UBC Theses and Dissertations

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UBC Theses and Dissertations

Competition and information among British Columbia salmon purse seiners Ledbetter, Max 1986

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COMPETITION AND INFORMATION AMONG BRITISH COLUMBIA SALMON PURSE SEINERS By MAX LEDBETTER .Sc., The U n i v e r s i t y o f B r i t i s h Columbia, 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department 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 as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVE£S-I-TY OF BRITISH COLUMBIA A p r i l 1986 © Max L e d b e t t e r , 1986 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of p O l l Q f t The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date D E - 6 ( 3 / 8 1 ) A b s t r a c t T r a d i t i o n a l f i s h e r i e s models a r e b a s e d upon s i m p l i s t i c P o i s s o n a s s u m p t i o n s c o n c e r n i n g f l e e t b e h a v i o r . F i s h i n g v e s s e l s a r e assumed t o o p e r a t e i n d e p e n d e n t l y o f one a n o t h e r and t o sample the f i s h p o p u l a t i o n i n a random f a s h i o n . T h i s d i s s e r t a t i o n p r o v i d e s a r e v i e w o f t h e major component p r o c e s s e s c o n t r i b u t i n g t o the o p e r a t i o n o f f i s h i n g f l e e t s and u s e s f i e l d d a t a on salmon p u r s e s e i n e r s t o p r e s e n t t e s t s o f the h y p o t h e s e s c o n t a i n e d i n t h e h i s t o r i c a l a s s u m p t i o n s . Data p e r t a i n i n g t o i n t e r f e r e n c e c o m p e t i t i o n and i n f o r m a t i o n were a n a l y z e d . S i n c e f i s h e r i e s management u s u a l l y e n t a i l s a s s u m p t i o n s c o n c e r n i n g the form o f e x p l o i t a t i o n r a t e r e s p o n s e s t o e f f o r t , t h e consequences o f non-random f i s h e r m a n b e h a v i o r were e x p l o r e d . A l t e r n a t i v e models o f the f i s h i n g p r o c e s s were p r o p o s e d and examined. I n B r i t i s h Columbia, salmon p u r s e s e i n e r s l i n e up a t f i s h i n g a c c e s s p o i n t s , f o r m i n g w e l l d e f i n e d queues. These queues were measured o v e r time i n J o h n s t o n e S t r a i t u s i n g a one d i m e n s i o n a l r e c o r d i n g s c a l e . The d i s t r i b u t i o n o f e f f o r t was f i t t o t h e o r e t i c a l t r u n c a t e d P o i s s o n and t r u n c a t e d n e g a t i v e b i n o m i a l d i s t r i b u t i o n s . Most d a t a f i t t h e n e g a t i v e b i n o m i a l r a t h e r t h a n t h e P o i s s o n . Movement p a t t e r n s and time s e r i e s o f c a t c h e s were a l s o non-random. A n a l y s i s o f v a r i a n c e methods i n d i c a t e d t h a t l i n e - u p l e n g t h s r e f l e c t e d s e t c a t c h r a t e s . W a i t i n g times were q u a n t i f i e d u s i n g f u n c t i o n a l and s t a t i s t i c a l models. U s i n g t h e w a i t i n g t i m e s , the f l e e t s e t e f f o r t and number o f s e t s p e r b o a t were c a l c u l a t e d . A l t h o u g h t h e f l e e t s e t e f f o r t was a n e a r l i n e a r f u n c t i o n o f t h e number o f b o a t s i n t h e a r e a , i n t e r f e r e n c e c o m p e t i t i o n p r o d u c e d an i n i t i a l d e c r e a s e i n s e t s p e r v e s s e l . Two models were p r e s e n t e d f o r e x p l o i t a t i o n r a t e s i n r e l a t i o n t o q u e u i n g p a t t e r n s . The o v e r f l i g h t model was b a s e d upon the l i n e - u p d i s t r i b u t i o n s and assumed t h a t i n f o r m a t i o n was good. The model f i t w e l l and the p a r a m e t e r e s t i m a t e s r e f l e c t e d a n e c d o t a l and s t a t i s t i c a l i n f o r m a t i o n about f i s h b e h a v i o r . The e x p l o i t a t i o n r a t e s s a t u r a t e d a t an e f f o r t l e v e l o f 100 v e s s e l s . As an a l t e r n a t i v e model, the n e g a t i v e b i n o m i a l d i s t r i b u t i o n was u s e d t o e s t i m a t e e x p l o i t a t i o n r a t e s from c a t c h p e r v e s s e l d i s t r i b u t i o n s . I t was assumed t h a t salmon abundance does n o t a f f e c t the shape o f the d i s t r i b u t i o n s . As e f f o r t i n c r e a s e d , the d i s t r i b u t i o n o f c a t c h p e r v e s s e l was p r e d i c t e d t o become more skewed t o the o r i g i n . The p a r a m e t e r d e s c r i b i n g t h e shape o f the d i s t r i b u t i o n , k, s h o u l d have t r a c k e d t h e f i s h i n g power o f the f l e e t ( d e c r e a s i n g as t h e d i s t r i b u t i o n became more skewed). A f t e r f i t t i n g t h e weekly d i s t r i b u t i o n s , i t was f o u n d t h a t t h e r e l a t i v e e x p l o i t a t i o n r a t e s from the s a l e s s l i p model d i d n o t s a t u r a t e l i k e t h e p a r a m e t e r s o f t h e o v e r f l i g h t model. An a l t e r n a t i v e d e r i v a t i o n i n d i c a t e d t h a t t h e shape o f c a t c h p e r u n i t e f f o r t d i s t r i b u t i o n s r e s p o n d s t o the s i z e and a g g r e g a t i v e p r o p e r t i e s o f the f l e e t and t o the magnitude o f the c a t c h . As the mean c a t c h p e r s e t i n c r e a s e s , k w i l l i n c r e a s e . Salmon abundance, f l e e t n u m e r i c a l r e s p o n s e s and v e s s e l a g g r e g a t i o n s a f f e c t the skewness o f the c a t c h p e r u n i t e f f o r t d i s t r i b u t i o n s . I n g e n e r a l , t r a d i t i o n a l model assumptions were r e j e c t e d . V e s s e l s d i d n o t o p e r a t e i n d e p e n d e n t l y . Boats were n o t d i s t r i b u t e d i n a random f a s h i o n . The o v e r f l i g h t model p r o v i d e d p r e d i c t e d e x p l o i t a t i o n r a t e s . The e x p l o i t a t i o n r e s p o n s e t o e f f o r t was q u a l i t a t i v e l y d i s t i n c t f rom the forms i n c o r p o r a t e d i n t r a d i t i o n a l models. i i i TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i ACKNOWLEDGEMENTS i x CHAPTER I . I n t r o d u c t i o n 1 Responses o f the F i s h i n g System 3 Components o f t h e F i s h i n g P r o c e s s 6 C o m p e t i t i o n 6 I n f o r m a t i o n 8 S a t u r a t i o n and S e l e c t i v i t y . . . . . 9 F i s h i n g Power 10 S k i l l , S t r a t e g y , and M o t i v a t i o n 11 S e a r c h 13 M o b i l i t y 14 The Models 16 CHAPTER I I . Salmon S e i n e Boats and the Jo h n s t o n e S t r a i t Salmon F i s h e r y 20 V e s s e l O p e r a t i o n . 21 The J o h n s t o n e S t r a i t F i s h e r y 27 CHAPTER I I I . Data C o l l e c t i o n and V e r i f i c a t i o n 33 V e r i f i c a t i o n 35 CHAPTER IV. Independence and D i s t r i b u t i o n o f E f f o r t 44 L i n e - u p D i s t r i b u t i o n s 44 Movement and A c t i v i t y 51 D i s c u s s i o n 57 i v CHAPTER V. C o m p e t i t i o n and Set S t r a t e g i e s 60 L i n e - u p and E f f o r t L e v e l s 60 E f f e c t s o f S e t S t r a t e g i e s on C a t c h p e r Set 72 D i s c u s s i o n 79 CHAPTER V I . Models o f the F i s h i n g P r o c e s s 84 The O v e r f l i g h t Model 88 The S a l e s S l i p Model 109 D i s c u s s i o n 126 CHAPTER V I I . G e n e r a l D i s c u s s i o n 131 L i t e r a t u r e C i t e d 138 v LIST OF TABLES T a b l e I Parameter e s t i m a t e s f o r t h e t r u n c a t e d n e g a t i v e b i n o m i a l and t r u n c a t e d P o i s s o n f i t s t o queue l e n g t h f r e q u e n c y d a t a 48 T a b l e I I A c c e s s p o i n t - f l i g h t ANOVA 50 T a b l e I I I S h o r t term v e s s e l movements 55 T a b l e IV S e t time components 69 T a b l e V One-way ANOVA f o r v e s s e l e f f e c t s 76 T a b l e VI S e t t y p e - l i n e - u p - w e e k ANOVA f o r 28 v e s s e l s 77 T a b l e V I I Average w e i g h t e d r a t i o s f o r s e t type and l i n e - u p c a t c h e s 80 T a b l e V I I I Monte c a r l o s i m u l a t i o n o f e r r o r i n t h e o v e r f l i g h t model 110 T a b l e IX The param e t e r v a l u e s ( k ) , s t a n d a r d e r r o r s and sample s i z e s f o r the n e g a t i v e b i n o m i a l f i t t o CPUE d a t a . . . 118 v i LIST OF FIGURES F i g u r e 1 A c o n c e p t u a l model o f f l e e t dynamics 4 F i g u r e 2 F i s h i n g i n n o v a t i o n s i n the salmon s e i n e f i s h e r y . . . . 22 F i g u r e 3 S e t s t r a t e g i e s 25 F i g u r e 4 The J o h n s t o n e S t r a i t s t u d y a r e a 29 F i g u r e 5 A b e a c h s e t queue 36 F i g u r e 6 C o d i n g e r r o r 38 F i g u r e 7 O b s e r v a t i o n e r r o r 39 F i g u r e 8 R e p o r t e d and o b s e r v e d e f f o r t 41 F i g u r e 9 A e r i a l v e s s e l c o u n t s 42 F i g u r e 10 Queue l e n g t h f r e q u e n c y d i s t r i b u t i o n s 45 F i g u r e 11 Beach s e t l i n e - u p s : low e f f o r t 52 F i g u r e 12 Beach s e t l i n e - u p s : medium e f f o r t 53 F i g u r e 13 Beach s e t l i n e - u p s : h i g h e f f o r t 54 F i g u r e 14 W i t h i n o p e n i n g f l e e t movements 56 F i g u r e 15 Queue r e s p o n s e h y p o t h e s e s 61 F i g u r e 16 Average l i n e - u p l e n g t h v s . e f f o r t 63 F i g u r e 17 Maximum l i n e - u p l e n g t h v s . e f f o r t 64 F i g u r e 18 Average b e a c h s e t l i n e - u p l e n g t h v s . e f f o r t 65 F i g u r e 19 Average open s e t l i n e - u p l e n g t h v s . e f f o r t 66 F i g u r e 20 O p e r a t i o n o f a queue . 68 F i g u r e 21 W a i t i n g times as a f u n c t i o n o f queue l e n g t h 70 F i g u r e 22 Average number o f s e t s p e r b o a t v s . e f f o r t 73 F i g u r e 23 T o t a l s e t e f f o r t v s . e f f o r t 74 F i g u r e 24 P r o p o r t i o n o f open s e t e f f o r t v s . e f f o r t 82 F i g u r e 25 The s e l e c t i o n r u l e f o r e n t r y and e x i t o f e f f o r t . . . . 91 F i g u r e 26 E x p l o i t a t i o n r a t e s as a f u n c t i o n o f e f f o r t 101 v i i F i g u r e 27 C a t c h and CPUE v s . c a t c h p e r s e t 104 F i g u r e 28 The time s e r i e s o f the f i s h skewness para m e t e r c . . . 106 F i g u r e 29 T o t a l f l e e t k v s . s t a t i o n a r y f l e e t k 119 F i g u r e 30 k v s . e f f o r t 120 v i i i Acknowledgements I would l i k e t o thank the B r i t i s h Columbia S c i e n c e C o u n c i l and the C a n a d i a n Sportsman's Fund f o r t h e i r f i n a n c i a l s u p p o r t . Dr. P. L a r k i n , Dr. R. H i l b o r n , Dr. C. J . W a l t e r s , Dr. C. S. H o l l i n g , Dr. N. J . W i l i m o v s k y , Dr. I . V e r t i n s k y and Dr. D. Ludwig p r o v i d e d academic commentary and a s s i s t a n c e . My r e s e a r c h a s s i s t a n t , M i a D a v i s , d i d an a d m i r a b l e j o b on the f i s h i n g b o a t s . I w ould a l s o l i k e t o thank the N a t i o n a l S c i e n c e and E n g i n e e r i n g R e s e a r c h C o u n c i l and t h e U n i v e r s i t y o f B r i t i s h Columbia f o r p r o v i d i n g s c h o l a r s h i p s . The B r i t i s h Columbia p u r s e s e i n e r f i s h e r m e n made the t h e s i s p o s s i b l e . i x CHAPTER I INTRODUCTION F i s h e r i e s management encompasses many o f the most complex s c i e n t i f i c , t e c h n o l o g i c a l and human problems documented t h r o u g h o u t w r i t t e n h i s t o r y . F i s h e r m e n and s c i e n t i s t s a r e u n a b l e t o a d e q u a t e l y o b s e r v e p o p u l a t i o n s o f f i s h e s i n the n a t u r a l environment and c a n n o t q u a n t i f y the e r r o r s a s s o c i a t e d w i t h abundance e s t i m a t e s . The r e s u l t i s a p e r v a d i n g r e l i a n c e upon i n d i c e s i n c o r p o r a t i n g t r a d i t i o n a l and u s u a l l y u n t e s t e d a s s u m p t i o n s . The s t a n d a r d i n d e x o f abundance i s c a t c h p e r u n i t e f f o r t (CPUE). I t i s u s u a l l y p r o p o s e d t h a t CPUE i s p r o p o r t i o n a l t o abundance. T h i s f o r m u l a t i o n i s b a s e d upon s i m p l i s t i c , P o i s s o n assumptions about f l e e t b e h a v i o r . T h i s d i s s e r t a t i o n p r o v i d e s a r e v i e w o f the major component p r o c e s s e s c o n t r i b u t i n g t o the o p e r a t i o n o f f i s h i n g f l e e t s and uses f i e l d d a t a on salmon p u r s e s e i n e r s t o p r e s e n t t e s t s o f t h e h y p o t h e s e s c o n t a i n e d i n t h e h i s t o r i c a l a s s u m p t i o n s . Management o f any f i s h e r y i s d i r e c t l y o r i n d i r e c t l y dependent upon the amount o f e f f o r t a p p l i e d d u r i n g each f i s h i n g s e a s o n ( i . e . , number o f b o a t s , b o a t days, t r i p s o r s e t s , and a c t i v i t y ) . Measurement o f e f f o r t t r a n s l a t e s t h e b i o l o g i c a l v a r i a b l e s o f growth, m o r t a l i t y and r e c r u i t m e n t i n t o c a t c h ( R o t h s c h i l d 1977). E f f o r t i s r e g u l a t e d i n o r d e r t o " o p t i m i z e " e i t h e r y i e l d o r c a t c h and management m a n i p u l a t i o n s a r e u s u a l l y m a n i f e s t e d as 1) c a t c h q u otas ( i n c l u d i n g s i z e l i m i t s , i . e . , biomass q u o t a s ) , 2) l e n g t h o f o p e n i n g s d u r i n g t h e s e a s o n and, 3) d i r e c t l i m i t a t i o n o f the amount o f e f f o r t a v a i l a b l e t o t h e f i s h e r y ( i . e . , l i m i t e d e n t r y ) . U n c e r t a i n t i e s i n management o f e f f o r t and p r e d i c t i o n o f t h e e f f e c t i v e n e s s o f f u t u r e e f f o r t a r e r e f l e c t i o n s o f our i g n o r a n c e o f the 1 2 q u a n t i t a t i v e e c o l o g y o f f l e e t s and f i s h e r m e n . A l t h o u g h thousands o f man y e a r s have been d e v o t e d to f i s h r e l a t e d r e s e a r c h , p a s t d e s c r i p t i o n s o f f l e e t s and f i s h e r m e n were p r i m a r i l y l i m i t e d t o s i m p l e , t h e o r e t i c a l models t h a t do n o t r e f l e c t t h e c o m p l e x i t i e s o f the f i s h i n g p r o c e s s (Baranov 1918; R i c k e r 1940, 1944; B e v e r t o n and H o l t 1957; Paloheimo and D i c k i e 1964) and s t a t i s t i c a l s t a n d a r d i z a t i o n o f the e f f o r t measures u s e d i n t h e s e models (Kennedy 1951; P a r r i s h 1951; G u l l a n d 1956a; Inove and Watanabe 1958; P a r r i s h and K e i r 1959; O s t v e d t 1964; Robson 1966; Z i j l s t r a and de Veen 1963; H o v a r t and M i c h i e l s o n 1975; Houghton 1977; J o n e s and S c h o l e s 1980). F i s h e r i e s s c i e n t i s t s have p r o v i d e d comments on the q u a l i t a t i v e e f f e c t s o f v i o l a t i o n s o f the a s sumptions u n d e r l y i n g the t h e o r e t i c a l f o r m u l a t i o n s (Pope 1970; Peterman e t a l . 1979). A n t h r o p o l o g i s t s have summarized t h e i r a n e c d o t a l o b s e r v a t i o n s c o n c e r n i n g t h e s o c i o l o g i c a l a d a p t a t i o n s o f f i s h e r m e n ( T u n s t a l l 1969; A n d e r s o n and Wadel 1972a, 1972b; G o o d l a d 1972; Wadel 1972; B r e t o n 1973; P o g g i e and Gersuny 1974; Lummis 1977; N o r r and N o r r 1978) and the components o f the f i s h i n g p r o c e s s ( S t i l e s 1972; Watanabe 1977). E m p i r i c a l , q u a n t i t a t i v e d e s c r i p t i o n s o f f l e e t dynamics a r e r a r e and s y n t h e s e s a t t e m p t i n g t o summarize group b e h a v i o r on t h e f i s h i n g grounds as th e p r o d u c t o f i n t e r r e l a t e d mechanisms a r e n o n - e x i s t e n t . F i s h e r i e s s c i e n t i s t s s t u d i e d a s u b s e t o f the components o f the f i s h i n g p r o c e s s i n d e t a i l ( e . g . , Maeda and Minami 1969, 1976; Todd and L a r k i n 1971; Hamley 1975; R i c k e r 1976, 1981) o r p r o d u c e d n u m e r i c a l o v e r v i e w s which were n o t s t r u c t u r e d f o r h y p o t h e s i s t e s t i n g due to the problems a s s o c i a t e d w i t h d a t a v e r i f i c a t i o n ( e . g . , Peterman 1980; Peterman and S t e e r 1981). F a c t o r s t h a t c o n f o u n d p r e c i s e r e g u l a t i o n and i n t e r p r e t a t i o n o f e f f o r t and which have n o t b e en a d e q u a t e l y i n c l u d e d i n the t h e o r e t i c a l o r e m p i r i c a l models a r e c o m p e t i t i o n , i n f o r m a t i o n ( b o t h n e g a t i v e and f a c i l i t a t o r y ) , s e a r c h , and s k i p p e r ' s s k i l l . 3 T h i s i n t r o d u c t o r y c h a p t e r w i l l r e v i e w the c u r r e n t s t a t e o f knowledge c o n c e r n i n g the s t r u c t u r e and dynamic r e s p o n s e s o f f i s h i n g f l e e t s . Problems w i t h th e r e l a t i o n between t h e s e r e s p o n s e s and f i s h abundance w i l l be o u t l i n e d . Subsequent c h a p t e r s w i l l t h e n p r e s e n t a f i e l d s t u d y on t h e b e h a v i o r o f salmon p u r s e s e i n e r s i n an a r e a i n B r i t i s h C o l u m b i a and e x p l o r e t h e consequences o f t h i s b e h a v i o r on e x p l o i t a t i o n r a t e s on t h e salmon s t o c k s . Responses o f the F i s h i n g : System F l e e t dynamics a r e d e f i n e d h e r e as t h e t e m p o r a l and s p a t i a l p a t t e r n s i n e f f o r t and c a t c h p e r u n i t e f f o r t (CPUE) g e n e r a t e d by r e s p o n s e s o f t h e f i s h i n g system t o c e r t a i n d r i v i n g v a r i a b l e s , s t a t e v a r i a b l e s and p a r a m e t e r s ( F i g u r e 1 ) . T h r e e major r e s p o n s e s have been i d e n t i f i e d i n p r e d a t i o n s y stems: the r e s p o n s e o f a t t a c k r a t e s t o p r e y d e n s i t y , t h e r e s p o n s e o f a t t a c k r a t e s t o p r e d a t o r d e n s i t y and t h e n u m e r i c a l r e s p o n s e o f p r e d a t o r abundance t o changes i n p r e y abundance (Solomon 1949; H o l l i n g 1959). A l t h o u g h t h e s e p r o c e s s e s were d i s c u s s e d i n t h e c o n t e x t o f non-human p r e d a t i o n i n f i s h e r i e s systems (Peterman and G a t t o 1978; L a r k i n 1979), e x p l i c i t a p p l i c a t i o n s o f t h i s c o n c e p t u a l s t r a t i f i c a t i o n t o f i s h e r m e n have b e e n l i m i t e d t o two p a p e r s (Peterman 1980, Peterman and S t e e r 1981). E x t e n s i o n o f the r e s p o n s e c l a s s i f i c a t i o n t o f i s h i n g v e s s e l s and s k i p p e r s f a c i l i t a t e s an o r d e r e d a p p r o a c h to the p r o b l e m o f d e s c r i b i n g f l e e t dynamics and promotes c o m p a r i s o n t o o t h e r p r e d a t o r - p r e y s i t u a t i o n s ( s e e H o l l i n g 1973) . The two f u n d a m e n t a l v a r i a b l e s t h a t d r i v e the t h r e e r e s p o n s e s i n s i m p l e p r e d a t i o n systems a r e p r e y d e n s i t y and p r e d a t o r d e n s i t y . I n Peterman's (1980) example ( t h e I n d i a n f o o d f i s h e r i e s on salmon i n B.C.), the a n a l y s i s RESPONSES COMPONENTS STATE VARIABLES FUNCTIONAL RESPONSE' TO PREY DENSITY , SATURATION .SELECTIVITY •SEARCH •FISHING POWER •SKIPPER'S SKILL, STRATEGY and MOTIVATION -COMPETITION • INFORMATION COMPETITION WITHIN SEASON / NUMERICAL (AGGREGATIVE) — INFORMATION RESPONSE \ ^ M O B I L I T Y FUNCTIONAL RESPONSE. TO PREDATOR DENSITY ' > REGULATORY SCIENTIFIC TECHNOLOGICAL -ECONOMIC PARAMETERS I N S T I T U T I O N A L E N V I R O N M E N T A L ANNUAL NUMERICAL RESPONSE A CONCEPTUAL MODEL OF FLEET DYNAMICS F i g u r e 1 5 can be r e s t r i c t e d t o t h e s e v a r i a b l e s . But, s i m i l a r d e s c r i p t i o n s o f maior f i s h e r i e s must i n c l u d e t h r e e a d d i t i o n a l c a t e g o r i e s o f s t a t e v a r i a b l e s --t e c h n o l o g i c a l - e c o n o m i c , r e g u l a t o r y and s c i e n t i f i c . These v a r i a b l e s a f f e c t t h e c o n d i t i o n o f t h e f i s h i n g system a t each s t a g e o f l a r g e r p r o c e s s e s and may be q u a n t i f i e d as an a g g r e g a t e o f measurements ( e . g . , the r e g u l a t o r y s t a t e v a r i a b l e c o u l d be d e f i n e d as a c o m b i n a t i o n o f f i s h i n g time and f i s h i n g a r e a ) . The g e n e r a l s t r u c t u r e o f a f i s h e r y can be c h a r a c t e r i z e d by r e l a t i v e l y c o n s t a n t e n v i r o n m e n t a l and i n s t i t u t i o n a l p a r a m e t e r s . The s t a t e v a r i a b l e s and p a r a m e t e r s a f f e c t the s c a l e and the q u a l i t a t i v e form o f the r e s p o n s e s (see F i g u r e 1). Feedback l o o p s c e r t a i n l y e x i s t . T e c h n o l o g i c a l - e c o n o m i c s t a t e v a r i a b l e s a r e r e f l e c t e d by changes i n f i s h i n g equipment ( e . g . , r a d i o s , s o u n d e r s , n e t s , e t c . ) . M o t i v a t i o n a l l e v e l s may be a f f e c t e d by s h o r t term changes w i t h i n t h e g e n e r a l r e g u l a t o r y s t r u c t u r e ( e . g . , s h o r t o p e n i n g s o r t r a n s i e n t b o u n d a r i e s may m o d i f y the amount o f time s p e n t s e a r c h i n g ) . The s c i e n t i f i c v a r i a b l e c a n be d e f i n e d as t h e c e r t a i n t y o f s c i e n t i f i c a l l y d e r i v e d i n f o r m a t i o n ( e . g . , knowledge o f f i s h d i s t r i b u t i o n a l f a c t o r s ) . R e g u l a t o r y schemes ( e . g . , v e s s e l q u o tas, c l o s e d s e a sons, e f f o r t q u o t as, e t c . ) and the h i e r a r c h i c a l s t r u c t u r e o f c o m mercial f i s h i n g o p e r a t i o n s a r e c l a s s i f i e d as the i n s t i t u t i o n a l p a r a m e t e r s ; t h e s e p a r a m e t e r s may d e t e r m i n e the i n t e n s i t y o f c o m p e t i t i o n and t h e q u a l i t y o f i n f o r m a t i o n exchange. The h i s t o r i c a l i m p o r t a n c e o f a f i s h i n g i n d u s t r y may a f f e c t the e v o l u t i o n o f t h e i n s t i t u t i o n a l p a r a m e t e r s . The e n v i r o n m e n t a l p a r a m e t e r s ( i n s h o r e o r o f f s h o r e , s p e c i e s b i o l o g y ) d e f i n e f i s h e r y s p e c i f i c c h a r a c t e r i s t i c s ( e . g . , s e a r c h , s i t e o r h o l d l i m i t a t i o n o f f l e e t c a t c h r a t e s ) . T h e re a r e a few documented examples o f t h e e f f e c t s o f t h e s e v a r i a b l e s and p a r a m e t e r s ; p u b l i s h e d a c c o u n t s w i l l be m e n t i o n e d i n o t h e r s e c t i o n s . The s u c c e s s o f the e m p i r i c a l a n a l y s i s o f the r e s p o n s e s t o f i s h and 6 p r e d a t o r d e n s i t i e s i s dependent upon two appr o a c h e s : 1) an i n d e p e n d e n t e s t i m a t e o f abundance i n the form o f c a t c h p e r u n i t e f f o r t o f a l t e r n a t i v e gear t y p e s ( i n c l u d i n g s a m p l i n g t e c h n i q u e s , e.g., B o t s f o r d e t a l . 1983) o r the spawning escapements p l u s c a t c h o f anadromous s p e c i e s and 2) d a t a r e l a t i n g group dynamics t o c a t c h r a t e s , f i s h d i s t r i b u t i o n s and v e s s e l d e n s i t i e s . The n u m e r i c a l r e s p o n s e , however, i s b e s t u n d e r s t o o d i n the f i s h e r i e s c o n t e x t as a r e s p o n s e t o i n f o r m a t i o n -- t h e p a s t c a t c h o f the gear t y p e u nder e x a m i n a t i o n . Components o f the F i s h i n g P r o c e s s The q u a l i t a t i v e forms o f p r e d a t i o n r e s p o n s e s a r e d e t e r m i n e d by t h e r e l a t i v e c o n t r i b u t i o n s o f components. F o r example, the r e s p o n s e t o p r e d a t o r d e n s i t y c a n be e x p r e s s e d as c o m p e t i t i o n and i n f o r m a t i o n components. Changes i n t h e c o n t r i b u t i o n s o f t h e s e components t o t h e r e s p o n s e a r e f u n c t i o n s o f t h e t e c h n o l o g i c a l - e c o n o m i c and r e g u l a t o r y s t a t e v a r i a b l e s . C o m p e t i t i o n Knowledge o f c o m p e t i t i o n among f i s h e r m e n has u s u a l l y been r e s t r i c t e d t o a n e c d o t a l a c c o u n t s by a n t h r o p o l o g i s t s and f i s h e r i e s s c i e n t i s t s . The s c i e n t i f i c l i t e r a t u r e l a c k s q u a n t i t a t i v e d e m o n s t r a t i o n s o f the e f f e c t s o f c o m p e t i t i o n . A n d e r s o n and S t i l e s (1973) examined r i v a l r y among Newfoundland t r a w l e r s . T h e i r r e s e a r c h s u g g e s t e d t h a t t h e s e f i s h e r m e n engaged i n 7 s p a t i a l l y o r i e n t e d c o m p e t i t i o n : f i s h i n g u n i t s i n the same techno-economic s e c t o r competed f o r a c c e s s p o i n t s . E x p l o i t a t i o n c o m p e t i t i o n was s e c o n d a r y t o a c t u a l i n t e r f e r e n c e . I n the Maine l o b s t e r f i s h e r y , i n t e r f e r e n c e c o m p e t i t i o n e v o l v e d i n t o a t e r r i t o r i a l system o f a c t i v e l y p r o t e c t e d b o u n d a r i e s . A l t h o u g h c l a i m s were n o t r e c o g n i z e d by the s t a t e , t h e y were b a c k e d by s u r r e p t i t i o u s v i o l e n c e (Acheson 1975). I n t e r f e r e n c e c o m p e t i t i o n ( b l o c k i n g a c c e s s ) i s n o t a s i g n i f i c a n t element i n the CYRA t u n a f i s h e r y (Shimada and S h a e f e r 1956; P e l l a and P s a r o p u l o s 1975; O r b a c h 1977), b u t e x p l o i t a t i o n c o m p e t i t i o n (competing f o r the same f i s h ) r e s u l t i n g from the o v e r l a p o f s e a r c h o p e r a t i o n s may be an i m p o r t a n t f a c t o r a f f e c t i n g c a t c h r a t e s . The e f f e c t s o f c o m p e t i t i o n a r e m o d i f i e d by t e c h n o l o g i c a l i n p u t s . Indeed, i n n o v a t i o n s c o u p l e d w i t h f i s h e r m e n ' s p e r c e p t i o n s o f c o m p e t i t i o n and o f l o n g term d e c l i n e s i n c a t c h may p r o d u c e a r e d i s t r i b u t i o n o f e f f o r t t h a t m i t i g a t e s t h e c o m p e t i t i v e e f f e c t s on c a t c h r a t e s . L o f g r e n (1972) documented the a d a p t a t i o n s o f Swedish t r a w l e r s t o c o m p e t i t i o n and d e c l i n i n g c a t c h e s . Due t o t e c h n o l o g i c a l advances, f i s h e r m e n expanded r e s o u r c e u t i l i z a t i o n by s p e c i a l i z i n g i n e x p l o i t i n g new n i c h e s s u c h as r o c k y bottoms o r r e g i o n s where s m a l l y i e l d s d i s c o u r a g e d o t h e r s from i n t r u d i n g . The a n t h r o p o l o g i c a l a p p roach p r o v i d e s v a l u a b l e i n p u t t o our p e r c e p t i o n s o f f i s h e r y systems, y e t s o c i a l s c i e n t i s t s may make c o n c e p t u a l e r r o r s i n e x t e n s i o n s o f a n e c d o t a l o b s e r v a t i o n s t o dynamics: McCay (1978) m a i n t a i n e d t h a t s p a c i n g mechanisms ( i . e . , m i n i m i z a t i o n o f c o m p e t i t i v e e f f e c t s ) d e c r e a s e the l i k e l i h o o d o f o v e r f i s h i n g . A more r e a l i s t i c v i ew i s t h a t d i s p e r s i o n o f e f f o r t due t o t e c h n o l o g i c a l and m o t i v a t i o n a l changes i s a major c a u s a l agent u n d e r l y i n g p o s s i b l e i n c r e a s e s i n e x p l o i t a t i o n r a t e s . 8 I n f o r m a t i o n Orbach (1977) documented the s t r u c t u r e o f code groups i n the San Diego t u n a f l e e t . The use o f w a l k i e - t a l k i e s by c o o p e r a t i n g p a i r s o f t r a w l e r s t h a t a v o i d e d r i s k i n g v a l u a b l e i n f o r m a t i o n o v e r o t h e r r a d i o c h a n n e l s was d i s c u s s e d by L o f g r e n (1972) . S t u s t e r (1978) o b s e r v e d t h a t many o f the more s u c c e s s f u l U.S. West c o a s t crews p r o d u c e d h a l f o f t h e i r t o t a l c a t c h u s i n g i n f o r m a t i o n o b t a i n e d from i n t e r c e p t e d and/or d e c i p h e r e d r a d i o t r a n s m i s s i o n s o r d i r e c t communication w i t h members o f o r g a n i z e d groups. A n d e r s o n and Wadel (1972b) r e p o r t e d t h a t f r a g m e n t a r y i n f o r m a t i o n d e t e r m i n e d t h e s u c c e s s o f Norwegian h e r r i n g f i s h e r m e n . They a s s e r t e d t h a t t h e d i s p e r s i o n o f t h e f l e e t i n 1966 (due t o movement o f v e s s e l s t o I c e l a n d w i t h the a dvent o f the p o w e r b l o c k ) was the c a u s a l agent u n d e r l y i n g a d e c r e a s e i n l o c a l c a t c h r a t e s . A nderson and Wadel d i d n o t i n d i c a t e t h a t o t h e r f a c t o r s ( e . g . , h e r r i n g p o p u l a t i o n s i z e o r s c h o o l i n g mechanisms) may have p r e c i p i t a t e d t h e d e c l i n e i n c a t c h p e r u n i t e f f o r t . M a j or p a p e r s r e l a t e d t o i n f o r m a t i o n management have r e p o r t e d t h a t i n f o r m a t i o n exchange i s u s u a l l y d e c e p t i v e and t h a t v e r y l i t t l e f a c i l i t a t i o n o c c u r s (Anderson 1972, 1973; S t i l e s 1972). Exchange o f n e g a t i v e i n f o r m a t i o n i s known t o be g e n e r a l l y c h a r a c t e r i s t i c o f e a s t e r n C a n a d i a n and U.S. t r a w l e r o p e r a t i o n s , and E n g l i s h , F r e n c h , P o r t u g u e s e , and S p a n i s h deep s e a f l e e t s ( A n derson 1973) . The p r e v a l e n c e o f d e c e p t i v e s t r a t e g i e s has s e r i o u s consequences f o r w i t h i n - s e a s o n management and f o r the e f f i c i e n c y o f c o m m e r c i a l o p e r a t i o n s . A Newfoundland f l e e t owner s t a t e d t h a t h i s o p e r a t i o n s a t t a i n e d t h e h i g h e s t l e v e l o f e f f i c i e n c y as v e s s e l s were d i s p a t c h e d on the b a s i s o f a c c u r a t e r e p o r t s from the s k i p p e r s . But, o b s e r v a t i o n o f the d a t a exchanges r e v e a l e d t h a t much o f the i n f o r m a t i o n was p u r p o s e l y d i s t o r t e d . These f i s h i n g o p e r a t i o n s were n o t as i n t e g r a t e d as a p p e a r a n c e s s u g g e s t e d (Anderson 1972). 9 The p r e v a l e n c e o f d e c e p t i v e i n f o r m a t i o n c a n be a t t r i b u t e d t o the i n s t i t u t i o n a l s t r u c t u r e . A n d e r s o n (1972, 1973) m a i n t a i n e d t h a t the c e n t r a l f a c t o r s g e n e r a t i n g t h i s phenomenon a r e the c o - a d v e n t u r e system o f crew payment ( i . e . , s h a r e s ) and th e v e r t i c a l l y i n t e g r a t e d form o f the i n d u s t r y . Many s k i p p e r s f e e l t h a t t h e i r p r o d u c t i v i t y i s d e t e r m i n e d by w e l l k e p t s e c r e t s . A l s o , the crew may r e s e n t o v e r t s h a r i n g o f i n f o r m a t i o n w i t h c o m p e t i t o r s . C a t c h s u c c e s s d e t e r m i n e s the s t a b i l i t y o f t h e crew and a c c e s s t o b e t t e r v e s s e l s and e a r n i n g s w i t h i n t h e company. F u r t h e r m o r e , S t u s t e r (1978) s t a t e d t h a t t h e f a c i l a t o r y and/or d e c e p t i v e n a t u r e o f i n f o r m a t i o n management i s r e l a t e d t o t h e p r e dominate f i s h i n g s t r a t e g y ( e . g . , h u n t e r o r t r a p p e r ) and t h e a v a i l a b l e t e c h n o l o g i e s . F i s h i n g s t r a t e g i e s a r e o f t e n d e t e r m i n e d by the e n v i r o n m e n t a l p a r a m e t e r ( e . g . , f i s h e r m e n t r a p l o b s t e r s and s e a r c h f o r t u n a ) . S a t u r a t i o n and S e l e c t i v i t y Gear s a t u r a t i o n was r e v i e w e d by R o t h s c h i l d (1977) . Hamley (1975) summarized the g i l l n e t s i z e s e l e c t i v i t y l i t e r a t u r e . The s e l e c t i v i t y o f o t h e r g e a r t y p e s has a l s o been s t u d i e d ( e . g . , ICNAF 1963). Shardlow (1983) g a t h e r e d f i e l d d a t a f o r t h e a t t a c k r a t e o f salmon t o s p o r t g e a r a t t a c h e d t o an u nderwater camera. He f o u n d t h a t as abundance i n c r e a s e d , t h e f i s h f a c i l i t a t e d s e a r c h . More salmon a t t a c k e d t h e l u r e and t h e f i s h f o l l o w e d each o t h e r i n t o t h e a t t a c k . Shardlow d i d n o t e n c o u n t e r enough salmon f o r g e a r s a t u r a t i o n e f f e c t s t o become e v i d e n t . A t t h a t p o i n t , the e f f e c t s o f salmon s e a r c h f a c i l i t a t i o n would be overwhelmed by the f i s h e r m a n ' s h a n d l i n g t i m e . The r e s p o n s e o f c a t c h r a t e s t o salmon abundance would s a t u r a t e . R i c k e r (1981) a n a l y z e d d a t a c o n c e r n i n g t h e s i z e s o f B r i t i s h Columbia salmon s p e c i e s and c o n c l u d e d t h a t the d e c r e a s e i n the i n d i v i d u a l w e i g h t s o f 10 p i n k and coho salmon can be e x p l a i n e d by the s e l e c t i v e a c t i o n s o f g i l l n e t and t r o l l g e a r . E n v i r o n m e n t a l v a r i a b l e s were n o t c o r r e l a t e d w i t h t h e r e d u c t i o n i n s i z e . R i c k e r a t t r i b u t e d t h e time t r e n d t o a change i n the t e c h n o l o g i c a l - e c o n o m i c s t a t e v a r i a b l e : t h e p r o c e s s o r s began t o buy salmon by the pound r a t h e r t h a n on a p i e c e b a s i s d u r i n g the 1940s; f i s h e r m e n r e s p o n d e d w i t h g e a r t h a t t a r g e t e d on t h e l a r g e s t f i s h . F i s h i n g Power G u l l a n d (1956a) d e f i n e d the a b s o l u t e f i s h i n g power o f a v e s s e l as the p r o p o r t i o n o f t h e v u l n e r a b l e f i s h t a k e n d u r i n g a g i v e n time i n t e r v a l i n a p a r t i c u l a r f i s h i n g a r e a . The a n a l o g o u s p a r a m e t e r f o r a f l e e t i s c a t c h a b i l i t y . S i n c e a b s o l u t e measurements a r e r a r e l y o b t a i n e d , f i s h e r i e s managers have u s u a l l y r e s t r i c t e d t h e i r a n a l y s e s t o r e l a t i v e q u a n t i t i e s . R e l a t i v e f i s h i n g power i s o f t e n d e f i n e d as t h e CPUE o f a v e s s e l r e l a t i v e t o t h e CPUE o f a s t a n d a r d v e s s e l ( G u l l a n d 1956a; Robson 1966; R o t h s c h i l d 1977). T r a d i t i o n a l methods f o r c a l c u l a t i n g r e l a t i v e f i s h i n g power e n t a i l n o r m a l i z a t i o n o f the d a t a . G u l l a n d (1956a) and B e v e r t o n and H o l t (1957) r e p o r t e d t h a t the l o g t r a n s f o r m s t a b i l i z e d the v a r i a n c e o f s u c c e s s i v e t r i p s b y t h e same or d i f f e r e n t b o a t s and p r o d u c e d a n o r m a l d i s t r i b u t i o n o f f i s h i n g power among b o a t s . R e l a t i v e f i s h i n g power i s t h e n r e l a t e d t o v e s s e l c h a r a c t e r i s t i c s s u c h as horsepower and tonnage by a n a l y s i s o f v a r i a n c e methods. T h i s a p p r o a c h has been u t i l i z e d many times d u r i n g the p a s t two and one h a l f decades, b u t the u n d e r l y i n g d i s t r i b u t i o n o f CPUE i s r a r e l y r e p o r t e d -- the l o g t r a n s f o r m appears t o have been a c c e p t e d on a p u r e l y p r a g m a t i c b a s i s . F i s h e r i e s s c i e n t i s t s have i g n o r e d v a l u a b l e i n f o r m a t i o n p e r t a i n i n g t o s k i p p e r ' s s t r a t e g i e s and s k i l l , i n f o r m a t i o n t h a t may be c o n t a i n e d i n t h e shapes o f the o r i g i n a l d i s t r i b u t i o n s ( s e e G u l l a n d 1964) and the c o r r e s p o n d i n g r e l a t i o n s h i p s 11 between the mean and the v a r i a n c e o f s u c c e s s i v e t r i p s . T r e s c h e v (1978) d e f i n e d f i s h i n g power as the r a t i o o f t h e a r e a o r volume o f t h e water f i s h e d t o the d u r a t i o n o f f i s h i n g . T h i s zone o f i n f l u e n c e i s c a l c u l a t e d i n terms o f the s t r u c t u r e and r a t e o f movement o f the f i s h i n g g e ar. More work i s n e c e s s a r y so t h a t the a p p a r e n t e f f e c t s o f horsepower and tonnage can be i n c o r p o r a t e d i n t o the p a r a m e t e r as, p erhaps, the shape o f the g e a r under d i f f e r e n t e n v i r o n m e n t a l c o n d i t i o n s . He t h e n d e f i n e d t h e c a p a b i l i t y o f t h e f i s h i n g u n i t as t h e CPUE d i v i d e d by t h e mean CPUE w i t h i n t h e same t i m e - a r e a s t r a t u m . T r e s c h e v d e v i s e d an a b s o l u t e parameter f o r the s t a n d a r d i z a t i o n o f r e l a t i v e c a p a b i l i t i e s . The (assumed) e f f e c t s o f t h e t e c h n o l o g i c a l - e c o n o m i c v a r i a b l e on gear and, u l t i m a t e l y , on the f u n c t i o n a l r e s p o n s e t o p r e y d e n s i t y c a n be o b j e c t i v e l y q u a n t i f i e d i n d e p e n d e n t l y o f h i s t o r i c a l c a t c h r e c o r d s . F i s h i n g c a p a b i l i t y , however, remains r e l a t i v e and c o n t a i n s an a d d i t i o n a l component: s k i p p e r s ' s k i l l , s t r a t e g y and m o t i v a t i o n . S k i l l . S t r a t e g y and M o t i v a t i o n A l t h o u g h f i s h e r i e s s c i e n t i s t s have r e c o g n i z e d t h a t d i f f e r e n c e s i n s k i p p e r ' s s k i l l , s t r a t e g y and m o t i v a t i o n may e x p l a i n much o f the v a r i a t i o n i n f i s h i n g power among b o a t s , a wide s c a l e a t t e m p t t o r e l a t e t h i s component t o c a t c h s u c c e s s has n o t been made. Orbach (1977) o b s e r v e d t h a t d i f f e r e n c e s i n s e a r c h s t r a t e g y w i t h i n the San D i e g o t u n a f l e e t were r e l a t e d t o p h y s i c a l c o n s t r a i n t s ( e . g . , o l d o r new b o a t s ) , m o t i v a t i o n ( e . g . , mortgages, f a m i l y ) and p e r s o n a l i t y . He d e f i n e d two s t r a t e g i e s -- the h u n t e r and t h e c h a s e r . H u n t e r s r e l i e d on t h e i r own e x p e r i e n c e and hunches t o f i n d f i s h . C h a s e r s u s e d r a d i o i n f o r m a t i o n from o t h e r b o a t s and o f t e n moved w i t h o r i n t o a g g r e g a t i o n s o f b o a t s . B o t h groups c o n t a i n e d s k i p p e r s t h a t a c c e p t e d d i f f e r e n t d e g r e e s o f r i s k b a s e d on s i m i l a r i n f o r m a t i o n . 12 Cove (1973) compared s t r a t e g i e s i n t h r e e f i s h e r i e s : t h e Newfoundland o f f s h o r e f i s h e r y , t h e B.C. i n s h o r e , salmon f i s h e r y and t h e o y s t e r f i s h e r y o f C o r n w a l l , E n g l a n d . He d e v e l o p e d a model f o r d i f f e r e n c e s i n r i s k t a k i n g b a s e d on the u n c e r t a i n t y o f the r e s o u r c e , the m o t i v a t i o n o f t h e s k i p p e r and t h e c a p a b i l i t y o f t h e gear ( i . e . , t e c h n o l o g y ) . H i s d e f i n i t i o n o f r i s k i n c l u d e d e n v i r o n m e n t a l f e a t u r e s ( s e t t i n g n e a r r o c k s , k e l p e t c . ) , s e l e c t i o n by l a r g e o r a v e r a g e c a t c h and i n d e p e n d e n t o r g r e g a r i o u s s t r a t e g i e s . The h i g h e s t l e v e l o f r i s k t a k i n g was p r e d i c t e d t o o c c u r when u n c e r t a i n t y was low, c a p a b i l i t y was low and m o t i v a t i o n was h i g h . Cove d i d n o t i n c l u d e an i m p o r t a n t f a c t o r -- p e r s o n a l i t y . I s the s k i p p e r ' s i n h e r e n t n a t u r e t h a t o f a h u n t e r o r a f o l l o w e r ( c h a s e r ) ? The reward s t r u c t u r e ( i . e . , i n s t i t u t i o n a l p a rameter) o f the Newfoundland and B.C. f i s h e r i e s were s i m i l a r ; the c o a d v e n t u r e system and th e i mportance o f r e l a t i v e p e r f o r m a n c e s t i m u l a t e d i n t e n s e c o m p e t i t i o n . M o t i v a t i o n a l l e v e l s were n e g a t i v e l y c o r r e l a t e d w i t h ownership and rank w i t h i n the company f l e e t . I n the C o r n w a l l o y s t e r f i s h e r y , t h e i n s t i t u t i o n a l p a r a m e t e r was c h a r a c t e r i z e d by i n d i v i d u a l o w n ership o f s m a l l b o a t s and t h e community s o c i a l s t r u c t u r e . The knowledge t h a t p a s t m a x i m i z a t i o n o f p r o d u c t i o n l e d to the n e a r d e s t r u c t i o n o f t h e f i s h e r y s t i m u l a t e d community demands f o r c o n f o r m i t y t o low r i s k t a k i n g b e h a v i o r and n o n - i m p l e m e n t a t i o n o f t e c h n o l o g i c a l p o t e n t i a l . P a l s s o n and D u r r e n b e r g e r (1982) p e r f o r m e d s t a t i s t i c a l a n a l y s e s o f I c e l a n d i c c o d c a t c h e s , v e s s e l c h a r a c t e r i s t i c s and s k i p p e r s ' e x p e r i e n c e . They c o n c l u d e d t h a t the s k i p p e r e f f e c t i s a myth u s e d f o r crew i m p r e s s i o n management ( i . e . , s k i p p e r ' s r h e t o r i c b o l s t e r s crew m o r a l e ) . The v e s s e l s i z e s and the number o f t r i p s made d u r i n g t h e s e a s o n a c c o u n t e d f o r most o f the v a r i a n c e i n c a t c h . There was no r e l a t i o n s h i p between e x p e r i e n c e and s u c c e s s . The h i g h c o r r e l a t i o n between v e s s e l s i z e and c a t c h may have 13 masked the l e a r n i n g r e s p o n s e -- s k i p p e r s ' e x p e r i e n c e was n e g a t i v e l y c o r r e l a t e d w i t h b o a t tonnage. A l s o , q u a n t i f i c a t i o n o f w i t h i n t r i p a c t i v i t y and e n e r g y e x p e n d i t u r e might have i n d i c a t e d d i f f e r e n c e s i n c o s t / b e n e f i t r a t i o s ; t h e crews c o u l d have resp o n d e d t o n e t c a s h r e t u r n s and i g n o r e d s k i p p e r s ' r h e t o r i c . The a u t h o r s s u g g e s t e d t h a t I c e l a n d i c f i s h e r m e n a v o i d e d r i s k y s t r a t e g i e s and c o n c e n t r a t e d t h e i r e f f o r t i n a r e a s p o s s e s s i n g a h i s t o r y o f c o n t i n u o u s c a t c h e s . S e a r c h Paloheimo and D i c k i e (1964) and Paloheimo (1971a, 1971b), u s i n g t h e o r e t i c a l models o f the p r e d a t i o n p r o c e s s , s t a t e d t h a t t h e d i s t r i b u t i o n s o f p r e d a t o r s e a r c h t i m e s and c a t c h e s a r e dependent upon t h e p r e y d i s t r i b u t i o n s . F u r t h e r m o r e , c a t c h p e r f i s h i n g day w i l l n o t r e f l e c t changes i n abundance i n s e a r c h f i s h e r i e s u n l e s s the s c h o o l d e n s i t y i s p r o p o r t i o n a l t o abundance. E f f o r t must be s t a n d a r d i z e d f o r the s e a r c h time i n v o l v e d i n l o c a t i n g s c h o o l s . S h o t t o n (1974) p r e s e n t e d a good r e v i e w o f s e a r c h models i n t h e f i s h e r i e s c o n t e x t and began h i s r e s e a r c h where Paloheimo l e f t o f f . He c o n s i d e r e d methods f o r o p t i m i z i n g s e a r c h and d e c i s i o n making when t h e f i s h d i s t r i b u t i o n was s p e c i f i e d b y e x p e r i m e n t a l f i s h i n g . Bayes' theorem was u s e d i n making d e c i s i o n s about f i s h i n g t a c t i c s . S h o t t o n d i d n o t s p e c i f y d e t e c t i o n f u n c t i o n s and c o m p e t i t i o n e f f e c t s were n o t i n c l u d e d . Orbach (1977) d e s c r i b e d s e a r c h f o r t u n a as b e i n g dependent on many f a c t o r s s uch as weather, water tempe r a t u r e and t h e b e h a v i o r o f o t h e r b o a t s . The random s e a r c h f u n c t i o n (see Koopman 1980), t h e r e f o r e , does n o t a p p l y . The i n v e r s e cube law o f d e t e c t i o n , however, c o n t a i n s an a d d i t i o n a l p a r a m e t e r t h a t d e s c r i b e s the o b s e r v e r ' s a b i l i t y and m o t i v a t i o n , weather and o t h e r f a c t o r s . 14 B o t h the random and i n v e r s e cube law f u n c t i o n s have an e x p o n e n t i a l form, r e s u l t i n g i n an i m p o r t a n t p r o p e r t y : t h e p r o b a b i l i t y o f d e t e c t i n g i n t h e n e x t time i n c r e m e n t , g i v e n f a i l u r e t o d e t e c t the t a r g e t , i s i n dependent o f p r e v i o u s i n c r e m e n t s (Stone 1975). Mangel (1982) u s e d the random s e a r c h f u n c t i o n i n h i s renewal model f o r s e a r c h e f f o r t and c a t c h r a t e s i n the tuna f i s h e r y . The p r i m a r y r e s u l t was t h a t c a t c h p e r u n i t e f f o r t i s more s e n s i t i v e t o s e a r c h a b i l i t y and r e l a t e d t e c h n o l o g y t h a n t o the time t a k e n t o complete a s e t . R e s e a r c h i s n e c e s s a r y f o r s p e c i f y i n g d e t e c t i o n f u n c t i o n s i n f i s h e r i e s where the p r o b a b i l i t y o f d e t e c t i n g c o n c e n t r a t i o n s o f f i s h i n s e q u e n t i a l time i n c r e m e n t s ( i . e . , days, o p e n i n g s e t c . ) i s n o t i n d e p e n d e n t o f p r e v i o u s i n c r e m e n t s . A l s o , d e t e c t i o n f u n c t i o n s w i l l change w i t h the t e c h n o l o g i c a l - e c o n o m i c v a r i a b l e and a p r i o r i p r o b a b i l i t i e s , whether " o b j e c t i v e l y " d e f i n e d by the s k i p p e r o r r e m a i n i n g as a s e t o f hunches and u n c o n s c i o u s w e i g h t i n g s o f the a v a i l a b l e i n f o r m a t i o n , w i l l change w i t h t h e q u a l i t y ( i . e . , c e r t a i n t y ) o f s c i e n t i f i c a l l y d e r i v e d i n f o r m a t i o n on d i s t r i b u t i o n a l f a c t o r s ( e . g . , water t e m p e r a t u r e ) . The r e g u l a t o r y s t a t e v a r i a b l e ( e . g . , s h o r t e r o p e n i n g s ) may a f f e c t t h e m o t i v a t i o n a l a s p e c t s o f s e a r c h . M o b i l i t y M o b i l i t y c a n be o p e r a t i o n a l l y d e f i n e d as the p o t e n t i a l f o r w i t h i n s e a s o n n u m e r i c a l ( a g g r e g a t i v e ) r e s p o n s e s t o i n f o r m a t i o n about f i s h abundance. I t i s a f f e c t e d by a l l t h r e e s t a t e v a r i a b l e s and i m p l e m e n t a t i o n o f e x i s t i n g p o t e n t i a l i s bounded by the c o m p e t i t i o n and i n f o r m a t i o n components. The I n t e r - A m e r i c a n T r o p i c a l Tuna Commission u s e d an i n d e x ( d e v e l o p e d by G u l l a n d 1956b) f o r m e a s u r i n g the s u c c e s s o f the f l e e t i n c o n c e n t r a t i n g i t s e f f o r t on h i g h e r t h a n average f i s h d e n s i t i e s ( G r i f f i t h s 1960; C a l k i n s 15 1961, 1963). The c o n c e n t r a t i o n i n d e x was d e f i n e d as the u n w e i g h t e d i n d e x o f f i s h d e n s i t y d i v i d e d by the w e i g h t e d i n d e x o f d e n s i t y . The unweighted i n d e x i s the t o t a l c a t c h d i v i d e d by the t o t a l e f f o r t and t h e w e i g h t e d i n d e x i s t h e sum o f the CPUE from e a c h e x p l o i t e d a r e a d i v i d e d by the t o t a l number o f e x p l o i t e d a r e a s : N I - (CT/ET)/(1/N Z C i / e i ) 1) i = l Where I = the c o n c e n t r a t i o n i n d e x CT = t o t a l c a t c h ET = t o t a l e f f o r t c = a r e a c a t c h e = a r e a e f f o r t N = t o t a l number o f a r e a s A c c o r d i n g t o t h i s view, i f e q u a l e f f o r t i s d e v o t e d t o t h e e x p l o i t e d a r e a s ( i . e . , u n i f o r m a p p l i c a t i o n o f e f f o r t ) , t h e two d e n s i t y i n d i c e s w i l l be e q u a l ; i f more e f f o r t i s a p p l i e d t o a r e a s where CPUE i s h i g h e r t h a n a v e r a g e , the u n w e i g h t e d i n d e x w i l l e x c e e d t h e w e i g h t e d i n d e x . T h e r e f o r e , i n d e x v a l u e s g r e a t e r t h a n one a r e i n d i c a t i v e o f s u c c e s s f u l c o n c e n t r a t i o n o f e f f o r t on f i s h . The p r o b l e m w i t h t h i s f o r m u l a t i o n i s t h a t c o m p e t i t i o n e f f e c t s a r e i g n o r e d . O p t i m a l d i s t r i b u t i on o f e f f o r t i n t h e p r e s e n c e o f c o m p e t i t i o n (and good i n f o r m a t i o n ) s h o u l d r e s u l t i n e q u a l CPUE among a r e a s , p r o d u c i n g a c o n c e n t r a t i o n i n d e x o f one. U n i f o r m and o p t i m a l a p p l i c a t i o n o f e f f o r t a c r o s s a r e a s r e s u l t s i n an i d e n t i c a l i n d e x v a l u e -- i n t e r p r e t a t i o n o f t h e dynamics o f t h e c o n c e n t r a t i o n i n d e x becomes vague. H i l b o r n and L e d b e t t e r (1979), u s i n g d a t a from the B.C. salmon f i s h e r y , i m p l i c i t l y i n c l u d e d c o m p e t i t i o n e f f e c t s on m o b i l i t y p a t t e r n s . I f b o a t s 16 o p t i m i z e w i t h r e s p e c t t o f i s h abundance and v e s s e l c o m p e t i t i o n , t h e n i n d i v i d u a l f i s h i n g u n i t s s h o u l d move between a r e a s t o e q u a l i z e the CPUE i n each a r e a . I n r e a l i t y , however, t h e r e were d i f f e r e n c e s i n the r a t i o s o f a r e a CPUE t o B.C. t o t a l CPUE. H i l b o r n and L e d b e t t e r a t t r i b u t e d t h e s e d i f f e r e n c e s t o a r e a s p e c i f i c d e s i r a b i l i t i e s and c o s t s o f f i s h i n g . They d i d n o t d i s c u s s a n o t h e r i m p o r t a n t f a c t o r : the p e r c e n t a g e o f m o b i l e b o a t s a b l e to s u c c e s s f u l l y f i s h an a r e a may have v a r i e d among a r e a s . F u r t h e r m o r e , t h e r e were 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 r e l a t i v e r a n k s o f th e a r e a s ; t h e s e changes may have b e e n r e l a t e d t o i m p e r f e c t i n f o r m a t i o n and t o the f i s h e r m e n ' s p e r c e p t i o n o f s p e c i e s v a l u e (some s e i n e s k i p p e r s seem t o p o s s e s s an i n e x p l i c a b l e d e s i r e t o chase sockeye r e g a r d l e s s o f t h e i r abundance r e l a t i v e t o o t h e r salmon s p e c i e s ) . L i a o (1979) p u b l i s h e d an economic a n a l y s i s o f shrimp v e s s e l m o b i l i t y i n t h e South A t l a n t i c s t a t e s ( U . S . ) . He c a l c u l a t e d a m o b i l i t y c l a s s i n d e x f o r e a c h v e s s e l , u s i n g a l i n e a r model c o n s i s t i n g o f c a t c h , v e s s e l c h a r a c t e r i s t i c s and s k i p p e r ' s s k i l l and m o t i v a t i o n . The s i g n i f i c a n c e o f t h e s e f a c t o r s v a r i e d from s t a t e t o s t a t e . A l i n e a r e n t r y f u n c t i o n f o r out o f s t a t e v e s s e l movement i n t o a f i s h e r y was s p e c i f i e d i n terms o f an i n d e x o f shrimp abundance ( w i n t e r weather) and th e a r e a s p e c i f i c e x - v e s s e l shrimp p r i c e s . L i a o c o n c l u d e d t h a t the d i f f e r e n c e s i n s t a t e p r i c e s were i m p o r t a n t and t h a t many o t h e r f a c t o r s must be i n c l u d e d (R = 0.6). The Models F i s h e r i e s models (Baranov 1918; R i c k e r 1940, 1944; B e v e r t o n and H o l t 1957; P e l l a 1969; C l a r k and Mangel 1979) have been p r e d i c a t e d on the a s s u m p t i o n t h a t t h e f i s h i n g p r o c e s s i s s i m i l a r t o random s a m p l i n g --c a t c h a b i l i t y remains c o n s t a n t . Even when h e t e r o g e n e i t i e s a r e examined and 17 c a t c h a b i l i t y i s shown t o change w i t h s c h o o l d i s t r i b u t i o n s and s i z e ( e . g . , P a l oheimo and D i c k i e 1964; Paloheimo 1971a, 1971b; S a i l a and F l o w e r s 1969), the models i n c o r p o r a t e what appears t o be an e x t r e m e l y u n r e a l i s t i c a s s u m p t i o n ; f i s h i n g u n i t s o p e r a t e i n d e p e n d e n t l y . The e f f e c t s o f d e p a r t u r e s from t h i s a s s u m p t i o n were n o t e d by G u l l a n d (1964), G a r r o d (1964), FAO (1975) , R a d o v i c h (1976) , and were d i s c u s s e d i n more d e t a i l by R o t h s c h i l d (1977). P e l l a (1969) and P e l l a and P s a r o p u l o s (1975) p r o d u c e d " r e a l i s t i c " , s t o c h a s t i c models f o r the o p e r a t i o n o f s e a r c h i n g p u r s e s e i n e f l e e t s , y e t t h e y i n c o r p o r a t e d s e a r c h as a P o i s s o n p r o c e s s . P e l l a e t a l . i g n o r e d the human i n t e r a c t i o n s documented by Orbach (1977), a s p e c t s o f group dynamics w h i c h may l e a d t o m a r k e d l y d i f f e r e n t d i s t r i b u t i o n s o f s e a r c h t i m e s . A n o t h e r s i m p l e P o i s s o n model was u t i l i z e d by C l a r k and Mangel (1979) and t h e y n o t e d t h a t t h e p r o b l e m o f a l l o c a t i o n o f e f f o r t o v e r non-random d i s t r i b u t i o n s o f f i s h has n o t been s o l v e d . Mangel (1982) d e r i v e d a model f o r c o o p e r a t i v e s e a r c h b a s e d upon Koopman's random s e a r c h model. The e f f e c t s o f i n f o r m a t i o n s h a r i n g upon c a t c h r a t e s were n o t a n a l y z e d . T r a d i t i o n a l s e a r c h t h e o r y a s s u m p t i o n s w i l l n o t be met i n f i s h e r i e s where f i s h e r m e n ' s s t r a t e g i e s r e f l e c t s p e c i a l i z e d s k i l l s , h i s t o r i c a l i n f o r m a t i o n and i n t i m a t e knowledge o f f i s h b e h a v i o r . R e c e n t l y , f i s h e r i e s s c i e n t i s t s examined p o s s i b l e mechanisms f o r c r i t i c a l d e p e n s a t i o n i n f i s h s t o c k s ( e . g . , C l a r k 1974; J ones and W a l t e r s 1976; Peterman 1977; C l a r k and Mangel 1979). G u l l a n d (1977) q u a l i t a t i v e l y i l l u s t r a t e d f i s h e r m e n as c r i t i c a l d e p e n s a t o r y a g e n ts when c a t c h a b i l i t y i n c r e a s e s as f i s h p o p u l a t i o n l e v e l s d e c r e a s e . He d i d n o t s p e c u l a t e about t h e m e c h a n i s t i c r e l a t i o n s h i p s between the f i s h i n g p r o c e s s and c a t c h a b i l i t y . Peterman (1980) r e l a t e d the q u a l i t a t i v e form o f an e m p i r i c a l c a t c h response t o f i s h d e n s i t y and p o s s i b l e c r i t i c a l d e p e n s a t i o n i n the B.C. n a t i v e I n d i a n 18 f o o d f i s h e r y . But, he a s s e r t e d t h a t f i s h e r i e s managers c a n d e t e r m i n e whether d e p e n s a t i o n i s o c c u r r i n g by u t i l i z i n g a model b a s e d on p r e s e a s o n f o r e c a s t s o f r u n s t r e n g t h s (which a r e v e r y u n c e r t a i n e s t i m a t e s ) and p a r a m e t e r s r e l a t e d t o c a t c h d a t a t h a t a r e u s u a l l y i n a c c e s s i b l e u n t i l a f t e r the f i s h e r y has.ended. Perhaps s p e c u l a t i v e r e s e a r c h on mechanisms f o r c a t a s t r o p h i c o r a c c e l e r a t e d d e c l i n e s o f f i s h s t o c k s s h o u l d i n c l u d e t h e p o s s i b i l i t i e s t h a t c o m p e t i t i o n d e c r e a s e s ( r e f e r t o the L o f g r e n (1972) example above) o r t h a t i n f o r m a t i o n q u a l i t y i n c r e a s e s ( r e s u l t i n g i n l a r g e r c a t c h c o e f f i c i e n t s ) as s t o c k s a r e d i m i n i s h e d . T h i s p a t t e r n i n t o t a l f l e e t r e s p o n s e may be f u n c t i o n a l l y r e l a t e d t o f i s h e r m e n ' s p e r c e p t i o n s o f d e c r e a s i n g f i s h abundance and changes i n the i n s t i t u t i o n a l p arameter, o r may s i m p l y m i r r o r t e c h n o l o g i c a l and s c i e n t i f i c advances t h a t p a r a l l e l t h e e f f e c t s o f o v e r f i s h i n g . Under the c o n s t r a i n t s o f p r e s e n t t e c h n o l o g y , i n d e p e n d e n t e s t i m a t e s o f s t o c k abundance a r e r a r e . But, o b s e r v a t i o n s o f f l e e t b e h a v i o r c a n be made and our models c a n be reworked i n t o a s l i g h t l y more c o m p l i c a t e d form. As R o t h c h i l d (1977) s t r e s s e d , measurements o f e f f o r t and t h e e x p l o i t a t i o n r e s p o n s e t o e f f o r t a r e n e c e s s a r y i n g r e d i e n t s o f o p t i m i z a t i o n p r o c e d u r e s . C o m p e t i t i o n , i n f o r m a t i o n , s a t u r a t i o n , s e a r c h and t e c h n o l o g y a f f e c t t h e e x p l o i t a t i o n r e s p o n s e s . T r a d i t i o n a l models a r e p r e d i c a t e d upon the a s s u m p t i o n t h a t e x p l o i t a t i o n r a t e s a r e a l i n e a r f u n c t i o n o f e f f o r t or s a t u r a t e w i t h an asymptote a t 100% o f the f i s h p o p u l a t i o n . V e s s e l c o m p e t i t i o n and i n f o r m a t i o n w i l l a f f e c t the q u a l i t a t i v e form o f the e x p l o i t a t i o n r e s p o n s e . The g r e a t e s t p o t e n t i a l f o r q u a n t i f y i n g t h e e f f e c t s o f i n f o r m a t i o n q u a l i t y and c o m p e t i t i o n i n d e p e n d e n t l y o f f i s h d e n s i t y e s t i m a t e s i n v o l v e s e x a m i n a t i o n o f s k i p p e r ' s r e s p o n s e s t o h e t e r o g e n e o u s d i s t r i b u t i o n s o f c a t c h r a t e s and q u a n t i f i c a t i o n o f i n t e r f e r e n c e 19 c o m p e t i t i o n . The B r i t i s h Columbia salmon s e i n e f l e e t p r o v i d e s an u n i q u e o p p o r t u n i t y f o r a s s e s s i n g i n f o r m a t i o n q u a l i t y and i n t e r f e r e n c e c o m p e t i t i o n : s k i p p e r s form queues a t d e f i n e d a c c e s s p o i n t s and p e r c e i v e a queue as r e f l e c t i n g t h e s e t c a t c h r a t e . F i s h e r m e n can be o b s e r v e d , h y p o t h e s e s can be t e s t e d and i n f e r e n c e s about the q u a l i t a t i v e forms o f e x p l o i t a t i o n r e s p o n s e s t o f i s h o r f i s h e r m e n abundance c a n be made. CHAPTER I I SALMON SEINE BOATS AND THE JOHNSTONE STRAIT SALMON FISHERY The B r i t i s h Columbia salmon s e i n e f l e e t i s a h e t e r o g e n e o u s group o f new and a g e i n g v e s s e l s s k i p p e r e d by i n d i v i d u a l s p o s s e s s i n g v a r y i n g d e g r e e s o f e x p e r i e n c e . B o a t s range i n s i z e from 40 f e e t t o 132 f e e t w i t h the m a j o r i t y a v e r a g i n g 50 t o 70 f e e t . New b o a t s a r e b e i n g b u i l t e v e r y y e a r , w h i l e t h e o l d e s t d a t e as f a r b a c k as 1903 ( F i s h i n g V e s s e l Owners A s s o c i a t i o n 1981). A l t h o u g h l i m i t e d e n t r y began i n 1969, t h e number o f s e i n e v e s s e l s f i s h i n g salmon i n c r e a s e d from 369 i n 1969 t o 532 i n 1980. The c o n t r i b u t i n g f a c t o r s t o t h i s growth were c r e a t i o n o f n a t i v e I n d i a n l i c e n s e s and t h e t r a n s f e r o f l i c e n s e s from the h a l i b u t f l e e t and from salmon t r o l l e r s and g i l l n e t t e r s ( P e a r s e 1982). The a v e r a g e g r o s s e a r n i n g s f o r salmon s e i n e s i n 1980 was 84,940 d o l l a r s . Some v e s s e l s p a r t i c i p a t i n g i n more t h a n one f i s h e r y a v e r a g e d 97,150 d o l l a r s f o r salmon and 62,500 d o l l a r s f o r o t h e r s p e c i e s ( P e a r s e 1982) . The s e i n e b o a t s o p e r a t e on a s h a r e system; t o t a l c a t c h v a l u e i s d i v i d e d among the b o a t , n e t , s k i p p e r and crew. The F e d e r a l F l e e t R a t i o n a l i z a t i o n Committee i n t e r v i e w e d p u b l i c a c c o u n t a n t s and o b t a i n e d r e p r e s e n t a t i v e samples o f s e i n e n e t incomes ( b o a t p l u s n e t s h a r e a f t e r e x p e n s e s ) . The average n e t income f o r 17 v e s s e l s f i s h i n g salmon o n l y was 16,377 d o l l a r s i n 1981. S i x t y - f i v e s e i n e s f i s h i n g salmon and h e r r i n g a v e r a g e d 39,126 d o l l a r s (Dept. o f F i s h e r i e s and Oceans, Canada 1982a). The s e i n e f l e e t t a r g e t s on sockeye (Oneorhvnchus n e r k a ) , p i n k (0.  g o rbuscha) and chum ( 0 ^ k e t a ) salmon and p r o d u c e s s m a l l e r l a n d i n g s o f c h i n o o k (CL. t s h a w v t s c h a ) and coho (Ch_ k i s u t c h ) . I n 1981, s e i n e r s l a n d e d 54.9 p e r c e n t o f t h e t o t a l s ockeye pack (11,307 m e t r i c t o n s , round w e i g h t ) , 20 63.7 p e r c e n t o f the p i n k c a t c h (23,807 m e t r i c t o n s ) , 45.7 p e r c e n t o f the chum p r o d u c t i o n (2,757 m e t r i c t o n s ) and l e s s t h a n 20 p e r c e n t o f the c h i n o o k and coho p a c k s . The s e i n e s e c t o r caught 40,092 m e t r i c t o n s o f salmon, amounting to 51.8 p e r c e n t o f the B r i t i s h Columbia l a n d i n g s (Dept. F i s h e r i e s and Oceans, Canada 1982b) w i t h a l a n d e d v a l u e o f 63.9 m i l l i o n d o l l a r s ( M i n i s t r y o f E nvironment, B.C. 1982). V e s s e l O p e r a t i o n Salmon s e i n e n e t s a r e d e s i g n e d t o c a t c h s c h o o l s o f f i s h . S e t s a r e c h a r a c t e r i z e d by f o u r s t a g e s : l e t t i n g go, towing, c l o s i n g and p u r s i n g . The s k i p p e r a l l o w s t h e movement o f the b o a t and t h e f r i c t i o n o f t h e water w i t h t h e n e t t o p u l l t h e n e t o f f the drum ( l e t t i n g go) and t h e n tows the n e t i n a s e m i c i r c l e u s u a l l y p e r p e n d i c u l a r t o the f l o w o f the t i d e . A f t e r a p e r i o d o f time (which may v a r y w i t h s p e c i e s , water c o n d i t i o n s o r t h e s k i p p e r ' s p e r c e p t i o n s o f f i s h abundance and b e h a v i o r ) t h e s k i p p e r b r i n g s t h e end o f the n e t t o g e t h e r ( c l o s i n g ) and t h e n b r i n g s t h e n e t a b o a r d as he p u r s e s the submerged edge. T h r e e i n n o v a t i o n s became p r e v a l e n t d u r i n g the 1960s and 1970s -- the s e i n e drum, the r u n n i n g l i n e and the b o w t h r u s t e r ( F i g u r e 2 ) . These t o o l s i n c r e a s e d t h e f i s h i n g power o f the f l e e t by d e c r e a s i n g t h e t i m e n e c e s s a r y f o r t h e s e t and t h e r i s k a s s o c i a t e d w i t h the n e t . The drum a l l o w s the crew t o s e t and r e t r i e v e t h e n e t q u i c k l y , p r o d u c i n g a g r e a t e r number o f s e t s p e r day. A s e t w i t h t h e o l d p o w e r b l o c k gear took 50 minutes (Cove 1973); modern drum s e i n e r s complete a s e t w i t h i n 35 m i n u t e s . S k i p p e r s can take b i g g e r r i s k s w i t h t h e i r n e t s ; i f n e t problems o c c u r , t h e crew can q u i c k l y b a c k h a u l the n e t onto the drum. The r u n n i n g l i n e c o n t r i b u t e s t o the shape o f the open s e t , 22 / — — s DRUM F i g u r e 2. F i s h i n g i n n o v a t i o n s i n the salmon s e i n e f i s h e r y . The drum and r u n n i n g l i n e equipment a r e r e c e n t improvements. These i n v e n t i o n s a l l o w t h e f i s h e r m e n t o make more s e t s p e r time p e r i o d and f a c i l i t a t e s e t s made o f f s h o r e . 23 p a r t i c u l a r l y i n h i g h winds o r s t r o n g c u r r e n t s ; the s e a a n c h o r - r u n n i n g l i n e c o m b i n a t i o n s u b s t i t u t e s f o r the s t a t i o n a r y hook ups u s e d d u r i n g s h o r e s e t s . F u r t h e r m o r e , the s k i f f a s s o c i a t e d w i t h the end o f the n e t c a n be d i s p e n s e d w i t h and, t h e r e f o r e , an e x t r a crew member i s on deck d u r i n g s e t s t h a t do n o t r e q u i r e a t i e up. The b o w t h r u s t e r i s a l s o h e l p f u l i n winds o r c u r r e n t s ; t h e s k i p p e r u s es t h i s f o r w a r d p o s i t i o n e d p r o p t o c o n t r o l the p o s i t i o n o f h i s bow r e l a t i v e t o the n e t and a v o i d s t h e p o s s i b i l i t y o f n e t c o l l a p s e a r o u n d t h e bow o f the b o a t . I n the ev e n t o f n e t c o l l a p s e , the c o r k l i n e ( i . e . , f l o a t s ) must be p i l e d by hand i n the s k i f f and rowed back a r o u n d t h e end o f t h e v e s s e l . S k i p p e r s p o s s e s s i n g l e s s t e c h n o l o g y may s e t w i t h r e s p e c t t o t h e s e a c o n d i t i o n s r a t h e r t h a n t h e f i s h . S e i n e r s l i n e - u p f o r s e t p o s i t i o n s . The queues v a r y f r o m 1 t o 18 b o a t s and p r e s u m a b l y r e f l e c t the p o t e n t i a l c a t c h p e r s e t a t p a r t i c u l a r f i s h i n g s p o t s . D i f f e r e n t s k i p p e r s adopt d i f f e r e n t l i n e - u p s t r a t e g i e s . Many b o a t s s i t i n l o n g l i n e - u p s a t low energy c o s t s (due t o t h e f a c t t h a t t h e y make fewer s e t s ) and r i s k m i s s i n g the b i g c a t c h e s d u r i n g t h e c r u c i a l p e r i o d s when a s c h o o l i s p r e s e n t and a n o t h e r b o a t i s i n s e t . O t h e r s f i s h a l o n e , m a x i m i z i n g t h e number o f s e t s made d u r i n g a f i s h i n g o p e n i n g . The c h o i c e o f s t r a t e g y i s o f t e n l i m i t e d by the s i z e o f t h e v e s s e l ; l a r g e v e s s e l s may c o n s e r v e f u e l by r e m a i n i n g i n l i n e - u p s where few s e t s ( l e s s f u e l ) a r e r e q u i r e d f o r a r e l a t i v e l y good t o t a l c a t c h . S t r a t e g i e s u s u a l l y v a r y w i t h e f f o r t l e v e l s : s k i p p e r s s e t t i n g a l o n e i n l e s s d e s i r a b l e a r e a s d u r i n g p e r i o d s o f h i g h e f f o r t w i l l j o i n l i n e - u p s when t h e r e a r e few v e s s e l s i n the f i s h e r y . The m a j o r i t y o f s k i p p e r s s e a r c h t h r o u g h d i f f e r e n t queue l e n g t h s and d e t e r m i n e s h o r t term s t r a t e g i e s w i t h r e s p e c t t o t h e d i s t r i b u t i o n o f the o t h e r b o a t s . A n o t h e r s t r a t e g y i s t o f i s h a good s p o t t h a t i s a s s o c i a t e d w i t h a h i g h d e g ree o f r i s k ( e . g . , a r o c k p i l e ) . The l i n e - u p i s u s u a l l y s m a l l r e l a t i v e t o t h e reward as many f i s h e r m e n a v o i d r i s k s t o t h e i r gear. 24 Salmon f i s h e r m e n p e r c e i v e a r i s i n g t i d e as t h e most p r o b a b l e time f o r a b i g c a t c h . A c c o r d i n g t o the s k i p p e r s , t h e salmon a r e most v u l n e r a b l e d u r i n g the f l o o d ( i . e . , r i s i n g w a t e r ) . I n some a r e a s , l i n e - u p s o s c i l l a t e w i t h t h e t i d e as b o a t s queue w i t h the f l o o d water. T h i s phenomenon i s s i m i l a r t o a r o u l e t t e game i n which each s k i p p e r hopes t o make an e x t r a o r d i n a r y s e t . L i n e - u p e t i q u e t t e i s e n f o r c e d by gentleman's agreement and by r e g u l a t i o n . Each b o a t w a i t s f o r i t s t u r n as d e t e r m i n e d by i t s p o s i t i o n i n the queue. Anyone s e t t i n g w i t h i n a n e t l e n g t h i n f r o n t o f a v e s s e l i n s e t i s s a i d t o have " c o r k e d " t h e o t h e r s k i p p e r and t h i s may be cause f o r w a r n i n g shotgun b l a s t s o r rough language o v e r t h e r a d i o (and t h e c u l p r i t w i l l be c o r k e d i n t h e f u t u r e ) . A s k i p p e r c a n l e g a l l y tow h i s n e t f o r no more t h a n twenty m i n u t e s and o t h e r f i s h e r m e n p o s s e s s the r i g h t t o c o r k i f a b o a t tows f o r a l o n g e r p e r i o d . As soon as a b o a t has f i n i s h e d t h e l e g a l tow and c l o s e d t h e n e t , a n o t h e r s k i p p e r c a n t a k e h i s s p o t . There a r e f o u r t y p e s o f s e t s t r a t e g y ( F i g u r e 3 ) : b e a c h s e t t i e up, b e a c h s e t , open s e t and open s e t on a l i n e . D u r i n g t h e b e a c h s e t t i e up, the s k i f f man and t h e t i e up man row a s h o r e and s e c u r e a l i n e a s s o c i a t e d w i t h t h e end o f t h e n e t t o a t r e e o r a n o t h e r s t a t i o n a r y o b j e c t . Depending upon t h e t i d e , t h e r e i s c o n s i d e r a b l e danger t o t h e t i e up man; s e r i o u s i n j u r i e s and de a t h s have o c c u r r e d i n the p a s t . The t i e up i s u s u a l l y a s s o c i a t e d w i t h t o p o g r a p h i c landmarks such as l e a d i n g p o i n t s . The r a t i o n a l e f o r t h i s t y p e o f s e t i s t h a t salmon t e n d t o f o l l o w t h e s h o r e l i n e t o p o g r a p h y a l o n g t h e i r m i g r a t i o n p a t h , s c h o o l i n t h e s e a r e a s and ca n n o t get ar o u n d the end o f the n e t , which i s t u c k e d i n c l o s e t o s h o r e . O t h e r s s p e c u l a t e t h a t i n c r e a s e d f i s h v u l n e r a b i l i t y may be due t o a r e l a t i o n s h i p between the way c u r r e n t s move a l o n g the s h o r e l i n e and the shape o f the n e t o r t h a t the salmon a s c e n d w i t h the t h e r m o c l i n e on t h e f l o o d , e n t e r i n g the 25 F i g u r e 3. S e t s t r a t e g i e s . T h r ee t y p e s o f s e t a r e made i n t h e B r i t i s h C o l umbia salmon s e i n e f i s h e r y . T i e ups i n v o l v e w r a p p i n g a l e a d i n g rope a s s o c i a t e d w i t h the end o f t h e n e t t o a s t a t i o n a r y o b j e c t on t h e s h o r e l i n e . Beach s e t s o c c u r o n s h o r e , b u t no t i e up i s made. Open s e t s a r e made away from s h o r e . L i n e - u p s a r e a l s o i l l u s t r a t e d . 26 e f f e c t i v e volume o f the n e t . Beach s e t s a r e p e r f o r m e d when the s k i p p e r s e t s c l o s e t o s h o r e , b u t does n o t t i e up due t o s t r o n g c u r r e n t s o r because t h e r e i s no m a t e r i a l upon which t o a t t a c h the l i n e ( e . g . , a t t h e bottom o f a c l i f f o r a l o n g s l o p i n g b e a c h ) . The open s e t o c c u r s away from the b each and i s c h a r a c t e r i z e d by a s h o r t e r l i n e - u p ; a l t h o u g h the f i s h e r m e n f e e l t h a t fewer f i s h a r e c aught per s e t , more s e t s a r e made. I n f a c t , many open s e t s i n v o l v e a s i n g l e b o a t making s e t a f t e r s e t and a v o i d i n g any w a i t i n g s t r a t e g y . S p e c i a l i z e d open s e t s a r e l o c a t e d n e a r r o c k p i l e s o r i n and a round k e l p beds. The r i s k i n v o l v e d i s h i g h e r and ( a c c o r d i n g t o t h e f i s h e r m e n ) the c a t c h i s a l s o h i g h e r . Rock p i l e s and k e l p beds s u p p o s e d l y a c t l i k e t o p o g r a p h i c a l landmarks on the s h o r e l i n e : the f i s h a r e more v u l n e r a b l e i n t h e s e s h a l l o w a r e a s and t h e o b s t a c l e s p r e v e n t escape from the n e t . I n an o r d i n a r y open s e t , t h e s k i p p e r w i l l keep a hook a t the end o f the n e t so t h a t t h e salmon w i l l f o l l o w t h e c u r v a t u r e and a r r i v e b a c k i n s i d e the n e t ( F i g u r e 2 ) . I f a n a t u r a l ( e . g . , depth c o n t o u r s ) o r manmade boundary i s p r e s e n t i n t h e f i s h i n g a r e a , t h e b o a t s w i l l u s u a l l y form a l i n e a l o n g t h e boundary and l o n g e r l i n e - u p s w i l l ensue. The l i n e s a r e p o p u l a r b e c a u s e t h e s k i p p e r s t a k e a f i r s t c r a c k a t the f i s h b e f o r e t h e y e n t e r the c e n t r a l p o r t i o n o f the f i s h e r y . B o a t s a r e c o n s t a n t l y j o c k e y i n g f o r p o s i t i o n and t h i s o f t e n l e a d s t o an o v e r s t e p p i n g o f t h e boundary. F i s h e r m e n a l s o e x p l o i t box b o u n d a r i e s a r o u n d s m a l l r i v e r s o r c r e e k s ; t h i s t y p e o f boundary i s r e c t a n g u l a r i n shape and u s u a l l y e s t a b l i s h e s a r e f u g e i n th e v i c i n i t y o f a s t r e a m o r r i v e r mouth. The s k i p p e r s hope t h a t the f i s h w i t h i n t h e boundary w i l l be swept ou t by the t i d e -- a l e g a l method o f c a t c h i n g o t h e r w i s e p r o t e c t e d salmon. I n f o r m a t i o n i s t r a n s m i t t e d v i a t r a d i t i o n ( a c c u m u l a t e d , h i s t o r i c a l i n f o r m a t i o n ) , v i s u a l i n s p e c t i o n o f c o m p e t i t o r ' s c a t c h e s , r a d i o communication and a e r i a l s u r v e y s . The queues a r e formed a t t r a d i t i o n a l 27 f i s h i n g s p o t s which have a p o t e n t i a l v a l u e a s s o c i a t e d w i t h them. A s k i p p e r may e n t e r a l i n e - u p , watch a few c a t c h e s b e i n g made and make the d e c i s i o n t o t r y somewhere e l s e . L i n e - u p s a l s o form around known h i g h l i n e r s ; the e x c e p t i o n a l f i s h e r m a n ' s r e p u t a t i o n a t t r a c t s o t h e r s k i p p e r s t o h i s f i s h i n g s p o t s . Many groups o f f i s h e r m e n i n t e r a c t t h r o u g h r a d i o c h a n n e l s and a c o n s i d e r a b l e amount o f money has been i n v e s t e d i n s c r a m b l e r s and d e s c r a m b l e r s as s k i p p e r s a s p i r e t o p r o t e c t t h e i r communication c h a n n e l s and t o b r e a k o t h e r s . S e n i o r s k i p p e r s sometimes d i r e c t the movements o f o t h e r s k i p p e r s i n t h e i r group o r a f i s h e r m a n may c o n t a c t t h e company d i s p a t c h e r f o r a d v i c e c o n c e r n i n g h i s d e c i s i o n s t r a t e g y . A few groups p o s s e s s a h i e r a r c h i c a l s e t o f s c r a m b l e d c h a n n e l s w i t h o n l y t h e i n n e r c i r c l e h a v i n g a c c e s s t o t h e most p r i v a t e o f t h e s e . Company o r p r i v a t e p l a n e s a r e u s e d f o r s p o t t i n g c a t c h e s and jumping salmon. The p i l o t s a l s o f l y o v e r f i s h i n g a r e a s a day b e f o r e t h e o p e n i n g s i n o r d e r t o s p o t l a r g e s c h o o l s o f salmon. Many s k i p p e r s w i l l n o t b r i n g t h e i r c a t c h a b o a r d i f an a i r p l a n e i s n e a r . A s k i p p e r w i t h 42 y e a r s e x p e r i e n c e s t a t e d t h a t t h e r e a r e no s e c r e t s anymore -- e v eryone f i s h e s a l l o f t h e s p o t s . A n o t h e r e x p e r i e n c e d f i s h e r m a n i n d i c a t e d t h a t good f i s h i n g s p o t s become r a p i d l y overcrowded due t o a e r i a l s u r v e i l l a n c e . R e l a t i v e t o most e c o l o g i c a l systems, i n f o r m a t i o n i s n e a r p e r f e c t . The J o h n s t o n e S t r a i t F i s h e r y The J o h n s t o n e S t r a i t f i s h e r y c o m p r i s e s s i x d i s t i n c t r e g i o n s : D i s c o v e r y Passage, J o h n s t o n e S t r a i t , B r o u g h t o n S t r a i t , Queen C h a r l o t t e S t r a i t , G o l e t a s Channel and Gordon Channel ( F i g u r e 4 ) . The w i d t h o f t h e c h a n n e l 28 F i g u r e 4. The J o h n s t o n e S t r a i t s t u d y a r e a . The map i s d i v i d e d i n t o two p o r t i o n s w i t h the n o r t h w e s t e r n s e c t i o n o f the f i s h e r y i l l u s t r a t e d i n t h e top h a l f o f the f i g u r e . 30 v a r i e s from l e s s t h a n 2.5 km. i n J o h n s t o n e S t r a i t and D i s c o v e r y Passage t o 26 km. i n Queen C h a r l o t t e S t r a i t . T i d e s p r o p a g a t e from the P a c i f i c Ocean n o r t h o f Vancouver I s l a n d and t i d a l c u r r e n t s l a g by 160 m i n u t e s between Queen C h a r l o t t e S t r a i t and D i s c o v e r y Passage. The ebb c u r r e n t s i n m i d c h a n n e l a r e o f t e n o v e r 1 kn. (50 cm./sec.) and sometimes e x c e e d 1.5 kn. (75 cm./sec.) d u r i n g s p r i n g t i d e s . T i d a l c u r r e n t s a s s o c i a t e d w i t h r i s i n g w a ter a r e always weaker t h a n 1 kn. and c u r r e n t s w i t h i n one h a l f m i l e o f the s h o r e a r e about 20 p e r c e n t o f t h o s e i n m i d c h a n n e l . C u r r e n t s may e x c e e d 6 kn. (3 m./sec.) i n the v i c i n i t y o f K e l s e y Bay. The f i s h e r y i s a f f e c t e d by m o r n i n g f o g s and h i g h winds (up t o 30 kn. -- 15 m./sec.) t h a t u s u a l l y peak i n t h e a f t e r n o o n (Thomson 1981). The Department o f F i s h e r i e s and Oceans a l l o c a t e s B r i t i s h Columbia salmon c a t c h e s t o 29 s t a t i s t i c a l a r e a s (see Map 1, H i l b o r n and L e d b e t t e r 1979). J o h n s t o n e S t r a i t i s d i v i d e d i n t o A r e a s 12 and 13 a t K e l s e y Bay. A r e a 12 i n c l u d e s a p p r o x i m a t e l y h a l f o f J o h n s t o n e S t r a i t and t h e Broughton S t r a i t , Queen C h a r l o t t e S t r a i t , G o l e t a s Channel and Gordon C h a n n e l r e g i o n s . The l o w e r p o r t i o n o f J o h n s t o n e S t r a i t and D i s c o v e r y Passage a r e i n c l u d e d i n A r e a 13. I n 1981, A r e a 12 was t h e l a r g e s t p r o d u c e r o f p i n k and s o c k e y e salmon, r a n k e d f o u r t h f o r chum and f i f t h f o r coho and c h i n o o k . A r e a 13 was the f o u r t h l a r g e s t f i s h e r y f o r sockeye and was n o t r e p r e s e n t e d among t h e t o p f i v e a r e a s f o r the o t h e r s p e c i e s (Dept. F i s h e r i e s and Oceans 1982b). The t o t a l J o h n s t o n e S t r a i t s e i n e c a t c h was 17,277.9 m e t r i c t o n s (7,106,069 p i e c e s ) and t h e pink:sockeye:coho:chum:chinook r a t i o ( b a s e d on l a n d e d w e i g h t ) was 38.7:29.5:2.1:2.0:1.0 (Dept. F i s h e r i e s and Oceans 1982c). The J o h n s t o n e S t r a i t , D i s c o v e r y Passage and Broughton S t r a i t f i s h e r i e s a r e d ominated by a b e a c h s e t t i e up s t r a t e g y . S k i p p e r s p e r c e i v e the t i e ups as the most p r o f i t a b l e s e t s and l i n e - u p s a r e p r e v a l e n t . Open s e t s a r e 31 u s u a l l y p e r f o r m e d by i n d i v i d u a l s who w i s h to m i n i m i z e t h e i r w a i t i n g time. When the e x t e n d e d Adam R i v e r b o u n d a r i e s a r e i n e f f e c t , an open s e t l i n e forms a l o n g the lower boundary and the b o a t s i n t e r c e p t t h e f i s h b e f o r e t h e y e n t e r t h e lower s t r a i t ( F i g u r e 4) . Queues are a s s o c i a t e d w i t h t h i s l i n e . R o c k p i l e f i s h i n g i s f o u n d a l o n g the n o r t h e r n s h o r e o f Hanson I s l a n d . O n l y a s m a l l p o r t i o n o f Queen C h a r l o t t e S t r a i t i s u t i l i z e d . The f i s h i n g a r e a s a r e the r e g i o n around White C l i f f I s l e t s n o r t h o f Hanson I s l a n d , t h e n o r t h and n o r t h w e s t s h o r e s o f M a l c o l m I s l a n d , t h e n e a r s h o r e w a t e r s o u t s i d e o f W e l l s Passage on the m a i n l a n d s h o r e , and t h e i s l a n d s a r ound D i l l o n P o i n t o u t s i d e o f P o r t Hardy. T i e ups a r e r a r e ; t h e open s e t on a l i n e s t r a t e g y i s p r e v a l e n t . The n o r t h w e s t s h o r e o f M a l c o l m I s l a n d i s the major f i s h i n g a r e a ; an open s e t l i n e forms d u r i n g p e r i o d s o f h i g h e f f o r t and t h e l i n e - u p s may become as l o n g as t h r e e o r f o u r b o a t s . F i s h e r m e n ' s f o l k l o r e i n d i c a t e s t h a t the salmon sweep s o u t h f o l l o w i n g the d e p t h c o n t o u r s , c h o o s i n g m i g r a t i o n p a t h s around the n o r t h e r n and s o u t h e r n s h o r e s o f M a l c o l m I s l a n d . A n o t h e r open s e t l i n e d e v e l o p s when the D i l l o n P o i n t - D o y l e I s l a n d boundary i s i n e f f e c t ( F i g u r e 4) . G o l e t a s C h a n n e l i s r a r e l y f i s h e d by s e i n e r s and was u s u a l l y c l o s e d t o f i s h i n g d u r i n g the 1981 season. Gordon Channel i s c h a r a c t e r i z e d by numerous r o c k p i l e s and r e e f s . Open s e t s a r e the p r i m a r y s t r a t e g y and o n l y 12 t i e ups a r e u t i l i z e d . W i t h i n - s e a s o n management (as w e l l as p r e s e a s o n p l a n n i n g ) r e s t r i c t s most f i s h i n g o p e n i n g s to 48 h o u r s ( s t a r t i n g a t 6 p.m. Sunday e v e n i n g ) and m a n i p u l a t e s b o u n d a r i e s i n o r d e r t o p r o t e c t v a r i o u s s t o c k s o f salmon. D u r i n g the 1981 season, temporary b o u n d a r i e s c l o s e d the Gordon Channel and M a l c o l m I s l a n d f i s h e r i e s f o r t h e c o n s e r v a t i o n o f e a r l y N i m p k i s h sockeye and m a i n l a n d p i n k s . B o u n d a r i e s from the s o u t h s h o r e o f M a l c o l m I s l a n d t o the Vancouver I s l a n d s h o r e e x c l u d e d the s e i n e r s from the p o o l i n g grounds o f the 32 N i m p k i s h sockeye. A box boundary p r o t e c t e d l o c a l sockeye e n t e r i n g the Adam R i v e r . The m a i n l a n d i n l e t s a d j o i n i n g J o h n s t o n e S t r a i t and D i s c o v e r y Passage were c l o s e d f o r the p r o t e c t i o n o f m a i n l a n d p i n k s and d u r i n g two o p e n i n g s the b o a t s were r e s t r i c t e d t o w i t h i n one h a l f m i l e o f t h e Vancouver I s l a n d s h o r e o v e r v a r i o u s p o r t i o n s o f J o h n s t o n e S t r a i t . D u r i n g t h e second week o f t h e season, A r e a 13 was c l o s e d f o r t h e p r o t e c t i o n o f j u v e n i l e coho and c h i n o o k salmon. A permanent box boundary a t K e l s e y Bay c o n t r i b u t e d t o the c o n s e r v a t i o n o f a l l salmon s p e c i e s spawning i n t h e Salmon R i v e r . CHAPTER I I I DATA COLLECTION AND VERIFICATION T h r e e t y p e s o f d a t a were c o l l e c t e d d u r i n g the 1980 and 1981 salmon s e a s o n s . F i r s t , o b s e r v e r d a t a were c o l l e c t e d d u r i n g t h e 1980 s e a s o n as a b a s i s f o r p l a n n i n g t h e s t r u c t u r e and emphasis o f d a t a c o l l e c t i o n d u r i n g 1981. S e i n e o p e r a t i o n s were o b s e r v e d on f i v e v e s s e l s and c o v e r e d the c o a s t between the two A m erican b o r d e r s . An o b s e r v e r g a t h e r e d d a t a on t e n b o a t s f i s h i n g v a r i o u s a r e a s d u r i n g t h e 1981 season. Second, 32 s k i p p e r s f i l l e d o u t l o g b o o k s f o r the J o h n s t o n e S t r a i t s t u d y a r e a . T h i r d , t h e p r i m a r y d a t a f o r t h e t h e s i s were c o l l e c t e d d u r i n g f l i g h t s i n a C e s s n a 180 o v e r J o h n s t o n e S t r a i t d u r i n g 1981. The o b s e r v e r d a t a c o n s i s t e d o f c a t c h e s p e r s e t and s p e c i e s ( p i e c e s ) , time components o f the s e t ( l e t t i n g go, towing, c l o s i n g and p u r s i n g ) , the amount o f time s p e n t i n d i f f e r e n t a c t i v i t i e s , queue l e n g t h s , w a i t i n g times and a n e c d o t a l i n f o r m a t i o n . Emphasis was p l a c e d on t h e d a t a p e r t a i n i n g t o time components, time a l l o c a t i o n , l i n e - u p l e n g t h s and w a i t i n g t i m e s . These d a t a were i m p o r t a n t f o r the f o r m u l a t i o n o f h y p o t h e s e s c o n c e r n i n g f l e e t b e h a v i o r . The l o g b o o k s were d e s i g n e d f o r s t a t i s t i c a l a n a l y s i s as w e l l as ease o f r e c o r d i n g . F o r example, l i n e - u p l e n g t h s were g i v e n as i n t e r v a l s and s e t t y p e s were d i s t i n g u i s h e d as t i e up and open s e t ( i . e . , e i t h e r / o r ) r a t h e r t h a n b e a c h s e t t i e up, b e a c h s e t , open s e t and open s e t on a l i n e . O t h e r d a t a i n c l u d e d i n t h e l o g b o o k s were the number o f b o a t s o b s e r v e d w i t h the u n a i d e d eye ( t h i s was n o t u s e d i n th e a n a l y s i s due t o b i a s e s i n t r o d u c e d by t o p o g r a p h y and f o g p a t c h e s ) , t h e time, the l o c a t i o n , the crew/gear p e r f o r m a n c e and the number o f f i s h caught p e r s e t and by s p e c i e s . A c q u i s i t i o n o f l o g b ook d a t a depended upon the c o o p e r a t i o n o f s k i p p e r s ; t h i s 34 r e q u i r e m e n t r e s t r i c t e d t h e s t a t i s t i c a l s u p p o r t a b i l i t y o f t h e sample though i t i s hoped t h a t r e p r e s e n t a t i v e d a t a were o b t a i n e d . T h e r e f o r e , t h e r e s u l t s o f t h e logbook d a t a a n a l y s i s cannot be r i g o r o u s l y e x t e n d e d t o t h e t o t a l f l e e t . S i x t y - o n e f l i g h t s were a t t e m p t e d and 51 were completed. Ten f l i g h t s were t e r m i n a t e d due t o f o g . L i n e - u p l e n g t h s and a c t i v i t i e s ( e . g . , tow, c l o s e , d i r e c t i o n o f movement, d e l i v e r i n g and w a i t i n g ) were r e c o r d e d once d u r i n g t h e Sunday n i g h t o p e n i n g and t w i c e a day on Monday and Tuesday. F l i g h t s were s p a c e d f o u r h o u r s a p a r t on the same day to c o n t r a s t p o s s i b l e t e m p o r a l changes i n f l e e t b e h a v i o r l i n k e d t o the t i d a l c y c l e o r t o s h o r t term f l u c t u a t i o n s i n f i s h abundance. The morning f l i g h t o r i g i n a t e d a t K e l s e y Bay and t e r m i n a t e d a t A l e r t Bay; t h e a f t e r n o o n f l i g h t r e t u r n e d t o K e l s e y Bay. An at t e m p t was made t o randomize t h e f l i g h t s o v e r 12 s t a g e s o f the t i d a l c y c l e (two h o u r s a p a r t ) b u t the c o m b i n a t i o n o f t i d e s and h o u r s o f d a y l i g h t r e n d e r e d t h i s arrangement i m p o s s i b l e . T h e r e f o r e , f l i g h t s were s t a g g e r e d t o a c h i e v e e q u a l numbers o f seven o f the two hour s t a g e s and a f l i g h t p l a n was f o l l o w e d e x c e p t d u r i n g f o g g y p e r i o d s when m u l t i p l e attempts were n e c e s s a r y . Sample e s t i m a t e s o f t o t a l f i s h i n g f l e e t ( f l e e t s i z e ) f o r the s t r a i t were o b t a i n e d f o r each f l i g h t . L i n e - u p s and a c t i v i t i e s were r e c o r d e d on an a c c e s s p o i n t b a s i s . An a c c e s s p o i n t was s i m p l y d e f i n e d as a p l a c e where a l i n e - u p o c c u r r e d (whether one o r more b o a t s ) . As mentioned i n the p r e v i o u s c h a p t e r , s e t s c l o s e r t h a n a n e t l e n g t h a p a r t v i o l a t e t h e f i s h e r m e n s ' r u l e s and may be cause f o r anger. T h i s f a c t a i d e d i n the i d e n t i f i c a t i o n o f a c c e s s p o i n t s i n an open s e t a r e a . The one d i m e n s i o n a l c h a r a c t e r o f t h e s e measurements a v o i d e d the problems a s s o c i a t e d w i t h g r i d s ( i . e . , the change o f the c h a r a c t e r o f d i s t r i b u t i o n s w i t h g r i d s i z e ) . 35 Queues were easy t o c o u n t f o r shor e s e t s ( F i g u r e 5 ) . One b o a t open s e t l i n e - u p s were common and spaced. F o r open s e t l i n e s , t h e number o f a c c e s s p o i n t s was c a l c u l a t e d as the number o f v e s s e l s l e t t i n g go, t o w i n g or c l o s i n g ( a p u r s i n g b o a t has a v e s s e l a s s o c i a t e d w i t h i t as men t i o n e d i n the p r e v i o u s c h a p t e r ) and p u r s i n g and w a i t i n g b o a t s were a l l o c a t e d t o t h e s e a c c e s s p o i n t s i n an i t e r a t i v e f a s h i o n ( v e s s e l s were a s s i g n e d t o eac h i d e n t i f i e d a c c e s s p o i n t one a t a time u n t i l a l l v e s s e l s were a c c o u n t e d f o r ) . T h i s method may have u n d e r e s t i m a t e d the maximum open s e t l i n e - u p . Open s e t s were r e c o r d e d by f i s h i n g a r e a . S i n c e a g r i d a n a l y s i s was i m p o s s i b l e w i t h o u t p h o t o g r a p h s , a r e a s o f a g g r e g a t i o n were s u b j e c t i v e l y . i d e n t i f i e d and d e s i g n a t e d as f i s h i n g a r e a s . T i e up l o c a t i o n s were r e p e a t e d l y o b s e r v e d ( t h e rope marks s h o u l d be v i s i b l e on the t r e e s ) and t h i s r e p e a t a b i l i t y a l l o w e d s i m p l e n u m e r i c a l i d e n t i f i c a t i o n . V e r i f i c a t i o n The o v e r f l i g h t d a t a were coded t w i c e . The c o d i n g s e s s i o n s were t e m p o r a l l y s e p a r a t e d i n o r d e r t o m i n i m i z e b i a s e s a s s o c i a t e d w i t h f i x a t i o n on a p a r t i c u l a r mode o f p a t t e r n r e c o g n i t i o n . One d a t a s e t c o n t a i n e d t h e d a t e , f l i g h t , l o c a t i o n , number o f a c c e s s p o i n t s , number o f b o a t s and a c t i v i t i e s . A n o t h e r s e t o f d a t a c o n t a i n e d the twenty minute i n t e r v a l d u r i n g w h i c h a b e a c h s e t a c c e s s p o i n t o r open s e t f i s h i n g a r e a was s p o t t e d . The two s e t s o f d a t a were t h e n compared f o r d i f f e r e n c e s i n a c c e s s p o i n t (or f i s h i n g a r e a ) i d e n t i f i c a t i o n and number; t h i s c o m p a r i s o n t e s t e d f o r c o d i n g o b s e r v a t i o n e r r o r and f o r the degree o f i n t e r p r e t a t i o n i n v o l v e d i n the assessment. ( A l t h o u g h l i n e - u p s were c h a r t e d as queues, a m i n i m a l amount o f i n t e r p r e t a t i o n was r e q u i r e d d u r i n g the c o d i n g p r o c e s s . ) The p e r c e n t e r r o r f o r m i s i d e n t i f i e d and m i s s i n g a c c e s s p o i n t s r e a c h e d 17 p e r c e n t , b u t most F i g u r e 5. A beach s e t queue. P u r s e s e i n e r s l i n e up a t h i s t o r i c a l a c c e s s p o i n t s and w a i t t h e i r t u r n to s e t . 37 p o i n t s were below 10 p e r c e n t . The t o t a l d i f f e r e n c e i n t h e number o f a c c e s s p o i n t s o r f i s h i n g a r e a s r e c o r d e d i n the two d a t a s e t s was f a i r l y c o n s t a n t ( c r i t i c a l rho a t a = 0.05 i s 0.2859, c a l c u l a t e d rho = 0.3503; a l l c o r r e l a t i o n p r e s e n t a t i o n s r e f e r to Spearman's r a n k c o r r e l a t i o n c o e f f i c i e n t ) . These d a t a a r e summarized i n F i g u r e 6. The l a r g e s t p e r c e n t e r r o r was 12 p e r c e n t and 34 out o f 48 measurements were l e s s t h a n 5 p e r c e n t . T h i s c o m p a r a t i v e a p p r o a c h i n d i c a t e d t h a t c o d i n g o b s e r v a t i o n e r r o r was low. F l i g h t s o r i g i n a t e d o r t e r m i n a t e d a t K e l s e y Bay ( t h e A r e a 12 and 13 b o u n d a r y ) . As a consequence, the A r e a 13 f i s h e r y was o b s e r v e d t w i c e d u r i n g a 40 minute i n t e r v a l o f each f l i g h t . These r e p e a t e d c o u n t s were summarized as t h e d i f f e r e n c e i n v e s s e l c o u n t s f o r v a r i o u s e f f o r t l e v e l s . T h e r e was no t r e n d i n the d a t a ; the a b s o l u t e e r r o r r e m a i n e d c o n s t a n t o v e r e f f o r t ( c r i t i c a l rho a t a = 0.05 i s 0.3313, c a l c u l a t e d rho = 0.2192). The p e r c e n t e r r o r e x p r e s s e d i n terms o f the f l i g h t s u s e d i n the a c t u a l a n a l y s i s was as h i g h as 11 p e r c e n t a t low e f f o r t . T w e n t y - f i v e o f 36 e r r o r measurements were l e s s t h a n 5 p e r c e n t ( F i g u r e 7 ) . A s u b s t a n t i a l p o r t i o n o f t h i s e r r o r was a t t r i b u t e d t o b o a t s moving a c r o s s the A r e a 12-13 boundary o r s e a r c h i n g beyond the s u b s i d i a r y c h a n n e l b o u n d a r i e s f o r f i s h t h a t moved o u t o f t h e c h a n n e l s on t h e ebb. Spot checks p r o d u c e d o b s e r v a t i o n s o f v e s s e l s s e a r c h i n g above the f i s h i n g b o u n d a r i e s . The e f f o r t e r r o r d a t a may i n d i c a t e t h a t a v e s s e l e n u m e r a t i o n l e a r n i n g r e s p o n s e o c c u r r e d . T h i s r e s p o n s e r a p i d l y s a t u r a t e d and d i d n o t c o n t r i b u t e any a p p r e c i a b l e b i a s t o the a n a l y s i s . The c o d i n g was n o t s y s t e m a t i c a l l y p e r f o r m e d o v e r e f f o r t l e v e l s and the t r e n d i n the p e r c e n t code e r r o r r e l a t i o n s h i p s r e f l e c t e d the f a i r l y c o n s t a n t a b s o l u t e o b s e r v a t i o n e r r o r . S k i p p e r s l a n d t h e i r f i s h a t p a c k e r s o r p r o c e s s i n g p l a n t s . The number and w e i g h t o f the f i s h by s p e c i e s , the a r e a f i s h e d and o t h e r p e r t i n e n t 38 1 0.12 r o o_ v> to IxJ o o < 0 . 0 9 ? 0 .06 UJ o z UJ or UJ Yr 0 . 0 3 o i r UJ h o o o CD O O O O COD -O Qg> < B CO OO CD O O QD O O ' O 0 O ' 7 5 150 2 2 5 3 0 0 E F F O R T (NO. OF BOATS) 3 7 5 F i g u r e 6. C o d i n g e r r o r : p e r c e n t d i f f e r e n c e o f the number o f a c c e s s p o i n t s c o u n t e d d u r i n g two c o d i n g s e s s i o n s . 39 O.I2 r 0.09 0.06 CD O 0.03 —Q-6-O O O O O CD C D O O J I n ob O 20 40 60 80 100 EFFORT (NO. OF BOATS) J 120 F i g u r e 7. O b s e r v a t i o n e r r o r : the p e r c e n t d i f f e r e n c e i n the number o f b o a t s o b s e r v e d i n A r e a 13 d u r i n g a 40 minute i n t e r v a l and two f l i g h t s . 40 i n f o r m a t i o n a r e r e c o r d e d on s a l e s s l i p s . E f f o r t f o r any f i s h i n g a r e a and o p e n i n g c a n be c a l c u l a t e d as the number o f b o a t s r e p o r t i n g t h e i r c a t c h as o r i g i n a t i n g from t h a t a r e a . F i g u r e 8 d emonstrates the r e l a t i o n s h i p between the r e p e a t e d a e r i a l e f f o r t c o u n t s and the s a l e s s l i p e f f o r t measurement f o r A r e a s 12 and 13 combined. The r e l a t i o n s h i p was q u i t e good e x c e p t f o r a few p o i n t s t h a t c a n e a s i l y be e x p l a i n e d . The p o i n t s l y i n g t o t h e f a r r i g h t o c c u r r e d when the J u a n de Fuca f i s h e r y was open. T h i s f i s h e r y i s i n C o n v e n t i o n w a t e r s a d m i n i s t e r e d by the I n t e r n a t i o n a l P a c i f i c Salmon Commission, where c a t c h and o p e n i n g s a r e r e g u l a t e d t o p r o d u c e e q u a l A m e r i c a n and C a n a d i a n c a t c h e s o f F r a s e r R i v e r sockeye and p i n k salmon. O b v i o u s l y , C a n a d i a n f i s h e r m e n a r e m o t i v a t e d t o r e p o r t J u a n de Fuca c a t c h e s as J o h n s t o n e S t r a i t . A n o t h e r e x p l a n a t i o n f o r t h i s d i f f e r e n c e i s t h a t b o a t s e n t e r e d t h e f i s h e r y from the c e n t r a l c o a s t as o t h e r s e x i t e d e a r l y f o r the J u a n de Fuca f i s h e r y and a l l v e s s e l s r e p o r t e d t h e i r c a t c h e s as J o h n s t o n e S t r a i t . The p o i n t l y i n g t o the l e f t o f the e q u a l e f f o r t l i n e r e p r e s e n t s the f i n a l o p e n i n g o f the s e a s o n . S k i p p e r s r e t u r n t o t h e i r home p o r t a t t h i s time and ( i n t h e r u s h ) o f t e n r e p o r t t h e c a t c h as o r i g i n a t i n g from the home p o r t a r e a . The e r r o r s i n t h e s a l e s s l i p d a t a a r e r e c o g n i z e d (see H i l b o r n and L e d b e t t e r 1979); a g g r e g a t e c a t c h e s a r e sometimes r e c o r d e d as o r i g i n a t i n g i n a s i n g l e a r e a and l a n d i n g s a r e o f t e n r e c o r d e d f o r weeks i n w h i c h the f i s h e r y was n o t open. The e r r o r i n t e r v a l s (two s t a n d a r d d e v i a t i o n s ) v e r i f y the a c c u r a c y o f th e o v e r f l i g h t c o u n t s . I n s p e c t i o n o f F i g u r e s 8 and 9 i n d i c a t e s t h a t t h e r e was no w e l l d e f i n e d r e l a t i o n s h i p o f v a r i a n c e t o e f f o r t ( s m a l l b o a t d e n s i t i e s a t t h e end o f o p e n i n g s , r e s u l t i n g from e a r l y d e p a r t u r e , were n o t i n c l u d e d i n t h e c a l c u l a t i o n o f s t a n d a r d d e v i a t i o n s ) . A l t h o u g h the l a r g e s t d e v i a t i o n s were a s s o c i a t e d w i t h h i g h e f f o r t , the s m a l l e s t d e v i a t i o n s a l s o o c c u r r e d a t the upper end o f t h e d i s t r i b u t i o n . A l a r g e p o r t i o n o f the v a r i a n c e can be 41 F i g u r e 8. R e p o r t e d and o b s e r v e d e f f o r t . R e p o r t e d e f f o r t was measured as the number o f v e s s e l s l a n d i n g c a t c h e s as J o h n s t o n e S t r a i t . O b s e r v e d e f f o r t i s p r e s e n t e d as the means o f t h e r e p e a t e d a e r i a l c o u n t s and the s t a n d a r d d e v i a t i o n s . 42 3 7 5 3 0 0 CO m 2 2 5 u_ o or 150 7 5 0 _ J _ o 8 8 J L O o 0 o o J L 6 8 WEEK 10 0 12 J I 14 F i g u r e 9. A e r i a l v e s s e l c o u n t s . M u l t i p l e e f f o r t c o u n t s were o b t a i n e d d u r i n g each w eekly f i s h i n g o p e n i n g d u r i n g June t o September, 1981. Much o f the w i t h i n - o p e n i n g v a r i a t i o n was e x p l a i n e d by the e n t r a n c e and e x i t o f v e s s e l s . 43 a t t r i b u t e d t o breakdowns, t o b o a t s l e a v i n g the f i s h e r y f o r J u a n de F u c a (which opened on Monday, Tuesday o r Wednesday e v e n i n g s ) o r exchanges w i t h t h e c e n t r a l c o a s t and to b o a t s l e a v i n g f o r Campbell R i v e r , Quadra I s l a n d and Vancouver e a r l y d u r i n g the l a s t day o f the o p e n i n g due t o p o o r t i d e s o r low c a t c h r a t e s ( a l l o f w h i c h have been o b s e r v e d from the a i r and n o t e d i n the l o g b o o k s ) . T h i r t y - t h r e e a e r i a l o b s e r v a t i o n s were made o f v e s s e l s t h a t c a r r i e d l o g b o o k s . D u r i n g t h e hour i n t e r v a l s s u r r o u n d i n g t h e s p o t c h e c k s , 31 o f the r e c o r d e d p o s i t i o n s were the same as t h o s e n o t e d from the a i r . One f i s h e r m a n ' s l o c a t i o n c o u l d n o t be i d e n t i f i e d from the l o g b o o k and a n o t h e r d i d n o t r e p o r t h i s a c t i v i t i e s d u r i n g t h e a f t e r n o o n o f t h e f l i g h t . CHAPTER IV INDEPENDENCE AND DISTRIBUTION OF EFFORT As many f i s h e r i e s s c i e n t i s t s have emphasized ( e . g . , Paloheimo 1971a), c l a s s i c a l f i s h e r i e s models a r e p r e d i c a t e d upon the a s sumptions t h a t f i s h i n g v e s s e l s o p e r a t e i n d e p e n d e n t l y and i n a random f a s h i o n . A n t h r o p o l o g i s t s have p r o v i d e d d e t a i l e d a n e c d o t a l i n f o r m a t i o n c o n c e r n i n g t h e b e h a v i o r o f f i s h e r m e n and t h e i r d e s c r i p t i o n s c o i n c i d e w i t h t h a t o u t l i n e d i n t h e p r e v i o u s c h a p t e r : f i s h e r m e n r e s p o n d t o p o t e n t i a l c a t c h r a t e s u s i n g v a r i o u s t y p e s o f i n f o r m a t i o n and compete f o r t h i s i n f o r m a t i o n and f o r f a v o u r a b l e s p o t s t o f i s h . The d i s t r i b u t i o n o f v e s s e l s and w a i t i n g t i m e s r e f l e c t the p e r f e c t i o n o f a c t i v e i n f o r m a t i o n ( d e f i n e d h e r e as i n f o r m a t i o n t h a t i s i n c o r p o r a t e d i n d e c i s i o n s t r a t e g i e s ) , the d i s t r i b u t i o n o f known f i s h c o n c e n t r a t i o n s and/or v u l n e r a b i l i t i e s and the i n t e n s i t y o f c o m p e t i t i o n . Random e f f o r t d i s t r i b u t i o n s a r e phenomena a s s o c i a t e d w i t h low v e s s e l abundance and th e l a c k o f i n f o r m a t i o n , o r a r e a r t i f a c t s o f g r i d m a n i p u l a t i o n i n d a t a r e c o r d i n g s . L i n e Up D i s t r i b u t i o n s Two a l t e r n a t i v e h y p o t h e s e s c o n c e r n i n g queue l e n g t h f r e q u e n c y d i s t r i b u t i o n s were t e s t e d : t h e s e s p a t i a l a r r a y s were e i t h e r randomly o r c o n t a g i o u s l y d i s t r i b u t e d . S i n c e the z e r o c a t e g o r y was i m p o s s i b l e t o a s c e r t a i n ( t h e r e b e i n g no p h y s i c a l l i m i t t o t h e number o f p l a c e s a s e t c o u l d be made) the t r u n c a t e d P o i s s o n and t r u n c a t e d n e g a t i v e b i n o m i a l d i s t r i b u t i o n s were f i t t e d t o the l i n e - u p d a t a by the maximum l i k e l i h o o d method (Cohen 1960; Sampford 1955). Examples o f the l i n e - u p d i s t r i b u t i o n s a r e p r e s e n t e d i n F i g u r e 10. 44 45 Queue l e n g t h f r e q u e n c y d i s t r i b u t i o n s . The graphs r e p r e s e n t t h e f r e q u e n c y o f l i n e - u p l e n g t h s o b s e r v e d d u r i n g d i f f e r e n t f l i g h t s and e f f o r t l e v e l s . E f f o r t was measured as the t o t a l number o f v e s s e l s p a r t i c i p a t i n g i n the f i s h e r y . 46 The t r u n c a t e d P o i s s o n p r o b a b i l i t y f u n c t i o n i s g i v e n by P(x) - e " X X x / x ! ( l - e - A ) 2) and t h e maximum l i k e l i h o o d e s t i m a t e o f X i s g i v e n by V ( l - e " X ) = x 3) where X i s the e s t i m a t e o f the p o p u l a t i o n mean and n i s t h e sample s i z e . A. The v a r i a n c e o f X i s g i v e n by V(X) -+(X)(X/n) 4) where + U ) = ( l - e - X ) 2 / a - ( A + l ) e - X ) 5) One f o r m u l a t i o n o f the n e g a t i v e b i n o m i a l i s P(x) = ( k + x - 1 ) ! / ( k - l ) ! x ! p x / ( l + P ) k + x x-1,2,3...; p,k>0 6) P(0) = l / ( l + p ) k 7) where k i s the d i s p e r s i o n c o e f f i c i e n t , p = m/k and m i s the mean. L e t t i n g w = 1/1+p, n = 1 -co, t h e t r u n c a t e d n e g a t i v e b i n o m i a l i s P(x) = <o k/(l-o) k) (k+x-1) ! / ( k - l ) !x! n x 8) The maximum l i k e l i h o o d e q u a t i o n s a r e nk/w(l-w k) - nm/(l-w) = 0 9) n l o g U ) / d - w k ) + I f i Z l / ( k + j - l ) - 0 10) i - 1 j - 1 47 T a b l e I . Parameter e s t i m a t e s f o r t h e t r u n c a t e d n e g a t i v e b i n o m i a l and t r u n c a t e d P o i s s o n f i t s t o queue l e n g t h f r e q u e n c y d a t a , ns = n o t s i g n i f i c a n t . 48 EFFORT ACCESS POINTS X a(X) 34 25 0.58 0.04 29 11 0.50 0.08 61 38 0.15 0.01 53 38 0.53 0.02 41 30 0.32 0.02 50 34 0.39 0.02 27 17 0.23 0.02 82 38 ns 84 48 ns 80 51 ns 85 47 ns 67 34 ns 111 64 ns 110 55 ns 105 43 ns 100 44 ns 95 36 ns 58 41 0.66 0.03 54 36 0.61 0.03 52 32 0.41 0.02 66 33 0.90 0.04 38 19 0.58 0.05 50 31 ns 55 29 ns 58 36 ns 114 51 ns 118 41 ns 120 56 ns 190 88 ns 178 83 ns 184 81 ns 166 67 ns 228 103 ns 260 133 ns 239 112 ns 241 109 ns 298 159 ns 280 136 ns 325 174 ns 341 138 ns 361 214 ns 363 178 ns 362 181 ns 263 127 ns 257 117 ns 255 111 ns 252 106 ns 279 167 ns 278 122 ns 289 178 ns 291 131 ns k a ( k ) w a(w) pa r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e 0.52 1.4 0.56 0.28 1.6 2.8 0.69 0.27 0.16 1.0 0.59 0.27 pa r a m e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e 1.5 2. .5 0. .70 0. .23 0.82 1. .1 0. .54 0. .19 0.05 0. .44 0. .27 0. .13 0.53 0. .87 0, .45 0. .19 2.1 2. .3 0. .61 0. .20 param e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e 22. 402. 0.98 0.30 53. 394. 0.98 0.12 param e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e 0.03 0.76 0.40 0.25 param e t e r e s t i m a t e n e g a t i v e p a r a m e t e r e s t i m a t e n e g a t i v e 1.7 1.4 0. 55 0.16 param e t e r e s t i m a t e n e g a t i v e 0.13 0.45 0. 40 0.14 0.19 0.52 0. 42 0.15 0.84 0.86 0. 53 0.15 20. 93. 0. 95 0.23 1.5 1.3 0. .60 0.15 0.43 0.49 0. .48 0.11 4.1 3.3 0. .77 0.13 1.1 0.93 0. .53 0.14 param e t e r e s t i m a t e n e g a t i v e 1.2 0.97 0. .60 0.13 1.5 1.4 0. .69 0.13 1.2 0.73 0 .51 0.11 3.6 4.3 0 .84 0.13 1.3 1.0 0 .65 0.12 param e t e r e s t i m a t e n e g a t i v e 1.0 0.99 0 .59 0.14 0.73 0.72 0 .51 0.13 0.95 0.76 0 .54 0.12 1.8 1.8 0 .65 0.16 0.95 1.2 0 .68 0.15 3.5 2.7 0 .74 0.13 7.4 13. 0 .91 0.14 0.90 0.73 0 .54 0.12 49 where n i s t h e sample s i z e , i s the f r e q u e n c y o f t h e i t h c a t e g o r y and X i s the l a r g e s t v a l u e o f x. The v a r i a n c e s o f to and k c a n t h e n be c a l c u l a t e d from t h e v a r i a n c e - c o v a r i a n c e m a t r i x (see Sampford 1955). T a b l e I g i v e s the para m e t e r e s t i m a t e s and s t a n d a r d d e v i a t i o n s f o r l i n e - u p d i s t r i b u t i o n s from a l l the o v e r f l i g h t s and i n d i c a t e s whether the f i t s were s i g n i f i c a n t f o r the t r u n c a t e d n e g a t i v e b i n o m i a l and t r u n c a t e d P o i s s o n s o l u t i o n s (a =0.05). The Kolmogorov-Smirnov t e s t was u s e d . I t i s o b v i o u s t h a t e f f o r t was o n l y d i s t r i b u t e d i n a random f a s h i o n when v e r y few b o a t s were p r e s e n t (50 b o a t s appears t o be t h e b r e a k p o i n t ) . The m a j o r i t y o f t h e h i g h e f f o r t queue d i s t r i b u t i o n s were a p p r o x i m a t e d by t h e t r u n c a t e d n e g a t i v e b i n o m i a l ( t h e P o i s s o n d i d n o t f i t ) . E f f o r t , t h e n , was u s u a l l y d i s t r i b u t e d i n a c o n t a g i o u s f a s h i o n and t h e o b v i o u s h y p o t h e s i s i s t h a t t h e s e non-random d i s t r i b u t i o n s r e f l e c t e d a r e s p o n s e t o salmon d e n s i t i e s o r v u l n e r a b i l i t i e s c o u p l e d w i t h c o m p e t i t i v e i n t e r a c t i o n s among f i s h e r m e n . I n summary, t h e d i s t r i b u t i o n s were d e s c r i b e d ( i . e . , p o s s e s s e d a s i g n i f i c a n t f i t ) by t h e P o i s s o n , o n l y , i n 10 o u t o f 51 d a t a s e t s ( a t low e f f o r t ) , the n e g a t i v e b i n o m i a l , o n l y , i n 31 s e t s , b o t h t h e o r e t i c a l d i s t r i b u t i o n s i n 2 i n s t a n c e s and n e i t h e r i n 8 samples. A n o t h e r way o f a p p r o a c h i n g t h e p r o b l e m i s t h r o u g h a n a l y s i s o f v a r i a n c e . I f the a c c e s s p o i n t s r e p r e s e n t e d a n o n - u n i f o r m d i s t r i b u t i o n o f salmon v u l n e r a b i l i t i e s and a c q u i r e d l i n e - u p s i n an o r d e r e d f a s h i o n o v e r e f f o r t l e v e l s , some o f t h e s e p o i n t s s h o u l d have d i f f e r e n t means ( i . e . , queue l e n g t h s d i d n o t f l u c t u a t e randomly among a c c e s s p o i n t s ) . A two-way ANOVA c o n t a i n i n g f l i g h t and a c c e s s p o i n t e f f e c t s was p e r f o r m e d f o r beach s e t l i n e - u p s t h a t were n o t a f f e c t e d by b o u n d a r i e s . Z e r o s were i n c l u d e d and t h e r e was one o b s e r v a t i o n p e r c e l l . T a b l e I I summarizes t h e d a t a : the a c c e s s p o i n t and f l i g h t e f f e c t s were s i g n i f i c a n t (p<0.001). Some a c c e s s p o i n t s were c h a r a c t e r i z e d by d i f f e r e n t queue l e n g t h s . F i g u r e s 11-13 50 T a b l e I I . A c c e s s p o i n t - f l i g h t ANOVA f o r beach s e t l i n e - u p s u n a f f e c t e d by b o u n d a r i e s . Z e r o l i n e - u p l e n g t h s were i n c l u d e d . SOURCE DF SS MS F-RATIO PROBABILITY a c c e s s p o i n t 155 1922.9 12.406 15.286 0.0000 f l i g h t 45 407.88 9.0641 11.168 0.0000 a c c e s s p o i n t - f l i g h t 6975 5660.9 0.81160 51 i l l u s t r a t e the d i s t r i b u t i o n o f beach s e t s f o r d i f f e r e n t b o a t d e n s i t i e s and b o u n d a r i e s . A s u b s e t o f a c c e s s p o i n t s ( u n a f f e c t e d by b o u n d a r i e s ) a c q u i r e d v e s s e l s as e f f o r t i n t e n s i f i e d w h i l e o t h e r f i s h i n g s p o t s were c h a r a c t e r i z e d by c o n s t a n t b o a t d e n s i t i e s . Movement and A c t i v i t y V e s s e l movements may be random o r d i r e c t i o n a l . D u r i n g a s h o r t time p e r i o d ( i . e . , a f l i g h t ) t h e n u l l h y p o t h e s i s i s t h a t e q u a l numbers o f b o a t s were moving up o r down the s t r a i t . B i n o m i a l o r c h i s q u a r e d t e s t s were p e r f o r m e d f o r f l i g h t s c h a r a c t e r i z e d by adequate sample s i z e s o f m o b i l e b o a t s . (The b i n o m i a l t e s t was p e r f o r m e d f o r sample s i z e s l e s s t h a n 25.) The n u l l h y p o t h e s i s was r e j e c t e d i n o n l y 15 o f the 46 d a t a s e t s ( T a b l e I I I ) . T h i s r a t i o was g r e a t e r t h a n the e x p e c t e d 1/20 r e j e c t i o n r a t i o f o r a l p h a e q u a l t o 0.05. When the d a t a s e t s were grouped, the n u l l h y p o t h e s i s was n o t r e j e c t e d ( c a l c u l a t e d X 2 = 0.46). The sum o f the i n d i v i d u a l t e s t p a r a m e t e r s w i t h 22 degrees o f freedom was s i g n i f i c a n t ( c a l c u l a t e d X 2 = 122.16). T h e r e f o r e , the samples were v e r y h e t e r o g e n e o u s : group s e a r c h b e h a v i o r was n o t c o n s t a n t . The a c c e s s p o i n t s and f i s h i n g a r e a s were d i g i t i z e d as a l o n g i t u d e - l a t i t u d e g r i d and were c o n v e r t e d t o d i s t a n c e s i n n a u t i c a l m i l e s from t h e lower f i s h i n g b oundary i n A r e a 13. F i g u r e 14 summarizes the f l e e t movement w i t h i n o p e n i n g s as the average v e s s e l d i s t a n c e from the lower boundary. F l e e t movement was d i r e c t i o n a l and p r o g r e s s e d t o the n o r t h w e s t ( w i t h i n - o p e n i n g f l i g h t s a r e c o n n e c t e d by s o l i d l i n e s ) . F i s h e r m e n caught the f i s h a l r e a d y p r e s e n t i n the f i s h i n g a r e a on Sunday n i g h t and th e n moved n o r t h t o i n t e r c e p t i n c o m i n g f i s h . B o u n d a r i e s a l s o had an e f f e c t , as n o t e d i n F i g u r e 14. The measurement o f t h i s d i r e c t i o n a l movement was somewhat F i g u r e 11. Beach s e t l i n e - u p s : low e f f o r t . Beach s e t and t i e up l i n e - u p l e n g t h s a r e i l l u s t r a t e d . The s o u t h e a s t e r n end of t h e Johnstone S t r a i t f i s h e r y appears near t h e v e r t i c a l a x i s . Salmon e n t e r from the northwest. F i g u r e 12. Beach s e t l i n e - u p s : medium e f f o r t . Beach s e t and t i e up l i n e - u p ^ l e n g t h s a r e i l l u s t r a t e d . The s o u t h e a s t e r n end o f the J o h n s t o n e S t r a i t f i s h e r y a p pears near the v e r t i c a l a x i s . Salmon e n t e r from the northwest. F i g u r e 13. Beach s e t l i n e - u p s : h i g h e f f o r t . Beach s e t and t i e up l i n e - u p l e n g t h s a r e i l l u s t r a t e d . The s o u t h e a s t e r n end of t h e Johnstone S t r a i t f i s h e r y appears near the v e r t i c a l a x i s . Salmon e n t e r from the northwest. 55 T a b l e I I I . S h o r t term v e s s e l movements. The b i n o m i a l and c h i s q u a r e d s t a t i s t i c s were used t o t e s t the h y p o t h e s i s t h a t e q u a l numbers o f b o a t s were moving up and down the s t r a i t d u r i n g a f l i g h t . C r i t i c a l c h i square (a = 0.05) = 3.84. X2 ( n > 2 5 ) BINOMIAL (n<25) SIGNIFICANT 9 6 NOT SIGNIFICANT 13 18 56 >-F L I G H T F i g u r e 14. W i t h i n - o p e n i n g f l e e t movements. The p o s i t i o n s o f a c c e s s p o i n t s were c o n v e r t e d t o d i s t a n c e s from the l o w e r f i s h i n g boundary. T h i s graph i l l u s t r a t e s the a verage v e s s e l d i s t a n c e from t h e lower boundary d u r i n g d i f f e r e n t f l i g h t s and o p e n i n g s . W i t h i n - o p e n i n g measurements a r e c o n n e c t e d by s o l i d l i n e s . M a j o r boundary r e s t r i c t i o n s a r e n o t e d . 57 s u b j e c t i v e : open s e t f i s h i n g a r e a s were s u b j e c t i v e l y i d e n t i f i e d as d i s t i n c t r e g i o n s o f a g g r e g a t i o n and t h e n d i g i t i z e d as a s i n g l e p o i n t . F i s h e r m e n a r e aware o f the t i d a l c y c l e and s t r u c t u r e t h e i r s t r a t e g i e s a r o u n d the c h a n g i n g c u r r e n t s . A c t i v i t y p a t t e r n s may thus be c o r r e l a t e d w i t h t i d e s and a n u l l h y p o t h e s i s i s t h a t e q u a l numbers o f b o a t s were a c t i v e d u r i n g t h e ebb and t h e f l o o d . I n the absence o f i m p o r t a n t r e s t r i c t i o n s , t h e a l t e r n a t i v e h y p o t h e s i s s h o u l d be s u p p o r t e d : a c t i v i t y o s c i l l a t e d w i t h t h e t i d a l c y c l e . A c t i v i t i e s f o r the A r e a 12 p o r t i o n o f t h e f i s h e r y were compared f o r r i s i n g and e b b i n g t i d e s a c c o r d i n g t o A l e r t Bay t i d a l d a t a ( A r e a 13 was n o t i n c l u d e d due t o the time l a g f o r t h e s t a g e s o f t h e t i d e ) . The p r o p o r t i o n s o f a c t i v e e f f o r t f o r the ebb and f l o o d were e q u a l (0.47) and r e m a i n e d so when w a i t i n g v e s s e l s were i n c l u d e d ( 0 . 8 2 ) . The o b s e r v e d numbers o f maximum c a t c h e s i n A r e a 12 were d i f f e r e n t : o n l y 68 maximum c a t c h e s o b t a i n e d by i n d i v i d u a l b o a t s d u r i n g an o p e n i n g were made on t h e ebb w h i l e 120 maximum c a t c h e s were o b t a i n e d on t h e f l o o d . The maximum c a t c h was an i m p o r t a n t component o f the g r o s s c a t c h . Four h u n d r e d and f o r t y - t h r e e s e t s were r e c o r d e d by o b s e r v e r s f o r 12 v e s s e l s and a t o t a l o f 16 o p e n i n g s . N i n e t e e n p e r c e n t o f t h e t o t a l v e s s e l c a t c h was t a k e n by t h e l a r g e s t s e t p e r o p e n i n g (3.6 p e r c e n t o f t h e t o t a l s e t s ) . D i s c u s s i o n The J o h n s t o n e S t r a i t f i s h e r y cannot be p e r c e i v e d as a random f i s h i n g p r o c e s s . L i n e - u p s were i n d i c a t i v e o f t h e s p a t i a l h e t e r o g e n e i t y and the queue l e n g t h s were d i s t r i b u t e d c o n t a g i o u s l y . L a r g e s c a l e movements were d i r e c t i o n a l and r e p r e s e n t r a t i o n a l b e h a v i o r -- c l e a n up t h e f i s h p r e s e n t i n the c e n t r a l p o r t i o n o f t h e f i s h e r y and t h e n move towards the boundary which a l l f i s h c r o s s . The s u p p o s i t i o n t h a t s h o r t term s e a r c h was random was n o t 58 r e j e c t e d most o f the time, b u t the d a t a s e t was c e r t a i n l y h e t e r o g e n e o u s . T h i s r e s u l t may be i n d i c a t i v e o f the u n c e r t a i n t y f a c e d by the s m a l l p r o p o r t i o n o f m o b i l e b o a t s ( l e s s t h a n 20 p e r c e n t on a v e r a g e ) . The n e g a t i v e k e s t i m a t e s i n d i c a t e d t h a t some o f the l i n e - u p d i s t r i b u t i o n s c o u l d n o t be d e s c r i b e d by the n e g a t i v e b i n o m i a l . A l s o , t h e s e e s t i m a t e s a r e d i f f i c u l t t o e x p l a i n i n terms o f p o s s i b l e a l t e r n a t i v e d i s t r i b u t i o n s . D u r i n g p e r i o d s o f h i g h e f f o r t , a n e g a t i v e k may have been i n d i c a t i v e o f a v e r y l a r g e number o f u n e x p l o i t e d a c c e s s p o i n t s ( z e r o s ) . However, t h i s v i e w does n o t e x p l a i n the o c c u r r e n c e o f n e g a t i v e e s t i m a t e s , a t low e f f o r t l e v e l s ; t h e s e d i s t r i b u t i o n s were d e s c r i b e d by t h e P o i s s o n d i s t r i b u t i o n . The n e g a t i v e b i n o m i a l approaches the P o i s s o n as k approaches i n f i n i t y ( r a t h e r t h a n some n e g a t i v e number). The r e s u l t s o f t h e a c c e s s p o i n t - f l i g h t ANOVA were l e s s vague and i n c l u d e d t h e w eekly n u m e r i c a l r e s p o n s e component. An e m p i r i c a l d e s c r i p t i o n o f l i n e - u p d i s t r i b u t i o n s i s p r e s e n t e d i n C h a p t e r V I . C o n s t r a i n t s o t h e r t h a n random b e h a v i o r p r o d u c e d c o n s t a n t f l e e t a c t i v i t y o v e r the t i d a l range. The o l d t i m e r s s t a t e d t h a t t h e i r a c t i v i t i e s change w i t h the t i d e and t h a t the r e c e n t o v e r c r o w d i n g o f the f i s h e r y w i t h i n e x p e r i e n c e d i n d i v i d u a l s r u n n i n g new, t e c h n o l o g i c a l l y advanced v e s s e l s p r o d u c e d c o n s t a n t a p p l i c a t i o n o f e f f o r t . Knowledgeable f i s h e r m e n d e f i n e d s k i l l i n terms o f making a few, t a r g e t e d , l a r g e s e t s ; c o s t s a r e m a i n t a i n e d a t a minimum l e v e l . T h i s s t r a t e g y r e q u i r e s e x t e n s i v e l o c a l knowledge and freedom o f a c t i o n f o r p r e c i s e t i m i n g . I n t h e p r e s e n t c o n g e s t e d f i s h e r y , s k i p p e r s a r e f o r c e d to m a i n t a i n t h e i r p o s i t i o n i n l i n e - u p s -- s e t t i m i n g w i t h r e s p e c t t o t i d e s i s h i n d e r e d . Young s k i p p e r s s u b s t i t u t e h a r d work, l o n g h o u r s and t e c h n o l o g y f o r s k i l l and o f t e n t r y to maximize t h e i r c a t c h by m a x i m i z i n g the number o f s e t s made d u r i n g an o p e n i n g r a t h e r t h a n f i n e t u n i n g t i m i n g . A l s o , t h e r e i s always a chance t h a t the equipment w i l l 59 b r e a k down o r t h a t an u n e x p e c t e d c a t c h w i l l be made i f one s e t s o f t e n enough. F i s h i n g expenses have p r o b a b l y i n c r e a s e d as young t e c h n o c r a t s e n t e r e d the f i s h e r y . The r e s u l t s i l l u s t r a t e the p e r v a d i n g s p a t i a l and t e m p o r a l h e t e r o g e n e i t y o f t h e system. F i s h e r m e n a r e c o g n i t i v e o f t h i s p a t c h i n e s s and a l i g n t h e m s e l v e s a c c o r d i n g t o t h e s e p e r c e p t i o n s . The r e s u l t i s i n t e r f e r e n c e c o m p e t i t i o n . CHAPTER V COMPETITION AND SET STRATEGIES R o t h s c h i l d (1977) r e v i e w e d the problems a s s o c i a t e d w i t h m e a s u r i n g f i s h i n g e f f o r t and d i s c u s s e d the e f f e c t s o f c o m p e t i t i o n upon t h e r e l a t i o n s h i p between e x p l o i t a t i o n r a t e s and common d e f i n i t i o n s o f e f f o r t . The a p p r o a c h was p r i m a r i l y t h e o r e t i c a l . The m a j o r i t y o f w o r l d f i s h e r i e s a r e managed on a c a t c h p e r u n i t e f f o r t b a s i s and any argument b a s e d on C P U E - e f f o r t r e l a t i o n s h i p s (where t h e same measure o f e f f o r t c o n t r i b u t e s t o the dependent and i n d e p e n d e n t v a r i a b l e s ) i s c i r c u l a r . M a j o r b a r r i e r s c o n f r o n t i n g q u a n t i f i c a t i o n o f the c o m p e t i t i v e p r o c e s s a r e e s t i m a t i o n o f f i s h abundance and a s s o c i a t e d measurement e r r o r s . W a l t e r s and Ludwig (1981) d i s c u s s e d t h e e f f e c t s o f measurement e r r o r s on a p p a r e n t c u r v i l i n e a r r e l a t i o n s h i p s and c o n c l u d e d t h a t o b s e r v a t i o n e r r o r s may have extreme e f f e c t s . Salmon s e i n e f i s h e r m e n , however, c a n be v i s u a l l y l o c a t e d on a one d i m e n s i o n a l s c a l e and a c c u r a t e c o u n t s a r e p o s s i b l e . O b s e r v a t i o n e r r o r s a r e r e l a t i v e l y s m a l l , p e r c e p t i o n s and r e a l i t y c a n be compared and c o o p e r a t i o n from f i s h e r m e n c a n be a s s u r e d and t e s t e d . L i n e - u p and E f f o r t L e v e l s The r e l a t i o n s h i p between average and maximum queue l e n g t h s and e f f o r t c a n be summarized by t h r e e a l t e r n a t i v e h y p o t h e s e s ( F i g u r e 15) wh i c h p r o c e e d from t h e e v i d e n c e t h a t , due t o i n f o r m a t i o n , s k i p p e r s r e s p o n d t o the d i s t r i b u t i o n o f f i s h i n a non-random f a s h i o n . 1) I n a system p o s s e s s i n g an u n l i m i t e d number o f e q u a l l y d e s i r a b l e 60 61 i EFFORT (NO. OF BOATS) F i g u r e 15. Queue r e s p o n s e h y p o t h e s e s . The p r e d i c t e d r e s p o n s e s o f average l i n e - u p l e n g t h t o salmon d i s t r i b u t i o n s a r e shown. These p r e d i c t i o n s a r e b a s e d upon the a s s u m p t i o n t h a t i n f o r m a t i o n i s good. 1) An u n l i m i t e d number o f e q u a l l y d e s i r a b l e a c c e s s p o i n t s . 2) A l i m i t e d number o f e q u a l l y d e s i r a b l e a c c e s s p o i n t s . 3) A d i s t r i b u t i o n o f d e s i r a b i l i t i e s . 62 a c c e s s p o i n t s , the r e l a t i o n s h i p s h o u l d p o s s e s s the form o f a s t r a i g h t l i n e w i t h s l o p e z e r o and i n t e r c e p t e q u a l t o one. The maximum l i n e - u p , o f c o u r s e , w i l l a l s o e q u a l one b o a t . 2) I f t h e r e a r e a l i m i t e d number o f e q u a l l y d e s i r a b l e s p o t s , a l i n e a r , i n c r e a s i n g r e l a t i o n s h i p s h o u l d be o b s e r v e d and the maximum l i n e - u p w i l l f o l l o w the same t r e n d . 3) A d i s t r i b u t i o n o f d e s i r a b i l i t i e s c o u p l e d w i t h r e s t r i c t i v e w a i t i n g t i m e s (which e q u a l i z e t h e t o t a l a v a i l a b l e c a t c h among a c c e s s p o i n t s ) w i l l p r o d u c e a s a t u r a t i n g o r dome shaped c u r v e p r o v i d e d t h a t t h e skew does n o t approach t h e s i t u a t i o n d e s c r i b e d by h y p o t h e s i s 2 ) ; t h e q u a l i t a t i v e form c a n n o t a p p r o a c h t h a t o f h y p o t h e s i s 1 ) , b u t may assume the c h a r a c t e r i s t i c s o f h y p o t h e s i s 2) a t e x t r e m e l y h i g h v e s s e l d e n s i t i e s . F i g u r e s 16-19 i l l u s t r a t e the l i n e - u p d a t a . The d i s t r i b u t i o n h y p o t h e s i s (3) was s u p p o r t e d and models i n c o r p o r a t i n g random o r u n i f o r m b e h a v i o r were r e j e c t e d . F u r t h e r e v i d e n c e f o r a d i s t r i b u t i o n o f p o t e n t i a l c a t c h e s i s p r e s e n t e d i n a f o l l o w i n g s e c t i o n . F i s h e r m e n s t a t e d t h a t the e x c e p t i o n a l l y l o n g l i n e - u p s r e f l e c t e d s h o r t term r e s p o n s e s t o e x c e p t i o n a l c a t c h e s . O b s e r v e d a g g r e g a t i o n s were c o n f i r m e d as t h e y o c c u r r e d and r e p r e s e n t e d r a p i d d i s s e m i n a t i o n o f i n f o r m a t i o n c o n c e r n i n g a s i n g l e l a r g e s e t . The s k i p p e r s e x p e c t e d the b i g s c h o o l s o f salmon t o f o l l o w a s i m i l a r p a t h on the n e x t t i d e ( s e e F i g u r e 17). W i t h i n - s e a s o n boundary changes p r o d u c e d s e v e r e r e s t r i c t i o n s o f the a v a i l a b l e s u r f a c e a r e a . These m a n i p u l a t i o n s a p p a r e n t l y d i d n o t a f f e c t q u e u i n g b e h a v i o r (measured as the average l i n e - u p l e n g t h ) , c o n s i d e r i n g the 63 to O CL CO CO UJ o o < CO o CO u. o 0_ i UJ UJ C5 < or UJ > < 2 . 2 5 r 2 . 0 0 h 1.75 1.50 1.25 1.00" O o o o o • 9 CD . CO Q 7 5 150 2 2 5 3 0 0 EFFORT (NO. OF BOATS) 3 7 5 F i g u r e 16. Average l i n e - u p l e n g t h v s . e f f o r t . The f i l l e d c i r c l e s r e p r e s e n t major boundary r e s t r i c t i o n s and the open c i r c l e s r e p r e s e n t d a t a r e c o r d e d when o n l y minor b o u n d a r i e s were i n e f f e c t . 64 O 0_ CO CO bJ O O < CO I— < o m u. o ZD i Lu I3 i 10 o o o o o o o o o o o o o« o X < mm _L 75 150 225 3 0 0 EFFORT (NO. OF BOATS) 375 F i g u r e 17. Maximum l i n e - u p l e n g t h v s . e f f o r t . The f i l l e d c i r c l e s r e p r e s e n t major boundary r e s t r i c t i o n s and t h e open c i r c l e s r e p r e s e n t d a t a r e c o r d e d when o n l y minor b o u n d a r i e s were i n e f f e c t . 65 O Q-CO CO LU t r Q. — CO o CD O d 0_ • LU CO X o < LU CD LU CD < or LU 2 . 5 r 5 2 . 2 1.9 1.6 1.3 • • • o° >o •o O 7 5 150 225 3 0 0 E F F O R T (NO. OF BOATS) 3 7 5 F i g u r e 18. Average beach s e t l i n e - u p l e n g t h v s . e f f o r t . The f i l l e d c i r c l e s r e p r e s e n t major boundary r e s t r i c t i o n s and the open c i r c l e s r e p r e s e n t d a t a r e c o r d e d when o n l y minor b o u n d a r i e s were i n e f f e c t . 66 o CL CO CO UJ o o < CO \— <t o CD U. o d z CL => i UJ UJ CO UJ CL O UJ o <t or UJ 2 . 2 5 r l . 9 0 h 1.55 1.20 0 . 8 5 O O o o 0 ^ 0 ° o • o o 0 . 5 0 1 J_ J_ JL 7 5 150 2 2 5 3 0 0 EFFORT (NO. OF BOATS) 3 7 5 F i g u r e 19. Average open s e t l i n e - u p l e n g t h v s . e f f o r t . The f i l l e d c i r c l e s r e p r e s e n t major boundary r e s t r i c t i o n s and the open c i r c l e s r e p r e s e n t d a t a r e c o r d e d when o n l y m i n o r b o u n d a r i e s were i n e f f e c t . 67 o v e r l a p o f p o i n t s i n F i g u r e s 16-19. The s a t u r a t i n g p o r t i o n s o f the beach s e t and open s e t c u r v e s were d i f f e r e n t and the l a r g e r b e a c h s e t l i n e - u p s r e f l e c t e d the f i s h e r m e n s ' p e r c e p t i o n s c o n c e r n i n g t h e i r r e l a t i v e p r o f i t a b i l i t y . The maximum l i n e - u p q u i c k l y s a t u r a t e d a t 8 o r 9 b o a t s . T o t a l s e t e f f o r t and average s e t s p e r b o a t were a l s o c a l c u l a t e d from the l i n e - u p d i s t r i b u t i o n s . The o p e r a t i o n o f a queue i s d e m o n s t r a t e d i n F i g u r e 20. A t e q u i l i b r i u m ( i . e . , a b o a t has n o t r e c e n t l y j o i n e d the l i n e - u p ) , a v e s s e l o n l y w a i t s f o r the l e t t i n g go, t o w i n g and c l o s i n g times o f t h e o t h e r b o a t s minus h i s own p u r s i n g t i m e . A s k i p p e r b e g i n s h i s s e t as the p r e c e d i n g b o a t b e g i n s t o p u r s e . The w a i t i n g time f o r an i n d i v i d u a l b o a t s h a r i n g a s p o t c a n be c a l c u l a t e d on the b a s i s o f f u n c t i o n a l d a t a as W = ( n - l ) S - P 11) where n i s t h e queue l e n g t h , S i s the sum o f t h e l e t t i n g go, t o w i n g and c l o s i n g t i m e s , P i s the time t a k e n t o p u r s e t h e n e t and b r i n g i t a b o a r d . The t o t a l time t o s e t i s t h e r e f o r e g i v e n by ST = (n-l)S-P+S+P - nS 12) E s t i m a t e s o f t h e time components f o r the o b s e r v e r d a t a from 1980-1981 a r e p r e s e n t e d i n T a b l e IV. E q u a t i o n 11 becomes W = ( n - l ) 2 1 . 3 - 1 3 . 1 13) O b s e r v e r d a t a on w a i t i n g times a r e p l o t t e d i n F i g u r e 21. The l i n e a r r e g r e s s i o n o f w a i t i n g time on queue l e n g t h p r o d u c e d t h e e q u a t i o n W = 29n-33 n>l 14) W = 0 n-1 14) 68 O WAITING TIME FOR BOAT 1 2 4 ^  o 3 ^ 1 BOAT NUMBER ^ L E T T I N G GO TOW o o CLOSE PURSE F i g u r e 20. O p e r a t i o n o f a queue. The s e t components and w a i t i n g times w i t h i n a queue a r e i l l u s t r a t e d f o r an e q u i l i b r i u m s i t u a t i o n ( i . e . , a v e s s e l has n o t r e c e n t l y e n t e r e d t h e l i n e - u p ) . Note the o v e r l a p between the p u r s i n g and l e t t i n g go components. 69 T a b l e IV. Set time components. O b s e r v e r measurements f o r t h e components a p u r s e s e i n e s e t . VARIABLE N MEAN a s h o o t ( s ) 472 3. .303 0. .9271 tow ( t ) 474 12. .77 4. .471 c l o s e ( c) 476 5. .164 2, .358 s+t+c 472 21. .28 5, .862 p u r s e 476 13. .09 6. .000 t o t a l s e t 467 34. .38 9 .007 70 2 7 5 r 0 2 4 6 8 10 L I N E - U P (NO. OF BOATS) F i g u r e 21. W a i t i n g t i m e s as a f u n c t i o n o f queue l e n g t h . B o t h the f u n c t i o n a l model d e r i v e d from the o p e r a t i o n o f a queue and the s t a t i s t i c a l model p r o v i d e d by l e a s t s q u a r e s r e g r e s s i o n a r e p r e s e n t e d h e r e . 71 which was h i g h l y s i g n i f i c a n t (p<0.0001, R=0.97). The f u n c t i o n a l ( e q u a t i o n 13) and s t a t i s t i c a l ( e q u a t i o n 14) p r e d i c t i o n s a r e a l s o compared i n F i g u r e 21. The d i f f e r e n c e between those p r e d i c t i o n s can be e x p l a i n e d by s k i p p e r s ' c a u t i o n . S k i p p e r s s a c r i f i c e d e f f i c i e n c y as th e y a v o i d e d n e t s . The number o f s e t s p e r f o r m e d by an i n d i v i d u a l b o a t p a r t i c i p a t i n g i n a g i v e n l i n e - u p l e n g t h i s Sb = T/(S+P+W) 15) where T i s the t o t a l f i s h i n g time. The average time f o r a s e t g i v e n an e f f o r t l e v e l i s E TS = ( Z ( S i + W i ) ) / E 16) i = l where E i s t h e number o f v e s s e l s p a r t i c i p a t i n g i n the f i s h e r y , S^ i s the t o t a l s e t time and Wj_ i s the w a i t i n g time f o r v e s s e l i . I f ES^/E i s e s t i m a t e d as t h e average s e t time ( S t ) from T a b l e IV (and w a i t i n g times a r e  e q u a l w i t h i n and between e q u a l queue l e n g t h s ) e q u a t i o n 16 becomes A A TS = S t + Z n ^ / Z n L 17) i = l i = l where A i s the t o t a l number o f a c c e s s p o i n t s , n^ i s the l i n e - u p l e n g t h a t a c c e s s p o i n t i and i s e s t i m a t e d from e q u a t i o n 14. U s i n g e q u a t i o n 17, the maximum number o f f i s h i n g h ours r e c o r d e d f o r a 48 hour o p e n i n g (T) and the l i n e - u p d i s t r i b u t i o n s , the average number o f s e t s p e r b o a t was e s t i m a t e d as Sb = T/TS 18) ( F i g u r e 22). The t o t a l number o f s e t s f o r the f l e e t was e s t i m a t e d as ESb 72 ( F i g u r e 2 3 ) . The s k i p p e r s ' s p a c i n g mechanisms p r o d u c e d an i n c r e a s i n g a b s o l u t e s e t e f f o r t as a f u n c t i o n o f b o a t d e n s i t y , ' b u t i n t e n s e i n t e r f e r e n c e c o m p e t i t i o n between b o a t s r e s u l t e d i n a d e c r e a s i n g a v e r age number o f s e t s p e r b o a t . The f l i p i n t h e c u r v e ( i . e . , the i n c r e a s e i n t h e number o f s e t s p e r b o a t a t h i g h v e s s e l d e n s i t i e s ) r e p r e s e n t s a change i n s t r a t e g y due t o o v e r c r o w d i n g ; v e s s e l s moved o f f s h o r e t o r e g i o n s o f low l i n e - u p s and made open s e t s . E f f e c t s o f S e t S t r a t e g i e s on C a t c h p e r S e t The l o g b o o k d a t a i n c l u d e d l i n e - u p i n t e r v a l s and s e t s t r a t e g i e s (open s e t o r t i e u p ) . The f o l l o w i n g s e c t i o n p r e s e n t s a n a l y s e s o f t h i s l o g b o ok d a t a and e x p l o r e s the e f f e c t s o f s e t s t r a t e g y and l i n e - u p l e n g t h on c a t c h p e r s e t . The l o g b o o k s were s t r u c t u r e d t o t e s t two h y p o t h e s e s : 1) l i n e - u p l e n g t h r e f l e c t s c a t c h p e r s e t and 2) open s e t s a r e l e s s d e s i r a b l e t h a n t i e ups. F i s h e r m e n r e c o r d e d c a t c h e s p e r s e t and l i n e - u p i n t e r v a l s i n l o g b o o k s . S i n c e v e r y few queues were o b s e r v e d i n the 6-10 range, o n l y two l i n e - u p i n t e r v a l s were u s e d i n t h e f o l l o w i n g ANOVA (1-2 and 3-5 b o a t s ) . The u n b a l a n c e d d a t a a r r a y ( i . e . , a l l b o a t s o v e r a l l weeks) p r o v e d t o be e x t r e m e l y cumbersome f o r a n a l y s i s w i t h e x i s t i n g U.B.C. s o f t w a r e . M a i n t e n a n c e o f a low f r e q u e n c y o f empty c e l l s e n t a i l e d a one-way ANOVA f o r b o a t e f f e c t s s t a n d a r d i z e d f o r week e f f e c t s ( t h e b o a t e f f e c t i n c l u d e d d i f f e r e n c e s i n l i n e - u p and s e t type s t r a t e g i e s ) and a three-way ANOVA f o r queue l e n g t h , s e t t y p e , week and i n t e r a c t i o n e f f e c t s . C a t c h e s p e r s e t f o r 32 v e s s e l s were e x p r e s s e d as s t a n d a r d d e v i a t i o n s from t h e w e e k l y means. The n a t u r a l l o g a r i t h m o f t h e d e v i a t i o n s p l u s 1.0 p r o d u c e d n o r m a l i t y . Due 73 5 0 r o CO to h-UJ to <s> < DC UJ > < 4 5 4 0 3 5 3 0 2 5 2 0 9 ? ° 15 « 0 0 8 o o o o o ^ o CO o o o O . Q ? 0 o o 7 5 150 2 2 5 3 0 0 EFFORT (NO. OF BOATS) 3 7 5 F i g u r e 22. Average number o f s e t s p e r b o a t v s . e f f o r t . The number o f s e t s was c a l c u l a t e d from t h e l i n e - u p d i s t r i b u t i o n s , the measured s e t time components and a p r e d i c t i v e r e g r e s s i o n e q u a t i o n f o r w a i t i n g t i m e s as f u n c t i o n o f l i n e - u p l e n g t h . 74 I 3 0 0 C V to 9000 LU CO o 5000 o o o OQO o o 1000 ° CX Oo 75 150 225 300 EFFORT (NO. OF BOATS) 375 F i g u r e 23. T o t a l s e t e f f o r t v s . e f f o r t . The number o f s e t s was c a l c u l a t e d from the l i n e - u p d i s t r i b u t i o n s , t h e measured s e t time components and a p r e d i c t i v e r e g r e s s i o n e q u a t i o n f o r w a i t i n g t i m e s as f u n c t i o n o f l i n e - u p l e n g t h . to t h e l a r g e number o f l e v e l s , the v a r i a n c e s were h e t e r o g e n e o u s . Boat e f f e c t s were s i g n i f i c a n t (p<0.0001) and the p e r c e n t a g e o f the t o t a l v a r i a n c e a t t r i b u t e d t o d i f f e r e n c e s among b o a t s was 5.3 ( T a b l e V ) . The n a t u r a l l o g a r i t h m s o f the c a t c h e s p e r s e t p l u s 1.0 c o n s t i t u t e d the i n p u t t o t h e s e t t y p e - l i n e - u p - w e e k ANOVA ( T a b l e V I ) : t w e n t y - e i g h t v e s s e l s were i n c l u d e d i n the a n a l y s i s . A l t h o u g h the t e s t f o r homogeneity o f v a r i a n c e i n d i c a t e d t h a t t h e s e t ty p e v a r i a n c e s were d i f f e r e n t , t h e a c t u a l v a l u e s were s i m i l a r (3.5 and 2.6) and i t was assumed t h a t t h e a n a l y s i s was r o b u s t . S e t t y p e s were d i f f e r e n t (p<0.003), b u t the ranges o f the t r a n s f o r m e d p r e d i c t e d means p l u s o r minus t h e i r s t a n d a r d e r r o r s were 32-36 and 28-29 f i s h p e r s e t f o r t h e t i e ups and open s e t s , r e s p e c t i v e l y . C o n s i d e r i n g the t e m p o r a l and s p a t i a l v a r i a b i l i t y and s k i l l e f f e c t s , t h e d i f f e r e n c e i n mean v a l u e s was n e g l i g i b l e . Queue i n t e r v a l s were a l s o d i f f e r e n t (p<0.00001) and the d i f f e r e n c e i n p r e d i c t e d means was i n d i c a t i v e o f d e f i n i t e economic e f f e c t s : t h e s h o r t queue, p r e d i c t e d mean was 27-28 salmon p e r s e t and the medium queue mean was 40-45 f i s h p e r s e t . Weeks, o f c o u r s e , were d i f f e r e n t (p=0.0) as t h e salmon r u n i n c r e a s e d and ebbed. A s e t t y p e - l i n e - u p i n t e r a c t i o n was p r e s e n t (p<0.04) and may be i n t e r p r e t e d s i m p l y from t h e d a t a means: open s e t s were l e s s p r o f i t a b l e t h a n b each s e t s made i n s h o r t queues; s e t t y p e s were e q u a l l y p r o f i t a b l e i n l o n g queues. The s e t type-week i n t e r a c t i o n r e f l e c t e d t h e f l u c t u a t i o n i n the r e l a t i v e r a n k s o f open s e t s and t i e ups among weeks (p<0.003). The a n a l y s i s i n d i c a t e d s i g n i f i c a n t d i f f e r e n c e s between g e o m e t r i c means o f c a t c h r a t e s p e r s e t , b u t the i m p o r t a n t measurements f o r f i s h e r m e n ' s d e c i s i o n s a r e t h e r a t i o s o f s e t type o r l i n e - u p c a t c h e s . The weekly r a t i o s were w e i g h t e d by t h e i r v a r i a n c e and an average w e i g h t e d r a t i o 76 T a b l e V. One-way ANOVA f o r v e s s e l e f f e c t s on c a t c h p e r s e t i n t h e logbook d a t a . SOURCE b o a t r e s i d u a l t o t a l DF 31 6443 6474 SS 136.13 2325.2 2461.3 MS F-RATIO 4.3913 12.168 0.36089 PROBABILITY 0.0000 77 T a b l e V I . Set t y p e - l i n e - u p - w e e k ANOVA f o r 28 v e s s e l s from the l o g b o o k d a t a , showing the e f f e c t s o f s t r a t e g y (open v e r s u s t i e - u p ) , l i n e - u p l e n g t h and week o f s e a s o n on c a t c h e s p e r s e t . SOURCE DF SS MS F-RATIO PROBABILITY s e t 1 19.650 19.650 l i n e - u p 1 96.614 96.614 week 13 2738.9 210.68 s e t - l i n e - u p 1 9.5900 9.5900 set-week 12 64.069 5.3391 l i n e - u p - w e e k 12 25.010 2.0841 s e t - l i n e - u p - w e e k 10 19.009 1.9009 r e s i d u a l 4448 9336.0 2.0989 t o t a l 4498 12360. 9.3621 46.030 100.38 4.5690 2.5438 0.99296 0.90566 0.00223 0.00000 0.0 0.03261 0.00238 0.45270 0.52684 FACTOR s e t l i n e up week BARTLETT X z 31.973 0.03404 163.78 HOMOGENEITY OF VARIANCE PROB. DF 0.00000 0.85361 0.00000 1 1 13 LAYARD X2 40.503 0.04477 182.95 PROB. 0.00000 0.83243 0.00000 78 f o r the s e a s o n was c a l c u l a t e d f o r each s e t type l i n e - u p c o m b i n a t i o n 2 2 _2 2 _2 S r ^ R i = S X i / X i + Syi/YL 19) where S r ^ , Sx^ and Sy^ a r e the v a r i a n c e s o f the r a t i o (R^) and t h e means (X^, Y ^ ) , r e s p e c t i v e l y , i n week i ; N 2 N 2 R = Z R i / S r i / Z 1 . 0 / S r i i - 1 i - 1 20) S r 2 = 1.0 / Z 1.0/Srj; i = l 21) where R i s th e mean w e i g h t e d r a t i o and S r ^ i s the mean r a t i o v a r i a n c e . Category-week c o m b i n a t i o n s w i t h sample s i z e s l e s s t h a n 20 were d i s c a r d e d . The r a t i o n a l e f o r t h i s ad hoc d i v i s i o n was t h a t s e t samples s m a l l e r t h a n the number o f s e t s made by a v e s s e l i n a day c o n t a i n e d v e r y l i t t l e i n f o r m a t i o n . The d a t a a r e summarized i n T a b l e V I I . O b v i o u s l y , the s e t t y p e and l i n e - u p e f f e c t s f l u c t u a t e . F i s h e r m e n work on l o n g t e r m averages and the samples h e r e a r e s m a l l compared to the number o f s e t s made d u r i n g a week. T h i s f a c t may e x p l a i n p a r t o f the f l u c t u a t i o n : the medium l i n e - u p  t i e up was v e r y under r e p r e s e n t e d . The most h i g h l y r e p r e s e n t e d c a t e g o r i e s a r e t h e open s e t and t h e s m a l l l i n e - u p . I n t h e s m a l l l i n e - u p c a t e g o r y , the r a t i o f o r b e a c h s e t t o open s e t i s o n l y 0.844, a v e r y s m a l l d i f f e r e n c e . The medium l i n e - u p t o low l i n e - u p r a t i o was 1.6 f o r the open s e t c a t e g o r y . T h i s r e s u l t i n d i c a t e d a s i g n i f i c a n t economic d i f f e r e n c e . The a n a l y s i s o f v a r i a n c e was r e p e a t e d f o r c a t c h v a l u e s : s e t c a t c h e s were m u l t i p l i e d by the a v e rage s e a s o n a l v a l u e p e r p i e c e ( f o r e a c h s p e c i e s ) c a l c u l a t e d from the 1981 s a l e s s l i p s . T w e n t y - e i g h t v e s s e l s were r e p r e s e n t e d . The s e t t y p e e f f e c t was n o t s i g n i f i c a n t (p<0.1) and the 79 l i n e - u p s and weeks were d i f f e r e n t (p<0.00001). The ranges o f the g e o m e t r i c means were 86-91 and 139-161 f o r the low and medium l i n e - u p s , r e s p e c t i v e l y . The s e t t y p e - l i n e - u p , l i n e - u p - w e e k and s e t t y p e - l i n e - u p - w e e k i n t e r a c t i o n s were n o t s i g n i f i c a n t (p>0.1) b u t the s e t type-week i n t e r a c t i o n c o n t r i b u t e d t o t h e model (p<0.01). L i t e r a t u r e d e s c r i b i n g the use o f d e c e p t i v e i n f o r m a t i o n was r e v i e w e d i n the i n t r o d u c t i o n . T h e r e i s a p o s s i b i l i t y t h a t the log b o o k s c o n t a i n l i e s . The w i t h i n v a r i a n c e o f l i n e - u p c a t a g o r i e s was i n c r e a s e d by t h e use o f i n t e r v a l s i n d a t a r e c o r d i n g s ; 1 s u s p e c t t h a t d a t a f o r i n d i v i d u a l v e s s e l s s h o u l d n o t u s u a l l y e x h i b i t s t a t i s t i c a l s i g n i f i c a n c e . I f t h e s k i p p e r s s y s t e m a t i c a l l y l i e d about the r e l a t i v e c a t c h e s f o r l i n e - u p i n t e r v a l s ( i . e . , a l l h i g h o r low c a t c h e s i n the medium l i n e - u p c a t e g o r y ) , one-way ANOVAS f o r i n d i v i d u a l b o a t s s t a n d a r d i z e d f o r week e f f e c t s s h o u l d e x h i b i t s t a t i s t i c a l s i g n i f i c a n c e w i t h a l a r g e amount o f the v a r i a n c e e x p l a i n e d by t h e e f f e c t . I n f a c t , o n l y 5 o f the 27 v e s s e l s p o s s e s s e d s i g n i f i c a n t d i f f e r e n c e s (p<0.05) and the maximum p e r c e n t o f the v a r i a n c e e x p l a i n e d was 8.4. O b s e r v e r r e c o r d s o f c a t c h e s f o r i n d i v i d u a l b o a t s and d i s c r e t e l i n e - u p l e n g t h s were a n a l y z e d . O n l y t h r e e o f the s e v e n b o a t s p o s s e s s e d a s l i g h t c a t c h r a t e r e s p o n s e t o l i n e - u p l e n g t h and two o f the r e l a t i o n s h i p s were s i g n i f i c a n t by rank c o r r e l a t i o n p r o c e d u r e s . L a r g e r sample s i z e s t h r o u g h o u t a s e a s o n might have p r o d u c e d d i f f e r e n t r e s u l t s . D i s c u s s i o n The h y p o t h e s i s t h a t f i s h e r m e n r e s p o n d t o a d i s t r i b u t i o n o f p o t e n t i a l c a t c h r a t e s and to w a i t i n g times was s u p p o r t e d . L i n e - u p s were a re s p o n s e to s e t c a t c h r a t e s . I n t e r f e r e n c e c o m p e t i t i o n i n the form o f w a i t i n g times r e s t r i c t e d the t o t a l c a t c h a v a i l a b l e a t an a c c e s s p o i n t . The dynamics o f 80 T a b l e V I I . Average w e i g h t e d r a t i o s f o r s e t type and l i n e - u p c a t c h e s . The weekly r a t i o s o f the average c a t c h e s p e r s e t f o r s e t type and l i n e - u p c a t e g o r i e s were w e i g h t e d by t h e i r v a r i a n c e s . T i e Up/Open S e t (Low L i n e - u p ) T i e Up/Open Set (Medium L i n e - u p ) Medium Line-up/Low L i n e - u p (Open Set) Medium Line-up/Low L i n e - u p ( T i e Up) R S r z Mean R a t i o Mean V a r i a n c e N 0.844 0.0072 615:3238 1.191 0.0060 144:427 1.601 0.0001 427:3238 0.804 0.0097 144:615 81 the f l e e t was d i c t a t e d by t h e s e f a c t o r s i n the p r e s e n c e o f good i n f o r m a t i o n and p r o d u c e d i n t e n s e i n t e r f e r e n c e c o m p e t i t i o n among v e s s e l s . T o t a l s e t e f f o r t i n c r e a s e d i n s p i t e o f the c o m p e t i t i v e e f f e c t , y e t h a r v e s t r a t e s must have v a r i e d w i t h e f f o r t i n a c u r v i l i n e a r f a s h i o n as v e s s e l s e n t e r e d l e s s d e s i r a b l e a r e a s . I t must be emphasized t h a t t h e l i n e - u p s r e f l e c t e d p o t e n t i a l c a t c h e s o n l y . The f i s h e r y i s a s t o c h a s t i c system w h i c h f i s h e r m e n v i e w i n terms o f d e t e r m i n i s t i c p o t e n t i a l s . S k i p p e r s d e s c r i b e d t h e i r e x p e c t a t i o n s as s u b j e c t i v e a v e r a g e s . Indeed, "average" i m p r e g n a t e d t h e i r r h e t o r i c . P a s t l a r g e s c a l e a g g r e g a t i v e r e s p o n s e s t o t h e J o h n s t o n e S t r a i t f i s h e r y were a l s o c o r r e l a t e d w i t h c a t c h r a t e s ( H i l b o r n and L e d b e t t e r 1979) and t h i s i n p u t was l a r g e r e l a t i v e t o t h e v a l u e r e t u r n e d i n the c o m p e t i t i v e s i t u a t i o n . H i l b o r n and L e d b e t t e r a t t r i b u t e d t h i s f a c t t o a r e a s p e c i f i c d e s i r a b i l i t y , b u t f i s h e r m e n e x p l a i n e d t h a t a major t r a d e o f f o c c u r s when the J u a n de Fuca f i s h e r y i s open. The Ju a n de F u c a f i s h e r y r e q u i r e s l a r g e b o a t s ; t h e e x a g g e r a t e d r e s p o n s e t o the J o h n s t o n e S t r a i t f i s h e r y may r e s u l t f rom t h e i m m o b i l i t y o f s m a l l b o a t s . As new b o a t s a r e b u i l t i n t h e f u t u r e , s k i p p e r s may o p t f o r the l u c r a t i v e Juan de Fuca f i s h e r y and c o m p e t i t i o n w i l l s u b s i d e i n J o h n s t o n e S t r a i t , u n l e s s a l a r g e r p r o p o r t i o n o f F r a s e r salmon a r e d i v e r t e d by temper a t u r e regimes t o the i n s i d e p a s s a g e . (A l a r g e p r o p o r t i o n o f the salmon w i l l e n t e r the s t r a i t when the water i s c o o l r e l a t i v e t o t e m p e r a t u r e s o f f the west c o a s t o f Vancouver I s l a n d . ) The p r o p o r t i o n o f open s e t e f f o r t i n c r e a s e d w i t h the d e n s i t y o f v e s s e l s as b e a c h s e t a c c e s s p o i n t s were s a t u r a t e d and s k i p p e r s s h i f t e d t o what t h e y c o n s i d e r e d t o be l e s s d e s i r a b l e open s e t a r e a s ( F i g u r e 24) . The Department o f F i s h e r i e s and Oceans has e x p r e s s e d c o n c e r n t h a t the r e c e n t r u n n i n g l i n e and b o w t h r u s t e r i n n o v a t i o n s (which improved open s e t f i s h i n g c o n d i t i o n s ) c o n t r i b u t e d t o i n c r e a s e d e x p l o i t a t i o n r a t e s as f i s h e r m e n 82 or o LU UJ CO Q. O or o o_ o or 0-0 . 5 r 0 .4 0 . 3 -^ 0 . 2 0.1 ' O O o o o gs> ° o o o o o o o o $ o o o o c9> 8o 7 5 150 2 2 5 3 0 0 E F F O R T (NO. OF BOATS) 3 7 5 F i g u r e 24. P r o p o r t i o n o f open s e t e f f o r t v s . e f f o r t . Open s e t e f f o r t was d e f i n e d as the number o f b o a t s making s e t s away from s h o r e . The A r e a 13 c l o s u r e d u r i n g the s e c o n d week o f the s e a s o n i s n o t i n c l u d e d h e r e . 83 d i s p e r s e d i n t o open water. The f a c t t h a t s e t ty p e s were c a t e g o r i z e d as t i e up o r open s e t ( i n o r d e r t o produce an e i t h e r / o r q u e s t i o n ) c o n f o u n d e d the a n a l y s i s : b e ach s e t s c l o s e t o shore were i n c l u d e d i n the open s e t c a t e g o r y . The r u n n i n g l i n e and b o w t h r u s t e r a l s o a i d t h e s k i p p e r d u r i n g b e a c h s e t s and t h i s s e t s t r a t e g y became common w i t h t h e s e i n n o v a t i o n s . I t may be t e n t a t i v e l y c o n c l u d e d t h a t the advent o f the open s e t s t r a t e g y c o n t r i b u t e d t o i n c r e a s i n g e x p l o i t a t i o n r a t e s and t h a t t h e f i s h e r m e n s ' p e r c e p t i o n s o f the b e a c h s e t d e s i r a b i l i t y may be b a s e d more on t r a d i t i o n and f o l k l o r e t h a n on f a c t . An i n c r e a s i n g t r e n d towards the open s e t s t r a t e g y w i l l p r o b a b l y take p l a c e i n the n e a r f u t u r e as f i s h e r m e n abandon o u t d a t e d i n f o r m a t i o n d e r i v e d from t r a d i t i o n s w h i c h were b a s e d on l e s s modern t e c h n o l o g i e s . C o n c e r n over i n c r e a s i n g e x p l o i t a t i o n r a t e s and the r o l e s o f the r u n n i n g l i n e and the b o w t h r u s t e r i n n o v a t i o n s i s w e l l founded. I f the average l i n e - u p has d e c r e a s e d as b o a t s d e v e l o p e d the e q u a l l y d e s i r a b l e open s e t s t r a t e g y , the h a r v e s t r a t e has i n t e n s i f i e d . L o g i c does n o t summon t h e c o r o l l a r y c o n c l u s i o n t h a t a c o n s t a n t average queue l e n g t h m a i n t a i n s a c o n s t a n t h a r v e s t r a t e -- a c t i n g on i n f o r m a t i o n g a i n e d t h r o u g h t e c h n o l o g y , f i s h e r m e n have p r o b a b l y s u b s t i t u t e d open s e t s f o r t h e l e a s t d e s i r a b l e t i e ups. The s t a t i s t i c a l a n a l y s i s o f the lo g b o o k d a t a p r o v i d e d c o n c l u s i o n s t h a t p e r t a i n t o t h i s p a r t i c u l a r sample o f f i s h e r m e n and to A r e a 12 ( v e r y few s e t s were r e c o r d e d f o r A r e a 13). A random sample c o u l d n o t be o b t a i n e d , y e t a wide range o f e x p e r i e n c e and s t r a t e g y was r e p r e s e n t e d and the r e s u l t s i n d i c a t e d t h a t a v e r y s m a l l amount o f the v a r i a n c e i n c a t c h p e r s e t was e x p l a i n e d by t h e s k i l l e f f e c t . A l s o , t h e c o r r e l a t i o n s o f c a t c h e s w i t h t i d e s and queue l e n g t h s s u p p o r t e d the f i s h e r m e n ' s t r a d i t i o n a l s t a t e m e n t s . O n l y t h e s t a t i s t i c a l r e p r e s e n t a t i o n o f the s e t type e f f e c t c o n t r a d i c t e d many s k i p p e r s ' o b s e r v a t i o n s . CHAPTER VI MODELS OF THE FISHING PROCESS F i s h i n g power has been examined many times i n the p a s t . These s t u d i e s i n v o l v e d a t t e m p t s t o s t a n d a r d i z e e f f o r t and c a t c h a b i l i t y . But d i s t r i b u t i o n s o f e f f o r t , f i s h and c a t c h p e r u n i t e f f o r t (CPUE) have u s u a l l y b e e n i g n o r e d . The c l a s s i c c a t c h e q u a t i o n s (Baranov 1918; R i c k e r 1940, 1944) a r e b a s e d upon t h e assumptions t h a t the p o p u l a t i o n o f f i s h i s d i s t r i b u t e d randomly o r u n i f o r m l y o v e r the p o p u l a t i o n a r e a and t h a t u n i t s o f e f f o r t o p e r a t e i n d e p e n d e n t l y (see Seber 1982). A d i r e c t consequence o f t h e s e a s s u m p t i o n s i s t h a t models a r e i n s e n s i t i v e t o d i s t r i b u t i o n changes o f f i s h and f i s h i n g u n i t s a t g i v e n p o p u l a t i o n d e n s i t i e s (Paloheimo and D i c k i e 1964). I t i s e v i d e n t from the p r e v i o u s c h a p t e r s and p r e v i o u s p u b l i c a t i o n s t h a t f i s h i n g o f t e n d e p a r t s from the random model ( G u l l a n d 1964; C a l k i n s 1961; W i l l i a m s 1970). The c a t c h p e r u n i t e f f o r t o v e r a time p e r i o d may be r e p r e s e n t e d by ( C / E ) t = qN t 22) where ( C / E ) t and N t a r e t h e average c a t c h p e r u n i t e f f o r t and t h e average p o p u l a t i o n s i z e , r e s p e c t i v e l y , o v e r time t . The c a t c h a b i l i t y c o e f f i c i e n t , q, i s d e f i n e d as t h e p r o p o r t i o n o f the f i s h p o p u l a t i o n t a k e n by one u n i t o f gear and, i f the as s u m p t i o n s d e s c r i b e d above a r e v a l i d , i s c o n s t a n t i n the absence o f t e c h n o l o g i c a l changes. where a r i s t h e a r e a swept by one u n i t o f gear, C r i s the f r a c t i o n o f the f i s h p o p u l a t i o n p r e s e n t i n a r caught by one u n i t o f gear, and A r i s the 84 85 a r e a o c c u p i e d by the t o t a l p o p u l a t i o n (Paloheimo and D i c k i e 1964). Paloheimo and D i c k i e (1964) d e v e l o p e d a s e a r c h model and a n a l y t i c a l l y d e m o n s t r a t e d t h a t the c a t c h a b i l i t y c o e f f i c i e n t , q, i s dependent upon s c h o o l s i z e s ( r a d i i ) and the numbers o f f i s h w i t h i n s c h o o l s . A l t h o u g h the t o t a l p o p u l a t i o n o f s c h o o l s was assumed t o be u n i f o r m l y d i s t r i b u t e d , h e t e r o g e n e i t y i n the f i s h s c h o o l s a f f e c t e d the p r o p o r t i o n c a u g h t ( C r ) i n the a r e a swept ( a r ) . W i l l i a m s (1970) p r e s e n t e d e v i d e n c e i n d i c a t i n g t h a t t h e d i s t r i b u t i o n o f s c h o o l i n g s k i p j a c k t u n a i s c o r r e l a t e d w i t h s e a s u r f a c e t e m p e r a t u r e s . A l l e n (1977) and A l l e n and P u n s l y (1984) i n c l u d e d the tem p e r a t u r e e f f e c t ( i . e . , h e t e r o g e n e i t y w i t h i n the p o p u l a t i o n a r e a ) i n t h e i r l i n e a r model f o r c a t c h r a t e s i n the Y e l l o w f i n R e g u l a t o r y A r e a (CYRA) o f t h e I n t e r - A m e r i c a n T r o p i c a l Tuna Commission. P e l l a and P s a r o p u l o s (1975) r e c o g n i z e d t h e p o s s i b l e e f f e c t s o f p o p u l a t i o n h e t e r o g e n e i t i e s w i t h i n the CYRA, b u t d i d n o t e x p l i c i t l y i n c l u d e t h o s e e f f e c t s i n t h e i r method o f s t a n d a r d i z a t i o n o f t u n a p u r s e s e i n e e f f o r t . C o m p e t i t i o n between u n i t s o f gear a f f e c t s the c a t c h a b i l i t y c o e f f i c i e n t . The i n t e n s i t y o f c o m p e t i t i o n s h o u l d be r e f l e c t e d i n t h e v a l u e s f o r C r and a r . Many s t u d i e s have i n d i c a t e d t h a t c a t c h a b i l i t y d e c l i n e s as f i s h abundance i n c r e a s e s (Peterman and S t e e r 1981; C r e c c o and Savoy 1985) and have d e m o n s t r a t e d t h i s r e l a t i o n s h i p u s i n g the power f u n c t i o n R+1 C/E = air 23) where C i s the c a t c h f o r a f l e e t , E i s the e f f o r t , N i s f i s h abundance, a and B a r e c o e f f i c i e n t s and 0 > B > -1. The a u t h o r s acknowledged t h a t f i s h abundance was measured w i t h e r r o r and, t h e r e f o r e , u s ed a g e o m e t r i c mean r e g r e s s i o n on l o g a r i t h m s . The l o g a r i t h m o f measurement e r r o r was assumed t o be 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 z e r o . I f t h e r e i s a b i a s i n e s t i m a t i o n o f N and the magnitude o f t h i s b i a s 86 changes w i t h N, the e f f e c t o f t h e s e e r r o r s may be r e p r e s e n t e d by ~ , . TB' +1 v N = a'N e where 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 z e r o and B' > 0 ( i . e . , abundance i s i n c r e a s i n g l y o v e r e s t i m a t e d as i t i n c r e a s e s ) . R e a r r a n g i n g , N - ( l / a ' } / ( B ' + 1 ) N ( " B ' / B ' + 1 ) + (B'+1)/(B'+D e - v / ( B » + l ) I f C/E = qN and the e x p r e s s i o n above i s s u b s t i t u t e d f o r N, t h e n t h e e s t i m a t e d B o b t a i n e d by f i t t i n g e q u a t i o n 23) t o C/E and N d a t a w i l l be n e g a t i v e and g r e a t e r t h a n -1. Peterman e t a l . (1985) s t a t e d t h a t t h e form o f t h e e r r o r term must be a s c e r t a i n e d b e f o r e h y p o t h e s i s t e s t i n g c a n be un d e r t a k e n . R e g a r d l e s s o f the e r r o r s t r u c t u r e , d e n s i t y dependent c a t c h a b i l i t y c o e f f i c i e n t s c a n n o t be r i g o r o u s l y a t t r i b u t e d t o non-random f i s h e r m a n b e h a v i o r . F i s h i n g g e a r t a r g e t o n l y upon v u l n e r a b l e f i s h . I f v u l n e r a b i l i t y (measured as the p r o p o r t i o n o f the f i s h p o p u l a t i o n t h a t i s s u s c e p t i b l e t o the g e a r ) i n c r e a s e s as the s t o c k s i z e d e c r e a s e s , c a t c h a b i l i t y measured r e l a t i v e t o v u l n e r a b l e p l u s i n v u l n e r a b l e f i s h w i l l be d e p e n s a t o r y . Arguments i n v o k i n g changes i n the s p a t i a l s c a l e o f f i s h d i s t r i b u t i o n s r e l a t i v e t o e f f o r t as f i s h abundance changes c a n be ex t e n d e d t o i n c l u d e changes i n the d e p t h d i s t r i b u t i o n o f the f i s h . I n dep t h r e g u l a t e d f i s h e r i e s , an i n c r e a s e i n t h e mean de p t h o f the f i s h w i t h i n c r e a s i n g abundance c o u l d c r e a t e d e p e n s a t o r y c a t c h a b i l i t y i n d e p e n d e n t l y o f the j o i n t f i s h / f i s h e r m a n d i s t r i b u t i o n w i t h i n the volume t h a t c a n be swept. S t u d i e s o f f i s h i n g power have u s u a l l y i g n o r e d the mechanics u n d e r l y i n g the p r o d u c t i o n o f CPUE d i s t r i b u t i o n s . B a n n e r o t and A u s t i n (1983) assumed 87 t h a t t h e s e d i s t r i b u t i o n s a r e n e g a t i v e b i n o m i a l and r e l a t e d t h e skewness o f the d i s t r i b u t i o n s t o the power model ( e q u a t i o n 23). They showed t h a t the parameter, k, o f the n e g a t i v e b i n o m i a l i s c o r r e l a t e d w i t h f i s h abundance. However, t h e y d i d n o t i n c l u d e an e x p l i c i t e x a m i n a t i o n o f the r e l a t i o n s h i p s between the mean c a t c h p e r u n i t e f f o r t and the v a r i a n c e o f t h e d i s t r i b u t i o n . T h i s r e l a t i o n s h i p d e t e r m i n e s the dynamics o f k, as w i l l be shown below. T r a d i t i o n a l models have i n c l u d e d the e f f e c t s o f s t o c k d e p l e t i o n ( B e v e r t o n and H o l t 1957), b u t have n o t r e p r e s e n t e d non-random human b e h a v i o r o r most forms o f v e s s e l c o m p e t i t i o n ( e . g . , i n t e r f e r e n c e o r s e a r c h o v e r l a p ) . I f v e s s e l a g g r e g a t i o n s r e f l e c t c a t c h r a t e s ( o r f i s h p a t c h s i z e s ) and the dynamics o f c o m p e t i t i o n and a g g r e g a t i o n a r e known, the parameters f o r a t r u n c a t e d form o f the p o t e n t i a l c a t c h ( o r v u l n e r a b l e f i s h p a t c h ) d i s t r i b u t i o n c a n be e s t i m a t e d . T h i s p r o c e d u r e l e a d s to e s t i m a t e s o f e x p l o i t a t i o n r a t e s f o r v u l n e r a b l e f i s h . F u r t h e r m o r e , g i v e n assumed d e c i s i o n r u l e s f o r v e s s e l a g g r e g a t i o n and d i s p e r s i o n , and h y p o t h e s e s r e g a r d i n g t h e a l l o c a t i o n o f v a r i a b l e c a t c h e s w i t h i n v e s s e l a g g r e g a t i o n s , a t h e o r y f o r t h e g e n e r a t i o n o f CPUE d i s t r i b u t i o n s c a n be f o r m u l a t e d . The p r e v i o u s d a t a a n a l y s e s and r e c o r d e d a n e c d o t e s p r o v i d e a s o l i d framework f o r the d e r i v a t i o n o f r e a l i s t i c models c o n c e r n i n g f l e e t b e h a v i o r , salmon d i s t r i b u t i o n s and CPUE d i s t r i b u t i o n s . Two d i s t r i b u t i o n a l models are p r e s e n t e d i n t h i s c h a p t e r . The f i r s t model was b a s e d upon measured e f f o r t d i s t r i b u t i o n s and the b e h a v i o r a l a s s u m p t i o n t h a t f i s h e r m e n p o s s e s s good i n f o r m a t i o n p e r t a i n i n g t o c a t c h o p p o r t u n i t i e s and use t h i s i n f o r m a t i o n r a t i o n a l l y . The s e c o n d model was d e r i v e d from a s e t o f s t a t i s t i c a l assumptions and i t s p a r a m e t e r s were found by f i t s t o CPUE d i s t r i b u t i o n s . Both models i n c l u d e d the d i s t r i b u t i o n s o f the f i s h and the f i s h e r m e n and gear c o m p e t i t i o n . Responses o f e x p l o i t a t i o n 88 r a t e s t o f i s h i n g v e s s e l abundance, o n l y , were examined. Complimentary d a t a s e t s f o r f l u c t u a t i n g salmon abundance on a s i m i l a r time s c a l e were n o t a v a i l a b l e . The O v e r f l i g h t Model Data p r e s e n t e d i n C h a p t e r s IV and V s u p p o r t the h y p o t h e s i s t h a t the f l e e t r a t i o n a l l y e x p l o i t s a d i s t r i b u t i o n o f salmon v u l n e r a b i l i t i e s ; a c c e s s p o i n t s d e v e l o p e d l i n e - u p s i n a non-random f a s h i o n as e f f o r t i n c r e a s e d , and queue l e n g t h s u s u a l l y r e f l e c t e d mean s e t c a t c h r a t e s . T h e r e f o r e , d e t e c t i o n o f r e l a t i v e d e s i r a b i l i t i e s was n o t i n d e p e n d e n t o f p r e v i o u s f i s h i n g openings and/or f i s h i n g s e a s o n s . I t i s p r o b a b l e t h a t t h e most d e s i r a b l e a c c e s s p o i n t s a c q u i r e d v e s s e l s i n i t i a l l y and, as queues became l o n g , e n t r a n t b o a t s d i s p e r s e d t o l e s s p r o f i t a b l e s p o t s . ( P r o f i t a b i l i t y , v u l n e r a b i l i t y and d e s i r a b i l i t y a r e d e f i n e d as the t o t a l c a t c h p e r a c c e s s p o i n t . ) The p r e c e d i n g d i s c u s s i o n s e c t i o n i s expanded h e r e as an i n t r o d u c t i o n t o the ass u m p t i o n s u n d e r l y i n g t h e d e r i v a t i o n o f an e x p l o i t a t i o n model. The r e s u l t s o f t h e a n a l y s i s o f v a r i a n c e o f s e t ty p e and l i n e - u p e f f e c t s were i n t e r p r e t e d as i n d i c a t i v e o f i m p e r f e c t i n f o r m a t i o n : a l t h o u g h f i s h e r m e n s t a t e d t h a t open s e t s a r e l e s s p r o f i t a b l e t h a n t i e ups, the ANOVA i n d i c a t e d t h a t the c a t c h r a t e s were s i m i l a r . However, i f f i s h e r m e n view the r e l a t i v e d e s i r a b i l i t i e s o f open and t i e up s e t s p o t s as a f u n c t i o n o f c a t c h r a t e s a l o n e ( i . e . , t h e y do n o t e n t e r open s e t a r e a s b e c a u s e t h e i r i n d e p e n d e n t s p i r i t s a r e r e p e l l e d by crowds o r because t h e y want t o maximize t h e i r chance o f b r i n g i n g i n the b i g s e t ) we s h o u l d e x p e c t t h e c a t c h r a t e s f o r t i e ups and open s e t s t a k e n i n s i m i l a r l y s i z e d queues t o be e q u a l ; the mean c a t c h r a t e s f o r t h e same l i n e - u p i n t e r v a l s s h o u l d be s i m i l a r . A l t h o u g h the ANOVA p r o d u c e d s i g n i f i c a n t d i f f e r e n c e s between s e t t y p e s , the 89 g e o m e t r i c means were v e r y c l o s e . The w e i g h t e d r a t i o s f o r t i e up/open s e t s were a l s o s i m i l a r . Comparison o f F i g u r e s 18 and 19 shows t h a t the ave r a g e open s e t l i n e - u p was s m a l l e r t h a n the average t i e up l i n e - u p . P e rhaps, i n a b r o a d sense, t h e f i s h e r m e n were c o r r e c t : open s e t a c c e s s p o i n t s a r e g e n e r a l l y l e s s p r o f i t a b l e t h a n t i e ups. The ANOVA r e s u l t s and f l e e t d i s t r i b u t i o n a l r e s p o n s e s i n d i c a t e t h a t t h e f i s h e r m e n p o s s e s s e d and u t i l i z e d good i n f o r m a t i o n . The ANOVA f o r c a t c h r a t e s measured as p i e c e s o f f i s h e x h i b i t e d i n t e r a c t i o n s ; i n t h e p r e v i o u s d i s c u s s i o n t h e s e i n t e r a c t i o n s were t e n t a t i v e l y a t t r i b u t e d t o sample s i z e e f f e c t s . However, when c a t c h r a t e s were computed as monetary v a l u e s , t h e s e t t y p e - l i n e - u p , l i n e - u p - w e e k and s e t t y p e - l i n e - u p - w e e k i n t e r a c t i o n s were n o t s i g n i f i c a n t . A l s o , t h e l i n e - u p e f f e c t was s i g n i f i c a n t and s e t t y p e s were n o t s i g n i f i c a n t l y d i f f e r e n t . These r e s u l t s i n d i c a t e t h a t i n t h i s mixed f i s h e r y ( p i n k s and sockeye) the f i s h e r m e n p o s s e s s e d good i n f o r m a t i o n : t h e y c o u l d a l l o c a t e t h e i r e f f o r t among m i x t u r e s o f d i s s i m i l a r l y v a l u e d s p e c i e s . The r e s i d u a l sum o f s q u a r e s f o r t h e s e t t y p e - l i n e - u p - w e e k ANOVA ( i n p i e c e s o f salmon) was l a r g e . The l a r g e p r e d i c t i o n e r r o r was p r o d u c e d by t h r e e f a c t o r s . F i r s t , the l i n e - u p c a t e g o r i e s were gro u p e d i n t o i n t e r v a l s and t h i s c o n t r i b u t e d t o t h e w i t h i n v a r i a n c e o f t h a t v a r i a b l e . Second, as the ANOVA b a s e d on monetary v a l u e s i n d i c a t e d , t h e l i n e a r model f o r c a t c h r a t e s measured as p i e c e s o f f i s h was n o t e x a c t ( i . e . , the model was n o t a p e r f e c t r e p r e s e n t a t i o n o f t h e r e l a t i o n s h i p s between dependent and i n d e p e n d e n t v a r i a b l e s ) . T h i r d , the v a r i a b i l i t y i n s e t c a t c h e s a t i n d i v i d u a l a c c e s s p o i n t s was l a r g e l y due t o salmon m i g r a t i o n r a t e s and s c h o o l i n g b e h a v i o r , t i d e s and o t h e r , "random" f a c t o r s . S i n c e s k i p p e r s form queues, t a l k i n terms o f av e r a g e s and o f t e n make many s e t s o v e r extended p e r i o d s a t s p o t s c h a r a c t e r i z e d by f l u c t u a t i n g c a t c h r a t e s , the v a r i a b i l i t y 90 and r e s u l t i n g o v e r l a p i n s e t c a t c h r a t e s among d i f f e r e n t s i t e s and queue s i z e s i s p r o b a b l y i g n o r e d i n f a v o u r o f l o n g term e x p e c t a t i o n s . Based upon the r e s u l t s p r e s e n t e d i n C h a p t e r s IV and V and upon the o v e r f l i g h t d a t a , an e x p l o i t a t i o n model was c o n s t r u c t e d . T h i s model i n c o r p o r a t e d the f o l l o w i n g assumptions. 1) F i s h e r m e n p o s s e s s p e r f e c t i n f o r m a t i o n c o n c e r n i n g t h e d i s t r i b u t i o n o f t o t a l c a t c h e s a t a c c e s s p o i n t s w i t h i n the f i s h e r y . They may n o t be a b l e t o p r e d i c t t h e v a r i a b l e s e t c a t c h e s w i t h i n queues o r the d i s t r i b u t i o n o f t h e s e c a t c h e s among b o a t s p a r t i c i p a t i n g i n the same l i n e - u p s , b u t th e y c a n p r e d i c t the mean c a t c h p e r b o a t f o r any queue. G i v e n the p r e v i o u s d a t a a n a l y s e s , t h i s assumption i s p r o b a b l y a b e t t e r r e f l e c t i o n o f r e a l i t y t h a n t h e t r a d i t i o n a l "random b e h a v i o r " a s s e r t i o n . 2) F i s h e r m e n use t h e i r i n f o r m a t i o n r a t i o n a l l y : s k i p p e r s e x p l o i t the most p r o f i t a b l e s i t e s f i r s t and, as c o m p e t i t i o n i n t e n s i f i e s w i t h i n c r e a s i n g v e s s e l e n t r y , t h e y move t o l e s s p r o f i t a b l e a c c e s s p o i n t s where w a i t i n g times a r e s h o r t e r (see F i g u r e 2 5 ) . T h i s d e f i n i t i o n o f r a t i o n a l i t y does n o t i n c l u d e a r e s p o n s e t o o p e r a t i n g c o s t s . Many f i s h e r m e n r e c e i v e bonuses b a s e d upon p r o d u c t i o n . T h e r e f o r e , i t i s assumed t h a t s k i p p e r s e q u a l i z e mean c a t c h p e r v e s s e l o r mean c a t c h v a l u e p e r v e s s e l r a t h e r t h a n mean c a t c h v a l u e p e r v e s s e l minus o p e r a t i n g c o s t s p e r v e s s e l . F o r example, i n s t e a d o f e n t e r i n g a two b o a t l i n e - u p where v a l u e minus c o s t i s r e l a t i v e l y h i g h , a s k i p p e r w i l l j o i n a one b o a t l i n e - u p where c a t c h v a l u e i s l a r g e r , y e t v a l u e minus c o s t i s lower due t o the f u e l c o s t a s s o c i a t e d w i t h the more f r e q u e n t s e t s ( i . e . , w a i t i n g t i m e s a r e s h o r t e r ) . 91 F i g u r e 25. The s e l e c t i o n r u l e f o r e n t r y and e x i t o f e f f o r t . Due to h i s t o r i c a l i n f o r m a t i o n r e g a r d i n g the r e l a t i v e d e s i r a b i l i t i e s o f known f i s h i n g s i t e s , the s k i p p e r s a r e a b l e t o e x p l o i t the most p r o f i t a b l e s p o t s f i r s t . As the f l e e t s i z e i n c r e a s e s and w a i t i n g times become l o n g , v e s s e l s d i s p e r s e t o l e s s d e s i r a b l e s i t e s . 92 3) S k i p p e r s ' t a c t i c a l c h o i c e s do n o t a f f e c t the o v e r a l l r e s p o n s e o f l i n e - u p l e n g t h s t o c a t c h r a t e s . The l o g b ook d a t a i n c l u d e d groups o f s k i p p e r s t h a t f i s h e d d i f f e r e n t l y (one group s p e c i a l i z e d i n e x p l o i t i n g r o c k p i l e s , a n o t h e r made open s e t s , and y e t a n o t h e r group s t r u c t u r e d t h e i r s t r a t e g y a c c o r d i n g t o t i d e s ) y e t c a t c h r a t e s among l i n e - u p c a t e g o r i e s were s i g n i f i c a n t l y d i f f e r e n t and t h e s k i p p e r / v e s s e l e f f e c t (which i m p l i c i t l y i n c l u d e d the s k i p p e r s ' c h o i c e s o f s e t t y p e s and queue l e n g t h s ) e x p l a i n e d v e r y l i t t l e o f the v a r i a n c e i n c a t c h p e r s e t . V i o l a t i o n s o f a s s u m p t i o n s 1) t h r o u g h 3) were e x p l o r e d u s i n g monte c a r l o s i m u l a t i o n s . 4) As i n C l a r k and Mangel (1979), the salmon a r e d i s t r i b u t e d among two p o p u l a t i o n s : a b a c k g r o u n d p o p u l a t i o n t h a t i s n o t v u l n e r a b l e t o f i s h i n g and a v u l n e r a b l e p o p u l a t i o n ( e . g . , t h e d e p t h o f th e s e i n e i s r e g u l a t e d i n o r d e r to m i n i m i z e the c a t c h o f deep swimming c h i n o o k ) . 5) The p r o b a b i l i t y o f c a p t u r e o f a v u l n e r a b l e f i s h a t an e x p l o i t e d a c c e s s p o i n t i s one. The volume o f water a s s o c i a t e d w i t h a l i n e - u p i s c o n s t a n t l y f i s h e d ; a l l v u l n e r a b l e f i s h p r e s e n t a t an e x p l o i t e d s i t e a r e caught. 6) As i n C h a p t e r I V , i t i s assumed t h a t v u l n e r a b l e salmon a r e p r e s e n t a t a v e r y l a r g e number o f a c c e s s p o i n t s . A s s u m p t i o n s 1) t h r o u g h 3) ( p e r f e c t i n f o r m a t i o n , r a t i o n a l b e h a v i o r and no s t r a t e g y e f f e c t ) l e a d t o n± =B C ± 24) 93 where and C^ a r e the l i n e - u p l e n g t h and t o t a l c a t c h f o r some time i n t e r v a l a t a c c e s s p o i n t i , r e s p e c t i v e l y , and 3 i s c o n s t a n t w i t h i n an o p e n i n g o r f l i g h t . T h e r e f o r e , s s n i / E n i = c i / E c i i - 1 i - 1 nL/E = C j / C 25) where En^ i s t h e t o t a l e f f o r t ( E ) , EC^ i s t h e t o t a l c a t c h f o r a l l v e s s e l s (C) and s i s t h e number o f l i n e - u p s i n the f i s h i n g a r e a . R e a r r a n g i n g 25), the mean c a t c h p e r v e s s e l i s p r e d i c t e d t o be e q u a l i z e d among a c c e s s p o i n t s C/E = C i / n i 26) Note t h a t c a t c h e s a r e n o t e q u a l i z e d among f i s h e r m e n . The t o t a l c a t c h a t an a c c e s s p o i n t (C^) i s t h e sum o f a d i s t r i b u t i o n o f s e t c a t c h e s . Due t o l u c k o r the a b i l i t y t o p i c k a p o s i t i o n w i t h i n a l i n e - u p i n o r d e r t o make a s e t when the most f i s h a r e p r e s e n t , some s k i p p e r s w i t h i n the same queue w i l l c a t c h more t h a n o t h e r s . The t o t a l f l e e t c a t c h t a k e n d u r i n g a time p e r i o d i s a p r o p o r t i o n o f the t o t a l c a t c h a v a i l a b l e t o the f l e e t . The t o t a l a v a i l a b l e c a t c h (CA) i s e q u i v a l e n t t o t h e v u l n e r a b l e p o p u l a t i o n o f salmon (see as s u m p t i o n s 4) and 5) -- p r o b a b i l i t y o f c a p t u r e i s one and the e x p l o i t e d a c c e s s p o i n t s a r e c o n s t a n t l y s w e p t ) . Thus the c a t c h may be e x p r e s s e d as C = ( l - b ) C A 27) where b i s the p r o p o r t i o n o f the a v a i l a b l e c a t c h t h a t i s n o t e x p l o i t e d . Note t h a t CA can be e x p r e s s e d as 94 A CA = i V a 28) a-1 where V a i s t h e v u l n e r a b i l i t y ( p r o f i t a b i l i t y o r d e s i r a b i l i t y i . e . , the number o f c a t c h a b l e f i s h ) p r e s e n t a t a c c e s s p o i n t a and A i s t h e t o t a l number o f a c c e s s p o i n t s a s s o c i a t e d w i t h v u l n e r a b l e salmon. I n o r d e r t o s i m p l i f y the f o l l o w i n g p r e s e n t a t i o n , a = A i s d e f i n e d as t h e i n d e x o f the most d e s i r a b l e a c c e s s p o i n t ( V a = A = VMAX). A l l o t h e r a c c e s s p o i n t s a r e c h a r a c t e r i z e d by v u l n e r a b i l i t i e s t h a t a r e l e s s t h a n o r e q u a l t o VMAX ( V a = 1 < V a = 2 < V a = A = VMAX). Assumptions 5) ( t h e p r o b a b i l i t y o f c a p t u r e o f a v u l n e r a b l e f i s h a t an e x p l o i t e d s i t e i s one) and 2) ( t h e b e s t f i s h i n g s p o t s a r e e x p l o i t e d f i r s t : C a _ k _ s + i < C a = A _ s + 2 < ^a=A^ i m p l y t h a t c a t c h e s a t e x p l o i t e d a c c e s s p o i n t s aire e q u i v a l e n t t o v u l n e r a b i l i t i e s : C a " v a 29) ( A c c e s s p o i n t c a t c h e s and l i n e - u p s a r e now s u b s c r i p t e d w i t h i n t h e framework o f t h e t o t a l p o p u l a t i o n o f u n e x p l o i t e d p l u s e x p l o i t e d a c c e s s p o i n t s r a t h e r t h a n t h e sample o f l i n e - u p s ; the i n d e x v a l u e s f o r the s m a l l e s t and l a r g e s t queues a r e A-s+1 and A, r e s p e c t i v e l y ) . The number o f u n e x p l o i t e d salmon i n the v u l n e r a b l e p o p u l a t i o n (bCA) i s , t h e r e f o r e , the p o t e n t i a l c a t c h a t the u n e x p l o i t e d a c c e s s p o i n t s and g i v e n a s s u m p t i o n 2) ( r a t i o n a l b e h a v i o r ) A-s b = Z V a/CA 30) a-1 O b v i o u s l y , t h e r e i s a d i s t r i b u t i o n o f v u l n e r a b i l i t i e s among a c c e s s p o i n t s . N o r m a l l y , t h i s type o f d i s t r i b u t i o n i s i l l u s t r a t e d w i t h the event ( v u l n e r a b i l i t y ) on the a b s c i s s a and the f r e q u e n c y o f the e v e n t ( t h e number o f a c c e s s p o i n t s c h a r a c t e r i z e d by a p a r t i c u l a r v u l n e r a b i l i t y ) on the o r d i n a t e . S i n c e i t i s assumed t h a t l i n e - u p l e n g t h s a r e p r o p o r t i o n a l to t o t a l a c c e s s p o i n t c a t c h e s ( e q u a t i o n 24) and t h a t c a t c h e s a r e e q u i v a l e n t to v u l n e r a b i l i t i e s ( e q u a t i o n 29), the t r u n c a t e d forms o f t h e s e f i s h p a t c h d i s t r i b u t i o n s were examined as the f r e q u e n c y d i s t r i b u t i o n s o f queue l e n g t h s i n C h a p t e r IV. I t was a p p a r e n t t h a t f i n d i n g a s i n g l e , t h e o r e t i c a l p r o b a b i l i t y d i s t r i b u t i o n t h a t f i t s a l l d a t a s e t s w e l l may be d i f f i c u l t . T h e r e f o r e , an e m p i r i c a l a p p r o a c h was c h o s e n and i s d e s c r i b e d below. An i m p o r t a n t q u a l i t a t i v e form becomes a p p a r e n t when v u l n e r a b i l i t i e s a r e p l o t t e d as a c u m u l a t i v e d i s t r i b u t i o n . The rank o r d e r sum o f v u l n e r a b i l i t i e s a t i n d i v i d u a l a c c e s s p o i n t s can be e x p r e s s e d as a f u n c t i o n o f the number o f a c c e s s p o i n t s c o n t r i b u t i n g t o t h a t sum. L e t t h e c u m u l a t i v e p r o p o r t i o n o f a v a i l a b l e f i s h summed from the l e a s t d e s i r a b l e a c c e s s p o i n t t o any a r b i t r a r y , e q u a l l y o r more d e s i r a b l e a c c e s s p o i n t (a=F) be d e f i n e d as Pp. Then F P F = Z V a/CA 31) a-1 and F a l s o r e p r e s e n t s a p o r t i o n o f t h e f i s h i n g a r e a (1 < F < A and V a = ^ < V a = 2 • • < V a = F ) -The p r o p o r t i o n o f t o t a l a c c e s s p o i n t s r e p r e s e n t e d by Pp i s F/A. I f Pp i s p l o t t e d a g a i n s t F/A ( w i t h Pp on t h e o r d i n a t e ) the q u a l i t a t i v e form w i l l be a s e t o f s t r a i g h t l i n e s w i t h i n c r e a s i n g s l o p e s ( i . e . , t h e elements o f the r a n k o r d e r sum i n c r e a s e i n magnitude) o r a smooth a c c e l e r a t i n g c u r v e , d e p e n d i n g upon the s i z e s o f groups o f a c c e s s p o i n t s c h a r a c t e r i z e d by the same salmon p a t c h s i z e s . I n t h e J o h n s t o n e S t r a i t d a t a s e t s , t h i s c u r v e can be a p p r o x i m a t e d n i c e l y by an e x p o n e n t i a l f u n c t i o n : 96 P p . F / A . e ^ ^ " 1 ) 32) where c i s a s c a l i n g c o n s t a n t d e s c r i b i n g the skewness o f t h e f i s h p a t c h d i s t r i b u t i o n . I f c i s z e r o , Pp v e r s u s F/A i s a s t r a i g h t l i n e r e p r e s e n t i n g a u n i f o r m d i s t r i b u t i o n o f v u l n e r a b i l i t i e s . I f c i s l a r g e , most o f the f i s h a r e p r e s e n t a t a few a c c e s s p o i n t s . Pp v a r i e s between z e r o and one. E q u a t i o n 32) r e p r e s e n t s the e m p i r i c a l a p p r o a c h r e f e r r e d t o above. S u b s t i t u t i n g e q u a t i o n 32) i n t o 30), b = P F = A . s = ( A - s ) / A e C « ( A - S > / A > - 1 > 33) R e c a l l t h e as s u m p t i o n s p e r t a i n i n g t o r a t i o n a l i t y and e x p l o i t a t i o n o f v u l n e r a b l e f i s h : t h e most d e s i r a b l e f i s h i n g s i t e s a r e f u l l y e x p l o i t e d ( a l l a v a i l a b l e f i s h a r e t a k e n ) ; the p r o p o r t i o n o f the a v a i l a b l e c a t c h t h a t i s n o t caught i s p r e s e n t a t the r e m a i n i n g , r e l a t i v e l y p o o r f i s h i n g s p o t s ( A - s ) . The p r o p o r t i o n o f v u l n e r a b l e f i s h p r e s e n t among u n e x p l o i t e d s i t e s p l u s some f i s h e d s i t e s (B) i s Pp=A-s+B ^ - B 5; s > v a = l ^ va=2 < V a = A . s < V a = A . s + B ) and P M . s + B = ( A . s + B ) / A e c ( ( ( A - S + B ) / A ) - l ) A-s A-s+B = Z V a/CA + Z V a/CA 34) a=l a=A-s+l S i n c e C a = V a ( e q u a t i o n 29) and n a / E = C a / ( l - b ) C A ( e q u a t i o n s 25 and 27, n a = A - s + l ^ na=A-s+2 • • • ^  na=A-s+B ^ na=A) A-s+B A-s+B A-s+B Z V a/CA = Z C a/CA = ( l - b ) / E Z n, a=A-s+l a=A-s+l a=A-s+l 97 A-s = PF=A-s+B " 2 V a / C A 35) a=l _ PF=A-s+B " b R e f e r r i n g t o e q u a t i o n s 33), 34) and 35) A-s+B Z a=A-s+l c ( ( ( A - s + B ) / A ) - l ) c ( ( ( A - s ) / A ) - l ) n a / E = (A-s+B)/A e - ( A - s ) / A e 36) 1 - (A - s ) / A e c ( ( ( A - s ) / A ) - l ) E q u a t i o n 36) i s an e m p i r i c a l model r e p r e s e n t i n g the r a t i o o f the e x p l o i t a t i o n r a t e p r o d u c e d by the b o a t s a t some s e t o f l o w e s t ranked, e x p l o i t e d a c c e s s p o i n t s (B) t o the t o t a l e x p l o i t a t i o n r a t e . I t r e p r e s e n t s a t r u n c a t e d d i s t r i b u t i o n . The c u m u l a t i v e d i s t r i b u t i o n o f l i n e - u p s (and, t h e r e f o r e , c a t c h e s ) i s a f u n c t i o n o f e x p l o i t a t i o n ( 1 - b ) , the t o t a l number o f a c c e s s p o i n t s (A) p r e s e n t i n the a r e a i n h a b i t e d by v u l n e r a b l e f i s h , the p o r t i o n o f the f i s h e d a r e a under e x a m i n a t i o n (B) and a param e t e r d e s c r i b i n g the salmon d i s t r i b u t i o n ( c ) . The e x p l o i t e d a c c e s s p o i n t s a r e a s s o c i a t e d w i t h two r a n k s w h i c h a r e d e t e r m i n e d by t h e c o r r e s p o n d i n g queue l e n g t h : t h e i r r a n k d e s i r a b i l i t y among e x p l o i t e d a c c e s s p o i n t s ( i = l . . . s ) and t h e i r r a nk d e s i r a b i l i t y among a l l a c c e s s p o i n t s (a=A-s+l...A). E q u a t i o n 36) r e d u c e s t o a one parameter model w i t h a few a p p r o x i m a t i o n s . A s s u m p t i o n 6) s t a t e s t h a t t h e r e a r e a l a r g e number o f a c c e s s p o i n t s i n the f i s h i n g a r e a . T h e r e f o r e , we can make the a p p r o x i m a t i o n s and s u b s t i t u t e t h i s i n t o the e q u a t i o n . Depending upon the magnitude o f the pa r a m e t e r c, making t h i s s u b s t i t u t i o n i n the e x p o n e n t i a l p o r t i o n o f the (A-s+B)/A o r (A - s ) / A * 1 37) 98 model c o u l d l e a d t o s e r i o u s e r r o r (and, o f c o u r s e , b w ould e q u a l one when the s u b s t i t u t i o n i s made i n b o t h the m u l t i p l i e r and the e x p o n e n t ) . S u b s t i t u t i n g t h e s e a p p r o x i m a t i o n s ( e q u a t i o n 37) i n t o e q u a t i o n s 33) and 32) c = -A/s l n ( b ) 38) P F = e c « - s + B ) / A ) 3 9 ) and s u b s t i t u t i n g e q u a t i o n 38) i n t o e q u a t i o n 39) t o g i v e P F = b ( s ' B ) / S 40) l e a d s f i n a l l y t o A-s+B B ( s - B ) / s Z n a / E = Z n j / E = (b - b ) / ( l - b ) 41) a=A-s+l i = l S i n c e A i s unknown, a r e l a t i v e v a l u e f o r c i s - l n ( b ) / s . T h i s one parameter model was e a s i l y f i t by n o n - l i n e a r l e a s t s q u a r e s . Four major h y p o t h e s e s were t e s t e d . 1) The e x p l o i t a t i o n r a t e (1-b) s h o u l d have s a t u r a t e d w i t h i n c r e a s i n g e f f o r t as f i s h e r m e n moved i n t o l e s s d e s i r a b l e a r e a s . The a v e r a g e l i n e - u p v e r s u s e f f o r t c u r v e s a t u r a t e d as e f f o r t i n c r e a s e d w h i l e the maximum l i n e - u p a l s o s a t u r a t e d ; more one and two b o a t l i n e - u p s appeared i n the f i s h e r y and, presumably, were i n d i c a t i v e o f movement i n t o l e s s p r o f i t a b l e s p o t s where w a i t i n g times were s h o r t . S i n c e salmon c o n s t a n t l y e n t e r t h e f i s h i n g a r e a , the p r e d i c t e d s a t u r a t i o n s h o u l d be p r i m a r i l y due to i n t e r f e r e n c e c o m p e t i t i o n . T h i s c o m p e t i t i o n can be measured as w a i t i n g times w i t h i n queues and a l s o a f f e c t s t h e v e s s e l d i s t r i b u t i o n . The d i s p a t c h e r f o r the C a n a d i a n F i s h Co. i n Campbell R i v e r c a l l e d t h i s 99 phenomenon the " f u n n e l e f f e c t . " Salmon a r e f u n n e l e d i n t o a s m a l l a r e a where t h e y become v u l n e r a b l e and the e x p l o i t a t i o n r a t e s a t u r a t e s as the few d e s i r a b l e s p o t s a r e f i l l e d . C a n a d i a n F i s h Co. does n o t i n c r e a s e t h e number o f p a c k e r s i n J o h n s t o n e S t r a i t as more e f f o r t e n t e r s the a r e a . E x p l o i t a t i o n c o m p e t i t i o n i s p r o d u c e d by v e s s e l s c a t c h i n g t h e f i s h b e f o r e t h e y r e a c h a c c e s s p o i n t s f u r t h e r down the s t r a i t . F i g u r e s 11 and 12 i n C h a p t e r IV a r e t h e d i s t r i b u t i o n o f b each queue l e n g t h s t h r o u g h o u t the f i s h i n g a r e a . The s o u t h e r n end o f the f i s h e r y i s l o c a t e d n e a r the v e r t i c a l a x i s ; salmon e n t e r from the n o r t h . The n o r t h e r n m o s t edge o f t h e l i n e - u p d i s t r i b u t i o n was a major boundary t h a t r e m a i n e d i n e f f e c t f o r t h e f i r s t h a l f o f the s e a s o n . Most o f the l e s s d e s i r a b l e open s e t a r e a s ( s m a l l e r queues) were l o c a t e d n o r t h o f t h a t boundary and were e x p l o i t e d a f t e r the b oundary was l i f t e d . As e f f o r t i n c r e a s e d and/or the boundary was l i f t e d , b o a t s a g g r e g a t e d t o t h e n o r t h w e s t o f the most p r o f i t a b l e s i t e s , i n t e r c e p t i n g some o f t h e salmon b e f o r e t h e y r e a c h e d t h e s e d e s i r a b l e a c c e s s p o i n t s . T h i s summary o f s p a t i a l dynamics l e a d s to a n o t h e r h y p o t h e s i s . 2) The p a r a m e t e r f o r the skewness o f t h e salmon d i s t r i b u t i o n ( c) s h o u l d have d e c r e a s e d as e f f o r t e n t e r e d the a r e a , e s p e c i a l l y a f t e r t h e major boundary was l i f t e d . T h i s r e s p o n s e was p r o d u c e d by salmon i n t e r c e p t i o n above the most d e s i r a b l e a r e a , which c r e a t e d a d e c r e a s e i n the r e l a t i v e d e s i r a b i l i t y o f t h e good s p o t s . Two a d d i t i o n a l h y p o t h e s e s were t e s t e d . 3) I f t h e e x p l o i t a t i o n r e s p o n s e t o f i s h e r m a n abundance s a t u r a t e s , t o t a l c a t c h p e r o p e n i n g s h o u l d be t h e b e s t i n d e x o f v u l n e r a b l e salmon abundance ( e x c l u d i n g the model o u t p u t ) . 100 4) The p a r a m e t e r c s h o u l d r e f l e c t the f i s h b e h a v i o r e x h i b i t e d by the l o g b o o k d a t a and d e s c r i b e d by the f i s h e r m e n . The salmon d i s t r i b u t i o n ( i . e . , the l i n e - u p r e p r e s e n t a t i o n o f f i s h p a t c h e s ) s h o u l d be l e s s skewed ( s m a l l e r c) on t h e ebb t i d e and a t t h e b e g i n n i n g o f the o p e n i n g . The r e s u l t s o f t h e l e a s t s q u a r e s f i t were good. A l l R 2 were h i g h (> 0.96). F i g u r e 26 shows a r a p i d l y s a t u r a t i n g r e s p o n s e o f e x p l o i t a t i o n r a t e s t o e f f o r t . The salmon d i s t r i b u t i o n became l e s s skewed as e f f o r t i n c r e a s e d . A r a n k c o r r e l a t i o n t e s t f o r the p a r a m e t e r c and t o t a l e f f o r t was s i g n i f i c a n t (rho = -0.6094, c r i t i c a l rho @ a = 0.05 i s 0.2829). However, c was a l s o n e g a t i v e l y c o r r e l a t e d w i t h f i s h abundance (measured as t o t a l c a t c h ) ; t h e salmon d i s t r i b u t i o n became l e s s skewed as abundance i n c r e a s e d ( rho = -0.8197, c r i t i c a l rho @ a = 0.05 i s 0.3643). I t i s a p p a r e n t t h a t g i v e n t h e s e r e s u l t s , a c l e a r c u t t e s t o f the h y p o t h e s i s t h a t e x p l o i t a t i o n c o m p e t i t i o n c r e a t e s a l e s s skewed d i s t r i b u t i o n o f v u l n e r a b i l i t i e s c a n n o t be made. A n o t h e r model p r e d i c t i o n was t h a t c a t c h i s a b e t t e r i n d e x o f abundance t h a n CPUE s i n c e the e x p l o i t a t i o n r a t e s a t u r a t e d r a p i d l y . The model f o r c a t c h r a t e s i s C = p N ( l - b ) 42) where 1-b i s t h e e x p l o i t a t i o n r a t e o f v u l n e r a b l e f i s h , N i s the t o t a l abundance o f salmon and p i s the p r o p o r t i o n o f the f i s h t h a t a r e v u l n e r a b l e t o the g e a r . A l t h o u g h e q u a t i o n 42) i s s i m i l a r t o the t r a d i t i o n a l e x p o n e n t i a l e q u a t i o n , the f i t t i n g p r o c e s s i n c l u d e d t h e d i s t r i b u t i o n o f the f i s h and f i s h e r m e n and the d e c i s i o n r u l e g o v e r n i n g f l e e t b e h a v i o r . Most 101 100 LU < or 90 80 70 60 <P ° 8 o o o fccog° o o o o o o o o o < r - 50 X LU 40 30 h 201 _L 100 200 300 EFFORT (NO. OF BOATS) 400 F i g u r e 26. E x p l o i t a t i o n r a t e s as a f u n c t i o n o f e f f o r t . These e s t i m a t e s were p r o d u c e d by the n o n - l i n e a r o v e r f l i g h t model f i t s t o l i n e - u p d i s t r i b u t i o n d a t a . 102 i m p o r t a n t , e x p l o i t a t i o n r a t e s were e s t i m a t e d i n d e p e n d e n t l y o f salmon abundance o r salmon c a t c h . The model s t a t e s t h a t the a v a i l a b l e salmon p o p u l a t i o n s i z e (pN) i s e q u i v a l e n t t o C / ( l - b ) . U s i n g the t o t a l c a t c h r e p o r t e d on s a l e s s l i p s , t h i s i n d e x a l o n g w i t h t h e t o t a l c a t c h (C) and CPUE were compared to two i n d e p e n d e n t abundance i n d i c e s -- the low and h i g h l i n e - u p mean c a t c h e s p e r s e t . The n o n - p a r a m e t r i c rho v a l u e s were 0.9702 and 0.9204 f o r the model i n d e x ( c r i t i c a l rho @ a = 0.05 i s 0.2829), 0.9766 and 0.9189 f o r t o t a l c a t c h ( c r i t i c a l rho @ a = 0.05 i s 0.5140) and 0.9341 and 0.9231 f o r CPUE. The Z p r o b a b i l i t i e s f o r extreme v a l u e s were 0.1814 and 0.1190 f o r the C / ( l - b ) -- CPUE and t o t a l c a t c h -- CPUE low l i n e - u p rho c o m p a r i s o n s , r e s p e c t i v e l y . The n u l l h y p o t h e s i s o f e q u a l c o r r e l a t i o n c o e f f i c i e n t s was n o t r e j e c t e d and t h e low sample s i z e s (13 d a t a p o i n t s ) f o r c a t c h and CPUE may have c o n t r i b u t e d t o t h i s r e s u l t . G r a p h i c a l l y , however, the CPUE i n d e x a p p e a r e d t o s a t u r a t e somewhat w h i l e t h e C i n d e x was l i n e a r ( F i g u r e 27). The time s e r i e s o f p a r a m e t e r c i n F i g u r e 28 e x h i b i t s a few p a t t e r n s . A t t h e b e g i n n i n g o f an o p e n i n g o r d u r i n g low t i d e s , t h e a p p a r e n t salmon d i s t r i b u t i o n was u s u a l l y l e s s skewed ( s m a l l e r c ) . P a t c h e s were d i s p e r s e d a t t h o s e t i m e s . But on t h e f l o o d , the salmon and f i s h e r m e n were d i s t r i b u t e d i n a c o n t a g i o u s manner ( l a r g e r c ) . A l t h o u g h t h e r e i s some v a r i a b i l i t y and o v e r l a p , t h e p a t t e r n s i l l u s t r a t e d i n F i g u r e 28 appear t o be d i s t i n c t . I n p r i n c i p l e , t h e o v e r f l i g h t model c o u l d be u s e d t o a d d r e s s an i m p o r t a n t management q u e s t i o n . How many f i s h i n g s e t l o c a t i o n s c a n be e c o n o m i c a l l y f i s h e d ? I f t h e o p t i m a l number o f f i s h e d a c c e s s p o i n t s i s d e f i n e d as the number o f s i t e s w i t h c a t c h v a l u e s g r e a t e r t h a n o r e q u a l to the c o s t o f o p e r a t i n g a v e s s e l , the f i t t e d model can be u s e d t o e s t i m a t e the o p t i m a l number o f e x p l o i t e d s i t e s : 103 F i g u r e 27. C a t c h and CPUE v e r s u s low l i n e - u p c a t c h p e r s e t . T o t a l c a t c h e s and CPUEs were o b t a i n e d from s a l e s s l i p d a t a . Average c a t c h p e r s e t was c a l c u l a t e d u s i n g l o g b o o k d a t a . Each d a t a p o i n t r e p r e s e n t s a weekly o p e n i n g . 104 < O m oo LU O LU Q_ O LU 4500 3000 ZD or 1500 o o X o < o o o X 0 50 100 150 CATCH PER SET (PIECES) x o r -< 1,500,000 U J 1,000,000 o LU CL 500,000 V-0 50 100 150 CATCH PER SET (PIECES) 105 F i g u r e 28. The time s e r i e s o f the f i s h skewness parameter c. Open c i r c l e s a r e ebb t i d e s and f i l l e d c i r c l e s a r e f l o o d t i d e s . The d a t a p o i n t s w i t h i n openings a r e c o n n e c t e d . O EBB • FLOOD MAJOR BOUNDARIES LIFTED oV o 30 40 50 FLIGHT 107 V ( C / ( l - b ) ) ( b ( x ~ 1 ) / s - D X / S ) / X v = 1 43) where x i s the number o f a c c e s s p o i n t s u t i l i z e d f o r optimum h a r v e s t , (s-B i n e q u a t i o n 41) X V i s the c o s t o f v e s s e l o p e r a t i o n and V i s the average v a l u e p e r f i s h . E q u a t i o n 43) s t a t e s t h a t the c u m u l a t i v e p r o p o r t i o n o f v u l n e r a b l e f i s h a t a l l the l o w e s t r a n k e d a c c e s s p o i n t s i n c l u d i n g the s p o t where c a t c h e q u a l s o p e r a t i n g c o s t s minus the p r o p o r t i o n p r e s e n t a t s i t e s where c a t c h v a l u e s a r e l e s s t h a n o p e r a t i n g c o s t s , t i m e s the v a l u e o f the t o t a l p o p u l a t i o n o f v u l n e r a b l e f i s h and d i v i d e d by t h e o p e r a t i n g c o s t o f a v e s s e l w i l l e q u a l one. R e a r r a n g i n g 43 ) , b x / s ( ( i - b 1 / s ) / b 1 / s ) = X v ( l - b ) / C V x - 1 + s ( l n ( X v ) + l n ( l - b ) - l n ( C ) - l n ( V ) - l n ( l - b 1 / s ) ) / l n ( b ) 44) U n f o r t u n a t e l y , a q u a n t i t a t i v e assessment c o u l d n o t be made s i n c e good d a t a f o r t h e o p e r a t i n g c o s t s o f s e i n e v e s s e l s were n o t a v a i l a b l e . Even the r e c e n t F l e e t R a t i o n a l i z a t i o n Committee R e p o r t (Dept. o f F i s h e r i e s and Oceans, Canada 1982a) c o n t a i n e d a d i s c l a i m e r c o n c e r n i n g t h e i r d a t a on expenses and e a r n i n g s . The importance o f c o l l e c t i n g l a r g e sample s i z e s o f t h i s k i n d o f d a t a i s e v i d e n t . A monte c a r l o s i m u l a t i o n o f the p r o b a b l e e r r o r s t r u c t u r e i n the l i n e - u p d a t a and t h e e f f e c t s upon parameter e s t i m a t i o n y i e l d e d some i n t e r e s t i n g r e s u l t s . E q u a t i o n 41) d e s c r i b e s the rank o r d e r c u m u l a t i v e d i s t r i b u t i o n o f queues as a f u n c t i o n o f the parameter b. R e a r r a n g i n g t h a t e q u a t i o n and t a k i n g the d i f f e r e n c e o f the c u m u l a t i v e d i s t r i b u t i o n s between a d j a c e n t p o i n t s p r o v i d e s e s t i m a t e s o f l i n e - u p l e n g t h s 108 B B - l n i = B = Z n t - I nj_ = E ( ( b ( s " B / s ) . b < s " B + 1 ) / s ) / ( l - b ) ) 45) i - 1 i - 1 where B i s the r a n k o f the l i n e - u p . Monte c a r l o d a t a s e t s f o r n^ were g e n e r a t e d by e q u a t i o n 45) and an added e r r o r component: n i = n i + U < n i / R ) 46) where u i s an i n d e p e n d e n t , n o r m a l l y d i s t r i b u t e d v a r i a b l e w i t h mean z e r o and a s t a n d a r d d e v i a t i o n n^/R. The maximum a b s o l u t e v a l u e o f the random normal d i s t r i b u t i o n d e f i n e d by a s t a n d a r d d e v i a t i o n o f 1 was between 3 and 4, d e p e n d i n g upon t h e number o f c a l l s made. T e s t v a l u e s o f R were l i m i t e d t o the range 4-8 t o i n s u r e t h a t t h e s m a l l e s t n e g a t i v e random number f o r a g i v e n l i n e - u p was n o t g r e a t e r i n a b s o l u t e v a l u e t h a n the magnitude o f the l i n e - u p . The random n o r m a l e r r o r s t r u c t u r e was u s e d t o d e s c r i b e what were assumed t o be many, s m a l l i n d e p e n d e n t and a d d i t i v e e r r o r i n p u t s . A p e r f e c t r e f l e c t i o n o f the salmon d i s t r i b u t i o n s by t h e l i n e - u p s was d i s t o r t e d by i n d i v i d u a l movements b a s e d upon i n a d e q u a t e i n f o r m a t i o n , i n f o r m a t i o n about s u b - a r e a s o n l y , s e a r c h , a g g r e g a t i v e e f f e c t s and s t r a t e g y . Note t h a t the s t a n d a r d d e v i a t i o n s i n c r e a s e w i t h queue l e n g t h ( n ) . I t was assumed t h a t t h e b e s t s p o t s may have been p o o r l y r e p r e s e n t e d due to s k i p p e r ' s s e c r e t s , s t r a t e g y and e x p e r i e n c e and a g g r e g a t i v e e f f e c t s t h a t c r e a t e o v e r l y l a r g e queue r e s p o n s e s t o c a t c h r a t e s . O b s e r v a t i o n e r r o r was a l s o i n c l u d e d . F o r a g i v e n number o f e x p l o i t e d a c c e s s p o i n t s ( s ) the monte c a r l o s i m u l a t i o n s p r o d u c e d more o r fewer f i s h e d s i t e s . Twenty t r i a l s were u s e d f o r two e f f o r t / a c c e s s p o i n t and f i v e v a r i a n c e c a t e g o r i e s . The i n i t i a l p a r a m e t e r s f o r low and h i g h e f f o r t l e v e l s (60 and 250) and 109 low and h i g h a c c e s s p o i n t l e v e l s (35 and 140), the p a r a m e t e r means and r a n g e s r e s u l t i n g from t h e d i s c r e t e n a t u r e o f th e v e s s e l r e s p o n s e s ( r o u n d i n g ) and from the v a r i a n c e l e v e l s a r e r e c o r d e d i n T a b l e V I I I . From i n s p e c t i o n i t i s o b v i o u s t h a t the parameter e s t i m a t e s become v e r y u n c e r t a i n a t low e x p l o i t a t i o n r a t e s ( h i g h b ) . Parameters above 0.5 f o r the p e r f e c t queue d i s t r i b u t i o n c o u l d n o t be d i s t i n g u i s h e d d u r i n g model f i t t i n g . T h i s r e s u l t was p r o b a b l y an e f f e c t o f a c c e s s p o i n t sample s i z e s . F o r t u n a t e l y , the p a r a m e t e r s e s t i m a t e d from the f i e l d d a t a u s u a l l y f e l l below 0.3. The d i s c r e t e n a t u r e o f t h e f i s h e r m a n p r e d a t o r c o u p l e d w i t h the r e l a t i v e l y s m a l l a g g r e g a t i o n s a t a c c e s s p o i n t s (compared t o i n s e c t s o r b a c t e r i a e t c . ) a l s o b i a s e d t h e e s t i m a t e s . A t h i g h e f f o r t , t h e s e b i a s e s were s l i g h t l y l e s s s e v e r e . L a r g e queue r e s p o n s e e r r o r v a r i a n c e s dampened the b i a s when e x p l o i t a t i o n r a t e s were h i g h (low b ) . The l a r g e e x p l o i t a t i o n r a t e s p r e d i c t e d by t h e f i e l d d a t a may have been s t a b i l i z e d by t h e s e c o n t r a d i c t o r y e f f e c t s . The s i m u l a t i o n s i n d i c a t e d t h a t , a l t h o u g h r e s p o n s e e r r o r s w i l l c e r t a i n l y a f f e c t t h e p r e c i s i o n and a c c u r a c y o f t h e e s t i m a t i o n p r o c e s s , t h e q u a l i t a t i v e form o f the e x p l o i t a t i o n - e f f o r t r e l a t i o n s h i p may r e main i n t a c t . The S a l e s S l i p Model S e i n e b o a t s d e l i v e r t o p a c k e r s o r t h e i r home p o r t s . When a d e l i v e r y i s made, the s k i p p e r f i l l s o ut a s a l e s s l i p . The v e s s e l number, s t a t i s t i c a l a r e a , number o f pounds and p i e c e s o f e a c h salmon s p e c i e s , the v a l u e o f t h e c a t c h and o t h e r p e r t i n e n t d a t a a r e r e c o r d e d . These d a t a s e r v e d as t h e i n p u t t o t h e f o l l o w i n g p r e d i c t i v e model f o r the d i s t r i b u t i o n o f c a t c h r a t e s among v e s s e l s and the t o t a l e x p l o i t a t i o n r a t e s . LOW EFFORT b 0.1 0.2 0 .4 0 .6 0 .7 d i s c r e t e 0 .16 0.22 0 .34 0 . 50 0 .50 H igh V a r i a n c e R 4 0.14 ( 0 . 1 1 - 0 . 1 8 ) 0.19 ( 0 . 1 3 - 0 . 2 2 ) 0 .25 ( 0 . 2 0 - 0 . 3 0 ) 0 .32 ( 0 . 2 6 - 0 . 3 7 ) 0 .32 ( 0 . 2 6 - 0 . 3 7 ) 5 0.15 ( 0 . 1 2 - 0 . 1 8 ) 0.20 ( 0 . 1 7 - 0 . 2 4 ) 0 .28 ( 0 . 2 4 - 0 . 3 2 ) 0 .37 ( 0 . 3 3 - 0 . 4 3 ) 0 .37 ( 0 . 3 3 - 0 . 4 3 ) 6 0.15 ( 0 . 1 3 - 0 . 1 8 ) 0.21 ( 0 . 1 7 - 0 . 2 4 ) 0 .29 ( 0 . 2 4 - 0 . 3 3 ) 0.41 ( 0 . 3 7 - 0 . 4 8 ) 0.41 ( 0 . 3 7 - 0 . 4 8 ) 7 0.16 ( 0 . 1 3 - 0 . 1 8 ) 0.22 ( 0 . 1 8 - 0 . 2 4 ) 0.31 ( 0 . 2 6 - 0 . 3 5 ) 0 .45 ( 0 . 3 8 - 0 . 5 0 ) 0 .45 ( 0 . 3 8 - 0 . 5 0 ) Low V a r i a n c e 8 0.16 ( 0 . 1 4 - 0 . 1 8 ) 0.22 ( 0 . 1 9 - 0 . 2 5 ) 0 .32 ( 0 . 2 8 - 0 . 3 5 ) 0 .47 ( 0 . 4 1 - 0 . 5 0 ) 0 .47 ( 0 . 4 1 - 0 . 5 0 ) T a b l e V I I I . Monte c a r l o s i m u l a t i o n of e r r o r i n the o v e r f l i g h t model. Randomly s e l e c t e d v a l u e s from normal d i s t r i b u t i o n s were added to l i n e - u p l e n g t h s p r e d i c t e d by the o v e r f l i g h t model. The model was then f i t to t h i s f a k e d a t a . The mean parameter e s t i m a t e s f o r twenty t r i a l s a r e g i v e n . The ranges a r e r e c o r d e d i n p a r e n t h e s e s . HIGH EFFORT b 0.1 0.2 0.4 0 .6 0 .7 d i s c r e t e 0.15 0.21 0 .38 0 .58 0 .58 H igh V a r i a n c e R 4 0.13 ( 0 . 1 1 - 0 . 1 4 ) 0.17 ( 0 . 1 5 - 0 . 1 8 ) 0 .24 ( 0 . 2 2 - 0 . 2 6 ) 0 .33 ( 0 . 3 1 - 0 . 3 7 ) 0 . 33 ( 0 . 3 1 - 0 . 3 7 ) 5 0.14 ( 0 . 1 1 - 0 . 1 5 ) 0.18 ( 0 . 1 6 - 0 . 1 9 ) 0 .27 ( 0 . 2 4 - 0 . 3 0 ) 0 .39 ( 0 . 3 5 - 0 . 4 3 ) 0 .39 ( 0 . 3 5 - 0 . 4 3 ) 6 0.14 ( 0 . 1 3 - 0 . 1 5 ) 0 .19 ( 0 . 1 7 - 0 . 1 9 ) 0 .29 ( 0 . 2 6 - 0 . 3 2 ) 0 .45 ( 0 . 4 0 - 0 . 4 9 ) 0 .45 ( 0 . 4 0 - 0 . 4 9 ) 7 0.14 ( 0 . 1 3 - 0 . 1 5 ) 0 .19 ( 0 . 1 8 - 0 . 2 0 ) 0.31 ( 0 . 2 9 - 0 . 3 3 ) 0 .50 ( 0 . 4 6 - 0 . 5 4 ) 0 .50 ( 0 . 4 6 - 0 . 5 4 ) Low V a r i a n c e 8 0.14 ( 0 . 1 3 - 0 . 1 5 ) 0 .20 ( 0 . 1 9 - 0 . 2 1 ) 0 .33 ( 0 . 3 1 - 0 . 3 4 ) 0 .53 ( 0 . 4 9 - 0 . 5 6 ) 0 .53 ( 0 . 4 9 - 0 . 5 6 ) T a b l e V I I I . Monte c a r l o s i m u l a t i o n of e r r o r i n the o v e r f l i g h t model. Randomly s e l e c t e d v a l u e s from ( c o n t i n u e d ) normal d i s t r i b u t i o n s were added to l i n e - u p l e n g t h s p r e d i c t e d by t h e o v e r f l i g h t model. The model was then f i t to t h i s f a k e d a t a . The mean parameter e s t i m a t e s f o r twenty t r i a l s a r e g i v e n . The ranges a r e r e c o r d e d i n p a r e n t h e s e s . 112 The b a s i c h y p o t h e s i s u n d e r l y i n g the f o r m u l a t i o n o f t h e model i s a g g r e g a t i o n and the r e s u l t i n g c o m p e t i t i o n between organisms skews the d i s t r i b u t i o n o f e f f e c t i v i t y . E f f e c t i v e n e s s i s d e f i n e d r e l a t i v e t o an i n t e n d e d e f f e c t -- k i l l i n g , c a p t u r i n g , a t t a c k i n g , c o r n e r i n g a market. U n l e s s the i n t e n t i s t o s t a r t a r i o t , crowds, c o m p e t i t i o n and i n t e r f e r e n c e u s u a l l y c u r t a i l e f f e c t i v i t y , e x c e p t when the i n d i v i d u a l i s t r a i n e d t o m i n i m i z e o t h e r ' s r e c i p r o c a l e f f e c t s o r i s l u c k y . A c c o r d i n g t o the e f f e c t i v i t y h y p o t h e s i s , t h e d i s t r i b u t i o n o f s k i p p e r / v e s s e l e f f e c t i v e n e s s w i t h i n a t i m e / a r e a s t r a t u m i s a f u n c t i o n o f a g g r e g a t i o n o f e f f o r t . The m a t h e m a t i c a l form and the dynamics o f the d i s t r i b u t i o n may be c h a r a c t e r i z e d by the f o l l o w i n g s u b s i d i a r y h y p o t h e s e s . 1) The f l e e t i n any t i m e / a r e a s t r a t u m i s composed o f h i g h l i n e r s ( t h o s e t h a t do e x t r e m e l y w e l l ) and poor t o a v e r a g e s k i p p e r s . As a c c e s s p o i n t s a r e f i l l e d w i t h b o a t s , t h e r e i s v e r y l i t t l e room or chance f o r s k i p p e r s t o adopt d i f f e r e n t s t r a t e g i e s due t o the i n c r e a s i n g i n t e n s i t y o f i n t e r f e r e n c e and e x p l o i t a t i o n c o m p e t i t i o n . A l t h o u g h the d i s t r i b u t i o n o f l i n e - u p s and c a t c h r a t e s p e r a c c e s s p o i n t may become l e s s skewed as e f f o r t and e x p l o i t a t i o n c o m p e t i t i o n i n c r e a s e (see the o v e r f l i g h t model o u t p u t ) the d i s t r i b u t i o n o f c a t c h e s o r v e s s e l e f f e c t i v i t y s h o u l d become more skewed. F i r s t , the d a t a p r e s e n t e d i n C h a p t e r IV i n d i c a t e d t h a t a t l e a s t 20% o f a v e s s e l ' s c a t c h i s t a k e n by one s e t . I t i s p r o b a b l e t h a t the l a r g e s t a c c e s s p o i n t s e t s b e s t r e p r e s e n t the d i s t r i b u t i o n o f salmon p a t c h e s over an e x t e n d e d time i n t e r v a l . T h e r e f o r e , o n l y a p o r t i o n o f t h e v e s s e l c a t c h e s w i l l r e f l e c t the f i s h d i s t r i b u t i o n ( i . e . , t h o s e t h a t s e t on the i n f r e q u e n t 113 l a r g e s c h o o l s ) . Second, a s m a l l e r p r o p o r t i o n o f the v e s s e l s i n the l e n g t h e n i n g queues w i l l e n c o u n t e r the i n f r e q u e n t , l a r g e s c h o o l s o f salmon. T h i r d , the d i s t r i b u t i o n o f the v e s s e l c a t c h e s w i l l change as more a c c e s s p o i n t s a r e f i l l e d : many s k i p p e r s e n t e r l e s s d e s i r a b l e s p o t s where the b i g c a t c h e s a r e s m a l l e r t h a n t h o s e a s s o c i a t e d w i t h l o n g e r queues. (Note t h a t the o v e r f l i g h t model s t a t e d t h a t o n l y the mean c a t c h p e r v e s s e l a t a c c e s s p o i n t s i s e q u a l i z e d ) . The r i g h t hand t a i l o f the e f f e c t i v i t y d i s t r i b u t i o n r e m a i n s s t a t i o n a r y ( i . e . , t h e l a r g e s t s e t c a t c h e s t a k e n from the l o n g e s t queues d e f i n e the h i g h e s t e f f e c t i v i t y and do n o t change w i t h v e s s e l e n t r y ) w h i l e t h e mode s h i f t s t o t h e o r i g i n . F o u r t h , i n e x p e r i e n c e d s k i p p e r s w i l l have fewer chances t o implement t h e i r l i m i t e d knowledge; h i g h l i n e r s however, w i l l r e m a i n e f f e c t i v e and l u c k y c a t c h e s a r e always p r e s e n t i n the f i s h e r y ( s e e H i l b o r n and L e d b e t t e r 1985). 2) I n summary, as v e s s e l s e n t e r l e s s d e s i r a b l e s p o t s and l i n e up a t o t h e r s , t h e mean c a t c h p e r u n i t e f f o r t s q u a r e d d e c r e a s e s more r a p i d l y t h a n t h e v a r i a n c e . The i m p l i c a t i o n s o f t h i s s t a t e m e n t w i l l become a p p a r e n t (see e q u a t i o n 4 9 ) . 3) R e peated l a n d i n g s from an i n d i v i d u a l v e s s e l a r e d e s c r i b e d by the P o i s s o n d i s t r i b u t i o n . 4) Salmon abundance does n o t a f f e c t t h e shape o f the CPUE d i s t r i b u t i o n , which i s n e g a t i v e b i n o m i a l . Many c o n c e p t u a l and m a t h e m a t i c a l models f o r the n e g a t i v e b i n o m i a l have been p r o p o s e d ( B l i s s 1953) . A t h e o r e t i c a l model f o r the d i s t r i b u t i o n o f CPUE f o l l o w s the f o r m u l a t i o n o f Greenwood and Y u l e (1920): the n e g a t i v e b i n o m i a l i s a compound d i s t r i b u t i o n . The d i s t r i b u t i o n o f average o r e x p e c t e d s k i p p e r / v e s s e l e f f e c t i v i t i e s may be r e p r e s e n t e d by a gamma 114 d i s t r i b u t i o n o f P o i s s o n p a r a m e t e r s (X) where k u n i q u e l y d e s c r i b e s the shape o f the d i s t r i b u t i o n and a i s a s c a l i n g parameter r e f l e c t i n g the a c t u a l d r i v i n g p r o c e s s o f the system (salmon abundance). f(X,k,ct) = a k e " X a X k"Vr(k) 47) Compounding the P o i s s o n c a t c h i n g p r o c e s s f o r the i n d i v i d u a l v e s s e l s t h r o u g h t h e gamma p r o d u c e s a n e g a t i v e b i n o m i a l d i s t r i b u t i o n o f c a t c h p e r b o a t . The p r o b a b i l i t y o f o b s e r v i n g a c a t c h p e r b o a t , x^, i s p r e d i c t e d by the n e g a t i v e b i n o m i a l t o be P ( X i ) = ( k / ( m + k ) ) k (m/(m+k)) m * ( k + j - l ) / j 48) 2 2 where the mean, m, = k/a, a = k/a + k/a and 2 2 k = m / o - m 2 a = m / a - m 49) F i t t i n g the n e g a t i v e b i n o m i a l t o the f r e q u e n c y d i s t r i b u t i o n o f CPUE, i t f o l l o w s t h a t the mean c a t c h p e r b o a t i s a f u n c t i o n o f k and a: A A. C/E = k / a 50) where C i s the t o t a l c a t c h i n a t i m e / a r e a s t r a t u m and E i s the t o t a l e f f o r t . E q u a t i o n 50) can be f u r t h e r c h a r a c t e r i z e d by h y p o t h e s e s c o n c e r n i n g k and a. The parameter k i s always d e f i n e d as r e p r e s e n t i n g the shape o f the n e g a t i v e b i n o m i a l d i s t r i b u t i o n . As the skewness o f a d i s t r i b u t i o n becomes l a r g e , k d e c r e a s e s . I n t h e c o n t e x t o f dynamics, k i s a v a r i a b l e and i s a 115 f u n c t i o n o f a) s k i p p e r s s k i l l , b) g e a r e f f e c t i v e n e s s , c) the d i s t r i b u t i o n o f salmon p a t c h e s , d) c o m p e t i t i o n , e) d i f f e r e n c e s i n volumes swept, f ) l u c k . I f i t i s assumed t h a t t h e s e f a c t o r s a r e ind e p e n d e n t gamma v a r i a t e s , the f o l l o w i n g theorem c a n be a p p l i e d (Kennedy and K e e p i n g 1951): I f XQ_, X2 . . . x n a r e independent gamma v a r i a t e s from d i s t r i b u t i o n s d e f i n e d by paramet e r s k^, • • • k n and a common parameter, a, X = Ex^ i s a gamma v a r i a t e w i t h p a r a m e t e r K = Zk^ T h e r e f o r e , k from the n e g a t i v e b i n o m i a l f i t s t o CPUE i s the sum o f the p a r a m e t e r s f o r many i n d e p e n d e n t d i s t r i b u t i o n s o f e f f e c t i v i t y components. Now, t h e p r i m a r y h y p o t h e s i s i s t h a t k i s a f u n c t i o n o f c o m p e t i t i o n f o r f i s h i n g s i t e s and f o r l a r g e s c h o o l s o f f i s h . Some k^s from t h e component gamma d i s t r i b u t i o n s a r e f u n c t i o n s o f v e s s e l a g g r e g a t i o n ( c o m p e t i t i o n ) w h i l e o t h e r s a r e n o t , so t h a t n k = ( I k t ) + e 51) i = l where t h e sum r e p r e s e n t s the d i s t r i b u t i o n s a f f e c t e d by c o m p e t i t i o n and e i s the sum o f p a r a m e t e r s t h a t v a r y i n d e p e n d e n t l y o f c o m p e t i t i o n . I f t h i s e r r o r term i s too l a r g e o r v a r i e s too much, no c o r r e l a t i o n between k and c o m p e t i t i o n w i l l be e v i d e n t . 116 A n o t h e r n e c e s s a r y h y p o t h e s i s f o r the complete f o r m u l a t i o n i s t h a t 1/a i s p r o p o r t i o n a l t o salmon abundance. The v a r i a b l e 1/a d e s c r i b e s t h e s c a l e o f t h e d i s t r i b u t i o n . A 1/a - hpN 52) where h i s a s c a l i n g c o n s t a n t and p i s the p r o p o r t i o n o f t h e salmon p o p u l a t i o n (N) t h a t i s v u l n e r a b l e w i t h i n t h e f i s h i n g a r e a . From e q u a t i o n s 50) and 52) C/E = k h p N A A C a = C/hpN = k E 53) Assuming t h a t t h e p a r a m e t e r s h and p a r e c o n s t a n t A A k E a (1-b) 54) kE, t h e n , i s t h e r e l a t i v e e x p l o i t a t i o n r a t e o f a v a i l a b l e salmon and s h o u l d v a r y i n the same f a s h i o n as the e x p l o i t a t i o n r a t e s e s t i m a t e d from the o v e r f l i g h t model. F o r 52)-54) t o h o l d , i t was assumed t h a t the v a r i a n c e i n CPUE i s (hp^N^+pN)(l-b)/E. T h i s e q u a t i o n was d e r i v e d by s u b s t i t u t i n g e q u a t i o n s 42) and 52) i n t o e q u a t i o n 4 9 ) . S i n c e the magnitude o f h d e t e r m i n e s the r e l a t i v e c o n t r i b u t i o n o f N 2, t h i s a s s u m p t i o n i n c o r p o r a t e s c o n s i d e r a b l e f l e x i b i l i t y . A few model p r e d i c t i o n s c a n be made. 1) The changes i n the d i s t r i b u t i o n and s i z e s o f queues were p r e d i c t e d t o a f f e c t the shape o f the CPUE d i s t r i b u t i o n . I f these l i n e - u p d i s t r i b u t i o n s a r e a f u n c t i o n o f the amount o f e f f o r t e n t e r i n g the a r e a (as the d a t a i n Chapter V and the o v e r f l i g h t model r e s u l t s i n d i c a t e d ) k i s h i g h l y , n e g a t i v e l y c o r r e l a t e d w i t h 117 e f f o r t . As the skewness o f the n e g a t i v e b i n o m i a l i n c r e a s e s , the magnitude o f k d e c r e a s e s . I f t h e v e s s e l d i s t r i b u t i o n c o n t r a c t s and expands s o l e l y as a f u n c t i o n o f f i s h b e h a v i o r , no c o r r e l a t i o n i s e x p e c t e d . 2) Temporal changes i n k do n o t r e f l e c t the e n t r y o f m a r g i n a l e f f o r t . Assuming t h a t l o c a l s k i p p e r s r e f l e c t the range and d i s t r i b u t i o n o f s k i l l , the p a r a m e t e r s o f the CPUE d i s t r i b u t i o n s f o r s t a t i o n a r y e f f o r t and t o t a l e f f o r t s h o u l d c o r r e l a t e w e l l . 3) E q u a t i o n 54) p r e d i c t s t h a t the r e l a t i v e e x p l o i t a t i o n r a t e (kE) s h o u l d s a t u r a t e . The n e g a t i v e b i n o m i a l was f i t t o the 1981 J o h n s t o n e S t r a i t s a l e s s l i p d a t a by t h e maximum l i k e l i h o o d method ( F i s h e r 1953) and goodness o f f i t was t e s t e d u s i n g the Kolmogorov-Smirnov t e s t . C a t c h was i n u n i t s o f p i e c e s o f f i s h . Ten out o f 14 weekly CPUE d a t a s e t s f i t the n e g a t i v e b i n o m i a l . T h i s r e s u l t was l a r g e r t h a n the e x p e c t e d 1/20 r e j e c t i o n r a t i o f o r an a o f 0.05. A l s o , t h e sample s i z e was s m a l l . Boats were s p l i t i n t o two c a t e g o r i e s : s t a t i o n a r y and m o b i l e . S t a t i o n a r y v e s s e l s r e p o r t e d c a t c h e s f o r a t l e a s t 10 o f t h e 14 o p e n i n g s . A l l d a t a s e t s f o r the s t a t i o n a r y b o a t s f i t t h e n e g a t i v e b i n o m i a l ( T a b l e I X ) . O n l y p r e d i c t i o n 2) was e x h i b i t e d by t h e d a t a ( F i g u r e 29); t h e p a r a m e t e r s f o r t o t a l and s t a t i o n a r y e f f o r t were c o r r e l a t e d . The r e s p o n s e o f k t o e f f o r t was d o m e - l i k e and s c a t t e r e d ( F i g u r e 30). The r e l a t i v e e x p l o i t a t i o n r a t e - e f f o r t r e l a t i o n s h i p d i d n o t s a t u r a t e . The s a l e s s l i p model i s v e r y u n c e r t a i n . I n a d d i t i o n t o the model e r r o r term, r e p o r t i n g e r r o r s c e r t a i n l y a f f e c t the t a i l s o f the CPUE 118 T a b l e IX. The parameter v a l u e s ( k ) , s t a n d a r d e r r o r s and sample s i z e s f o r the n e g a t i v e b i n o m i a l f i t to CPUE d a t a . T o t a l F l e e t k a(k) n 0.9 0. .2 34 1.3 0. .2 50 0.9 0, .1 82 1.5 0. .2 109 2.4 0, .4 60 1.7 0. .2 118 2.4 0. .1 193 2.5 0, .1 247 1.5 0. .1 330 1.5 0. .1 388 2.1 0. .1 376 0.8 0. .1 253 1.2 0. .1 291 1.3 0. .1 224 S t a t i o n a r y F l e e t ( f i s h e d > 10 o p e n i n g s ) k o-(k) n 0.7 0. ,2 23 1.8 0. ,4 38 1.2 0. .2 52 1.6 0. ,3 56 2.8 0. .5 45 2.2 0. .4 55 3.0 0. .5 59 2.3 0. .4 65 1.6 0. .3 64 2.4 0. .4 65 3.3 0. ,5 66 0.8 0. ,1 60 0.8 0. .3 65 1.4 0. .2 57 119 2.4 2.2 2.0 1.8 >- 1.6 or < O 1.4 < o o CO 1.2 1.0 0.8 0.6 o o o 1.0 2.0 3.0 TOTAL K 4.0 F i g u r e 29. T o t a l f l e e t k v e r s u s s t a t i o n a r y f l e e t k. The e s t i m a t e s f o r t h e n e g a t i v e b i n o m i a l p a r a m e t e r , k, were o b t a i n e d f o r the t o t a l f l e e t CPUE d i s t r i b u t i o n s and from the CPUE o f v e s s e l s f i s h i n g a t l e a s t 10 o f the 14 o p e n i n g s . 120 • 2 9 •2.8 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0* 6 >02 mo.5 I #0-2 J. 0 100 200 300 EFFORT (NO. OF BOATS) O k • k' * r e p o r t i n g er ror 400 F i g u r e 30. k v s . e f f o r t . The parameter e s t i m a t e s and s t a n d a r d e r r o r s were computed f o r f i t s o f the n e g a t i v e b i n o m i a l t o GPUE f r e q u e n c y d i s t r i b u t i o n s . The maximum l i k e l i h o o d method was used. These e s t i m a t e s appear as open c i r c l e s . The f i l l e d c i r c l e s r e p r e s e n t p r e d i c t e d k' v a l u e s . These p r e d i c t i o n s were p r o v i d e d by the o v e r f l i g h t model e s t i m a t e s o f l i n e - u p l e n g t h s and a model f o r the v a r i a n c e o f v e s s e l c a t c h e s w i t h i n l i n e - u p s . 121 d i s t r i b u t i o n s . These e r r o r s were d i s c u s s e d w i t h i n the c o n t e x t o f i n d e p e n d e n t e f f o r t c o u n t s i n Cha p t e r IV ( F i g u r e 8 ) . V e s s e l s o f t e n r e p o r t t h e i r c a t c h e s i n t h e wrong s t a t i s t i c a l a r e a s . A l s o , c a t c h i s sometimes r e c o r d e d as w e i g h t and t h e n c o n v e r t e d t o p i e c e s b a s e d upon t h e mean weight o f salmon t h a t d i d n o t comprise a random sample. An a l t e r n a t i v e e x p l a n a t i o n was e x p l o r e d the salmon abundance v a r i a n c e component i s p r o p o r t i o n a l t o abundance (when mean c a t c h p e r s e t i s p r o p o r t i o n a l t o abundance); k v a r i e s w i t h t o t a l c a t c h . The f o l l o w i n g d e r i v a t i o n o f f e r s a p o s s i b l e e x p l a n a t i o n f o r t h e dynamics o f k. The v a r i a b l e c a t c h i n g p r o c e s s a t i n d i v i d u a l a c c e s s p o i n t s was compounded t h r o u g h the l i n e - u p d i s t r i b u t i o n s . A c c o r d i n g t o K e n d a l l , S t u a r t and Ord (1983) t h e minimum v a r i a n c e e s t i m a t o r f o r t h e mean o f a f i n i t e p o p u l a t i o n (N) sampled randomly b u t w i t h o u t r e p l a c e m e n t i s the sample mean (m). The v a r i a n c e o f the d i s t r i b u t i o n o f sample means i s V(m) = a 2 (1/n - 1/N) 55) where n i s the sample s i z e and a 2 i s the p o p u l a t i o n v a r i a n c e . The c o m p e t i t i v e p r o c e s s w i t h i n queues i s p r o b a b l y b e t t e r r e p r e s e n t e d as s a m p l i n g w i t h o u t r e p l a c e m e n t , b u t w i t h v a r i a b l e s e l e c t i o n p r o b a b i l i t i e s . T h i s c o m p l e x i t y was a v o i d e d h e r e . The v a r i a n c e o f t h e mean c a t c h p e r s e t w i t h i n a queue was assumed t o be V(Cs"i) = O i 2 ( 1 / t i - l / t i n i ) 56) where Cs^ i s the mean c a t c h p e r s e t f o r an i n d i v i d u a l b o a t , o ^ 2 i s now the p o p u l a t i o n v a r i a n c e o f c a t c h p e r s e t , t ^ i s the number o f s e t s made p e r b o a t and n^ i s the number o f v e s s e l s p a r t i c i p a t i n g i n queue i . I t was assumed t h a t 122 2 cfi = iCsp-L = iCspi T/n^t^ = T C / E t i 57) where Csp^ i s the p o p u l a t i o n mean c a t c h p e r s e t , T — n±^i i s the t o t a l number o f s e t s made a t t h e a c c e s s p o i n t and x i s a c o n s t a n t . S i n c e Csp^ T/n^ i s the mean c a t c h p e r b o a t and i t was p r e v i o u s l y assumed t h a t t h i s mean i s e q u a l among queues, i t can be r e p l a c e d by the mean c a t c h p e r v e s s e l ( C / E ) . E q u a t i o n 56) r e p r e s e n t s the e x p e c t e d sum o f s q u a r e s o f the v e s s e l mean c a t c h p e r s e t - p o p u l a t i o n mean c a t c h p e r s e t d i f f e r e n c e s , d i v i d e d by the degre e s o f freedom ( n ^ - 1 ) . M u l t i p l y i n g by t ^ 2 t r a n s f o r m s t h e e x p r e s s i o n i n t o one o f t o t a l c a t c h p e r v e s s e l . S S i = TC/E ( ( n i - l ) / n i ) ( n i - 1) s V(CPUE) = xC/E (E - 2s + Z l/nL)/E 58) i - 1 where SS^ i s the sum o f s q u a r e s f o r the v e s s e l c a t c h e s a t a c c e s s p o i n t i , s i s t h e number o f e x p l o i t e d a c c e s s p o i n t s and V(CPUE) i s the p r e d i c t e d p o p u l a t i o n v a r i a n c e o f v e s s e l c a t c h e s . S i n c e mean c a t c h e s a r e e q u a l i z e d among queues, t h e r e i s no "among" sum o f s q u a r e s . The t o t a l p o p u l a t i o n o f b o a t s i s r e p r e s e n t e d , so £SS^ i s d i v i d e d by the p o p u l a t i o n s i z e . E x p r e s s i o n s f o r p a r a m e t e r s analogous t o those o f the n e g a t i v e b i n o m i a l can be d e r i v e d from the moment e q u a t i o n s (49) k' - C / ( T [ E - 2s + Z l/n±] -E) i - 1 s a' = E / ( x [ E - 2s + Z 1/njJ - E) i - 1 59) 123 k', t h e n , i n c l u d e s the salmon abundance and f l e e t e x p l o i t a t i o n r a t e e f f e c t s (C = ( l - b ) p N ) . The v e s s e l d i s t r i b u t i o n i s c a p t u r e d by t h e e x p r e s s i o n i n b r a c k e t s . I f a l l v e s s e l s f i s h a l o n e , £l/n^ ^  s • E "= s, t h e b r a c k e t e d e x p r e s s i o n i s z e r o , and the denominator i s -E. k' i s n e g a t i v e i n d i c a t i n g a u n i f o r m d i s t r i b u t i o n . As e f f o r t i n c r e a s e s beyond 2s ( a n a v e r a g e l i n e - u p o f 2) the e x p r e s s i o n becomes l a r g e (and £l/n^ becomes s m a l l ) , r e s u l t i n g i n s m a l l e r k' v a l u e s . Between t h e s e two extremes, the n e g a t i v e v a l u e o f (E - 2s) o f f s e t s £l/n^. The param e t e r a' does n o t r e p r e s e n t t h e p h y s i c a l d r i v i n g p r o c e s s (salmon abundance) b u t r e f l e c t s the f l e e t s i z e and the s c a l e o f i t s s p a t i a l d i s t r i b u t i o n . k' was c a l c u l a t e d f o r each f l i g h t u s i n g e q u a t i o n 5 9 ) , t h e s a l e s s l i p c a t c h e s t i m a t e s and t h e o v e r f l i g h t model p r e d i c t i o n s f o r queue l e n g t h s a t o b s e r v e d e f f o r t and a c c e s s p o i n t l e v e l s ( e q u a t i o n 4 5 ) . The o v e r f l i g h t model p r e d i c t i o n s were rounded up and down i n o r d e r t o r e p r e s e n t the d i s c r e t e queues. The r e s u l t s a r e p r e s e n t e d i n F i g u r e 30) and r e p r e s e n t a v e r a g e k' v a l u e s f o r eac h o p e n i n g . The number o f o v e r f l i g h t s p e r o p e n i n g d i d n o t always c o n s t i t u t e a random sample o f f l e e t d i s t r i b u t i o n s . C o n s e q u e n t l y , s t a n d a r d e r r o r s f o r mean k's were n o t i n c l u d e d . A t low e f f o r t (< 109 v e s s e l s ) x = 2000; T = 5000 was u s e d f o r a l l o t h e r o p e n i n g s . T h i s m a n i p u l a t i o n was n e c e s s a r y t o d u p l i c a t e the s c a l e o f the k re s p o n s e and i n d i c a t e d t h a t the r e l a t i o n s h i p between the mean and v a r i a n c e o f c a t c h p e r s e t changed as p i n k s e n t e r e d what had been a p r e d o m i n a n t l y sockeye f i s h e r y . The b a s i c form o f the k r e s p o n s e was d u p l i c a t e d . Openings c h a r a c t e r i z e d by d i s c r e p a n c i e s between o b s e r v e d and r e p o r t e d e f f o r t a r e n o t e d ( c f . F i g u r e 8 ) . A t t h o s e t i m e s , v e s s e l s f i s h e d p a r t o f t h e weekly o p e n i n g i n J u a n de Fuca S t r a i t o r the n o r t h - c e n t r a l a r e a s and a p p a r e n t l y r e p o r t e d t h e i r t o t a l c a t c h as J o h n s t o n e S t r a i t f i s h . The d a t a p o i n t a t 124 224 v e s s e l s / k = l . 3 r e p r e s e n t s the f i n a l o p e n i n g o f the season; s k i p p e r s r e p o r t e d t h e i r J o h n s t o n e S t r a i t c a t c h as homeport a r e a f i s h . R e p o r t i n g c a t c h e s i n t o the a r e a d e c r e a s e d k r e l a t i v e t o k', w h i l e r e p o r t i n g c a t c h e s o u t o f t h e a r e a i n c r e a s e d k r e l a t i v e t o k'. k' was a l s o i n e r r o r . R e p o r t i n g c a t c h e s i n t o the a r e a b i a s e d k' upwards ( r e p o r t e d c a t c h was l a r g e r t h a n a c t u a l c a t c h ) w h i l e r e p o r t i n g o u t o f t h e a r e a p r o d u c e d s m a l l e r k ' s . A l s o , two low e f f o r t d a t a p o i n t s a r e l a b e l l e d . A g a i n , v e s s e l s a r r i v e d from o r d e p a r t e d t o o t h e r f i s h i n g a r e a s , c o n t r i b u t i n g t o the v a r i a b i l i t y i n e f f o r t c o u n t s and b i a s i n g t h e CPUE d i s t r i b u t i o n s . E i g h t k' v a l u e s f e l l v e r y c l o s e t o t h e i r k c o u n t e r p a r t s , 4 d e v i a t i o n s from k r e p r e s e n t e d d i s c r e p a n c i e s c a u s e d by r e p o r t i n g e r r o r s and t h e d i f f e r e n c e s between k' and k d u r i n g two o p e n i n g s c a n n o t be e x p l a i n e d . G i v e n t h e r e p o r t i n g e r r o r s , the s m a l l number o f o v e r f l i g h t s made w i t h i n e a c h o p e n i n g and the v a r i a b i l i t y o f t h i s sample s i z e among o p e n i n g s , the r e s u l t s were q u i t e good. W i t h i n T l e v e l s (x •= 2000 a t low e f f o r t and 5000 a t h i g h e f f o r t ) the r e s p o n s e o f k' r e f l e c t e d b o t h c a t c h and t h e d i s t r i b u t i o n o f v e s s e l s . k' g e n e r a l l y i n c r e a s e d w i t h c a t c h . The f l e e t d i s t r i b u t i o n term f o l l o w e d a s i g m o i d r e s p o n s e t o e f f o r t . V a r i a b i l i t y a r o u n d t h i s e f f o r t p a t c h r e s p o n s e a f f e c t e d the o r d e r i n g o f k' and, presumably, k. The r e s p o n s e t o t o t a l c a t c h e x p l a i n s t h e h i g h c o r r e l a t i o n between t o t a l f l e e t ks and s t a t i o n a r y f l e e t k s . A l t h o u g h t h e s k i p p e r s may have f i s h e d d i f f e r e n t l y , t h e y e x p l o i t e d the same salmon p o p u l a t i o n s i z e s . A s i m u l a t i o n w i t h c a t c h e q u a l t o t h e e s t i m a t e d e x p l o i t a t i o n r a t e s (1-b) t i m e s a c o n s t a n t salmon abundance p r o d u c e d a r a p i d d e c r e a s e i n k' as e f f o r t i n c r e a s e d . Thus t h e n u m e r i c a l r e s p o n s e o f t h e f i s h i n g f l e e t may skew t h e d i s t r i b u t i o n o f e f f e c t i v e n e s s . When queue r e s p o n s e e r r o r s were i n c l u d e d as d i f f e r e n c e s among mean c a t c h r a t e s ( t h e d e v i a t i o n s o f t h e 125 p r e d i c t e d queue l e n g t h s from t h e i r i n t e g r a l m a n i f e s t a t i o n ) the k' r e sponse d i d n o t change s i g n i f i c a n t l y . I t i s i n t e r e s t i n g t o n o t e t h a t the average l i n e - u p s a t u r a t e d b e f o r e E r e a c h e d 2s. The E-2s term was u s u a l l y n e g a t i v e and d i d n o t c o n t r i b u t e p o s i t i v e l y t o f l u c t u a t i o n s i n k'. T h i s f a c t r e f l e c t s two p r o p e r t i e s o f the system: t h e r e a r e few e x c e l l e n t a c c e s s p o i n t s and w a i t i n g t i m e s s e t a upper l i m i t on t h e s i z e o f t h e a g g r e g a t i o n s a t t h o s e s i t e s . D i s t r i b u t i o n s o f c a t c h e s w i t h e q u a l means and d i s s i m i l a r v a r i a n c e s were d e s c r i b e d by a c t u a l v e s s e l d i s t r i b u t i o n s r a t h e r t h a n P o i s s o n p a r a m e t e r s by t h e o r e t i c a l gamma d i s t r i b u t i o n s . T h e r e i s no d i r e c t method f o r o b t a i n i n g e s t i m a t e s o f e x p l o i t a t i o n r a t e s o r salmon abundance from the d i s t r i b u t i o n s o f CPUE. B o t h v a r i a b l e s a r e r e p r e s e n t e d as t o t a l c a t c h i n t h e f u n c t i o n a l e q u a t i o n f o r k'. l / ( a ' x ) i s a measure o f f l e e t a g g r e g a t i o n w e i g h t e d by the i n v e r s e o f the f l e e t s i z e . A clumped v e s s e l d i s t r i b u t i o n ( l a r g e r 1/a'T) i s i n d i c a t i v e o f a skewed salmon d i s t r i b u t i o n and a r e l a t i v e l y l a r g e number o f e x p l o i t e d a c c e s s p o i n t s -- few f i s h a r e p r e s e n t o u t s i d e the e f f o r t a g g r e g a t i o n and e x p l o i t a t i o n r a t e s a r e h i g h . T h i s i n d e x i s n o t e q u i v a l e n t t o c s i n c e the s i z e o f t h e f l e e t and the number o f e x p l o i t e d a c c e s s p o i n t s s t i l l c o n t r i b u t e t o t h e magnitude o f a'. The 1/a'x v e r s u s e f f o r t r e s p o n s e s a t u r a t e d a t a p p r o x i m a t e l y 100 v e s s e l s . O m i t t i n g t h e o p e n i n g s t h a t c o n t a i n e d r e p o r t i n g e r r o r s , 1/ax a l s o s a t u r a t e d and may be an i n d e x o f r e l a t i v e e x p l o i t a t i o n r a t e s . An e s t i m a t e o f x must be o b t a i n e d from t e s t f i s h i n g o p e r a t i o n s . S i n c e t h e o v e r f l i g h t model e s t i m a t i o n r e s u l t s i n d i c a t e d t h a t e x p l o i t a t i o n s a t u r a t e d r a p i d l y ( i . e . , became c o n s t a n t ) , i t may be b e s t t o assume t h a t c a t c h i s p r o p o r t i o n a l to abundance when e f f o r t exceeds 100 b o a t s . 126 D i s c u s s i o n The c r i t i c a l a s s u m p t i o n i n the o v e r f l i g h t model, and one w h i c h was not d i r e c t l y t e s t e d , i s t h a t a l l f i s h e r m e n p o s s e s s p e r f e c t i n f o r m a t i o n c o n c e r n i n g a c c e s s p o i n t c a t c h r a t e s ( c a t c h p e r time i n t e r v a l ) . The s u p p o r t i n g e v i d e n c e was d i s c u s s e d i n d e t a i l a t t h e b e g i n n i n g o f t h i s c h a p t e r . Model r e s u l t s appear t o s u p p o r t t h i s a s s u mption: t h e dynamics o f p a r a m e t e r c c o i n c i d e d w i t h a n e c d o t a l a c c o u n t s o f salmon and f i s h e r m a n b e h a v i o r . A c c o r d i n g t o t h e f i s h e r m e n , t h e f i s h a r e d i s p e r s e d on t h e ebb t i d e and a t the b e g i n n i n g o f the o p e n i n g . F i g u r e 28 m i r r o r s t h e s k i p p e r ' s a s s e r t i o n s . I n the l o g b o o k a n a l y s i s , the l a r g e s t c a t c h e s u s u a l l y appeared on t h e f l o o d t i d e . T h a t r e s u l t a g r e e s w i t h t h e a p p a r e n t p a t t e r n s i n queue/salmon d i s t r i b u t i o n skewness. The n e g a t i v e c o r r e l a t i o n between the skewness parameter, c, and e f f o r t was c o n f o u n d e d by a s i m i l a r c o r r e l a t i o n w i t h t h e i n d e x o f salmon abundance. T h e r e was a sudden change i n c as f i s h i n g b o u n d a r i e s were l i f t e d . T h i s r e s u l t p r o b a b l y r e f l e c t e d the i n c l u s i o n o f a new s u b s e t o f salmon v u l n e r a b i l i t i e s i n t o t h e f i s h e r y . I f the c o r r e l a t i o n between c and e f f o r t was a r e s u l t o f t h e c o r r e l a t i o n between e f f o r t and abundance and a salmon d i s t r i b u t i o n - a b u n d a n c e c a u s e / e f f e c t r e l a t i o n s h i p i s p o s t u l a t e d , i t appears t h a t t h e f i s h s p r e a d o u t and o c c u p i e d a g r e a t e r volume ( r a t h e r t h a n f o r m i n g more c o n c e n t r a t e d s c h o o l s ) as abundance i n c r e a s e d . T h i s phenomenon may a l s o r e f l e c t t h e change i n s p e c i e s c o m p o s i t i o n . P i n k salmon e n t e r e d the f i s h e r y d u r i n g t h e m i d d l e o f the s e a s o n and were more abundant t h a n s o c k e y e . The e x p l o i t a t i o n r a t e (1-b) on a v a i l a b l e f i s h s a t u r a t e d r a p i d l y . T h i s r e s u l t was s u p p o r t e d by the l e s s e v i d e n t s a t u r a t i o n o f CPUE as a f u n c t i o n o f s e t c a t c h r a t e s . S i n c e e f f o r t and v u l n e r a b l e abundance were c o r r e l a t e d 127 and e f f o r t was w e i g h t e d too h e a v i l y i n the CPUE i n d i c e s w h i l e e x p l o i t a t i o n s a t u r a t e d , t h e CPUE c u r v e f l a t t e n e d as r e l a t i v e abundance i n c r e a s e d . E r r o r s i n r e p o r t i n g c a t c h e s do n o t a f f e c t t h i s c o n c l u s i o n . The e r r o r s a t h i g h e f f o r t i n v o l v e d r e p o r t i n g c a t c h i n t o the a r e a , i n c r e a s i n g t h e s l o p e o f t h e c a tch-abundance r e l a t i o n s h i p . The r e s p o n s e o f e x p l o i t a t i o n r a t e s to e f f o r t s a t u r a t e d a b r u p t l y a t 100 v e s s e l s . I f t h e p r o d u c e r s w i s h t o maximize salmon p r o d u c t i o n and m i n i m i z e o p e r a t i o n c o s t s a t t h a t maximum ( r a t h e r t h a n a d v o c a t e a l a b o u r i n t e n s i v e s i t u a t i o n ) , 100 v e s s e l s i s p r o b a b l y optimum. E c o n o m i s t s , however, o f t e n c o n s i d e r s o c i a l a s p e c t s as w e l l . B i o l o g i c a l managers may d e c i d e t h a t an e f f o r t l e v e l o f 100 b o a t s i s too l a r g e ; the e x p l o i t a t i o n r a t e i s a r ound 80% o f t h e v u l n e r a b l e f i s h . The assumed e r r o r s t r u c t u r e i n the monte c a r l o s i m u l a t i o n s i n d i c a t e d t h a t t h e q u a l i t a t i v e form o f the e x p l o i t a t i o n r a t e r e s p o n s e i s p r e s e r v e d . W a l t e r s and Ludwig (1981) 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 models which i n c l u d e d o b s e r v a t i o n e r r o r . T h e i r r e s u l t s i n d i c a t e d t h a t t h i s e r r o r c a n p r o d u c e f a l s e q u a l i t a t i v e forms. These c o n t r a d i c t o r y r e s u l t s may be e x p l a i n e d by the d i f f e r e n c e s i n the d e t e r m i n i s t i c components o f the o v e r f l i g h t and s t o c k - r e c r u i t m e n t models, the d i f f e r e n c e s i n the e r r o r f o r m u l a t i o n s , o r the f a c t t h a t the e f f o r t v a r i a b l e i n the e x p l o i t a t i o n - e f f o r t r e l a t i o n s h i p was measured w i t h o u t e r r o r . More e r r o r s i n v a r i a b l e s r e s e a r c h i s r e q u i r e d . The r e l a t i o n s h i p between c a t c h a b i l i t y ( ( l - b ) / E ) and weekly, v u l n e r a b l e abundance w i l l be d e p e n s a t o r y when e f f o r t i s c o r r e l a t e d w i t h abundance. A n e g a t i v e c o r r e l a t i o n w i l l p roduce a compensatory e f f e c t . I f the weekly r e s p o n s e s o f e x p l o i t a t i o n t o e f f o r t do n o t change w i t h the a n n u a l salmon abundance, the r e l a t i o n s h i p between a n n u a l c a t c h a b i l i t y and a n n u a l salmon abundance w i l l be a f u n c t i o n o f v a r i a b l e salmon r u n t i m i n g s , a n n u a l n u m e r i c a l r e s p o n s e s , the r e l a t i o n s h i p s between weekly salmon abundance and 128 weekly e f f o r t l e v e l s , v a r i a b l e v u l n e r a b i l i t i e s and the number and l e n g t h o f o p e n i n g s . The f i s h e r m e n s t a t e t h a t , f o r a g i v e n e f f o r t l e v e l , t h e s p a t i a l d i s t r i b u t i o n o f the f l e e t w i l l c o n t r a c t as abundance d e c r e a s e s . I f abundance i n c r e a s e s , any i n c r e a s e i n t h e volume o c c u p i e d by t h e f i s h w i l l be t r a c k e d by an i n c r e a s e i n the volume f i s h e d by the f l e e t . A l l o t h e r t h i n g s b e i n g e q u a l ( o p e n i n g l e n g t h s , r u n t i m i n g s e t c . ) Peterman and S t e e r ' s (1981) mechanism f o r d e p e n s a t o r y c a t c h a b i l i t y may n o t h o l d h e r e : the r a t i o o f volume swept to the volume o c c u p i e d by the f i s h may n o t d e c r e a s e as f i s h abundance i n c r e a s e s . Indeed, as c d e c r e a s e d , e x p l o i t a t i o n r e m a i n e d f a i r l y c o n s t a n t f o r e q u i v a l e n t e f f o r t l e v e l s . The o v e r f l i g h t model o u t p u t appears t o r e p r e s e n t the dynamics o f the f i s h e r y : o b s e r v a t i o n e r r o r was s m a l l ; the component a s s u m p t i o n s were s u p p o r t e d by p r e v i o u s a n a l y s e s and the dynamics o f the e s t i m a t e d parameters f u l f i l l e d a p r i o r i p r e d i c t i o n s b a s e d upon independent d a t a and a n e c d o t a l a c c o u n t s . The r e s u l t s o b t a i n e d by compounding the v a r i a b l e c a t c h i n g p r o c e s s t h r o u g h the v e s s e l d i s t r i b u t i o n s appear t o s u p p o r t t h e o v e r f l i g h t model s t r u c t u r e . B annerot and A u s t i n (1983) s t a t e d t h a t i n c r e a s e d skewness ( s m a l l e r k) o f CPUE d i s t r i b u t i o n s w i t h d e c r e a s i n g f i s h abundance (N) i s c o n s i s t e n t w i t h c a t c h a b i l i t y b e i n g n e g a t i v e l y r e l a t e d t o N. They a l s o s t a t e d t h a t the v a r i a n c e o f t h e i r CPUE d i s t r i b u t i o n s t e n d e d t o be p r o p o r t i o n a l t o N. I n t h i s c a s e , c o r r e l a t i o n s between skewness o r k and N s h o u l d be e x p e c t e d even when c a t c h a b i l i t y i s c o n s t a n t . I f C/E = qN and k i s e x p r e s s e d as i t s moment e s t i m a t e , t h e n k - ( q N ) 2 / ( T N - qN) - q 2N/(x-q) where T i s the c o n s t a n t o f p r o p o r t i o n a l i t y f o r the v a r i a n c e - a b u n d a n c e 129 r e l a t i o n s h i p . I f C/E s a t u r a t e s w i t h i n c r e a s i n g N ( i . e . , c a t c h a b i l i t y d e c r e a s e s ) and t h e v a r i a n c e c o n t i n u e s t o i n c r e a s e w i t h N, t h e n k s h o u l d i n i t i a l l y i n c r e a s e w i t h N and t h e n d e c r e a s e as the v a r i a n c e i n c r e a s e s w i t h C/E c o n s t a n t . These arguments r e q u i r e n n n B+l E (Cj/EiVn - lCi/lEi = qN o r aN i - 1 i = l i - 1 • where 0 > B > -1. C^ and a r e c a t c h and e f f o r t measurements f o r b o a t i . B a n n e r o t and A u s t i n d i d n o t comment on t h e s e r e l a t i o n s h i p s . F o r t h e i r u n p o o l e d d a t a , c a t c h a b i l i t y was e s s e n t i a l l y c o n s t a n t f o r most o f the range o f e s t i m a t e d N. C/E, t h e n , s h o u l d have been a good i n d e x o f N. R f o r the C/E - N c o m p a r i s o n was g r e a t e r t h a n the v a l u e c a l c u l a t e d f o r the maximum l i k e l i h o o d k - N com p a r i s o n . T h i s r e s u l t i n d i c a t e d t h a t x v a r i e d . I n J o h n s t o n e S t r a i t , e f f o r t was c o r r e l a t e d w i t h salmon abundance ( r e p r e s e n t e d as t o t a l c a t c h ) ; k d i d d e c r e a s e a t h i g h e f f o r t ( t h e k' e s t i m a t e s were b i a s e d upward when c a t c h e s were r e p o r t e d i n t o t h e s t r a i t from o t h e r a r e a s ) ; the o v e r f l i g h t model p r e d i c t e d d e p e n s a t o r y c a t c h a b i l i t y and CPUE s a t u r a t e d as a f u n c t i o n o f c a t c h p e r s e t i n d i c e s o f abundance. Perhaps f i s h e r i e s s c i e n t i s t s s h o u l d m o n i t o r t h e s i z e s and s p a t i a l d i s t r i b u t i o n s o f f l e e t s and the k e s t i m a t e s from CPUE d i s t r i b u t i o n s . I f c h a n g i n g d i s t r i b u t i o n s o f e x p l o i t e d f i s h p a t c h e s i s v i e w e d as a random v a r i a b l e , d e v i a t i o n s o f CPUE k e s t i m a t e s from p r e d i c t i v e e q u a t i o n s w h i c h i n c l u d e f l e e t s i z e and d i s t r i b u t i o n as v a r i a b l e s c o u l d be r e l a t e d t o changes i n the s i z e o f t h e v u l n e r a b l e f i s h p o p u l a t i o n and x. At t e m p t s t o q u a n t i f y e x p l o i t a t i o n as salmon d e p l e t i o n w i t h i n a f i s h i n g o p e n i n g c a n n o t be s u p p o r t e d . I t i s i m p o s s i b l e t o o b t a i n a sample o f s e t c a t c h e s t h a t i s ran d o m i z e d o v e r s k i p p e r s , t i d e s and a c c e s s p o i n t s . C a t c h r a t e s v a r y w i t h t h e t i d a l c y c l e ; d e c r e a s i n g t r e n d s i n w i t h i n - o p e n i n g 130 c a t c h e s p e r s e t may j u s t r e f l e c t the p o s i t i o n o f the f i s h i n g o p e n i n g w i t h i n t h e l u n a r c a l e n d a r . I f t o t a l samples o f s e t c a t c h e s were o b t a i n e d f o r m u l t i p l e o p e n i n g s and the mean c a t c h r a t e s were s t a n d a r d i z e d f o r salmon abundance and the t i d a l c y c l e s , t h e s e means c o u l d n o t be r e l a t e d t o d e p l e t i o n o r e x p l o i t a t i o n c o m p e t i t i o n : e n t r a n t v e s s e l s move t o l e s s d e s i r a b l e s p o t s due to i n t e r f e r e n c e -- average c a t c h a b i l i t y d e c r e a s e s . The d i s t r i b u t i o n s o f c a t c h r a t e s and e f f o r t may p r o v i d e b e t t e r i n f o r m a t i o n . The e x p l o i t a t i o n r a t e s e s t i m a t e d w i t h the o v e r f l i g h t model were n o t i n d e p e n d e n t o f t h e e f f o r t measurements u s e d i n t h e f i t t i n g p r o c e s s . The p l o t o f (1-b) v e r s u s e f f o r t e s t i m a t e d from f l i g h t s c a n n o t be c o n s i d e r e d a r i g o r o u s p r o c e d u r e . Y e t , t h i s g r a p h i c a l a n a l y s i s p r o v i d e s an i m p o r t a n t c o n c l u s i o n : F i g u r e 8 e x h i b i t s a n e a r c o n s t a n t 1:1 r a t i o f o r a e r i a l e f f o r t c o u n t s and s a l e s s l i p measurements; t h e r e s p o n s e o f (1-b) t o t h e in d e p e n d e n t , s a l e s s l i p e f f o r t e s t i m a t e s w i l l be c l o s e t o t h a t p r e s e n t e d i n F i g u r e 26. S i m i l a r l y , k and kE were n o t e s t i m a t e d i n d e p e n d e n t l y o f s a l e s s l i p e f f o r t e s t i m a t e s , b u t the g e n e r a l form o f the k-E r e s p o n s e w i l l n o t change when o v e r f l i g h t e s t i m a t e s o f e f f o r t a r e s u b s t i t u t e d f o r s a l e s s l i p measurements. k' was e s t i m a t e d i n d e p e n d e n t l y o f s a l e s s l i p e f f o r t . CHAPTER V I I GENERAL DISCUSSION The J o h n s t o n e S t r a i t f i s h e r y i s a g a u n t l e t i n which salmon a r e s u b j e c t t o r e p e a t e d e x p l o i t a t i o n a l o n g t h e i r m i g r a t i o n r o u t e . T h i s t y p e o f f i s h e r y was d e s c r i b e d by B e v e r t o n and H o l t (1957). They p r e s e n t e d a c o m p e t i t i o n model f o r b each s e t s and open s e t l i n e s , y e t a major a s s u m p t i o n was t h a t the f i s h were d i s t r i b u t e d u n i f o r m l y . The d a t a p r e s e n t e d h e r e i n d i c a t e t h a t the f i s h e x h i b i t e d d i f f e r e n t v u l n e r a b i l i t i e s a l o n g the g a u n t l e t . Gardner (1980) u s e d a c a t c h model b a s e d upon power f u n c t i o n s o f e f f o r t and salmon biomass f o r the g a u n t l e t f i s h e r i e s a p p r o a c h i n g the F r a s e r R i v e r i n B r i t i s h C o lumbia. H i s p a r a m e t e r e s t i m a t e s f o r c a t c h and escapement d a t a s u p p o r t e d gear c o m p e t i t i o n h y p o t h e s e s , b u t once a g a i n t h e d a t a q u a l i t y was s u s p e c t . The o v e r f l i g h t and s a l e s s l i p models i n c l u d e d t h e g a u n t l e t e f f e c t . The d i s t r i b u t i o n o f f i s h e r m e n s h o u l d change as e x p l o i t a t i o n c o m p e t i t i o n a f f e c t s the abundance o f salmon a l o n g the m i g r a t i o n r o u t e . I t i s c o n c e i v a b l e t h a t e x p l o i t a t i o n c o m p e t i t i o n p r o d u c e s a more u n i f o r m d i s t r i b u t i o n o f c a t c h e s as f i s h a r e t a k e n b e f o r e t h e y r e a c h s i t e s o f h i g h v u l n e r a b i l i t y . Indeed, t h e d e c r e a s e i n skewness t h r o u g h o u t the s e a s o n , and the f a c t t h a t an a b r u p t change o c c u r r e d when b o u n d a r i e s were l i f t e d ( F i g u r e 28), may r e f l e c t the e f f e c t s o f e x p l o i t a t i o n c o m p e t i t i o n . A c c o r d i n g to the s k i p p e r s , the change i n f i s h and v e s s e l d i s t r i b u t i o n s a f t e r the Sunday n i g h t o p e n i n g was a r e s u l t o f e x p l o i t a t i o n c o m p e t i t i o n ; the u n i f o r m d i s t r i b u t i o n o f f i s h a t the b e g i n n i n g o f an o p e n i n g i s " c l e a n e d up" l e a v i n g a more skewed d i s t r i b u t i o n o f v u l n e r a b i l i t i e s . W i t h i n the c o n t e x t o f the s a l e s s l i p model, the theorem o f Kennedy and K e e p i n g (1951) p o s t u l a t e s t h a t the g a u n t l e t e f f e c t c a n be q u a n t i f i e d by an i n d e p e n d e n t gamma k. 131 132 An a l t e r n a t i v e h y p o t h e s i s to e x p l o i t a t i o n c o m p e t i t i o n i s t h a t f i s h d i v e below the n e t s and e x p l o i t a t i o n c o m p e t i t i o n i s m i n i m i z e d by salmon b e h a v i o r . F i s h i n g s t r a t e g i e s take t h i s phenomenon i n t o a c c o u n t : beach s e t s and r o c k p i l e s e t s p r e v e n t f i s h from e s c a p i n g under the n e t . F i s h e r m e n o f t e n use p l u n g e r s t o c r e a t e underwater t u r b u l e n c e and n o i s e w h i c h keep the f i s h from d i v i n g under the b o a t as the n e t i s p u r s e d . The salmon must pass t h r o u g h a g a u n t l e t o f n e t s , b u t the same f i s h a r e p r o b a b l y n o t v u l n e r a b l e a t a l l f i s h i n g s p o t s . S c h o o l s o f salmon do n o t f o l l o w t h e same p a t h and p o r t i o n s o f t h e p o p u l a t i o n may o n l y e n t e r t h e v u l n e r a b l e d e p t h a t p a r t i c u l a r f i s h i n g s i t e s . The h y p o t h e s i s c o n c e r n i n g t h e d i s p e r s a l o f salmon v e s s e l s i n t o l e s s d e s i r a b l e a r e a s was s u p p o r t e d by th e " f l i p s " i n the graphs o f the average l i n e - u p and s e t s p e r b o a t ( F i g u r e s 16 and 22). The a v e r a g e l i n e - u p s i z e d e c r e a s e d a t h i g h e f f o r t , i n d i c a t i n g t h a t more b o a t s were e x p l o i t i n g the l e s s d e s i r a b l e one b o a t l i n e - u p s i t e s . The number o f s e t s p e r b o a t i n c r e a s e d a t h i g h e f f o r t . The " f l i p " a l s o appeared i n a c u r v e r e l a t i n g the p r o p o r t i o n o f s i n g l e b o a t l i n e - u p s t o e f f o r t . Open s e t s a r e p e r c e i v e d as l e s s d e s i r a b l e . The p r o p o r t i o n o f v e s s e l s making open s e t s i n c r e a s e d w i t h e f f o r t . The maximum l i n e - u p remained c o n s t a n t . F i s h e r m e n were a p p a r e n t l y moving away from the h i g h l i n e - u p a r e a s and e n t e r i n g l e s s d e s i r a b l e s p o t s where t h e y c o u l d make more s e t s . An a l t e r n a t i v e h y p o t h e s i s c o n c e r n i n g the movement o f f i s h e r m e n to l e s s d e s i r a b l e a r e a s i s t h a t the o v e r a l l s t r a t e g y o f the f l e e t changed a t h i g h e f f o r t , as f i s h e r m e n w i t h a maximize the number o f s e t s s t r a t e g y e n t e r e d the f i s h e r y . From f i e l d o b s e r v a t i o n s , the maximize the number o f s e t s s t r a t e g y was e v i d e n t a t a l l l e v e l s o f e f f o r t . T h i s f a c t was s u p p o r t e d by a n e c d o t a l a c c o u n t s , l o g book a c c o u n t s and o v e r f l i g h t o b s e r v a t i o n s . S k i p p e r s ' s k i l l was i n c o r p o r a t e d i n the s a l e s s l i p model as a gamma 133 v a r i a t e . The o v e r f l i g h t model d i d n o t e x p l i c i t l y i n c l u d e s k i l l e f f e c t s . S k i p p e r / v e s s e l e f f e c t s a c c o u n t e d f o r o n l y 5 p e r c e n t o f the v a r i a n c e i n c a t c h p e r s e t . The o v e r f l i g h t model was f o r m u l a t e d as a f u n c t i o n o f c a t c h p e r s e t and s h o r t time i n t e r v a l s . S k i l l , t h e r e f o r e , may n o t c o n t r i b u t e much t o a r e v i s e d model. V e s s e l d i f f e r e n c e s a r e compounded t h r o u g h o u t an o p e n i n g : H i l b o r n and L e d b e t t e r (1985), w o r k i n g w i t h s a l e s s l i p d a t a , f o u nd t h a t the s k i p p e r / v e s s e l e f f e c t e x p l a i n e d 30 p e r c e n t o f the v a r i a n c e i n c a t c h p e r b o a t week. P e r s o n a l o b s e r v a t i o n s i n d i c a t e d t h a t t h e b e s t s k i p p e r s l e a r n e d t o t a k e t h e l a r g e s t r i s k s f o r t h e most p r o f i t a b l e s e t s b a s e d upon h i s t o r i c a l and r e a l time i n f o r m a t i o n . Mangel and C l a r k (1983) i n c l u d e d a b r i e f d e s c r i p t i o n o f t h e B r i t i s h C o l u m b i a salmon p u r s e s e i n e f i s h e r y as an i n t r o d u c t i o n to t h e i r s e a r c h and e f f o r t a l l o c a t i o n model f o r m u l t i p l e f i s h i n g a r e a s . T h e i r d e f i n i t i o n o f a f i s h i n g c e l l ( a p p r o x i m a t e l y 18 km. s q u a r e ) i m p l i e s t h a t many s u c h c e l l s e x i s t w i t h i n the J o h n s t o n e S t r a i t f i s h e r y . A c c o r d i n g t o the movement d a t a and t h e t e m p o r a l t r e n d s i n c, good c a t c h e s a r e e x p e c t e d i n many o f t h e s e s m a l l c e l l s ( r a t h e r t h a n w i t h i n 3 c e l l s as p r e s e n t e d by Mangel and C l a r k ) b u t t h e number d i m i n i s h e s as the o p e n i n g p r o g r e s s e s ( i . e . , v e s s e l s moved n o r t h w e s t and t h e i r d i s t r i b u t i o n became more clumped). The l a r g e s c a l e movement p a t t e r n s , s e t c a t c h e s and t h e dynamics o f t h e parameter c i n d i c a t e d t h a t movement and r e d i s t r i b u t i o n o f e f f o r t were the r e s u l t o f knowledge and common se n s e . Random e n c o u n t e r s ( o r t h e i r r e p r e s e n t a t i o n w i t h i n f i s h e r i e s s e a r c h t h e o r y ) d i d n o t shape the f i s h e r y . A l l o c a t i o n o f c o o p e r a t i v e e f f o r t w i t h i n a c e l l i s an enormous a n a l y t i c a l p r o b l e m when the f a c t o r s c o n s i d e r e d by f i s h e r m e n a r e t a k e n i n t o a c c o u n t : t i d e s , m u l t i p l e a c c e s s p o i n t s and queue s i z e s , l o c a l knowledge and s t r a t e g i e s . A l l o c a t i o n o f e f f o r t a c r o s s c e l l s i n c l u d e s a n o t h e r l e v e l o f c o m p l e x i t y . Mangel and C l a r k acknowledged t h i s " c u r s e o f d i m e n s i o n a l i t y . " 134 Y e t f i s h e r m e n c a r v e out a n i c h e w i t h i n t h i s d i m e n s i o n a l i t y , measure t h i s n i c h e i n terms o f t r a d i t i o n a l i n f o r m a t i o n , c o m p e t i t i o n , l o c a l knowledge and s k i l l , and do q u i t e w e l l when l u c k comes t h e i r way and as t h e y d e v e l o p the a b i l i t y t o " t h i n k l i k e a [non-random] f i s h . " T e c h n o l o g i c a l advances a f f e c t v e s s e l d i s t r i b u t i o n s and, t h e r e f o r e , the p r o p o r t i o n o f a v a i l a b l e f i s h caught i n a f i s h i n g a r e a and the volume swept by one u n i t o f e f f o r t . The advent o f the r u n n i n g l i n e and open s e t s t r a t e g y (and the drum) a f f e c t e d the volume swept and th e p r o p o r t i o n o f the f i s h i n g a r e a u t i l i z e d . F i s h e r m e n were a b l e to move o f f s h o r e away from the b e a c h and crowded c o n d i t i o n s . The average number o f s e t s p e r b o a t must have i n c r e a s e d as the f l e e t moved i n t o l e s s d e s i r a b l e b u t l e s s crowded a r e a s . D i r e c t i n t e r f e r e n c e c o m p e t i t i o n d e c r e a s e d . I n the CYRA t u n a o p e r a t i o n s , the r a p i d c o n v e r s i o n o f b a i t b o a t s t o p u r s e s e i n e r s d u r i n g the l a t e 1950's i n c r e a s e d the f i s h i n g power o f the f l e e t and a f f e c t e d t h e s p a t i a l d i s t r i b u t i o n o f e f f o r t ( A l v e r s o n 1963; C a l k i n s 1963, 1975; C a l k i n s and C hatwin 1967, 1971). F u r t h e r m o r e , t e c h n o l o g i c a l improvements o f p u r s e s e i n e v e s s e l s i n the 1960's i n c r e a s e d t h e i r s e t e f f i c i e n c i e s , c r u i s i n g speeds and, c o n s e q u e n t l y , t h e i r s e a r c h a r e a s ( P e l l a and P s a r o p u l o s 1975). R o t h s c h i l d (1977) emphasized t h a t changes i n f i s h i n g s t r a t e g i e s a l s o a f f e c t f i s h i n g power. Tuna f i s h e r m e n moved f u r t h e r o f f s h o r e , f o u n d new a g g r e g a t i o n s o f f i s h and s e a r c h o v e r l a p ( c o m p e t i t i o n ) was m i n i m i z e d when some s k i p p e r s were w i l l i n g t o l e a v e the group. The s i t u a t i o n was s i m i l a r t o the t e c h n o l o g i c a l r e v o l u t i o n w i t h i n the B r i t i s h Columbia salmon s e i n e f l e e t , b u t the a r e a was much l a r g e r and d i s p e r s i o n a l l o w e d the s k i p p e r s t o f i s h p r e v i o u s l y u n e x p l o i t e d , l a r g e a g g r e g a t i o n s o f t u n a . F r a n c i s (1974) p r e s e n t e d d a t a t h a t s u p p o r t e d the c o n c l u s i o n t h a t the e f f i c i e n c y o f the f l e e t , i n terms o f c a t c h a b i l i t y , i n c r e a s e d w i t h the e x p a n s i o n i n t o o f f s h o r e a r e a s . I n d i v i d u a l v e s s e l s were 135 d o i n g b e t t e r . B o t h the CYRA and B.C. salmon f l e e t s u s e d t e c h n o l o g i c a l i n n o v a t i o n s t o d i s p e r s e t o new a r e a s , b u t B.C. f i s h e r m e n m a i n t a i n t h a t they d i d n o t e n c o u n t e r new, l a r g e a g g r e g a t i o n s o f f i s h . T h e i r b e h a v i o r r e f l e c t e d t h i s p e r c e p t i o n . I n t e r f e r e n c e c o m p e t i t i o n a f f e c t e d t h e B.C. s e i n e f l e e t i n two ways. H i s t o r i c a l l y , the e x p l o i t a t i o n r a t e i n c r e a s e d as i n n o v a t i o n s made open s e t s p o s s i b l e . But, t h e a v e r a g e c a t c h p e r l i n e - u p d e c r e a s e d as f i s h e r m e n e n t e r e d l e s s d e s i r a b l e a r e a s . P a s t s a t u r a t i o n o f e x p l o i t a t i o n r a t e s would have been due t o f l e e t c o n f i n e m e n t w i t h i n a l i m i t e d number o f a c c e s s p o i n t s . A t some t h r e s h o l d p o i n t , d i s p e r s a l was i m p o s s i b l e . F i s h e r i e s s c i e n t i s t s have d i s c u s s e d t h e v a r i o u s mechanisms u n d e r l y i n g p o s s i b l e d e p a r t u r e s o f f i s h and f i s h e r m a n b e h a v i o r from t h e h i s t o r i c a l , "random b e h a v i o r " a s s u m p t i o n s . The p r e v i o u s c h a p t e r s p r o v i d e d many t e s t s o f t h e s e t r a d i t i o n a l a s s u m p t i o n s . A n a l y s i s o f v a r i a n c e and d e s c r i p t i o n s o f queue l e n g t h d i s t r i b u t i o n s i n d i c a t e d t h a t salmon s e i n e s were d i s t r i b u t e d i n a non-random f a s h i o n . L a r g e s c a l e movement p a t t e r n s were d i r e c t i o n a l and t h e l a r g e s t s e t c a t c h e s a p p eared most f r e q u e n t l y d u r i n g f l o o d t i d e s . A n a l y s i s o f l o g b o o k d a t a s u p p o r t e d the h y p o t h e s i s t h a t queue l e n g t h s a r e m easurable r e s p o n s e s t o l o c a l c a t c h r a t e s . A d e t a i l e d i n t e r p r e t a t i o n o f t h e s e r e s u l t s p r o v i d e d the g e n e r a l c o n c l u s i o n t h a t i n f o r m a t i o n q u a l i t y was q u i t e good. The non-random v e s s e l d i s t r i b u t i o n s were a p p a r e n t l y p r o d u c e d by f l e e t r e s p o n s e s t o good i n f o r m a t i o n c o n c e r n i n g t h e d i s t r i b u t i o n o f v u l n e r a b l e salmon and to the r e s u l t i n g i n t e r f e r e n c e c o m p e t i t i o n . A l t h o u g h i n t e r f e r e n c e c o m p e t i t i o n was e v i d e n t , v e s s e l d i s p e r s i o n t o a r e a s c h a r a c t e r i z e d by s m a l l l i n e - u p s c r e a t e d a n e a r l i n e a r r e l a t i o n s h i p between the number o f s e t s made by the f l e e t and the f l e e t s i z e . The o v e r f l i g h t model i l l u s t r a t e d the f a c t t h a t e x p l o i t a t i o n r a t e s c a n n o t be p r e d i c t e d by t h i s n o m i n a l , s e t u n i t o f e f f o r t . P r e d i c t e d e x p l o i t a t i o n 136 s a t u r a t e d as e n t r a n t v e s s e l s moved i n t o l e s s d e s i r a b l e a r e a s ; c a t c h a b i l i t y d e c r e a s e d . A n a l y s i s o f CPUE d i s t r i b u t i o n s i n d i c a t e d t h a t changes i n c a t c h a b i l i t y may be r e f l e c t e d by changes i n the f r e q u e n c y d i s t r i b u t i o n s o f c a t c h p e r b o a t . But, a major p r o b l e m may be e n c o u n t e r e d d u r i n g f u t u r e a n a l y s e s : the v a r i a n c e o f t h e CPUE d i s t r i b u t i o n s c a n f l u c t u a t e i n an u n p r e d i c t a b l e f a s h i o n and i n d e p e n d e n t l y o f f i s h i n g e f f o r t , f i s h abundance o r c a t c h a b i l i t y . I n summary, the f i s h and the f i s h e r m e n d i d n o t e x h i b i t random b e h a v i o r w i t h i n t h e J o h n s t o n e S t r a i t salmon f i s h e r y . The h i s t o r i c a l a ssumptions were r e j e c t e d . An a l t e r n a t i v e e x p l o i t a t i o n model was p r o p o s e d . T h i s model i n c o r p o r a t e d assumptions r e g a r d i n g the non-random b e h a v i o r o f f i s h e r m e n and u t i l i z e d d a t a c o n c e r n i n g t h e d i s t r i b u t i o n o f v e s s e l s . Model pa r a m e t e r e s t i m a t e s i n d i c a t e d t h a t c o m p e t i t i o n and good i n f o r m a t i o n p r o d u c e d s a t u r a t i n g r e s p o n s e s o f e x p l o i t a t i o n r a t e s t o e f f o r t . C a t c h p e r u n i t e f f o r t was n o t p r o p o r t i o n a l t o an i n d e x o f abundance and th e e x p o n e n t i a l f o r m u l a t i o n o f B e v e r t o n and H o l t (1957) w i l l n o t c a p t u r e the v e r y r a p i d s a t u r a t i o n o f e x p l o i t a t i o n r a t e s t o a l e v e l below 90% o f t h e v u l n e r a b l e p o p u l a t i o n o f f i s h . The f i s h i n g power o f f l e e t s s h o u l d be a s s e s s e d by l o o k i n g a t t h e d i s t r i b u t i o n s o f CPUE and the f l e e t . An i m p o r t a n t a s p e c t o f the o v e r f l i g h t model i s t h a t a c c e s s p o i n t s a r e i d e n t i f i e d . A g r i d a n a l y s i s and t h e r e s u l t i n g , r e l a t i v e p a r a m e t e r e s t i m a t e s a r e a v o i d e d . I n t h e CYRA tuna f i s h e r y , t h e a c c e s s p o i n t a p p r o a c h may work w e l l f o r l o g o r p o r p o i s e s e t s . The major p r o b l e m i s i d e n t i f y i n g a c c e s s p o i n t s t h a t have been f i s h e d more t h a n once. Perhaps a t a g g i n g a p proach would work as e a c h s k i p p e r marks the d e b r i s a f t e r s e t t i n g on i t . I n t h e l a r g e s e a r c h f i s h e r i e s f o r tuna and h e r r i n g , the o v e r f l i g h t 137 model may d e s c r i b e the dynamics i n a v e r y s m a l l s u b - a r e a d u r i n g p e r i o d s o f h i g h e f f o r t . I n f o r m a t i o n about f i s h d i s t r i b u t i o n s i n l a r g e s e a r c h a r e a s w i l l be v e r y u n c e r t a i n . I n o t h e r f i s h e r i e s , the o v e r f l i g h t model w i l l not f u l f i l l a d e s c r i p t i v e o r p r e d i c t i v e r o l e . D e v e l o p i n g f i s h e r i e s a t low e f f o r t l e v e l s have n o t a c c u m u l a t e d h i s t o r i c a l i n f o r m a t i o n a b o u t f i s h d i s t r i b u t i o n s . H o l d l i m i t e d f i s h e r i e s w i l l e x h i b i t e x p l o i t a t i o n r a t e s a t u r a t i o n due t o s a t i a t i o n and h a n d l i n g t i m e s . E x p l o i t a t i o n r a t e s a r e p r o b a b l y p r i m a r i l y a f u n c t i o n o f s k i p p e r s ' s k i l l f o r e x p l o i t i n g l o c a l r e g i o n s i n f i s h e r i e s where s p a t i a l c o m p e t i t i o n i s n o t i n t e n s e . LITERATURE CITED Acheson, J . M. 1975. The l o b s t e r f i e f s : economic and e c o l o g i c a l e f f e c t s o f t e r r i t o r i a l i t y i n the Maine l o b s t e r i n d u s t r y . Human E c o l o g y , 3: 183-207. A l l e n , R. 1977. S t a n d a r d i z a t i o n o f y e l l o w f i n p u r s e s e i n e c a t c h r a t e s . 1977 Tuna C o n f e r e n c e (CYRA/IATTC) Lake Arrowhead. A l l e n , R. and R. P u n s l y . 1984. C a t c h r a t e s as i n d i c e s o f abundance o f y e l l o w f i n t u na, Thunnus a l b a c a r e s . i n the E a s t e r n P a c i f i c Ocean. Inter-Am. T r o p . Tuna Comm., B u l l . 18: 77pp. A l v e r s o n , F. G. 1963. 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