68 . 0 12 . 69 . 0 12 . 70. 12 . 7 1 . 0 12 . 72 . 738 046 .815 234 860 185 0.013 0.094 0.0 .812 0.178 0.0 ro C H U M AREA YEAR 3 4 5 1. 57 . 2 . 57 . 2 . 58 . 2 . 59 . 2 . 60. 2 . 6 1 . O . 330 O . 680 0 .020 2 . 62 . 2 . 63 . 2 . 64 . O . 220 O 780 0 .0 2 . 65 . 0 .050 0. 920 0 .030 2 . 66 . 2 . 67 . 2 . 68 . 2 . 69 . 2 70. 2 . 7 1 . O .090 O. 870 0 .040 2 . 72 . 0. . 160 0. 7 50 0 .080 2 . 73 . 0 . 100 0. 7 50 0 . 150 2 . 74 . O . 1 10 0. 750 0 . 140 2 . 75 . 0 .220 0. 740 0 ,O40 2 . 76 . 0. .000 0'. 940 0 .060 2 . 77 . 2 . 78 . 2 . 79 . o. . 563 0. 332 0 . 105 3 . 57 . o. 108 0. 776 0 .116 3 . 58 . o. . 125 0. 734 0 .14 1 3 . 59 . 0 . 169 0. 622 0 . 209 3 . 60. 0. 183 0. 803 0 .014 3 . 6 1 . 0. .045 0. 917 0. 038 3 . 62 . 0. 377 0. 331 0. 292 3 . 63 . 0. 2 15 0. 768 0. 014 3 . 64 . 0. 056 0. 9 17 0 027 3 . 65 . 0. .068 0. 7 23 0. . 208 3 . 66 . o. 058 0. 893 0. 049 3 . 67 . o. .2 19 0. 580 0 201 3 . 68 . 0. 018 0. 909 0, ,068 3 . 69 . 0. . 150 o. 559 o. , 291 3 . 70. o .028 0. 96 1 0. ,011 3 . 7 1 . 0 173 0. 433 o . 394 3 . 72 . o 017 0. 945 0. ,036 3 . 73 . 3 . 74 . 3 . 75 . 3 . 76 . 3 . 77 . 3 . 78 . 3 . 79 . 4 . 57 . 0 .039 0. 926 0. .035 4 . 58 . 0 .068 0. 829 o 103 4 . 59 . 4 . 60. o . 186 0. 791 0 .023 4 . 6 1 . o .089 o. 873 0 .038 AREA YEAR 3 4 5 4 . 62 . 0 . 274 0 . 5 10 0 . 2 16 4 . 63 . O . 286 0 .690 0 .024 4 . 64 . 0 .095 0 . 852 0 .053 4 . 65 . 0 .0 1 .000 0 .0 4 . 66 . 0 .020 0 . 980 0 .0 4 . 67 . 0 . 285 0 . 402 0 .3 13 4 . 68 . 0 .017 0 . 952 0 .025 4 . 69 . 0 . 264 0 . 49 1 0 . 245 4 . 70. 0 .0 0 .867 0 . 133 4 . 7 1 . 0 . 153 0 . 553 0 . 294 4 . 72 . 0 .009 0 . 935 0 .056 4 . 73 . 4 . 74 . 0 .0 0 . 809 0 .19 1 4 . 75 . 0 .0 0 . 875 0 . 125 4 . 76 . 0 .0 1 .000 0 .0 4 . 77 . 0 ,0 0 929 o .07 1 4 . 78 . 4 . 79 . 5 . 57 . 0 177 0, 734 0 .089 5 . 58 . O. 092 0. 873 0 .036 5 . 59 . 0. 350 0 530 0 120 5 . 60. 0, 599 0. 392 0. ,009 5 . 6 1 . 0. 379 0. 605 0. 015 5 . 62 . 0. 352 0. 608 0. 039 5 . 63 . 0. 532 0. 446 0. 02 1 5 . 64 . 0. 108 0. 869 0. 023 5 . 65 . 0. 18 1 0. 662 0. 157 5 . 66 . 0. 149 0. 833 0. 017 5 . 67 . 0. 315 0. 528 0. 156 5 . 68 . 0. 068 0. 915 0. 016 5 . 69 . 0. 553 0. 336 0. 109 5 . 70. 0. 077 0. 92 1 0. 002 5 . 7 1 . 0. 2 10 0. 692 0. 098 5 . 72 . 0. 085 0. 875 0. 039 5. 73 . 5 . 74 . 5 . 75 . 5 . 76 . -5 . 77 . 5 . 78 . 5 . 79 . 6 . 57 . 6 . 58 . 0. 1 14 0. 869 0. 017 6 . 59 . 0. 398 0. 530 0. 072 6 . 60. 0. 73 1 0. 260 0. 009 6 . 6 1. 0. 339 0. 642 0. 019 6 . 62 . o. 225 0. 754 0. 02 1 6 . 63 . 0. 6 10 o. 376 0. 014 6 . 64 . 0. 12 1 o. 867 0. 01 1 6 . 65 . 0. 16 1 0. 683 0. 156 6 . 66 . 0. 167 0. 807 0. 026 6 . 67 . 0. 387 0. 513 0. ioo AREA YEAR 3 4 5 6. 68 . 0 .047 0 . 945 0 .007 6 . 69 . 0 .7 16 0 . 182 0 . 101 6 . 70. O .113 0 .885 0 .001 6 . 7 1 . 6 . 72 . 6 . 73 . 6 . 74 . 6 . 75 . 6 . 76 . 6 . 77 . 6 . 78 . 6 . 79 . 7 . 57 . 7 . 58 . 0 . 209 0 783 0 .008 7 . .59 . 0, . 336 0, .643 0 .020 7 . 60. O, , 4 16 0, 573 0 O10 7 . 61 . 0. , 1 10 0. 866 0. ,024 7 . 62 . 0. , 703 0. 270 0 027 7 . 63 . 0. 375 0. 619 0. 006 7 . 64 . 0. , 133 0. 849 0, 018 7 . 65 . 0. 093 0. 826 0. 078 7 . 66 . 0. 261 0. 686 0. .052 7 . 67 . 0. 442 o. 492 0. 066 7 . 68 . 0. 192 0. 803 0. 005 7 . 69 . O. 402 0. 544 0, 054 7 . 70. 0. 057 o. 936 0. 007 7 . 7 1 . 0. 34 1 o. 502 0. 157 7 . 72 . 0. 072 o. 907 0. 020 7 . 73. 7 . 74 . 7 . 75. 7 . 76 . 7 . 77 . 7.. 78 . 7 . 79. 8 . 57 . 8 . 58 . 8 . 59. 0. 344 0. 642 0. 010 8 . 60. 0. 503 0. 488 0. 008 8 . 6 1 . 0. 197 0. 800 0. 003 8 . 62 . 0. 797 0. 181 0. 022 8 . 63 . 0. 280 o. 7 16 o. 0 8 . 64 . o. 638 0. 340 0. 0 8 . 65 . 8 . 66 . 8 . 67 . 8 . 68 . 8 . 69 . 8 . 70. 8 . 7 1 . 8 . 72 . o. 039 o. 94 1 0. O 8 . 73 . AREA YEAR 3 4 5 8 . 74 . 8 . 75 . 8 . 76 . 8 . 77 . 8 . 78 . 8 . 79 . 9 . 57 . 0 259 0 .697 0 . 044 9 . 58 . 0 57 1 0 424 0 .005 9 . 59 . 0 408 O 587 0 .005 9 . 60. 0 346 0 643 0 O i l 9 . 6 1 . 0 156 0 824 0 .020 9 . 62 . 0 772 0 206 0 .022 9 . 63 . 0 289 0 707 0 004 9 . 64 . 0 147 0 832 0 02 1 9 . 65 . 0 02 1 0 970 0 009 9 . 66 . 0 070 0 908 O 022 9 . 67 . 0 549 0 423 0 028 9 . 68 . 0 203 O 79 1 0 006 9 . 69 . 0 405 0 573 0 22 9 . 70. 0 090 0 906 0 004 9 . .71. 0 354 0 545 0 101 9 . 72 . 0 02 1 0 976 0 003 9 . 73 . 0 033 0 804 0 163 9 . 74 . 0 192 0 568 0 240 9 . 75 . 0 537 0 444 0 019 9 . 76. 0 172 0 823 0 005 9 . 77 . 0 237 0 742 0 02 1 9 . 78 . 0 132 0 851 0 017 9 . 79 . 0 258 0 606 0 136 10. 57 . 10. 58 . 0 7 16 0 264 0 018 10. 59 . o 297 o 695 o 004 10. 60. o 674 0 320 0 006 10. 6 1 . 0 266 0 725 o 009 10. 62 . 0 840 0 148 0 012 10. 63 . 0 490 0 503 0 005 10 64 . 0 7 16 0. 272 o 001 10. 65 . 0. 1 14 o. 882 0 004 10. 66 . 0. 45 1 o. 500 0 04 7 10. 67 . 0. 598 0. 389 0 013 10. 68 . 0. 186 0. 800 0 013 10. 69 . 0. 167 o. 802 0 003 10. 70 0. 262 0. 724 0 014 10. 7 1 . 0. 508 o. 447 0. 04 5 10. 72 . 0. 020 o. 973 0. 007 10. 73 . 10. 74 . 10. 75 . 10. 76 . 10. 77 . 10. 78 . 10. 79 . AREA YEAR 3 4 5 1 1 57 . 1 1 . 58 . 1 1 . 59 . 0 4 1 1 0 .560 0 .022 1 1 . 60. 0 440 0 552 0 .008 1 1 . 6 1 . 0 482 0 494 O .019 1 1 . 62 . 0 57 1 O 4 14 0 .004 1 1 . 63 . 0 500 0 492 0 0 1 1 . 64 . 1 1 . 65,. 1 1 . 66 . 1 1 . 67 . 1 1 . 68 . 1 1 . 69 . 0 187 0 480 0 0 1 1 . 70. 0 388 0 578 6 024 1 1 . 7 1 . 0 452 0 518 0 03 1 1 1 . 72 . 0 052 0 934 0 013 1 1 . 73 . 0 026 0 552 0 42 1 1 1 . 74 . 0 261 0 404 0 32 1 1 1 . 75 . 0 3 10 0 673 0 017 1 1 . 76 . 0 138 0 846 0 014 1 1 . 77 . 0 407 0 535 0 025 1 1 . 78 . 0 167 0 459 0 034 1 1 . 79 . 12 . 57 . 12 . 58 . 12 . 59. 0 583 0 401 0 013 12 . 60. 0 764 0 233 0 003 12 . 6 1 . 0 208 0 78 1 0 010 12 . 62 . o 463 0 52 1 0 012 12 . 63 . o 613 0 374 0 01 1 12 . 64 . 0 326 0. 67 1 0 O 12.. 65 . 12 . 66 . 12 . 67 . 12 . 68 . 12 . 69 . 0. 194 o. 139 0 0 12 . 70. 0. 3 12 0. 666 12 . 7 1. 0. 348 0. 578 0. 071 12 . 72 . 0. 1 12 0. 864 0. 02 1 12 . 73 . 0. 084 0. 752 0. 162 12 . 74 . 0. 260 0. 592 0. 143 12. 75 . 0. 136 0. 799 0. 057 12 . 76 . 0. 1 19 0. 496 0. 033 12. 77 . 0. 599 o. 382 0. 020 12 . 78 . 12 . 79 . 165 Age c o m p o s i t i o n of c a t c h and escapement ( s p r i n g ) a r e a 40 = s t a t . A r e a 20-27 a r e a 41 = s t a t . A r e a 13-19+28 a r e a 42 = s t a t . A r e a 6-12 a r e a 43 = s t a t . A r e a 1-5 a r e a 29 = s t a t . A r e a 29 # = number s a m p l e d S P R I N G AREA YEAR 2/1 3/1 43 52 0 53 43 53 74 474 43 54 14 247 43 55 1 12 243 43 56 43 57 43 58 43 59 43 60 43 61 43 62 43 63 43 64 1 205 43 65 43 66 17 36 1 43 67 2 339 43 68 43 69 43 70 43 7 1 43 72 43 73 43 74 43 75 101 351 43 76 183 495 43 77 34 546 43 78 0 43 79 40 52 3 10 610 40 53 149 561 40 54 144 448 40 55 105 648 40 56 32 608 40 57 35 577 40 58 16 470 40 59 9 374 40 60 40 61 40 62 40 63 40 64 25 585 40 65 36 558 40 66 6 538 40 67 1 497 40 68 1 489 40 69 40 70 40 7 1 4/1 5/1 6/1 2/2 789 158 0 0 37 1 1 1 0 0 595 123 0 0 336 178 9 0 532 107 3 1 1 38 1 1 10 1 51 370 131 10 33 378 1 12 5 24 242 69 1 8 369 34 1 3 60 0 0 0 108 1 1 0 0 299 0 0 0 199 14 0 3 264 6 0 0 282 32 2 0 277 30 0 2 424 32 0 0 244 19 0 0 293 19 1 0 37 1 35 0 0 398 50 1 0 436 33 0 0 3/2 4/2 5/2 6/2 0 0 0 0 4 1 18 1 1 0 0 14 27 0 37 28 57 0 78 60 3 0 64 14 2 0 80 33 1 0 19 5 1 0 3 0 0 0 7 5 0 0 20 0 0 0 119 52 0 0 52 52 5 0 6 22 3 ' 0 29 55 6 0 15 47 5 0 50 108 45 2 9 107 36 9 36 76 16 0 16 58 18 1 5 34 10 0 1 41 1 1 • 0 4 28 8 0 H AREA 19 40 175 40 73 40 107 40 40 40 40 40 4 1 41 41 4 1 2116 4 1 4 1 ? 41 5031 4 1 4 1 4 1 4 1 4 1 4 1 4 1 41 1564 41 1 174 41 926 41 41 41 115 4 1 269 4 1 194 41 361 41 31 1 4 1 602 41 560 41 439 4 1 29 29 29 29 9315 29 7576 29 6204 29 7101 29 4076 29 29 29 29 YEAR : 2/1 3/1 4/1 72 73 74 75 78 553 276 76 60 585 297 77 43 689 243 78 23 506 4 14 79 52 4 10 570 10 53 97 822 48 54 103 647 174 55 156 682 156 56 135 723 101 57 153 490 222 58 130 576 150 59 40 618 222 60 61 62 63 64 215 544 150 65 40 669 203 66 209 591 154 67 120 702 149 68 58 552 347 69 70 7 1 72 73 74 75 95 601 249 76 8 766 215 77 78 14 695 274 79 52 340 140 260 53 136 340 175 54 50 325 275 55 56 366 169 56 40 476 323 57 126 188 334 58 8 174 305 59 0 51 4 14 60 61 62 63 5/1 6/1 2/2 3/2 35 1 1 38 48 0 0 3 17 0 0 3 29 0 0 8 0 0 0 10 0 0 0 33 0 0 4 22 0 o 0 3 0 0 0 7 7 0 0 84 14 0 0 51 1 1 0 7 51 5 0 59 26 8 0 33 35 7 0 24 13 4 0 8 14 7 0 14 18 24 0 18 12 8 0 0 2 8 0 2 6 0 0 0 170 19 0 0 155 0 0 0 225 0 o 0 225 46 5 0 59 16 0 3 176 35 o 0 54 58 0 0 7 4/2 5/2 6/2 16 1 0 2936 6 0 0 3986 3 1 0 3758 13 6 0 4745 0 0 0 156 0 0 0 62 41 9 0 224 3 0 0 288 20 14 0 148 36 7 0 275 72 7 0 293 36 15 0 275 2 0 0 2923 9 0 0 1773 3 0 0 5814 3 0 0 3 183 3 0 0 3937 1 0 0 2642 0 0 0 1959 1 0 0 2499 90 0 0 35 1 17 58 0 103 100 25 0 40 184 0 0 71 40 8 3 372 1 10 44 0 318 225 188 11 368 199 261 10 293 AREA YEAR 2/1 3/1 4/1 5/1 6/1 2/2 3/2 4/2 5/2 6/2 # 29 64 24 1 1 1 392 23 0 23 161 265 2 0 4674 29 65 14 1 1 1 256 45 0 64 269 23 1 10 0 4091 29 66 31 2 18 405 31 0 13 177 123 1 0 2701 29 67 29 68 29 69 29 70 29 7 1 29 72 29 73 29 74 29 75 170 439 306 61 0 25 0 0 0 0 172 29 76 0 422 5 10 66 0 1 0 1 0 0 362 29 77 6 1 500 37 1 3 0 6 17 38 6 0 332 29 78 0 226 644 17 0 0 25 88 0 0 303 29 79 42 52 42 53 42 54 42 55 42 56 42 57 42 58 42 59 42 60 42 6 1 42 62 42 63 42 64 42 65 2 278 484 126 3 5 56 47 0 0 860 42 66 53 456 289 98 2 17 68 14 3 0 2 190 42 67 26 437 339 130 2 12 38 16 1 0 3161 42 68 15 321 457 134 2 15 35 23 0 0 1229 42 69 42 70 42 71 42 72 42 73 42 74 42 75 8 279 43 1 190 2 29 36 24 0 0 1606 42 76 170 354 344 1 12 0 2 7 7 3 0 553 42 77 1 15 484 164 145 0 0 12 12 23 46 55 42 78 42 79 0* 1^ AREA SOCKEYE CHUM SPRING 4 5 6 3 4 5 3 4 5 6 1 . 29 .65 .05 . 18 . 75 .07 30 .40 . 20 0. 2 . 29 . 65 .05 . 18 . 75 .07 30 . 40 . 20 0. 3 . 29 .65 05 . 13 74 -.13 . 30 .40 . 20 0. 4 . 45 .53 .02 .09 . 80 . 10 .20 . 45 . 35 0. 5 ' .51 . 4 1 .03 . 26 . 68 .06 .30 .45 . 25 0. G . 43 . 54 .02 . 32 . 64 .04 . 30 .45 . 25 0. 7 . 70 . 29 .01 . 28 . 69 .04 . 30 . 45 . 25 0. 8 .88 . 1 1 0. .40 . 59 .01 .30 .45 . 25 0. 9 .91 .08 O. . 27 . 69 .05 . 20 .60 . 20 0. 10 . 89 .08 .01 . 42 . 56 .01 . 20 .60 . 20 0. 1 1 . 66 . 32 .01 . 32 . 57 .06 . 20 .60 . 20 0. 12 . 37 . 55 .05 . 34 . 55 .04 . 20 .60 . 20 O. APPENDIX IC. OVERALL AVERAGE AGE DISTRIBUTION BY AREA BY SPECIES 169 APPENDIX I_I_ T h i s a p p e n d i x summarizes s t o c k - r e c r u i t m e n t r e l a t i o n s h i p s f o r t h e major salmon p r o d u c t i o n u n i t s i n B.C. E a c h p r o d u c t i o n u n i t i s r e p r e s e n t e d by one page of i n f o r m a t i o n c o n t a i n i n g f o u r g r a p h s , a t a b l e o f optimums, a s h o r t summary of key u n c e r t a i n t i e s i n t h e r e c r u i t m e n t a n a l y s i s and t h e m a j o r management p r o b l e m s a s s o c i a t e d w i t h t h a t p r o d u c t i o n u n i t . The f i r s t g r a p h f o r e a c h s t o c k shows t h e t i m e s e r i e s o f e s c a p e m e n t s and t o t a l s t o c k . E a c h y e a r , e s c a p e m e n t i s t h e a d u l t p o p u l a t i o n e s t i m a t e d t o be i n t h e r i v e r s y s t e m s of t h a t a r e a , w h i l e t o t a l s t o c k i s t h e escapement p l u s a l l t h e c a t c h e s e s t i m a t e d (by b a c k - c a l c u l a t i o n ) t o have p r o d u c e d by t h e s t o c k o v e r a l l h a r v e s t i n g a r e a s . Some of t h e t i m e s e r i e s e x t e n d o n l y back t o t h e 1960's, b e c a u s e of l a c k o f i n f o r m a t i o n f o r s e p a r a t i n g mixed c a t c h e s . The s t o c k - r e c r u i t m e n t g r a p h p r e s e n t s e a c h d a t a p o i n t as a number r e p r e s e n t i n g t h e y e a r of s p a w n i n g . R e c r u i t m e n t i s t h e t o t a l number of f i s h p r o d u c e d by t h a t s p a w n i n g p o p u l a t i o n and h a v i n g s u r v i v e d t o be c a u g h t by t h e f i s h e r y o r e s c a p e d t o spawn. The d i a g o n a l d o t t e d l i n e i s t h e " r e p l a c e m e n t l i n e " when r e c r u i t s e q u a l s p a w n e r s . T h r e e c u r v e s a r e f i t t e d t h r o u g h t t h e d a t a p o i n t s w i t h o u t c o r r e c t i n g f o r s p a w n i n g c o u n t e r r o r s and e a c h p o i n t i s g i v e n e q u a l w e i g h t r e g a r d l e s s o f i t s c r e d i b i l i t y . A dome-shaped R i c k e r model ( - ), a s a t u r a t i n g B e v e r t o n - H o l t model ( v • ), and a Power model (-! - - ) a r e p r e s e n t e d i n most c a s e s . When t h e i t e r a t i o n scheme f o r e s t i m a t i n g t h e B e v e r t o n - H o l t model p a r a m e t e r s f a i l s , o n l y t h e R i c k e r and Power m o d e l s a r e shown. 170 The n e x t g r a p h shows t h e t i m e s e r i e s d e v i a t i o n s o f o b s e r v e d l o g r e c r u i t s p e r spawner from t h e v a l u e s p r e d i c t e d by t h e R i c k e r c u r v e . T h i s g r a p h m e a s u r e s t r e n d s i n p r o d u c t i v i t y p e r spawner t h a t c a n n o t be a t t r i b u t e d s i m p l y t o t r e n d s i n s p a w n ing s t o c k s i z e a l o n e . The l a s t g r a p h shows t h e a u t o - c o r r e l a t i o n p a t t e r n i n t h e r e g r e s s i o n r e s i d u a l s ( d e v i a t i o n i n l o g r e c r u i t s p e r spawner from R i c k e r p r e d i c t i o n ) a t d i f f e r e n t l a g s ( i n y e a r s ) . S i g n i f i c a n t c o r r e l a t i o n a t any l a g i n d i c a t e s t h e p r e s e n c e o f d a t a e r r o r s or b i o l o g i c a l p r o c e s s e s t h a t may i n v a l i d a t e t h e a s s u m p t i o n of a s t a t i o n a r y d i s t r i b u t i o n of r e c r u i t s f o r any f i x e d spawning s t o c k . F o r c h i n o o k , s i g n i f i c a n t c o r r e l a t i o n s a t l a g s 1-5 a r e common, and a r e t h o u g h t t o r e f l e c t c h a n g e s i n age c o m p o s i t i o n ; i n our c a l c u l a t i o n s , s t r o n g y e a r c l a s s e s may be a s s i g n e d i n c o r r e c t l y t o s e v e r a l p r o d u c t i o n y e a r s . The t a b u l a t e d optimum e s c a p e m e n t s and p r o b a b l e bounds a r e e s t i m a t e d as d e s c r i b e d i n c h a p t e r IV - by s t a t i s t i c a l a n a l y s e s t e m p e r e d w i t h j u d g e m e n t s a b o u t d a t a p r o b l e m s , h i s t o r i c a l p e r f o r m a n c e , and a v a i l a b l e h a b i t a t . E s t i m a t e s o f optimum e x p l o i t a t i o n r a t e s a r e s i m p l y t h e c a t c h / ( c a t c h + e s c a p e m e n t ) from t h e same col u m n o f t h e t a b l e . C u r r e n t e s c a p e m e n t and c a t c h a r e f i v e y e a r a v e r a g e s f r o m 1975-1979 ( f i v e - c y c l e a v e r a g e s f o r p i n k s from 1970-1979). A s h o r t v e r b a l summary of key u n c e r t a i n t i e s i n t h e r e c r u i t m e n t a n a l y s i s and key management p r o b l e m s f o l l o w s t h e t a b l e of optimums. T h e s e p r o b l e m s were e x p l a i n e d t o us by y government b i o l o g i s t s , o r m e n t i o n e d i n t h e u n p u b l i s h e d G e o g r a p h i c a l W o r k i n g G r o u p summaries p r e p a r e d r e c e n t l y f o r t h e S a l m o n i d Enhancement Program. 171 c Q . C . 1 C O H O PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 70,000 74,000 .51 35,000 140,000 .80 15,000 120,000 .89 75,000 240,000 .76 I. Major Unc e r t a i n t i e s In Analysis 1. large uncertainty i n catch a l l o c a t i o n 2. age composition not a v a i l a b l e 3. Alaska i n t e r c e p t i o n not a v a i l a b l e I I . Impediments to Improved Management 1. i n t e r c e p t i o n by Alaska t r o l l f l e e t 2. no opportunity f o r terminal f i s h e r y Q.C.2 COHO 173 as ESCAPEMENT r''n CATCH EXPLOITATION RATE PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER 48,000 52,000 .52 80,000 100,000 .53 50,000 50,000 .54 140,000 110,000 .50 I. Major Uncertainties in Analysis 1. large uncertainty in catch allocation 2. age composition not available 3. Alaska interception not available 4. escapement estimates are extremely unreliable (many holes in escapement records) II. Impediments to Improved Management 1. interception by Alaska t r o l l fleet 2. no opportunity for terminal fishery N R S S C O H O 174 * TOTAL 5 f o o t • ESCftPEMEfr ESCAPEMENT CATCH EXPLOITATION RATE CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER 26,000 61,000 .70 30,000 120,000 .80 10,000 70,000 .88 60,000 140,000 .70 I. Major Uncertainties in Analysis 1. large uncertainty in catch allocation 2. age composition, not available 3. Alaska interception not available 4. escapements before 1964 are less reliable II. Impediments to Improved Management 1. interception by Alaska t r o l l fleet SKEENR COHO 17 PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 35,000 96,000 .73 54,000 130,000 .73 10,000 120,000 .79 120,000 180,000 .67 I. Major Uncertainties in Analysis 1. large uncertainty i n catch allocation 2. age composition not available 3. Alaska interception not available II. Impediments to Improved Management 1. interception by Alaska t r o l l fleet C . C . COHO • TOTAL STOCK » ESCflPEnEVT PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 127,000 337,000 .73 135,000 670,000 .83 80,000 550,000 .91 240,000 800,000 .67 I. Major Uncertainties i n Analysis 1. large uncertainty i n catch a l l o c a t i o n ; r i ; " 2. a decreasing trend of r e c r u i t s per spawner i n recent years may i n d i c a t e lower q u a l i t y of habi t a t 3. Alaska i n t e r c e p t i o n not a v a i l a b l e I I . .Impediments to Improved Management 1. i n t e r c e p t i o n by Alaska t r o l l f l e e t R-S COHO 177 TOTAL STOCK ESCflPEMEf/T SPRVNERS CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 5 , 0 0 0 1 0 , 0 0 0 4 , 0 0 0 ? CATCH 9 4 , 0 0 0 1 8 0 , 0 0 0 1 2 0 , 0 0 0 ? EXPLOITATION RATE . 9 5 . 9 7 . 9 6 Major Uncertainties in Analysis 1. large uncertainty in catch allocation 2 . production at higher escapement i s highly uncertain but seems to be favourable II. Impediments to Improved Management J . S . COHO 178 a • r o CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 52,000 530,000 .91 100,000 580,000 .85 40,000 250,000 .85 180,000 700,000 .79 I. Major Uncertainties In Analysis 1. uncertainty in sports fishing estimates 2. large uncertainty in catch allocation II. Impediments to Improved Management 1. interception during chum fishery 2. incidental catch of j u v e n i l e f i s h G . S . C O H O 179 CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 155,000 630,000 .80 201,000 567,000 .74 100,000 400,000 .80 400,000 600,000 .60 I. Major Uncertainties in Analysis 1. uncertainty in sports fishing estimates 2. uncertainty i n the contribution of Washington produced fi s h 3. increasing hatchery output i n recent years II. Impediments to Improved Management 1. interception by Big Qualicum chum fishery 2. large sports fishing a c t i v i t i e s 3. incidental catch of juvenile fish F R A S E R C O H O 1 8 0 .' 1 i a CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 61,000 380,000 .86 54,000 406,000 .88 20,000 370,000 .95 100,000 400,000 .80 I. Major Uncertainties i n Analysis 1. uncertainty i n sports f i s h i n g estimates 2. increased e f f o r t i n escapement counts i n recent years 3. large uncertainty i n catch a l l o c a t i o n 4. uncertainty i n the con t r i b u t i o n of Washington produced f i s h II. Impediments to Improved Management 1. mixed stock problem with chum and pink f i s h e r y 2. i n t e r c e p t i o n by Point Roberts f i s h e r y S . W . V . I . C O H O 181 CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 48,000 135,000 .74 100,000 150,000 .60 50,000 100,000 .67 200,000 160,000 .44 I. Major Uncertainties in Analysis 1. large uncertainty in catch allocation 2. uncertainty in the contribution of Washington produced fish II. Impediments to Improved Management 1. West coast t r o l l fishery N . W . V . I . C O H O 1 8 2 SO TOTRL STOCK ESCAPEMENT -+-S5 C5 TERR 70 75 80 CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 27,000 116,000. .81 35,000 125,000 .78 20,000 x 100,000 .83 50,000 125,000 .71 Major U n c e r t a i n t i e s i n A n a l y s i s 1. l a r g e u n c e r t a i n t y i n catch a l l o c a t i o n 2. u n c e r t a i n t y i n the c o n t r i b u t i o n of Washington produced f i s h I I . Impediments to Improved Management 1. West coast t r o l l f i s h e r y NflSS SOCKEYE 183 TOTAL STOCK ESCAPEMENT 2 M CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 195,000 317,000 .62 181,000 350,000 .66 120,000 240,000 .67 360,000 360,000 .50 I . Major Uncertainties i n Analysis 1. escapement counts before 1964 are u n r e l i a b l e 2. uncertainty i n catch a l l o c a t i o n of Skeena and Nass f i s h 3. Alaska i n t e r c e p t i o n not included I I . Impediments t.^ Impioved Management 1. mixed f i s h e r y problem with Skeena sockeye, pink a n d ' l o c a l pink stocks 2. i n t e r c e p t i o n by Alaska f i s h e r y SKEENh SOCKEYE • TOTAL -STOCK 1 . ESCAPf.ttf>/T i TEAR _ S P f l U " E R S £ T ~ T CURRENT OPTIMUM . PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT . CATCH EXPLOITATION RATE 820,000 834,000 .50 868,000 800,000 .48 600,000 830,000 .58 1,500,000 1,000,000 .40 I. Major Uncertainties i n Analysis 1. substock composition i s changing r a p i d l y to predominantly enhanced stocks 2. e f f e c t s of s u b s t a n t i a l increase of smolt output from spawning channels are uncertain 3. Alaska i n t e r c e p t i o n not included 4. uncertainty i n catch a l l o c a t i o n II. Impediments tc Improved Management 1. mixed f i s u e r y problem with pink and enhanced stocks 2. i n t e r c e p t i o n by Alaska, Q.C.1, Nass and upper C . C . . f i s h e r i e s C . C , S O C K E Y E 1 8 5 TOTAL STOCK ESCAPEMEWT •+-SO 55 60 65 TEAR 70 75 60 CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 100,000 280,000 .74 200,000 283,000 .59 100,000 220,000 .69 400,000 350,000 .47 I. Major Uncertainties in Analysis 1. age composition data available from 1959-1972 only 2. may include f i s h destined for Skeena in the catch II. Impediments to Improved Management 1. d i f f i c u l t to set up small terminal fisheries 2. mixed fisheries problem with local pinks -CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 390,000 A80,000 .55 500,000 1, 200,000 .71 400,000 1,000,000 .83 2,000,000 1,500,000 .43 I. Major U n c e r t a i n t i e s i n A n a l y s i s 1. substocks not t r e a t e d s e p a r a t e l y I I . Impediments to Improved Management 1. mixed f i s h e r y problem w i t h pinks J . S . S O C K E Y E 187 • TOTAL STOCK T . ESCAPEnEWT 1 3> CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 37,000 1 7 ? CATCH 44,000 1 ? ? EXPLOITATION RATE .54 1 1 ? I. Major Uncertainties i n Analysis 1. age composition data a v a i l a b l e from 1958-1975 only 2. native food f i s h e r y not included 3. m i s a l l o c a t i o n of catches destined for the Fraser River 4. extreme uncertainty in.optimal escapement estimation I I . Impediments to Improved Management 1. i n t e r c e p t i o n during Johnstone S t r a i t f i s h e r y f o r Fraser sockeye 2. unable to move f i s h i n g boundaries due to gear a l l o c a t i o n problem F R R S E R S O C K E Y E 188 TOTRL STOCK ESCRPEflEMT .»4 1.C8 2.S2 3.36 SPRUMERS CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 1,370,000 4,460,000 ,77 4,000,000 8,000,000 .67 2,000,000 7,000,000 .78 8,000,000 11,000,000 .58 II. Major Uncertainties in Analysis 1. substocks not treated separately c 2. cyclic dominance not considered 3. in 1958 only 2 million fish allowed to spawn in Adams River Impediments to Tir.pioved Management 1. allocation of equal share to U.S. and Canadian fishermen 2. interception by Johnstone Strait net fishery and W.V.I, t r o l l fishery 3. potential disease problem in rebuilding high spawning densities 4. substock mixed fishery problem 5 . W . V . I . S O C K E Y E 189 TOTAL STOCK ESCAPEMEMT JO c i X LAG TJME CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH" EXPLOITATION RATE 260,000 600,000 .70 300,000 500,000 .63 100,000 150,000 .60 1,000,000 1,000,000 .50 Major Uncertainties in Analysis 1. f e r t i l i z a t i o n of Great Central Lake increased production in recent years 2. age composition data available from 1960-64 and 1967-72 3. 1970-74 S-R aata has a totally different pattern than previous years 4. current upward production trend occurred before f e r t i l i z a t i o n (note upwaid trend residuals began in 1968) II. Impediments to Improved Management 1. limited geographical area for terminal fishery 2. impact of lake f e r t i l i z a t i o n on the long term production of sockeye is s t i l l uncertain Q . C . 1 C H U M 190 - TOTAL STOCK . ' , • ESCAPEMEWT / CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 78,000 ? 7 1 CATCH 8,000 1 7 1 EXPLOITATION RATE .10 ? ? 1 I. Major Uncertainties in Analysis 1. age composition data not available 2. extreme uncertainty in optimal escapement estimation II. Impediments to Improved Management 1. d i f f i c u l t y in setting up terminal fishery 0.C.2 CHUM -I f - — i 1 1 1 1 ° +—i—i—i—i—i—i—i—i—i— i 50 55 60 65 70 75 80 . 0 .28 .56 .«4 S.12 1 .4 TERR SPRVNERS CURRENT OPTIMUM PROBABLE LIMI1 rS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 155,000 85,000 .34 600,000 200,000 .25 206,000 100,000 .33 1,000,000 300,000 .23 I. Major Uncertainties in Analysis 1. age composition data available in 1961, 1964-65 and 1971-1976 2. poor escapement estimate in 1956, 1959 3. early 50's data did not account for Japanese high seas interception II. Impediments to Improved Management 1. d i f f i c u l t y in setting up terminal fishery NRSS CHUM 192 • TOTAL STOCK - ESCAPEMENT V. CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 53,000 ? 7 CATCH 112,000 ? 7 7 EXPLOITATION RATE .68 7 ? I. Major Uncertainties i n Analysis 1. age composition data a v a i l a b l e from 1957-72 only 2. included unknown, but s i g n i f i c a n t number of Alaska chum i n the catch 3. extreme uncertainty i n optimal escapement estimation I I . Impediments to Improved Management 1. i n t e r c e p t i o n of Alaska chum 2. mixed f i s h e r y problem with Skeena and l o c a l pinks C . C . C H U M 193 • TOTRL STOCK •• ESCRPEnEiVT CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 380,000 470,000 .55 684,000 808,000 .54 400,000 400,000 .54 1,000,000 800,000 .44 I. Major U n c e r t a i n t i e s i n A n a l y s i s 1. age composition data a v a i l a b l e from 1957-72 only 2. d e c l i n e of p r o d u c t i v i t y i n recent years may i n d i c a t e h a b i t a t d e t e r i o r a t i o n I I . Impediments to Improved Management 1. mixed stock f i s h e r y with l o c a l pinks J . S . C H U M 194 TOTAL STOCK ESCAPEMENT i J . CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 242,000 94,000 .28 210,000 250,000 .54 150,000 150,000 .50 350,000 250,000 .42 I. Major Uncertainties in Analysis 1. age composition data available from 1958-72 only 2. uncertainty in catch allocation II. Impediments to Improved Management 1. mixed fishery with Big Qualicum, Fraser and Washington fish 2. terminal fishery produce poor quality fish G.S. CHUM 195 41 O TOTAL STOCK ESCAPEMENT 3> | S > —* SO 55 60 65 TEAR 70 75 60 3> —, O > J . PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER , UPPER ESCAPEMENT 472,000 415,000 300,000 , 500,000 CATCH 246,000 488,000 200,000 500,000 EXPLOITATION RATE .34 .54 .40 .50 I. Major Uncertainties in Analysis 1. age composition data available from 1958-64 only 2. Big Qualicum enhancement in recent years 3. uncertainty in catch allocation II. Impediments to Improved Management 1. mixed fishery with Big Qualicum, Fraser and Washington f i s h CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 435,000 341,000 .44 1,000,000 1,200,000 .55 600,000 600,000 .50 3,000,000 2,000,000 .40 I. Major Uncertainties In Analysis 1. uncertainty in catch allocation 2. d i f f i c u l t y in setting upper bound for optimal escapement II. Impediments to Improved Management 1. interception by Point Roberts fishery CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 471,000 58,000 .11 372,000 217,000 .37 300,000 150,000 .33 500,000 300,000 .38 I. Major U n c e r t a i n t i e s i n Analysis 1. age composition data a v a i l a b l e from 1959-63, and 1969-78 I I . Impediments to Improved Management N . W . V . I . CHUM 198 -X. Is) i n SO —I— S5 TOTRl STOCK ESCAPEMENT 60 + 65 TERR 70 75 80 m o c • CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 117,000 48,000 .29 150,000 ioo.ooo .40 100,000 80,000 .44 200,000 120,000 .38 I. Major Uncertainties In Analysis -1. age composition data available from 1959-64, and 1969-77 II. Impediments to Improved Management NRSS SPRING 199 CURRENT PROBABLE LIMITS ON OPTIMUM OPTIMUM LOWER UPPER ESCAPEMENT 7,00Q 8,300 6,000 10,000 CATCH 13,000 27,000 20,000 26,000 EXPLOITATION RATE .65 . 76 .77 .72 I. Major Uncertainties in Analysis 1. fish intercepted by Alaska fisheries not included 2. time specific age structure not available 3. large uncertainty in catch allocation II. Impediments to Improved Management 1. interception by Alaska t r o l l SKEENR SPRING 200 • CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 22,000 19,000 . .46 22,000 25,000 .53 20,000 20,000 .53 50,000 30,000 .38 I. Major Uncertainties in Analysis 1. f i s h intercepted by Alaska fisheries not included 2. native food fishery not included 3. time specific age structure not available 4. large uncertainty in catch allocation II. Impediments to Improved Management 1. increasing native food fishery demands 2. interception by Alaska t r o l l C C . SPRING 201 • TOTAL STOCK • ESCAPEMENT -CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 29,000 44,000 .60 30,000 56,000 .65 16,000 50,000 .76 50,000 50,000 .5 I. Major Uncertainties in Analysis 1. fis h intercepted by Alaska fisheries not included 2. time specific age structure not available 3. large uncertainty in catch allocation II. Impediments to Improved Management 1. interception by Alaska t r o l l R-S SPRING 202 Ol PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER "UPPER ESCAPEMENT 3,000 A, 000 3,000 8,000 CATCH 29,000 33,000 30,000 25,000 EXPLOITATION RATE .91 .89 .91 .76 I. Major Uncertainties in Analysis 1. fish intercepted by Alaska fishery not included 2. ' time specific age structure not available 3. large uncertainty in catch allocation II. Impediments to Improved Management 1. increasing sports fishing a c t i v i t i e s 2. interception by Alaska t r o l l J . S . SPRING 2 0 3 4 1 1 1 1 1 1 « 4 — — i — i — i — i — i — h — i — i — i — i SO S5 60 65 VO 75 80 0 .012 .37.4 .036 .3-tf .36 TERR SPACERS ' 1 ' CURRENT PROBABLE LIMITS ON OPTIMUM OPTIMUM LOWER UPPER ESCAPEMENT 17,000 18,000 10,000 30,000 CATCH 64,000 61,000 60,000 50,000 EXPLOITATION RATE .79 .77 .86 .63 I . Major U n c e r t a i n t i e s i n A n a l y s i s 1. f i s h i n t e r c e p t e d by Al a s k a f i s h e r i e s not in c l u d e d 2. l a r g e u n c e r t a i n t y i n catch a l l o c a t i o n 3. time s p e c i f i c age s t r u c t u r e not a v a i l a b l e 4. u n c e r t a i n t y i n spo r t s f i s h i n g estimates 5. u n c e r t a i n t y i n the c o n t r i b u t i o n of Washington produced f i s h I I . Impediments to Improved Management 1. i n c i d e n t a l catch of j u v e n i l e f i s h 2. i n t e r c e p t i o n by Alaska t r o l l FRASER SPRING 204 T O T f i l STOCK E S C R P E M E W T 2 * t jo c - t ^ H 1 1 1 \ 1 i V • 0 2 . 9 4 . 0 6 . 01.99 T E R R o m < • PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 68,000 578,000 .89 200,000 788,000 .80 100,000 700,000 .88 400,000 1,200,000 .75 I I . Major U n c e r t a i n t i e s i n A n a l y s i s 1. l a r g e u n c e r t a i n t y i n catch a l l o c a t i o n 2. f i s h i n t e r c e p t e d by Alaska f i s h e r i e s not i n c l u d e d 3. time s p e c i f i c age structure not a v a i l a b l e 4. u n c e r t a i n t y i n s p o r t s f i s h i n g estimates 5. u n c e r t a i n t y i n the c o n t r i b u t i o n of Washington produced f i s h Impediments to Improved Management  1.. mixed f i s h e r y problem w i t h l o c a l sockeye, pink and chum f i s h e r y 2. u n c e r t a i n t y i n the mechanisms and extent of " r e s i d e n t " verses "ocean" type behavior 3. i n t e r c e p t i o n by Ala s k a t r o l l G.S. SPRING CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 19,000 70,000 •79 32,000 62,000 .66 . 20,000 40,000 .67 50,000 50,000 .50 I. Major Uncertainties in Analysis 1. fish intercepted by Alaska fisheries not included 2. uncertainty in the contribution of Washington produced fish 3. time specific age structure not available 4. uncertainty in sports fishing estimates 5. increasing output from local hatcheries 6. large uncertainty in catch allocation - - — II. Impediments to Improved Management 1. incidental catch of juvenile fish 2. uncertainty in the mechanisms and extent of "resident" verses "ocean" type behavior 3. interception by Alaska t r o l l •S.W.V.J. SPRING 2 0 6 TOTRl STOCK ESCRPEMEVT • CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 15,000 ? 7 ? CATCH 62,000 ? 7 7 EXPLOITATION RATE .81 ? ? ? Major Uncertainties i n Analysis 1. large uncertainty i n catch a l l o c a t i o n 2. f i s h intercepted by Alaska f i s h e r i e s not included 3. uncertainty i n the contribution of Washington and Columbia River produced f i s h 4. time s p e c i f i c age structure not a v a i l a b l e 5. extreme uncertainty in. optimal escapement estimation 6. inc r e a s i n g output from l o c a l hatchery I I . Impediments to Improved Management 1. i n c i d e n t a l catch of j u v e n i l e f i s h 2. i n t e r c e p t i o n by Alaska t r o l l 3. West coast t r o l l f i s h e r y NRSS ODD PINK -CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 130,000 ? 1 ? • N CATCH 844,000 ? 1 ? EXPLOITATION RATE .87 9 ? ? I. Major U n c e r t a i n t i e s i n Analysis 1. included s u b s t a n t i a l number of intercepted f i s h of unknown o r i g i n 2. escapement counts before 1963 are l e s s r e l i a b l e 3. extreme uncertainty i n optimal escapement estimation I I . Impediments to Improved Management 1. lack of information on the o r i g i n of f i s h caught i n t h i s area S K E E N H ODD P I N K 208 TOTAL STOCK ESCAPEMENT < CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 1,120,000 854,000 .43 701,000 1,220,000 .64 500,000 1,000,000 .67 - 900,000 .1,000,000 .53 Major Unc e r t a i n t i e s i n Analysis 1. i n t e r c e p t i o n by Alaska f i s h e r y not known 2. i n t e r c e p t i o n by Nass f i s h e r y not considered I I . Impediments to Improved Management 1. mixed f i s h e r y problem with sockeye C.C. ODD PINK 2 0 9 TOTAL STOCK ESCRPEMEVT < CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 1,020,000 3,280,000 2,000,000 7 CATCH 1,340,000 3,650,000 2,500,000 ? EXPLOITATION RATE .57 .53 .56 1 I. Major Uncertainties in Analysis 1. did not account for substock effects 2. may include some fish destined for Skeena 3. extreme uncertainty in setting upper bound for optimal escapement II. Impediments to Improved Management 1. mixed fishery problem with local chums J . S . O D D P I N K 2 1 0 TOTRL STOCK ESCAPEMENT ro * is o ja c." C.9 13 LRS TIME PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 600,000 790,000 .57 600,000 800,000 .72 400,000 1,000,000 .71 1,000,000 1,000,000 .5 I. Major Uncertainties in Analysis 1. uncertainty in catch allocation II. Impediments to Improved Management 1. mixed fishery problem with Georgia Strait and Fraser pinks, and Fraser socke>e G.S. ODD PINK 211 TOTfiL STOCK ESCAPEMENT r -u vt o < 1 . 4 CURRENT OPTIMUM ' PROBABLE LIMIT S ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 86,000 190,000 .69 362,000 665,000 .65 250,000 350,000 .58 2,000,000 2,000,000 .5 1.^ Major Uncertainties i n Analysis 1. uncertainty i n catch a l l o c a t i o n I I . Impediments to Improved Management 1. mixed f i s h e r y problem with Fraser pink and sockeye F R A S E R O D D P . I N K 212 cn CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 2,440,000 7,000,000 .74 2,000,000 4,000,000 .67 .1,500,000 3,500,000 .70 6,000,000 8,000,000 .57 I. Major Uncertainties in Analysis 1. uncertainty in catch allocation 2. d i f f i c u l t y in setting upper bound for optimal escapement II. Impediments to Improved Management 1. • allocation of equal shares to U.S. and Canadian fishermen 2. interception Johnstone Strait fishery 3. mixed fishery problem with sockeye and chum Q . C . I E V E N P I N K 213 TOTAL STOCK ESCAPEMENT 30 U l c 1st 64 66 50 .84 J.68 2.52 3.36 SPAMERS CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 251,000 41,000 .14 750,000 1,000,000 .57 600,000 900,000 .6 2,500,000 2,000,000 .44 I. Major Uncertainties In Analysis 1. may include fish distined for Skeena II. Impediments to Improved Management 1. d i f f i c u l t y in setting up terminal fishery O.C.2 EVEN PINK 214 • CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 692,000 1,065,000 .61 576,000 1,020,000 .64 400,000 500,000 .56 1,000,000 1,100,000 • 52 I. Major U n c e r t a i n t i e s i n A n a l y s i s 1. may include f i s h destined for other areas I I . Impediments to Improved Management 1. d i f f i c u l t y i n s e t t i n g up terminal f i s h e r y N f i S S E V E N P I N K TOTRL STOCK ESCRPEMEVT o z o m < M Q 50 m 215 )6 PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT 278,000 ? 200,000 ? CATCH 1,440,000 7 600,000 7 EXPLOITATION RATE .84 ? .75 7 Major U n c e r t a i n t i e s i n Analysis 1. included s u b s t a n t i a l number of intercepted f i s h of unknown o r i g i n 2. escapement counts before 1964 are less r e l i a b l e 3. extreme uncertainty i n optimal escapement estimation I I . Impediments to Improved Management 1. lack of knowledge on the o r i g i n of f i s h caught i n t h i s a so 55 TOTAL STOCK F.SCAPET1D/T S K E E N A EVEN PINK 2 1 6 60 C5 TEAR 70 75 80 c • CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 700,000 294,000 •30 600,000 1,140,000 .66 500,000 1,000,000 .67 1,000,000 1,000,000 .5 Major Uncertainties In Analysis 1. interception by Alaska fishery not known 2. interception by Nass fishery not considered I I . Impediments to Improved Management 1. mixed fishery problem with sockeye C . C . E V E N P I N K 217 TOTHL STOCK F.SCRPErOT o cn a n < 50 » CO — IV) CURRENT OPTIMUM " PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 3,300,000 5,160,000 3,000,000 ? CATCH 4,310,000 10,100,000 8,000,000 ? EXPLOITATION RATE .57 .66 .73 7 II. Major U n c e r t a i n t i e s i n Ana l y s i s 1. did. not account f o r substock. e f f e c t s 2. may include some f i s h destined f o r Skeena 3. extreme uncertainty i n s e t t i n g upper bound f o r optimal escapement Impediments to Improved Management . 1. mixed f i s h e r y problem with l o c a l chums R - S E V E N P I N K 218 • PROBABLE LIMITS ON OPTIMUM CURRENT OPTIMUM LOWER UPPER ESCAPEMENT 193,000,, 155,000 100,000 • CATCH 468,000 1,120,000 600,000 EXPLOITATION RATE .71 .88 .86 ? I. Major Uncertainties in Analysis 1. extreme uncertainty in setting upper bound for optimal escapement II. Impediments to Improved Management 1. mixed fishery problem with local chums \ • CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 1,350,000 ? 1,000,000 7 CATCH 2,620,000 7 1,000,000 7 EXPLOITATION RATE .66 7 .50 7 I. Major Uncertainties in Analysis 1. extreme uncertainty in optimal escapement estimates II. Impediments to Improved Management 1. mixed fishery problem with Fraser sockeye S-.W.V. I . EVEN PINK CURRENT OPTIMUM PROBABLE LIMI TS ON OPTIMUM LOWER UPPER ESCAPEMENT CATCH EXPLOITATION RATE 7,000. 43,000 .86 ? ? ? 25,000 35,000 .58 ? ? ? I. Major Uncertainties in Analysis 1. extreme uncertainty in optimal escapement estimation II. Impediments to Improved Management CURRENT OPTIMUM PROBABLE LIMITS ON OPTIMUM LOWER UPPER ESCAPEMENT 131,000 ? 150,000 ? CATCH 128,000 ? 200,000 ? EXPLOITATION RATE .49 ? .57 ? I. Major Uncertainties in Analysis 1. extreme uncertainty in optimal escapement estimation II. Impediments to Improved Management 

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