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An evaluation of the current minimum legal size limit for the Dungeness crab (Cancer magister Dana) fishery… Smith, Barry Douglas 1988

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AN EVALUATION OF THE CURRENT MINIMUM LEGAL SIZE LIMIT FOR THE DUNGENESS CRAB (Cancer magister DANA) FISHERY NEAR TOFINO, BRITISH COLUMBIA By BARRY DOUGLAS SMITH B . S c , The U n i v e r s i t y of New Brunswick, 1974 M . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We accept t h i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1988 (c) Barry Douglas Smith, 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) ABSTRACT The Dungeness crab (Cancer magi s t e r Dana) t r a p f i s h e r y i n B r i t i s h Columbia has been r e g u l a t e d by a minimum l e g a l s i z e l i m i t of 165 mm s p i n e - t o - s p i n e carapace w i d t h (CW, 154 mm n o t c h - t o -notch CW) s i n c e e a r l y t h i s c e n t u r y . E v a l u a t i o n of the s i z e l i m i t by y i e l d - and e g g s - p e r - r e c r u i t a n a l y s e s has been p r e c l u d e d by a lack of i n f o r m a t i o n on b a s i c p o p u l a t i o n v a r i a b l e s such as growth , m o r t a l i t y , movement and mat ing b e h a v i o r . I n f o r m a t i o n on these v a r i a b l e s was o b t a i n e d i n an i n t e n s i v e two year s tudy of the Dungeness crab f i s h e r y near T o f i n o , B . C . from A p r i l 1985 u n t i l March 1987. A cohort of p r e - r e c r u i t males and females was f o l l o w e d as the males e n t e r e d the f i s h e r y and were s u b s e q u e n t l y e x p l o i t e d , y i e l d i n g i n f o r m a t i o n on moult i n c r e m e n t s - a t - s i z e , l e n g t h of i n t e r m o u l t p e r i o d s , s i z e - a t - m a t u r i t y , s i z e of mat ing p a i r s , m o r t a l i t y , movement, commercial f i s h i n g succes s and e x p l o i t a t i o n r a t e s . Male C .magi s t e r e n t e r e d the f i s h e r y d u r i n g t h e i r f o u r t h year a f t e r s e t t l e m e n t . S i z e f requency a n a l y s i s r e v e a l e d tha t n e a r l y a l l l e g a l - s i z e d (>154 mm n o t c h - t o - n o t c h CW) males are w i t h i n the 155.0+11.2 mm i n s t a r (*50% of t h i s i n s t a r ) . S u b l e g a l - s i z e d males i n t h i s i n s t a r have a h i g h a n n u a l n a t u r a l m o r t a l i t y r a t e ( M = 2 . 8 - 4 . 5 ) , hence a low p r o b a b i l i t y (<10%) of s u r v i v i n g to l e g a l s i z e . L e g a l - s i z e d males have a h i g h annual f i s h i n g m o r t a l i t y r a t e ( F = 5 . 1 - 6 . 9 ) . C o n s e q u e n t l y , a smal l component of the commercial c a t c h i s composed of males i n l a r g e r i n s t a r s . Page i i D e s p i t e females not b e i n g l a n d e d , the n e g a t i v e s lope of female c a t c h curves from four r e g i o n a l f i s h e r i e s was s t eepes t for the most h e a v i l y f i s h e d r e g i o n and sha l lowes t for the most l i g h t l y f i s h e d r e g i o n . Females mate a f t e r m o u l t i n g w h i l e accompanied by a l a r g e r male , and i n a h e a v i l y f i s h e d p o p u l a t i o n l a r g e r males may be absent . T h u s , the c a t c h curves suggested the p o s s i b i l i t y of reduced mat ing and m o u l t i n g , and c o n s e q u e n t l y fewer l a r g e f emales , i n h e a v i l y f i s h e d p o p u l a t i o n s . Y i e l d - p e r - r e c r u i t a n a l y s i s suggests l a n d i n g s might be markedly improved by l o w e r i n g the minimum l e g a l s i z e l i m i t . However, e g g s - p e r - r e c r u i t a n a l y s i s , which modeled the p o s s i b l e consequences of removing l a r g e male s , suggests tha t for a h e a v i l y f i s h e d p o p u l a t i o n the c u r r e n t s i z e l i m i t may r e s u l t i n up to a 50% d e c l i n e i n p o p u l a t i o n egg p r o d u c t i o n r e l a t i v e to an u n f i s h e d p o p u l a t i o n . The h i s t o r i c a l p r e s u m p t i o n that the c u r r e n t minimum l e g a l s i z e l i m i t for males does not impact on p o p u l a t i o n egg p r o d u c t i o n s h o u l d be r e c o n s i d e r e d . To f a c i l i t a t e c a l i b r a t i o n of t r a p samples b i a s e d by d i f f e r e n c e s i n soak t i m e s , parameters for models d e s c r i b i n g changes i n b a i t e f f e c t i v e n e s s over t i m e , and a g o n i s t i c i n t e r a c t i o n s between crabs w i t h i n a t r a p and those a t t e m p t i n g to enter tha t t r a p , were e s t i m a t e d . Parameter e s t imates were o b t a i n e d by s i m u l a t i n g the e n t r y and e x i t of crabs i n t o and out of t r a p s based on experiments which (1) emphasized the above two p r o c e s s e s , and (2) e s t imated the d a i l y p r o b a b i l i t i e s of crabs of d i f f e r e n t s i z e s e scap ing t r a p s . Page i i i Table of Contents A b s t r a c t i i L i s t of T a b l e s v i L i s t of F i g u r e s ix Acknowledgments xv 1 INTRODUCTION 1 2 DESCRIPTION OF STUDY AREAS 6 3 FIELD METHODS 13 3.1 MORPHOMETRICS 13 3.2 BEAM TRAWL SAMPLING 15 3 .3 TRAP SAMPLING 16 3.4 FEMALE SIZE-AT-MATURITY 16 3 .5 MATING PAIRS 17 3.6 TRAP DISTRIBUTION 17 3 .7 TRAP PERFORMANCE EXPERIMENTS 18 3 .7 .1 TRAP TYPES 20 3 .7 .2 CATCH RATES OF TRAPS IN GRIDS - 21 3 .7 .3 ESCAPE OF CRABS FROM TRAPS 21 3 .7 .4 SOAK TIME EXPERIMENT 22 3 . 7 . 5 BAIT-EFFECTIVENESS EXPERIMENT 23 3.8 MARK-RECOVERY PROGRAM 2 4 4 RESULTS 2 7 4.1 SPECIES COLLECTED 27 4.2 MORPHOMETRICS 27 4.3 FEMALE SIZE-AT-MATURITY 28 4.4 MATING PAIRS 30 4.5 MOULT INCREMENTS 3 2 Page i v 4 .6 GROWTH 3 6 4.7 TRAP PERFORMANCE EXPERIMENTS 43 4 .7 .1 CATCH RATES OF TRAPS IN GRIDS 43 4 .7 .2 ESCAPE OF CRABS FROM TRAPS 44 4 . 7 . 3 SOAK TIME AND BAIT EFFECTS 50 4.8 TRAP DISTRIBUTION 68 4.9 COMMERCIAL EXPLOITATION OF MALES 70 4.10 MALE MATING ACTIVITY 78 4.11 SPATIAL AND TEMPORAL DISTRIBUTIONS 84 4.12 TAG RETENTION AND TAG INDUCED MORTALITY 95 4.13 FISHING AND NATURAL MORTALITY OF MALES 96 4.14 FISHING INTENSITY AND FEMALE CATCH CURVES IN SELECTED FISHERIES .107 5 Y I E L D - AND EGGS - PER-RECRUIT MODEL I l l 5.1 DEVELOPMENT I l l 5.2 RESULTS 117 6 DISCUSSION 123 6.1 TRAP PERFORMANCE EXPERIMENTS 123 6.2 SPATIAL AND TEMPORAL DISTRIBUTIONS 128 6.3 GROWTH AND MORTALITY 131 6.4 Y I E L D - AND EGGS-PER-RECRUIT 137 6.5 SUMMARY 148 7 LITERATURE CITED 153 Page v L i s t of Tables T a b l e 4 . 5 . 1 . L i n e a r r e g r e s s i o n models for male C . m a g i s t e r moult i n c r e m e n t s - a t - s i z e for four da ta sets c o l l e c t e d from B r i t i s h Columbia ( B . C . ) and C a l i f o r n i a ( C a l . ) . 33 Tab le 4 . 5 . 2 . L i n e a r r e g r e s s i o n models for female C . magi s t e r moult i n c r e m e n t s - a t - s i z e for three data se t s c o l l e c t e d from B r i t i s h C o l u m b i a ( B . C . ) and C a l i f o r n i a ( C a l . ) . 33 T a b l e 4 . 6 . 1 . Mean and s t a n d a r d d e v i a t i o n s (SD, sd) f o r carapace widths d e f i n i n g i n s t a r s of male C . magis ter >80 mm CW. 40 Tab le 4 . 6 . 2 . Mean and s t a n d a r d d e v i a t i o n s (SD, sd) f o r carapace widths d e f i n i n g i n s t a r s of female C . mag i s t er >80 mm CW. 40 Tab le 4 . 6 . 3 . The r e l a t i v e p r o p o r t i o n s of male C . magi s t e r >80 mm CW w i t h i n c o n s e c u t i v e i n s t a r s for a t ime s e r i e s of beam t r a w l samples . The va lue for each date i n c l u d e s a l l males c a p t u r e d w i t h i n two weeks of tha t d a t e . The dominant i n s t a r i s h i g h l i g h t e d by an a s t e r i s k . 41 Tab le 4 . 6 . 4 . The r e l a t i v e p r o p o r t i o n s of female C . mag i s t er >80 mm CW w i t h i n c o n s e c u t i v e i n s t a r s for a t ime s e r i e s of beam t r a w l samples . The va lue for each date i n c l u d e s a l l females c a p t u r e d w i t h i n two weeks of t h a t d a t e . The dominant i n s t a r i s h i g h l i g h t e d by an a s t e r i s k . 42 Tab le 4 . 7 . 1 . 1 . Comparison of the mean number of C . mag i s t er caught per t r a p for 16 p e r i m e t e r versus n ine i n t e r i o r t r a p s i n two 5 by 5 g r i d s , and between a l l t r a p s i n each g r i d . 43 T a b l e 4 . 7 . 2 . 1 . The r e l a t i v e r e t e n t i o n of crabs <155 mm CW, for Traps C - D , and crabs <145 mm CW, for T r a p B, r e l a t i v e to T r a p A . The r e l a t i v e r e t e n t i o n for a t r a p type i s the number o f crabs caught by tha t t r a p type d i v i d e d by the number caught by T r a p A a f t e r e q u i v a l e n t one day soaks . For T r a p A n = 536 for crabs <155 mm CW, and n = 322 for crabs <145 mm CW. 47 T a b l e 4 . 7 . 2 . 2 . The p r o b a b i l i t i e s of male C . magi s t e r b e i n g r e t a i n e d by Traps A - D for 24 h . 47 Page v i T a b l e 4 . 7 . 3 . 1 . Comparison of d i f f e r e n t models e x p l a i n i n g d e n s i t i e s and s i z e f r e q u e n c y d i s t r i b u t i o n s of C . mag i s t er i n sets of t r a p s which e x p e r i e n c e d d i f f e r e n t soak t imes and b a i t ages d u r i n g e q u i v a l e n t exper iments i n 1985 and 1986. The o b j e c t i v e f u n c t i o n (A) i s the s e p a r a t i o n s t a t i s t i c of Schnute and F o u r n i e r (1980) . P i s the number of parameters i n the model . AIC (see t e x t ) measures model p e r f o r m a n c e , the lower the va lue the more s u i t a b l e the mode l . 57 Tab le 4 . 1 0 . 1 . The p e r c e n t of male C . magi s t e r , tagged when s o f t - s h e l l e d , which were h a r d - s h e l l e d when r e c o v e r e d . The r e s u l t s are r e p o r t e d f o r 30 day i n t e r v a l s of t i m e - a t - l a r g e . The carapace widths of r e c o v e r e d males were a p p r o x i m a t e l y n o r m a l l y d i s t r i b u t e d ( 1 5 3 . 4 ± 6 . 0 mm) and ranged from 135-173 mm. 80 Tab le 4 . 1 1 . 1 . Abundance of female C . magi s t e r >145 mm CW i n commercial t r a p s i n May and June of 1985 and 1986 . 88 Tab le 4 . 1 1 . 2 . D e n s i t i e s of two to three year o l d (*75-145 mm CW) C . magis ter from beam t r a w l samples near I n d i a n I s l a n d . 88 Tab le 4 . 1 1 . 3 . Summary of tag r e c o v e r i e s , by l o c a t i o n , of s u b l e g a l - and l e g a l - s i z e d male C . magis ter between A p r i l 1985 and August 1986. The number of t r a p h a u l s was determined by i n t e r v i e w i n g f i s h e r m e n . Only r e c o r d s from f ishermen whose e f f o r t was known are r e p o r t e d . Except where noted , r e c o v e r i e s were from w i t h i n the study a r e a as d e f i n e d i n F i g . 2.1 (page 9 ) . .89 T a b l e 4 . 1 1 . 4 . Summary of t a g r e c o v e r i e s , by l o c a t i o n , of female C . magi s t e r between A p r i l 1985 and August 1986. The number of t r a p h a u l s was d e t e r m i n e d by i n t e r v i e w i n g f i s h e r m e n . Only r e c o r d s from f i s h e r m e n whose e f f o r t was known are r e p o r t e d . A l l r e c o v e r i e s were from w i t h i n the s tudy a r e a as d e f i n e d i n F i g . 2.1 (page 9 ) . 90 Tab le 4 . 1 3 . 1 . S t a t i s t i c s of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13.1 from which the annual ins tantaneous r a t e of d i sappearance of s u b l e g a l - s i z e d (145-155 mm CW) male C . magi s t e r was e s t i m a t e d . The r e l a t i o n s h i p has the form Y = a+b-X; where Y i s the l o g a r i t h m of the number of r e c o v e r i e s w i t h i n c o n s e c u t i v e one month i n t e r v a l s , and X i s the t i m e - a t - l a r g e i n d a y s . 97 Page v i i T a b l e 4 . 1 3 . 2 . S t a t i s t i c s of the q u a d r a t i c r e l a t i o n s h i p i n F i g . 4 .13 .1 which suggests the m o r t a l i t y r a t e may i n c r e a s e as the t i m e - a t - l a r g e for s u b l e g a l - s i z e d (145-155 mm CW) male C . magi s t e r i n c r e a s e s . The r e l a t i o n s h i p has the form Y = a + b - X + c - X 2 ; where Y i s the l o g a r i t h m of the number of r e c o v e r i e s w i t h i n c o n s e c u t i v e one month i n t e r v a l s , and X i s the t i m e - a t - l a r g e i n d a y s . 97 T a b l e 4 . 1 3 . 3 . S t a t i s t i c s of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13 .2 from which the annual ins tantaneous r a t e of d i s a p p e a r a n c e (Z) of l e g a l - s i z e d male C . magi s t e r was e s t i m a t e d . The r e l a t i o n s h i p has the form Y = a+b-X; where Y i s the l o g a r i t h m of the number of r e c o v e r i e s w i t h i n c o n s e c u t i v e 15 day i n t e r v a l s , and X i s the t i m e - a t - l a r g e i n days . 98 T a b l e 4 . 1 3 . 4 . S t a t i s t i c s of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13 .4 e s t i m a t i n g the mean t i m e - a t - l a r g e for r e c o v e r e d tagged s u b l e g a l - s i z e d male C . magi s t e r . The r e l a t i o n s h i p has the form Y = a+b-X; where Y i s the time to r e c o v e r y ( i n d a y s ) , and X i s the p r e - m o u l t carapace w i d t h . 99 T a b l e 4 . 1 3 . 5 . Summary of s u r v i v o r s h i p to l e g a l s i z e of male C . m a g i s t e r which were tagged when s u b l e g a l s i z e , and r e c o v e r e d when l e g a l s i z e , for 5 mm i n t e r v a l s from 125-155 mm CW. 102 T a b l e 4 . 1 4 . 1 . Comparisons among d i f f e r e n t measures of f i s h i n g e f f o r t , and f i s h i n g i m p a c t , on male* C . mag i s t er p o p u l a t i o n s i n four r e g i o n a l f i s h e r i e s d e f i n e d by S t a t i s t i c a l Area ( S A ) . The s t a t i s t i c a l areas do not d i f f e r markedly i n a r e a . Annual s t a t i s t i c s i n c l u d e the m e t r i c tonnes landed ( t ) and the number of days f i s h i n g ( D F ) . 109 T a b l e 5 . 1 . 1 . The mean and s t a n d a r d d e v i a t i o n (mm) of n o r m a l l y d i s t r i b u t e d male and female C . mag i s t er i n s t a r s for the age and t ime of year when they are n e a r l y f u l l y formed. Males become s e x u a l l y a c t i v e i n the 155.0 mm i n s t a r . 112 Page v i i i L i s t of Figures F i g u r e 2 . 1 . Map of the main s tudy a r e a near T o f i n o , B r i t i s h C o l u m b i a . The s t i p p l e d areas are i n t e r t i d a l m u d f l a t s . The dashed l i n e s d e l i m i t the main s tudy a r e a . S e l e c t e d s i t e s are r e f e r e n c e d by c a p i t a l l e t t e r s . The arrow i n d i c a t e s the main channel out to sea . I n s e r t I l o c a t e s the Dixon E n t r a n c e f i s h e r y ( a ) . I n s e r t II l o c a t e s the main s tudy a r e a , the H o l b e r g I n l e t f i s h e r y ( a ) , and the F r a s e r d e l t a f i s h e r y ( b ) . 9 F i g u r e 2 . 2 . Time s e r i e s of the annual tonnage of C . magi s t e r l anded i n the S t a t i s t i c a l Area 1, 24 and 29 f i s h e r i e s . 10 F i g u r e 2 . 3 . Time s e r i e s of the annual number of days f i s h i n g for C . magi s t e r i n the S t a t i s t i c a l Area 1, 24 and 29 f i s h e r i e s . 11 F i g u r e 2 . 4 . Time s e r i e s of the annual number of v e s s e l s which r e p o r t e d l a n d i n g s of C . m a g i s t e r from the S t a t i s t i c a l Area 24 f i s h e r y near T o f i n o , B . C . 12 F i g u r e 3 . 7 . 1 . Layout of t r a p g r i d s d e s i g n e d to emphasize the e f f e c t s of d i f f e r e n t soak t imes ( A ) , changes i n b a i t e f f e c t i v e n e s s ( B ) , and t r a p s e l e c t i v i t y ( C ) , on the d e n s i t y and s i z e f requency d i s t r i b u t i o n of C . magi s t e r . For (A) and (B) soak t ime ( i n days ) i s e n c i r c l e d , for (C) t r a p type i s e n c i r c l e d . 19 F i g u r e 4 . 3 . 1 . The p e r c e n t of female C . mag i s t er inseminated as a f u n c t i o n of carapace w i d t h . 29 F i g u r e 4 . 4 . 1 . Carapace widths of C . magi s t e r mat ing p a i r s . The l i n e s ( E q n s . 4 .4 .1 and 2) d e f i n e the apparent l i m i t s i n carapace w id ths r e q u i r e d for a mat ing embrace. C i r c l e s r e p r e s e n t da ta from B u t l e r (unpub. d a t a ) , squares r e p r e s e n t d a t a from t h i s s t u d y . 31 F i g u r e 4 . 5 . 1 . Male C . magi s t e r moult increments as a f u n c t i o n of p r e - m o u l t carapace w i d t h . The p l o t uses d a t a from B r i t i s h Co lumbia and C a l i f o r n i a . Data from t h i s study are r e p r e s e n t e d by s q u a r e s . 34 Page ix F i g u r e 4 . 5 . 2 . Female C . magi s t e r moult increments as a f u n c t i o n of p r e - m o u l t carapace w i d t h . The p l o t uses d a t a from B r i t i s h Columbia and C a l i f o r n i a . Data from t h i s s tudy are r e p r e s e n t e d by s q u a r e s . 35 F i g u r e 4 . 6 . 1 . S i z e f requency d i s t r i b u t i o n s for a l l male and female C . magi s t e r c o l l e c t e d i n beam t r a w l samples from June 1985 u n t i l September 1986. 37 F i g u r e 4 . 7 . 2 . 1 . The p e r c e n t of male C . magi s t e r r e t a i n e d by Trap A for 24 h , as a f u n c t i o n of carapace w i d t h . 48 F i g u r e 4 . 7 . 2 . 2 . S i z e f requency d i s t r i b u t i o n s of C . mag i s ter caught i n Traps A - D . Female carapace w id ths are expressed as m a l e - e q u i v a l e n t carapace widths for the same body l e n g t h s . 49 F i g u r e 4 . 7 . 3 . 1 . Comparison of s i z e frequency d i s t r i b u t i o n s of C . magi s t e r i n t r a p s soaked 24 h i n the soak t ime (ST, 20 t r a p s ) and b a i t e f f e c t i v e n e s s ( B E , 16 t r a p s ) exper iments i n 1985 and 1986. Female carapace widths are e x p r e s s e d as m a l e - e q u i v a l e n t carapace widths for the same body l e n g t h s . 61 F i g u r e 4 . 7 . 3 . 2 . S i z e f requency d i s t r i b u t i o n s of C . m a g i s t e r for se ts of 20 type A t r a p s w i t h d i f f e r e n t soak t imes from e q u i v a l e n t exper iments i n 1985 and 1986. S o l i d c i r c l e s p r o f i l e p r e d i c t e d s i z e frequency d i s t r i b u t i o n s u s i n g Model '4 ' ( T a b l e 4 . 7 . 3 . 1 ) . Female carapace w id ths are expressed as m a l e - e q u i v a l e n t carapace widths for the same body l e n g t h s . 62 F i g u r e 4 . 7 . 3 . 3 . The r e l a t i v e r a t e at which C . magi s t e r enter Trap A , as a f u n c t i o n of the r a t i o between the weight of crabs i n a t r a p , and the weight of the c r a b a t t e m p t i n g to enter the t r a p . T h i s p l o t uses the best parameter e s t imates for E q n . 4 . 7 . 3 . 3 from Model '4 ' ( T a b l e 4 . 7 . 3 . 1 ) . 63 F i g u r e 4 . 7 . 3 . 4 . The r e l a t i v e e n t r y r a t e of C . magi s t e r i n t o Trap A as a f u n c t i o n of b a i t age . T h i s p l o t uses the best parameter e s t imates for Eqn . 4 . 7 . 3 . 5 from Model '4 ' (Table 4 . 7 . 3 . 1 ) . 64 Page x F i g u r e 4 . 7 . 3 . 5 . Response s u r f a c e of the p r e d i c t e d changes i n the s i z e f requency d i s t r i b u t i o n of C . magi s t e r w i t h i n 20 type A t r a p s , as a f u n c t i o n of t i m e . These r e s u l t s use the best parameter e s t imates for Eqns . 4 . 7 . 3 . 3 and 5 from Model '4 ' (Tab le 4 . 7 . 3 . 1 ) . Female carapace widths are expressed as m a l e - e q u i v a l e n t carapace w id ths for the same body l e n g t h s . 65 F i g u r e 4 . 7 . 3 . 6 . Response s u r f a c e of the p r e d i c t e d s i z e f requency d i s t r i b u t i o n s of C . magi s t e r w i t h i n 10 se t s of 16 type A t r a p s . Each set used b a i t r a n g i n g i n age from zero to e i g h t days , soaked for one day . The b a i t was removed for the n i n t h day . The v e r t i c a l l i n e s show the observed da ta for a p a r t i c u l a r combinat ion of b a i t age and carapace w i d t h , for d i f f e r e n c e s g r e a t e r than one . These r e s u l t s use the best parameter e s t imates for E q n s . 4 . 7 . 3 . 3 and 5 from Model '4 ' ( T a b l e 4 . 7 . 3 . 1 ) . Female carapace widths are expres sed as male - e q u i v a l e n t carapace w i d t h s for the same body l e n g t h s . 66 F i g u r e 4 . 7 . 3 . 7 . The percent of s o f t - s h e l l e d l e g a l - s i z e d male C . magi s t e r i n Trap A , as a f u n c t i o n of soak t i m e . These r e s u l t s were o b t a i n e d from the soak t ime experiment per formed near Ind ian I s l a n d (H; F i g . 2 . 1 , page 9) i n 1986. Above the S . D . bars i s the number of l e g a l - s i z e d males caught i n 20 t r a p s . 67 F i g u r e 4 . 8 . 1 . (A) Time s e r i e s comparison of the number of t r a p buoys counted i n Lemmens I n l e t , and the number of t r a p s e s t i m a t e d by i n t e r v i e w i n g f i s h e r m e n . (B) Time s e r i e s of the number of t r a p s e s t i m a t e d by i n t e r v i e w i n g f i s h e r m e n . The ' E l s e w h e r e ' ca tegory i n c l u d e s t r a p s f i s h e d o u t s i d e the s tudy a r e a i n S t a t i s t i c a l Area 24 by f i shermen who a l s o f i s h i n the s tudy a r e a . The c a p i t a l l e t t e r s i n p a r e n t h e s e s i d e n t i f y these areas i n F i g . 2.1 (page 9 ) . 69 F i g u r e 4 . 9 . 1 . Diagram e x p l a i n i n g how the degree of e x p l o i t a t i o n of male C . magi s t e r i n the 155.0111.2 mm i n s t a r was e s t i m a t e d . The p r o p o r t i o n e x p l o i t e d (A-s-[A + B]) was de termined by s i z e f r e q u e n c y a n a l y s i s . 73 F i g u r e 4 . 9 . 2 . The percent of l e g a l - s i z e d male C . mag i s t er removed from the 155.0 mm i n s t a r by f i s h i n g , as de termined by s i z e frequency a n a l y s i s of t r a p samples . The e n c i r c l e d data p o i n t s are for upper Lemmens I n l e t . The remainder are for the r e s t of the s tudy a r e a . 74 Page x i F i g u r e 4 . 9 . 3 . L i n e a r r e g r e s s i o n of v i r t u a l e n t r y r a t e s of male C . magi s t e r 145-155 mm CW i n t o t r a p s over t i m e . Data from upper Lemmens I n l e t , a poor c r a b h a b i t a t , are not i n c l u d e d i n t h i s p l o t . 75 F i g u r e 4 . 9 . 4 . Time s e r i e s of commercial c a t c h r a t e s of l e g a l - s i z e d male C . m a g i s t e r . The c a p i t a l l e t t e r s i n parentheses i d e n t i f y these areas i n F i g . 2.1 (page 9 ) . 76 F i g u r e 4 . 9 . 5 . V i r t u a l e n t r y r a t e s of l e g a l - s i z e d male C . magi s t e r i n t o t r a p s over t i m e . Data from upper Lemmens I n l e t , a poor c r a b h a b i t a t , are not i n c l u d e d i n t h i s p l o t . 77 F i g u r e 4 . 1 0 . 1 . The p e r c e n t of male C . magi s t e r w i t h mat ing marks ( B u t l e r 1960) as a f u n c t i o n of carapace w i d t h . The minimum l e g a l s i z e l i m i t i s « 1 5 4 mm CW. 81 F i g u r e 4 . 1 0 . 2 . Time s e r i e s of the percent of h a r d - s h e l l e d l e g a l - s i z e d (>154 mm CW) male , l e g a l - s i z e d male w i t h mating marks ( B u t l e r 1960) , and s u b l e g a l - s i z e d (140-154 mm CW) male C . magi s t e r w i t h mat ing marks . Except where n o t e d , a l l sample s i z e s are >100 c r a b s . 82 F i g u r e 4 . 1 0 . 3 . Time s e r i e s i n d i c a t i n g that the r e l a t i v e l e v e l of mat ing a c t i v i t y by l e g a l - s i z e d male C . magi s t e r i n 1986 was »29% of the l e v e l i n 1985. The s u b l e g a l : l e g a l mat ing r a t i o i s o b t a i n e d by d i v i d i n g the p e r c e n t of l e g a l - s i z e d males w i t h mat ing marks by the p e r c e n t of s u b l e g a l - s i z e d males w i t h mat ing marks . The r a t i o for May 1986 was e x c l u d e d from the comparison for reasons g i v e n i n the t e x t . 83 F i g u r e 4 . 1 1 . 1 . Time s e r i e s of d e n s i t i e s for one year o l d ( « 4 0 - 7 5 mm CW) male and female C . magi s t e r i n the entrance to Lemmens I n l e t ( A ) , and on the sha l low sand bottom of an exposed shore ( B ) . Time s e r i e s of d e n s i t i e s of two to three year o l d ( « = 7 5 - 1 4 5 mm CW) male and female C . m a g i s t e r i n the main channel out to sea ( C ) . The c a p i t a l l e t t e r s i n parentheses i d e n t i f y these areas i n F i g . 2.1 (page 9 ) . 91 F i g u r e 4 . 1 1 . 2 . Time s e r i e s of d e n s i t i e s for two to t h r e e year o l d (*75-145 mm CW) male and female C . m a g i s t e r i n Lemmens I n l e t . The c a p i t a l l e t t e r s i n parenthese s i d e n t i f y these areas i n F i g . 2.1 (page 9 ) . 92 Page x i i F i g u r e 4 . 1 1 . 3 . Time s e r i e s comparison of two i n d i c e s of abundance for female C . magi s t e r ( >145 mm CW) i n the study-a r e a , but e x c l u d i n g Lemmens I n l e t , Browning Passage , and near Ind ian I s l a n d , where female d e n s i t i e s were g e n e r a l l y low ( T a b l e 4 . 1 1 . 1 ) . ' V i r t u a l e n t r y r a t e s ' were e s t i m a t e d as i n S e c t i o n 4 . 9 . 93 F i g u r e 4 . 1 1 . 4 . Frequency d i s t r i b u t i o n s of mean d a i l y movement r a t e s for male and female C . m a g i s t e r . Crabs were r e c o v e r e d a f t e r a mean of » 1 5 0 d a y s - a t - l a r g e . 94 F i g u r e 4 . 1 3 . 1 . L i n e a r and q u a d r a t i c r e g r e s s i o n s of r e c o v e r i e s over t ime for tagged male C . magi s t e r r e l e a s e d and r e c o v e r e d as s u b l e g a l - s i z e d crabs 145-155 mm CW. Most t a g g i n g was done from M a y - J u l y 1985. The open c i r c l e s were not i n c l u d e d i n the r e g r e s s i o n a n a l y s e s because f i shermen were not w e l l p r e p a r e d for the m a r k - r e c o v e r y program at t h i s t i m e . 103 F i g u r e 4 . 1 3 . 2 . L i n e a r r e g r e s s i o n of r e c o v e r i e s over t ime for 341 tagged male C . magi s t e r r e l e a s e d and r e c o v e r e d as l e g a l - s i z e d c r a b s , m o s t l y i n s p r i n g 1986. 104 F i g u r e 4 . 1 3 . 3 . (A) Frequency d i s t r i b u t i o n of r e l e a s e dates of s u b l e g a l - s i z e d male C . m a g i s t e r . (B) Frequency d i s t r i b u t i o n of r e c o v e r y dates f o r those crabs r e l e a s e d i n (A) and r e c o v e r e d as l e g a l - s i z e d c r a b s . 105 F i g u r e 4 . 1 3 . 4 . L i n e a r r e g r e s s i o n of t i m e - a t - l a r g e for male C . m a g i s t e r . tagged and r e l e a s e d when s u b l e g a l s i z e and r e c o v e r e d when l e g a l s i z e , on p r e - m o u l t carapace w i d t h . 106 F i g u r e 4 . 1 4 . 1 . Comparison of c a t c h curves ( R i c k e r 1975) for females from four r e g i o n a l C . magi s t e r f i s h e r i e s d e f i n e d by S t a t i s t i c a l Area i n B r i t i s h C o l u m b i a . 110 F i g u r e 5 . 2 . 1 . R e l a t i v e egg p r o d u c t i o n by C . magis ter p o p u l a t i o n s as a f u n c t i o n of the F : M mat ing r a t i o , and for t h r e e e s t i m a t e s of M. These r e s u l t s are not n o t i c e a b l y s e n s i t i v e to the annual r a t e of decrease i n egg p r o d u c t i o n by females who f a i l to mate and moult i n p r e v i o u s y e a r s . 120 F i g u r e 5 . 2 . 2 , Y i e l d - p e r - r e c r u i t (YPR) for i n c r e a s i n g f i s h i n g m o r t a l i t y ( F ) . The r e s u l t s a r e r e p o r t e d r e l a t i v e to F=<». 121 Page x i i i F i g u r e 5 . 2 . 3 . Y i e l d - p e r - r e c r u i t i s r e p o r t e d r e l a t i v e to 1.0 at 165 mm CW ( S - S ) . E g g s - p e r - r e c r u i t are r e p o r t e d r e l a t i v e to an u n f i s h e d p o p u l a t i o n . The b r e a d t h of the r e l a t i o n s h i p s i n d i c a t e the range when the annual decrease i n egg p r o d u c t i o n by females t h a t d i d not mate and moult i n p r e v i o u s years i s v a r i e d from 0 . 0 - 1 . 0 t imes the egg p r o d u c t i o n of the p r e v i o u s y e a r . Both n o t c h - t o - n o t c h (N-N) and s p i n e - t o - sp ine ( S - S ) carapace w i d t h s , and the c u r r e n t Canadian (C) and American (A) l e g a l s i z e s , are n o t e d . 122 Page x i v ACKNOWLEDGMENTS T h i s s tudy b e n e f i t e d from the i n i t i a t i v e , s u p e r v i s i o n and support of D r . Glen S, J a m i e s o n , Department of F i s h e r i e s and Oceans , P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo, B r i t i s h C o l u m b i a . I extend my thanks to him f o r p r o v i d i n g t h i s o p p o r t u n i t y and for e n s u r i n g t h a t the work proceeded w i t h minimum u n c e r t a i n t y and p u r s u i t of dead ends, and few missed o p p o r t u n i t i e s . My r e s e a r c h committee , headed by D r . C . C . L i n d s e y of the Department of Z o o l o g y , U n i v e r s i t y of B r i t i s h C o l u m b i a , p r o v i d e d encouragement d u r i n g t h i s s t u d y , and I thank them. The s k i l l and wisdom of the t e c h n i c a l s t a f f at the P a c i f i c B i o l o g i c a l S t a t i o n ensured a p r o d u c t i v e , e f f e c t i v e and e n j o y a b l e f i e l d program. I e s p e c i a l l y thank M e s s r s . Wolfgang C a r o l s f e l d , Wayne H a r l i n g , Dwight H e r i t a g e , Antan P h i l l i p s and t h e i r s tudent a s s i s t a n t s for a s s u r i n g e f f i c i e n t , and above a l l , safe f i e l d work. I admire and envy t h e i r s k i l l s . My g r e a t e s t a p p r e c i a t i o n i s f or the p a r t i c i p a t i o n of the f i s h e r m e n , which was e s s e n t i a l f o r for s u c c e s s f u l c o m p l e t i o n of t h i s work. In p a r t i c u l a r , M e s s r s . Danny B a r r , Ken B a r r , Joe B a r t o n , John F r a s e r , B a r r y Grumbach, Jamie Sloman and Peter White i n v i t e d me -to; sample t h e i r c a t c h on b o a r d t h e i r v e s s e l s from time t o t i m e . M e s s r s . Danny B a r r , Ken B a r r , John F r a s e r , B a r r y Grumbach and L e i g h H i l b e r t not o n l y r e t a i n e d tags from l e g a l - s i z e d crabs which they caught , but r e c o r d e d a l l encounters of tagged c r a b s . M e s s r s . Mike D a n i e l s , A l e x E r i c k s o n , Page xv John F r a s e r , B a r r y Grumbach, Dave R a e - A r t h u r , Jamie Sloman, Ralph T i e l m a n and L e i g h H i l b e r t p r o v i d e d p r e c i s e p o s t - m o u l t measurements of tagged c r a b s , or r e t a i n e d l e g a l - s i z e d crabs so I c o u l d measure them l a t e r . Many other f i shermen r e t u r n e d tags or r e t a i n e d them for c o l l e c t i o n l a t e r . M r . Andre T u r p i n of T r i - S t a r Seafood S u p p l y L i m i t e d , V a n c o u v e r , B . C . c o l l e c t e d and r e t u r n e d tags from crabs purchased by h i s employer . I thank M r . Doug S w i f t , Department of F i s h e r i e s and Oceans , T o f i n o , B . C . for p r o v i d i n g s torage space for r e s e a r c h equipment and f o r h e l p i n g w i t h t h i s work i n other ways. I am v e r y g r a t e f u l to M r . T e r r y H . B u t l e r for p e r m i t t i n g me to use u n p u b l i s h e d data he c o l l e c t e d i n Dixon E n t r a n c e d u r i n g the 1950's . D u r i n g t h i s s tudy I was s u p p o r t e d by a graduate s c h o l a r s h i p from the C a n a d i a n Department of F i s h e r i e s and Oceans . A l l d a t a are t h e i r p r o p e r t y and are m a i n t a i n e d at the P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo, B r i t i s h C o l u m b i a . Page x v i 1 INTRODUCTION The Dungeness c r a b (Cancer magi s t er Dana) i s f i s h e d c o m m e r c i a l l y from A l a s k a to c e n t r a l C a l i f o r n i a a lon g the P a c i f i c coast of Nor th A m e r i c a . In American waters o n l y males g r e a t e r than 171 mm (6.75 i n ) carapace w i d t h (CW), measured from t i p to t i p of the t e n t h a n t e r o l a t e r a l s p i n e s , can be r e t a i n e d l e g a l l y . In B r i t i s h C o l u m b i a , the minimum l e g a l s i z e l i m i t i s 165 mm CW. Both males and females can be r e t a i n e d , but i n p r a c t i c e females are r a r e l y r e t a i n e d because (1) few reaclv l e g a l s i z e , (2) f i shermen b e l i e v e i t i s poor c o n s e r v a t i o n p o l i c y , and (3) the market i s f a m i l i a r o n l y w i t h m a l e s . The Dungeness crab f i s h e r y i s one of the most v a l u a b l e i n v e r t e b r a t e f i s h e r i e s i n B r i t i s h Columbia ($5.15 m i l l i o n landed value i n 1986) yet there has been l i t t l e r e s e a r c h a t t e n t i o n s i n c e the 1950's , p a r t l y because C . mag i s t er r e p r e s e n t s o n l y 1% of the landed value of sea p r o d u c t s i n B r i t i s h Columbia (Jamieson 1985) . A d d i t i o n a l l y , B r i t i s h C o l u m b i a C . magi s t e r f i s h e r i e s have had few p e r c e i v e d problems r e q u i r i n g s c i e n t i f i c i n t e r v e n t i o n , due i n p a r t to an «40% annual t u r n o v e r of f i shermen , and no core group of f i shermen to lobby for a t t e n t i o n (Jamieson 1985, 1986) . With the e x c e p t i o n o f a p r e c i p i t o u s , and as yet u n e x p l a i n e d , d e c l i n e i n C . mag i s t er l a n d i n g s a lon g the east coas t o f the Queen C h a r l o t t e I s l ands about 1970 (Jamieson 1985, 1986) , t h e r e appear to be no o u t s t a n d i n g t r e n d s or p a t t e r n s i n the l a n d i n g s t a t i s t i c s for major r e g i o n a l f i s h e r i e s i n B r i t i s h C o l u m b i a . In c o n t r a s t , S e c t i o n 1 Page 1 C . magi s t e r l a n d i n g s from C a l i f o r n i a , Oregon, and Washington have shown coherent c y c l i c a l f l u c t u a t i o n s w i t h a p e r i o d i c i t y of 9-10 years s i n c e at l e a s t the e a r l y 1950 ' s , a p p a r e n t l y r e f l e c t i n g male abundance ( B o t s f o r d 1986a) . I t i s not known whether c y c l e s are n o n e x i s t e n t in B r i t i s h Columbia f i s h e r i e s , or the l a n d i n g s t a t i s t i c s do not r e f l e c t abundance . Because of t h e i r a p p a r e n t l y p r e d i c t a b l e c y c l i c p a t t e r n and h i g h va lue ( B a r r y 1985, Demory 1985, Warner 1985, Methot 1986) , American Dungeness crab f i s h e r i e s have a t t r a c t e d much s c i e n t i f i c a t t e n t i o n . S e v e r a l mechanisms have been proposed as causes of these c y c l e s . those i n v o l v i n g d e n s i t y - d e p e n d e n t r e c r u i t m e n t were among the f i r s t e v a l u a t e d , and i n c l u d e d : (1) r e d u c e d female f e c u n d i t y due to an e g g - p r e d a t o r worm (Wickhara 1979) , (2) c a n n i b a l i s m of a d u l t s on j u v e n i l e s ( B o t s f o r d and Wickham 1978) , and (3) d e n s i t y - d e p e n d e n c e i n e a r l y l i f e h i s t o r y (McKelvey et a l . 1980 ) . A p r e d a t o r - p r e y h y p o t h e s i s , w i t h f i shermen as the p r e d a t o r , has been r e j e c t e d as an e x p l a n a t i o n of the c y c l e s ( B o t s f o r d et a l . 1983 ) . Salmon p r e d a t i o n on crab l a r v a e ( B o t s f o r d et a l . 1982, Thomas 1985) , a l s o seems u n l i k e l y to have caused the c y c l e s . Recent r e s e a r c h i s f o c u s i n g on the h y p o t h e s i s tha t the c y c l e s may have been caused by a c y c l i c a l p a t t e r n i n wind s t r e s s , p o s s i b l y i n c o n j u n c t i o n w i t h d e n s i t y - d e p e n d e n t p r o c e s s e s (Johnson et a l . 1986, B o t s f o r d 1986b) . S e c t i o n 1 Page 2 There have been no y i e l d - or e g g s - p e r - r e c r u i t a n a l y s e s of the minimum l e g a l s i z e l i m i t f or C . mag i s t er because r e l i a b l e e s t imates of growth and m o r t a l i t y have not been a v a i l a b l e (Methot 1986) . A lack of i n f o r m a t i o n on growth and m o r t a l i t y was acknowledged as a l i m i t a t i o n i n most of the models proposed to e x p l a i n the c y c l i c p a t t e r n of l a n d i n g s . A c c u r a t e e s t i m a t e s of p o p u l a t i o n parameters are o f t e n d i f f i c u l t to a c q u i r e because of the l o g i s t i c problems of p e r f o r m i n g exper iments and sampl ing on an unbounded, exposed c o a s t . The purpose of t h i s s tudy was to e s t imate the v i t a l s t a t i s t i c s of growth, m o r t a l i t y , m o u l t i n g , movement and r e p r o d u c t i o n for a r e l a t i v e l y c l o s e d C . magi s t e r p o p u l a t i o n i n order to e v a l u a t e the c u r r e n t minimum l e g a l s i z e l i m i t for C . magi s t e r . The c u r r e n t s i z e l i m i t of 165 mm s p i n e - t o - s p i n e CW ( » 1 5 4 mm n o t c h - t o - n o t c h CW) has been i n p l a c e i n B r i t i s h Co lumbia s i n c e at l e a s t e a r l y t h i s c e n t u r y , but there i s no documentat ion of how t h i s s i z e was chosen (Jamieson 1985) . Wi th i n f o r m a t i o n from t h i s s tudy (supplemented by i n f o r m a t i o n from Hankin et a l . (1985) on female growth , s u r v i v o r s h i p , and f e c u n d i t y ) y i e l d - and e g g s - p e r - r e c r u i t were a n a l y z e d t o e v a l u a t e the assumpt ion tha t the c u r r e n t minimum l e g a l s i z e l i m i t p r o v i d e s a h i g h y i e l d w h i l e e n s u r i n g a h i g h l e v e l of egg p r o d u c t i o n ( C l e a v e r 1949, Poole and G o t s h a l l 1965, Methot 1986) . T o f i n o , B . C . was chosen as the main s i t e for t h i s two year s tudy because of i t s a c c e s s i b i l i t y and w e l l - b o u n d e d f i s h e r y for C . magi s t e r . T o f i n o has been a t r a d i t i o n a l crab f i s h i n g r e g i o n S e c t i o n 1 Page 3 for most of t h i s c e n t u r y . Sampl ing in other c o a s t a l r e g i o n s supplemented the i n f o r m a t i o n c o l l e c t e d near T o f i n o . A two year o l d cohort of male and female C . magi s t e r was f o l l o w e d for 18 months as i t matured , and i n the case of ma le s , en tered the f i s h e r y . S p a t i a l , temporal and s i z e f requency d i s t r i b u t i o n s of s u b l e g a l - s i z e d males and females were o b t a i n e d from beam t r a w l samples . By a p p l y i n g s i z e f requency a n a l y s i s , which i n c l u d e d i n f o r m a t i o n on moult i n c r e m e n t s - a t - s i z e , to beam t r a w l samples , the t r a n s i t i o n of sm a l l e r i n s t a r s to l a r g e r i n s t a r s was f o l l o w e d . I n f o r m a t i o n on n a t u r a l and f i s h i n g m o r t a l i t y , movement, growth , and the e n t r y of males i n t o the f i s h e r y was g a t h e r e d from a m a r k - r e c o v e r y program. C a t c h r a t e s were de termined by sampl ing t r a p ca tches on board commercial f i s h i n g v e s s e l s . The p r o p o r t i o n of l e g a l - s i z e d males taken by the f i s h e r y was e s t i m a t e d by s i z e f requency a n a l y s i s on da ta from t r a p samples . T r a p g e n e r a l l y p r o v i d e s i z e f requency d a t a b i a s e d by the dynamics of e n t r y and e x i t of c r a b s , changes i n b a i t e f f e c t i v e n e s s over t ime , and a g o n i s t i c i n t e r a c t i o n s among crabs (Caddy 1979) . To reduce such b i a s , exper iments were performed to e s t imate parameters for models d e s c r i b i n g e n t r y and e x i t r a t e s as m o d i f i e d by changes i n b a i t e f f e c t i v e n e s s and a g o n i s t i c i n t e r a c t i o n s . Exper iments were a l s o performed to measure r e t e n t i o n p r o b a b i l i t i e s for d i f f e r e n t s i z e s of crabs by d i f f e r e n t t r a p t y p e s . A g e n e r a l model of the dynamic i n t e r a c t i o n s between S e c t i o n 1 Page 4 crabs and traps was constructed from the re su l t s of these experiments to help standardize data obtained from d i f f erent trap types and after d i f f erent soak times. Section 1 Page 5 2 DESCRIPTION OF STUDY AREAS Most f i e l d work was performed near T o f i n o , B r i t i s h C o l u m b i a . Sampling was l i m i t e d to those waters e n c l o s e d by the dashed l i n e s in F i g . 2.1, and i n c l u d e d Lemmens I n l e t , Browning Passage and the water s u r r o u n d i n g Ind ian I s l a n d . These s i t e s are w i t h i n S t a t i s t i c a l Area ( S A ) 24, as d e f i n e d by the Canadian Department of F i s h e r i e s and Oceans, and support most of the f i s h e r y i n SA 24. S t a t i s t i c a l Area 24 accounted for 13 and 20% of the t o t a l weight of C . magi s t e r landed i n B r i t i s h Co lumbia i n 1985 and 1986, r e s p e c t i v e l y . No crab f i s h i n g occurs i n waters i n l a n d of t h i s s tudy area due to poor crab h a b i t a t . The f i s h e r y was e x p l o i t e d y e a r - r o u n d , a l t h o u g h some f i shermen swi t ched to crab f i s h i n g o n l y a f t e r a summer of salmon f i s h i n g . The waters of the s tudy a r e a are sha l low (a=5-15 m depth) and w e l l mixed . The s u b s t r a t e v a r i e s from sand i n the more exposed areas to mud at the head of Lemmens I n l e t . Annual s u r f a c e seawater temperature ranges from *6-12° C , but summer temperatures may r e a c h 18° C i n s u r f a c e waters of upper Lemmens I n l e t or near I n d i a n I s l a n d . A l t h o u g h no l a r v a l s e t t l ement was d e t e c t e d d u r i n g t h i s s t u d y , the t r a d i t i o n of a p r o d u c t i v e crab f i s h e r y i n t h i s r e g i o n may be due to the e x t e n s i v e mudf la t s ( s t i p p l e d a r e a , F i g . 2.1) which p r o v i d e h i g h q u a l i t y h a b i t a t for newly s e t t l e d and f i r s t - y e a r crabs (Armstrong and Gunderson 1985). S e c t i o n 2 Page 6 In format ion from t h r e e o ther r e g i o n a l f i s h e r i e s i s i n c l u d e d i n t h i s s t u d y . The Dixon E n t r a n c e f i s h e r y (SA 1) i s c o n c e n t r a t e d i n shoal water n o r t h of the Queen C h a r l o t t e I s l a n d s ( F i g . 2 . 1 , I n s e r t I , ' a ' ) and accounted for 14 and 16% of r e p o r t e d l a n d i n g s i n 1985 and 1986, r e s p e c t i v e l y . The Ho lberg I n l e t f i s h e r y (SA 27) i s a smal l f i s h e r y near the nor thern end of Vancouver I s l a n d ( F i g . 2 . 1 , I n s e r t I I , ' a ' ) and accounted for <1% of r e p o r t e d l and ings i n 1985 and 1986. The F r a s e r d e l t a f i s h e r y (SA 29) near Vancouver ( F i g . 2 . 1 , Inser t I I , ' b ' ) a c c o u n t e d for 30 and 23% of r e p o r t e d l a n d i n g s i n 1985 and 1986, r e s p e c t i v e l y . F i g u r e s 2.2 and 3 d e s c r i b e h i s t o r i c a l trends i n c a t c h and e f f o r t , r e s p e c t i v e l y , for a l l but the H o l b e r g In le t f i s h e r y . In the H o l b e r g I n l e t f i s h e r y annua l l a n d i n g s seldom exceeded 5 t , and e f f o r t exceeded 200 days f i s h i n g o n l y once ( i n 1971) . Time s e r i e s a n a l y s e s were performed on the l a n d i n g and e f f o r t s t a t i s t i c s for a l l but the Ho lberg I n l e t f i s h e r y t o t e s t for t rends over t i m e . Time s e r i e s i n t e r v e n t i o n a n a l y s i s (an ARMA(1,0) l i n e a r or t r e n d i n t e r v e n t i o n , see Noakes 1986) u s i n g the M c L e o d - H i p e l a l g o r i t h m ( H i p e l and McLeod 1987) found no s i g n i f i c a n t (a=.05) t r e n d s i n the l a n d i n g s t a t i s t i c s for the SA 24 ( T o f i n o ) f i s h e r y , or i n the l a n d i n g and e f f o r t s t a t i s t i c s for the SA 29 ( the F r a s e r d e l t a ) f i s h e r y . A s i g n i f i c a n t t r e n d would i n d i c a t e a l i n e a r i n c r e a s e or decrease i n the l a n d i n g s t a t i s t i c s over t i m e . S i m i l a r l y , there were no s i g n i f i c a n t t r e n d s i n the l a n d i n g and e f f o r t s t a t i s t i c s for the SA 1 (Dixon S e c t i o n 2 Page 7 E n t r a n c e ) f i s h e r y . Both c o u l d be d e s c r i b e d by an ARMA(9,0) p r o c e s s w i t h s i g n i f i c a n t a u t o c o r r e l a t i o n terms o n l y at lags of 1 and 9 y e a r s , the term for the 9 year l a g b e i n g n e g a t i v e . The extent of the i n c r e a s e i n e f f o r t i n SA 24 (p<.05 for an ARMA(0,1) l i n e a r i n t e r v e n t i o n b e g i n n i n g i n 1965) i s m i s l e a d i n g s i n c e i n r e c e n t years the q u a l i t y of e f f o r t has d e c r e a s e d due to a h i g h t u r n o v e r of f i shermen (Jamieson 1985). A l s o , there are fewer e x p e r i e n c e d f i shermen and fewer t r a p s f i s h e d per f i sherman (as d e t e r m i n e d from i n t e r v i e w s o f f i shermen d u r i n g t h i s s t u d y ) . Most f i shermen f i s h e d 50-150 t r a p s . Two of the more e s t a b l i s h e d f i shermen f i s h e d « = 2 0 0 - 3 0 0 t r a p s and one f i s h e d *800 t r a p s . Twenty-seven (27) and 59 v e s s e l s r e p o r t e d l a n d i n g s from SA 24 d u r i n g 1985 and 1986, r e s p e c t i v e l y . As e v i d e n t i n F i g . 2 . 4 , the number of f i shermen r e p o r t i n g l a n d i n g s from SA 24 has i n c r e a s e d d r a m a t i c a l l y i n r e c e n t y e a r s . T h i r t y (30) of the 59 v e s s e l s which landed crabs i n 1986 are known to have f i s h e d i n the s tudy a r e a , as de termined by matching l a n d i n g s t a t i s t i c s w i t h my knowledge of f i s h i n g a c t i v i t i e s . These 30 v e s s e l s accounted for a p p r o x i m a t e l y 80% of the 265 t l anded from SA 24 i n 1986. S e c t i o n 2 Page 8 Figure 2.1 . Map of the main study area near Tof ino , B r i t i s h Columbia. The s t i p p l e d areas are i n t e r t i d a l mudflats. The dashed l ines de l imi t the main study area. Selected s i tes are referenced by c a p i t a l l e t t e r s . The arrow indicates the main channel out to sea. Insert I locates the Dixon Entrance f i shery (a) . Insert II locates the main study area, the Holberg Inlet f i shery (a) , and the Fraser d e l t a f i shery (b ) . Figure 2.1 Page 9 1 9 5 0 I 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 Y E A R F i g u r e 2 .2 . Time s e r i e s of the annua l tonnage of C . m a g i s t e r landed i n the S t a t i s t i c a l A r e a 1, 24 and 29 f i s h e r i e s . F i g u r e 2.2 Page 10 1 9 5 0 I 9 6 0 1 9 7 0 1 9 8 0 1 9 9 0 Y E A R F i g u r e 2 . 3 . Time s e r i e s of the annual number of days f i s h i n g for C . m a g i s t e r i n the S t a t i s t i c a l Area 1, 24 and 29 f i s h e r i e s . F i g u r e 2.3 Page 11 6 0 - i 4 0 H 2 0 H 0 1 9 6 5 1 9 7 0 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 Y E A R F i g u r e 2 . 4 . Time s e r i e s of the annual number of v e s s e l s which r e p o r t e d l a n d i n g s of C . magi s t e r from the S t a t i s t i c a l Area 24 f i s h e r y near T o f i n o , B . C . F i g u r e 2.4 Page 12 3 FIELD METHODS In order to evaluate the current minimum legal size l i m i t for C. magi ster, a cohort of pre-recruit males and females was followed over time as the males entered the fishery and were subsequently exploited. Commercial fi s h i n g success, exploitation rates, s p a t i a l , temporal and size frequency d i s t r i b u t i o n s , size-at-maturity, and sizes of males and females in mating embraces were determined from sampling on board commercial and research vessels, and trawling. The trap samples were standardized by correcting for the effects of trap retention c a p a b i l i t i e s , changes in bait effectiveness, and agonistic interactions between crabs, based on experiments which analyzed these processes. Moult increments-at-size, length of intermoult periods, mortality, movement, and recruitment to the fishery were obtained from a mark-recovery program. 3.1 MORPHOMETRICS The standard measure of C. magi ster size is carapace width (CW) measured between the notches just anterior to the tenth anterolateral spines (notch-to-notch). Except where noted, carapace width refers to the notch-to-notch measurement truncated to the nearest millimeter. Trap standardization experiments required relationships to convert notch-to-notch carapace width to body length for both males and females. A l l crabs measured to determine these relationships were obtained near Tofino. Section 3 Page 13 Because some e a r l i e r work measured carapace w i d t h between the t i p s of the t e n t h a n t e r o l a t e r a l sp ines ( s p i n e - t o - s p i n e ), a r e l a t i o n s h i p was e s t a b l i s h e d to conver t s p i n e - t o - s p i n e carapace w i d t h to the e q u i v a l e n t n o t c h - t o - n o t c h measurement f o r the f u l l range of male and female carapace widths o b s e r v e d . S p i n e - t o -sp ine carapace w i d t h was d e t e r m i n e d from n o t c h - t o - n o t c h carapace w i d t h by r e g r e s s i o n . Both measurements were o b t a i n e d for at l e a s t one c r a b of each sex i n each 1 mm i n t e r v a l from 100-190 and 100-170 mm CW, for males and f e m a l e s , r e s p e c t i v e l y . The s i z e at which C . magi s t e r can be l e g a l l y taken by f i shermen i s 165 mm CW ( s p i n e - t o - s p i n e , 154 mm n o t c h - t o - n o t c h CW). The p r o b a b i l i t y of a male of a p a r t i c u l a r n o t c h - t o - n o t c h carapace w i d t h b e i n g l e g a l s i z e was de termined from the j o i n t d i s t r i b u t i o n of n o t c h - t o - n o t c h and s p i n e - t o - sp ine carapace widths for 100 crabs 152-156 mm CW ( n o t c h - t o - n o t c h ) . T w e n t y - f i v e (25) crabs were measured w i t h i n each 1 mm i n t e r v a l w i t h i n t h i s range . Some a n a l y s e s i n t h i s s tudy r e q u i r e d a measure of body l e n g t h , so r e l a t i o n s h i p s c o n v e r t i n g n o t c h - t o - n o t c h carapace w i d t h to body l e n g t h for males and females were a l s o e s t a b l i s h e d . In order to e s t a b l i s h a r e l a t i o n s h i p between n o t c h - t o - n o t c h carapace w i d t h and body l e n g t h for males and females , s i x p a i r s of measurements were taken for each 1 mm i n t e r v a l from 120-185 and 120-175 mm CW, for males and f e m a l e s , r e s p e c t i v e l y . Body l e n g t h was measured from the t i p of the r o s t r u m to the most p o s t e r i o r e x t e n s i o n of the abdominal segments . S e c t i o n 3.1 Page 14 3.2 BEAM TRAWL SAMPLING S p a t i a l , t emporal and s i z e frequency d i s t r i b u t i o n s of mos t ly s u b l e g a l - s i z e d male and female C . magi s t e r were o b t a i n e d p r i m a r i l y by beam t r a w l i n g . The t r a w l d e s i g n was as d e s c r i b e d by Gunderson et a l . ( 1985 ). The e f f e c t i v e swept w i d t h i s 2.3 m. The d i s t a n c e towed was de termined by r a n g i n g landmarks at the b e g i n n i n g and end of a tow of 5-10 min , then e s t i m a t i n g the d i s t a n c e towed from h i g h r e s o l u t i o n a e r i a l p h o t o g r a p h s . Most tows were 200-500 m. C r a b d e n s i t i e s were e s t i m a t e d by d i v i d i n g the number of crabs caught by the a r e a swept by the beam t r a w l . Because beam t r a w l s are not 100% e f f i c i e n t , d e n s i t i e s s h o u l d be i n t e r p r e t e d o n l y as i n d i c e s of a b s o l u t e abundance. D u r i n g summer 1985 « 6 0 tows a s s e s s e d s p a t i a l d i s t r i b u t i o n throughout the s tudy a r e a . In s e l e c t e d s i t e s where crabs were abundant , tows were made at a p p r o x i m a t e l y monthly i n t e r v a l s from mid-1985 u n t i l September 1986. The d a t e , tow d e p t h , bottom t y p e , and a r e a swept were r e c o r d e d . D e t a i l s of s p e c i f i c t r a w l s and t h e i r r e s u l t s are g i v e n i n S e c t i o n 4 . 1 1 . A l l crabs c a p t u r e d by beam t r a w l i n g were i d e n t i f i e d to s p e c i e s . For C . magi s t e r , sex, s h e l l h a r d n e s s , and the presence of mat ing marks on male claws ( B u t l e r 1960) , were no ted; and carapace w i d t h was measured. A crab was c o n s i d e r e d h a r d - s h e l l e d i f the e x o s k e l e t o n of i t s legs c o u l d r e s i s t moderate p r e s s u r e a p p l i e d by the thumb and index f i n g e r . S e c t i o n 3.2 Page 15 3.3 TRAP SAMPLING Size f requency d i s t r i b u t i o n s of male and female C . magi s t e r from commercial t r a p s were de termined by sampl ing the c a t c h of commercial f i s h i n g v e s s e l s at a p p r o x i m a t e l y monthly i n t e r v a l s from A p r i l 1985 u n t i l September 1986. I a c c e p t e d the i n v i t a t i o n of four f i shermen to sample on b o a r d t h e i r v e s s e l s . These data were complemented by f i s h i n g ' r e s e a r c h ' t r a p s , which l a c k e d escape p o r t s , over the same time p e r i o d . Research t r a p s h e l p e d a s se s s the abundance of s m a l l e r crabs which o f t e n were absent from commercial t r a p s . The f i s h e r y was open to commercial f i s h i n g for the d u r a t i o n of t h i s s tudy . A l l crabs c a p t u r e d i n t r a p s were i d e n t i f i e d to s p e c i e s and assessed as i n S e c t i o n 3 . 2 . S p e c i f i c d e t a i l s of the t r a p sampl ing times and l o c a t i o n s are g i v e n i n S e c t i o n 4 . 9 . Commercial C . magi s t e r ca tches were sampled i n other r e g i o n a l f i s h e r i e s between 1983 and 1986. The H o l b e r g I n l e t f i s h e r y was sampled i n December 1984, and March and J u l y 1986. The Dixon E n t r a n c e f i s h e r y was sampled in October of 1983 and 1984 ( G . S . Jamieson , unpub. d a t a ) . The F r a s e r d e l t a f i s h e r y was sampled i n October of 1984 and 1985 ( P . A . B r e e n , unpub. d a t a ) . The d a t e , t o t a l number of t r a p s h a u l e d , l o c a t i o n , soak t i m e , t r a p t y p e , and b a i t t y p e , were r e c o r d e d . 3.4 FEMALE SIZE-AT-MATURITY From June 1985 u n t i l September 1986 females >80 mm CW c o l l e c t e d i n t r a p s or t r a w l s near T o f i n o were d i s s e c t e d to Sect i on 3.3 Page 16 determine i f a pair of sperm packs, placed by a male during mating, was present in their spermathecae (Butler 1960). At least 10 females in each 5 mm interval from 80-160 mm CW were dissected. In March and July 1986 «=50 large females c o l l e c t e d in Holberg Inlet (SA 27) were also dissected. 3.5 MATING PAIRS When mating pairs of C. magi ster were collected in traps or trawls, carapace widths of both individuals were measured. Mating pairs are e a s i l y recognized as a male clasping a smaller female with her abdomen against his (Butler 1960, Snow and Neilsen 1966). When convenient, the pair was retained and monitored in an enclosure u n t i l mating was complete to obtain pre- and post-moult carapace widths from the female. 3 . 6 TRAP DISTRIBUTION The number of crab traps fished in the study area was determined by interviewing fishermen at approximately monthly intervals from June 1985 u n t i l September 1986. Because fishermen generally f i s h s p e c i f i c s i t e s (e.g. Lemmens In l e t , Browning Passage, near Indian Island) trap d i s t r i b u t i o n was also assessed. To v e r i f y information from fishermen, the number of traps reported fished in Lemmens Inlet was compared with the number of trap buoys counted there each month for the duration of the study. With few exceptions each trap buoy indicated one trap. Traps were counted during calm weather from a moving boat. Section 3.4 Page 17 3.7 TRAP PERFORMANCE EXPERIMENTS S e v e r a l processes c o n t r i b u t e to the number, sex r a t i o and s i z e f requency d i s t r i b u t i o n of crabs w i t h i n t r a p s . Exper iments were per formed to measure the f o l l o w i n g p r o c e s s e s for the purpose of s t a n d a r d i z i n g commercial samples w i t h d i f f e r e n t soak t i m e s . 1. The escape of crabs from t r a p s as a f u n c t i o n of carapace w i d t h . 2. The r e d u c t i o n i n the e n t r y r a t e of crabs i n t o t r a p s due to a g o n i s t i c i n t e r a c t i o n s among c r a b s . 3 . The r e d u c t i o n i n the e n t r y r a t e of crabs i n t o t r a p s due to changes i n b a i t e f f e c t i v e n e s s . P e r f o r m i n g these exper iments w i t h i n the two bays i n upper Lemmens I n l e t and near I n d i a n I s l a n d ( A , H ; F i g . 2 . 1 , page 9) a s s u r e d e x c e l l e n t working c o n d i t i o n s and easy e x e c u t i o n of e x p e r i m e n t a l a c t i v i t i e s , e . g . s e t t i n g and m a i n t a i n i n g g r i d p a t t e r n s , t r a p h a u l i n g , crab measurement and da ta r e c o r d i n g . These two l o c a t i o n s were f i s h e d c o m m e r c i a l l y , the I n d i a n I s l a n d s i t e b e i n g more p r o d u c t i v e . The water depth at these l o c a t i o n s was «=7-12 m. Traps used i n these exper iments were set i n g r i d p a t t e r n s ( F i g . 3 . 7 . 1 ) w i t h a d i s t a n c e between a d j a c e n t t r a p s of =*75 m. A p p r o x i m a t e l y 0.5 kg per t r a p of geoduck clam (Panope a b r u p t a ( R a n d a l l ) ) was used for b a i t . Geoduck was the c h o i c e of most commercial f i s h e r m e n . S e c t i o n 3.6 Page 18 GRID LAYOUT FOR TRAPPING EXPERIMENTS © © ® © @ © ® © @ ® ® ® ® ® © @ ® ® ©@® ©o© ® ® © @ © © ® @ ® ® ® © A) SOAK TIME EXPERIMENT B) BAIT AGE EXPERIMENT ®©o© ©oo© ©©©© o©o© C) SELECTIVITY EXPERIMENT © ® © ® © @ © © © ® ® © © © © © ® ® ® ® ®® ® © © @ ® ® @ ® © © © © © © F i g u r e 3 . 7 . 1 . Layout of t r a p g r i d s d e s i g n e d to emphasize the e f f e c t s of d i f f e r e n t soak t imes ( A ) , changes i n b a i t e f f e c t i v e n e s s ( B ) , and t r a p s e l e c t i v i t y ( C ) , on the d e n s i t y and s i z e f requency d i s t r i b u t i o n of C . magi s t e r . For (A) and (B) soak time ( i n d a y s ) i s e n c i r c l e d , f or ( C ) t r a p type i s e n c i r c l e d . F i g u r e 3 .7 .1 Page 19 3.7.1 TRAP T Y P E S The b a s i c c o m m e r c i a l t r a p i s c i r c u l a r w i t h s t a i n l e s s s t e e l o r r u b b e r - w r a p p e d i r o n f r a m e s r a n g i n g i n d i a m e t e r f r o m 9 0 - 1 0 5 cm. T r a p h e i g h t i s 25 c m . Two i r o n w e i g h t b a r s p l a c e d on t h e b o t t o m o f a t r a p g i v e i t a w e i g h t o f 1 5 - 2 5 k g . Two d i a m e t r i c a l l y o p p o s e d 2 1 - 2 5 b y 10 cm e n t r a n c e t u n n e l s r e c e s s e d 25 cm f r o m t h e t r a p p e r i m e t e r r e q u i r e a c r a b t o a s c e n d a 2 0 ° s l o p e t o e n t e r t h e t r a p . Two o n e - w a y t r i g g e r s o p e n i n g t o w a r d t h e c e n t e r o f t h e t r a p p r o h i b i t a n e a s y e x i t . T r a p s a r e e n c l o s e d b y a 1 mm s t a i n l e s s s t e e l w i r e m e s h f o r m i n g a 7 b y 4 cm d i a m o n d c o n f i g u r a t i o n . B a i t i s p l a c e d i n t h e c e n t e r o f t h e t r a p i n a p e r f o r a t e d 500 mL p l a s t i c j a r . The b a i t j a r i s r e p l a c e d a n d c r a b s r e m o v e d b y o p e n i n g a f o l d - o v e r t r a p l i d n o r m a l l y h e l d s h u t b y a h o o k on a s t r e t c h e d r u b b e r s t r a p . P h o t o g r a p h s o f t r a p s o f t h i s g e n e r a l d e s i g n c a n be s e e n , i n H i g h ( 1 9 7 6 a ) a n d M i l l e r ( 1 9 7 8 , 1 9 7 9 ) . F o u r t r a p t y p e s w e r e d i s t i n g u i s h e d b y t h e number a n d i n s i d e d i a m e t e r o f t h e i r e s c a p e p o r t s . E s c a p e p o r t s a r e l o c a t e d h i g h i n t h e s i d e o f a t r a p p e r p e n d i c u l a r t o t h e e n t r a n c e t u n n e l s . P a i r e d e s c a p e p o r t s a r e d i a m e t r i c a l l y o p p o s e d . T r a p A No e s c a p e p o r t s ( r e s e a r c h t r a p s ) T r a p B 1 1 0 2 . 5 + 0 . 5 mm e s c a p e p o r t T r a p C 1 1 0 9 . 2 + 1 . 5 mm e s c a p e p o r t T r a p D 2 1 0 9 . 2 ± 1 . 5 mm e s c a p e p o r t s T r a p A i s n o t l e g a l f o r c o m m e r c i a l f i s h i n g b u t was u s e d i n a l l g r i d e x p e r i m e n t s t o a c h i e v e h i g h e r r e t e n t i o n o f s m a l l e r c r a b s . T r a p s B a n d D a r e l e g a l f o r c o m m e r c i a l f i s h i n g a n d w e r e S e c t i o n 3 . 7 . 1 Page 20 used l o c a l l y by the f i shermen whose ca t ch I sampled. A l t h o u g h not used l o c a l l y , T r a p C was i n c l u d e d i n a s e l e c t i v i t y experiment ( S e c t i o n 3 . 7 . 3 ) to p r o v i d e an i n t e r m e d i a t e escapement between Traps B and D. 3 .7 .2 CATCH RATES OF TRAPS IN GRIDS The f o l l o w i n g f i s h i n g exper iments which use a g r i d sampl ing format assume tha t a l l t r a p s i n a g r i d are e q u i v a l e n t sampl ing u n i t s . By comparing the c a t c h r a t e s of the p e r i m e t e r and i n t e r i o r t r a p s i n a g r i d , t h i s assumption was t e s t e d . In J u l y 1985 two 5 by 5 g r i d s were a r r a n g e d i n each of the two bays i n upper Lemmens I n l e t (A; F i g . 2 . 1 , page 9 ) . A f t e r a 24 h soak a l l t r a p s i n b o t h g r i d s were h a u l e d . For each t r a p , a l l crabs were a s se s sed as i n S e c t i o n 3 . 2 , and the t r a p l o c a t i o n i n the g r i d was r e c o r d e d . 3 . 7 . 3 ESCAPE OF CRABS FROM TRAPS The p e r c e n t of C . magi s t e r e s c a p i n g Trap A i n 24 h was e s t i m a t e d by t a g g i n g s e v e r a l a p p a r e n t l y h e a l t h y c r a b s , p l a c i n g them i n a t r a p , then c o u n t i n g the number r e m a i n i n g a f t e r a 24 h soak. A f t e r each t r a p h a u l untagged crabs were tagged a n d , a long w i t h p r e v i o u s l y tagged c r a b s , mon i tored for a s u c c e s s i v e 24 h p e r i o d . The t a g g i n g p r o c e d u r e i s d e s c r i b e d i n S e c t i o n 3 . 8 . Crabs w i t h tags that were r e t a i n e d by a t r a p for 24 h were presumed to r e p r e s e n t independent o b s e r v a t i o n s for the next 24 h S e c t i o n 3 .7 .1 Page 21 p e r i o d . For example, observing a tagged crab in a trap for f ive consecutive days is considered equivalent to having observed five d i f ferent crabs after 24 h. Traps were loaded to t y p i c a l densit ies (*5-10 per trap) and placed in a 5 by 5 g r i d in upper Lemmens In le t , or in pa irs near Indian Island (A, H; F i g . 2.1, page 9), at =7-10 m depth. This experiment was performed in termi t tent ly from June-August of 1985 and 1986 with traps being hauled for up to 10 consecutive days. Performing th i s experiment in di f ferent l oca t ions , without changing the bai t and 'reus ing ' tagged crabs, helped reduce biases that may have re su l t ed i f only fresh b a i t , newly captured crabs, or a s ingle s i t e were consis tent ly used. Thus, these escapement rates should be genera l ly appl icable to the commercial f i shery throughout the study area . The s e l e c t i v i t i e s of Traps B-D r e l a t i v e to Trap A were determined by simultaneously f i sh ing nine traps of Traps A-D in a regular pattern in a 6 by 6 g r i d ( F i g . 3 .7 .1c ) . Each day, for seven days, a l l 36 traps were hauled after a 24 h soak, the bait changed and traps replaced . A l l crabs in each trap type were assessed as in Section 3 .2 . 3 .7.4 SOAK TIME EXPERIMENT A 6 by 6 g r i d ( F i g . 3.7.1a) was used to determine the densi t ies and size frequency d i s t r i b u t i o n s of C. magi ster within Trap A traps hauled after soak times of 1, 2, 5 and 10 days. This g r i d was arranged in upper Lemmens Inlet in August 1985 and Section 3.7.3 Page 2 2 near I n d i a n I s l a n d in June 1986. The e n c i r c l e d numbers i n d i c a t e randomly d i s t r i b u t e d soak t imes for t r a p s composing the g r i d . Twenty (20) hauls were made for each soak time t r i a l by h a u l i n g the a p p r o p r i a t e t r a p s on 10 c o n s e c u t i v e days a c c o r d i n g to the f o l l o w i n g s c h e d u l e . 1. Two 1 day soak t r a p s h a u l e d every day . 2. Four 2 day soak t r a p s h a u l e d every second d a y . 3 . Ten 5 day soak t r a p s h a u l e d every f i v e d a y s . 4. Twenty 10 day soak t r a p s h a u l e d a f t e r 10 d a y s . A separate 5 by 4 g r i d was a r r a n g e d 20 days p r i o r to the p r e v i o u s l y d e s c r i b e d g r i d to p r o v i d e 20 r e p l i c a t e s for a 20 day soak. Because the 20 day t r i a l was not f i s h e d s i m u l t a n e o u s l y w i t h the s h o r t e r soak t ime t r i a l s , i t was r e p e a t e d a f t e r the s h o r t e r soak time t r i a l s t o a s s e s s any t r e n d i n the c a t c h r a t e over t i m e . No d i f f e r e n c e s were e v i d e n t so the e a r l i e r t r i a l was used i n b o t h the 1985 and 1986 e x p e r i m e n t s . A f t e r each t r a p h a u l crabs were r e l e a s e d and the was b a i t changed. A l l crabs were a s s e s s e d as i n S e c t i o n 3 . 2 . Traps were r e p l a c e d where they were h a u l e d . 3.7.5 BAIT-EFFECTIVENESS EXPERIMENT Changes i n d e n s i t i e s and s i z e frequency d i s t r i b u t i o n s of crabs w i t h i n Trap A r e s u l t i n g from changes in b a i t e f f e c t i v e n e s s were a s s e s s e d over the same 10 day time p e r i o d as the 1, 2, 5 and 10 day soak time t r i a l s ( S e c t i o n 3 . 7 . 4 ) . The 4 by 4 g r i d used for t h i s experiment ( F i g . 3 . 7 . 1 b ) was arranged near the "6 by 6 soak time g r i d i n upper Lemmens I n l e t in August 1985 and near Sect i o n 3.7 .4 Page 23 I n d i a n I s l a n d in June 1986. In upper Lemmens I n l e t the soak time and b a i t age exper iments were s e p a r a t e d by 2 km, w i t h one g r i d in each of the two bays (A; F i g . 2 . 1 , page 9 ) . Near I n d i a n I s l a n d the two g r i d s were w i t h i n 200 m of each other (H; F i g . 2 . 1 ) . Both g r i d s at each s i t e were presumed to sample crab p o p u l a t i o n s w i t h s i m i l a r s i z e f requency d i s t r i b u t i o n s . At the b e g i n n i n g of the experiment a l l 16 t r a p s were set w i t h f r e s h b a i t . A f t e r 24 h , for e i g h t c o n s e c u t i v e d a y s , a l l 16 t r a p s were h a u l e d , the crabs r e l e a s e d , and the t r a p s r e p l a c e d wi thout changing the b a i t . On the n i n t h day the b a i t j a r was removed and the t r a p s r e p l a c e d wi thout b a i t . A l l crabs were a s s e s s e d as i n S e c t i o n 3 . 2 . 3.8 MARK-RECOVERY PROGRAM Male and female C . magi s t e r were tagged and r e l e a s e d between A p r i l 1985 and May 1986. Most males were s u b l e g a l s i z e , a l l females were s u b l e g a l s i z e . Re lease and r e c o v e r y l o c a t i o n s were de termined w i t h a g r i d i d e n t i f i c a t i o n system (0.9 by 1.2 km) and landmarks . Crabs for t a g g i n g were o b t a i n e d from ' r e s e a r c h ' t r a p s , f i s h e r m e n , or t r a w l i n g . Be fore b e i n g r e l e a s e d , the d a t e , l o c a t i o n and t a g number were r e c o r d e d . Crabs were a s s e s s e d as i n S e c t i o n 3 . 2 . B l u e , i n d i v i d u a l l y numbered, 4.1 cm anchor tags ( F l o y Tag and M a n u f a c t u r i n g C o . , P . O . Box 5357, S e a t t l e , Washington , U . S . A . ) were i n s e r t e d g e n t l y t h r o u g h the r i g h t p o s t e r i o r e p i m e r a l su ture l i n e w i t h a t a g g i n g gun , t a k i n g care not to puncture Sect i on 3 . 7 . 5 Page 2 4 i n t e r n a l o r g a n s . The c o l o u r b lue was chosen for the tags because i t c o n t r a s t e d w e l l w i t h the n a t u r a l c o l o u r a t i o n of C. magis ter , t h e r e b y i n c r e a s i n g v i s i b i l i t y . P l a c i n g the tag through the e p i m e r a l su ture l i n e i s assumed to as sure a h i g h r e t e n t i o n r a t e when the o l d s h e l l i s d i s c a r d e d d u r i n g a m o u l t . To t e s t t h i s a s s u m p t i o n , tag r e t e n t i o n was a s s e s s e d by double t a g g i n g 850 s u b l e g a l - s i z e d male C. magi s t e r . Two tags were i n s e r t e d as d e s c r i b e d above except tha t the second tag was i n s e r t e d though the l e f t p o s t e r i o r e p i m e r a l s u t u r e l i n e . Most r e c o v e r i e s were o b t a i n e d from f i shermen and r e s e a r c h t r a p s . Four f i shermen r e c o r d e d the d a t e , l o c a t i o n and tag number of a l l tagged crabs they r e c o v e r e d on s p e c i a l forms. Three f i shermen a l s o measured carapace w i d t h u s i n g c a l i p e r s . Females and s u b l e g a l - s i z e d males were r e l e a s e d , but l e g a l - s i z e d males were g e n e r a l l y r e t a i n e d . Whether a crab was r e t a i n e d or r e l e a s e d was r e c o r d e d by the f i s h e r m e n . Most other f i s h e r m e n g e n e r a l l y i g n o r e d r e c o v e r i e s of s u b l e g a l - s i z e d c r a b s , but r e t a i n e d tags from l e g a l - s i z e d males . The ex ten t of i n f o r m a t i o n p r o v i d e d w i t h a t a g r e t u r n v a r i e d among f i s h e r m e n . Tags were e i t h e r g i v e n to me or an a s s o c i a t e , or I had p e r m i s s i o n to b o a r d a f i s h e r m a n ' s v e s s e l at the dock and r e t r i e v e tags set a s i d e . Some f i shermen kept tagged l e g a l - s i z e d males i n l i v e w e l l s u n t i l I c o u l d measure them. The i n f o r m a t i o n o b t a i n e d from a tag r e c o v e r y was sometimes supplemented by my knowledge of where p a r t i c u l a r f i shermen f i s h e d , and the f requency w i t h which I checked w i t h them Sect i on 3.8 Page 2 5 r e g a r d i n g r e c o v e r i e s . From A p r i l u n t i l August i n 1985 and 1986 I saw most f i shermen at l e a s t b i w e e k l y , at other t i m e s , month ly . I i n c r e a s e d the number of tag r e c o v e r i e s by a t t e n d i n g dock s ide b u y i n g and s o r t i n g s e s s i o n s . One major b u y e r , T r i - S t a r Seafood Supply L i m i t e d of Vancouver , B . C . r e c o v e r e d tags from crabs they p u r c h a s e d and m a i l e d them to me. S e c t i o n 3.8 Page 2 6 4 RESULTS 4.1 SPECIES COLLECTED Three Cancer spp. were c o l l e c t e d i n t r a p s and beam t r a w l s . C . produc tus R a n d a l l , the r e d rock c r a b , and C . gr ac i 1 i s Dana, the g r a c e f u l c r a b , accounted for <5% of the t o t a l c a t c h by these methods, a l t h o u g h i n c e r t a i n areas they were more abundant . Only C . magi s t e r was c o n s i d e r e d i n the f o l l o w i n g a n a l y s e s . 4.2 MORPHOMETRICS N o t c h - t o - n o t c h carapace w i d t h (CW, mm) i s de termined from s p i n e - t o - s p i n e carapace w i d t h (S , mm) for male and female C . magi s t e r , r e s p e c t i v e l y , by the f o l l o w i n g l i n e a r r e l a t i o n s h i p s (SAS I n s t i t u t e I n c . 1985) v a l i d for a l l observed carapace w i d t h s . M a l e s : CW = 0 .937-S; p<.0001, r 2 >99.9%, n=509 ( 4 . 2 . 1 ) Females: CW = 0 .950-S; p<.0001, r 2 >99.9%, n=478 ( 4 . 2 . 2 ) The p r o b a b i l i t y of a male , whose carapace w i d t h was measured n o t c h - t o - n o t c h , exceed ing the minimum l e g a l s i z e l i m i t of 165 mm CW ( s p i n e - t o - sp ine ) was de termined from the p r o p o r t i o n of males >165 mm CW ( s p i n e - t o - s p i n e ) for 25 crabs w i t h i n each 1 mm CW i n t e r v a l from 152-156 mm ( n o t c h - t o - n o t c h ) . S e c t i o n 4 Page 27 The p r o b a b i l i t y of a male b e i n g l e g a l s i z e when i t s n o t c h - t o - n o t c h carapace w i d t h l i e s w i t h i n a 1 mm i n t e r v a l between 153-155 mm CW i s l i s t e d below. Male n o t c h - 1 o - n o t c h carapace w i d t h (mm) P r o b a b i l i t y of b e i n g l e g a l s i z e <153 153- 154 154- 155 >155 0 .00 0.40 0 .72 1 . 00 The f o l l o w i n g l i n e a r r e l a t i o n s h i p s between n o t c h - t o - n o t c h carapace w i d t h (CW, mm) and body l e n g t h ( L , mm) are v a l i d f o r 120-185 and 120-175 mm CW, f o r male and female C. m a g i s t e r , r e s p e c t i v e l y . Some e x t r a p o l a t i o n of these r e l a t i o n s h i p s beyond the s e ranges w i l l not i n t r o d u c e s i g n i f i c a n t e r r o r . L = 1.94+0.718-CW; p<.0001, r 2=95.5%, n=330 (4.2.5) 4.3 FEMALE SIZE-AT-MATURITY In t h i s s t u d y a l l females >115 mm CW up t o the l a r g e s t s i z e d i s s e c t e d of 180 mm CW had been mated r e g a r d l e s s of the l o c a t i o n or t h e time of year when t h e y were c o l l e c t e d ( F i g . 4.3.1). In the H o l b e r g I n l e t f i s h e r y , where l a r g e females were most abundant, a l l of *50 l a r g e ( 150-180 mm CW) females d i s s e c t e d c o n t a i n e d a p a i r of sperm p a c k s . Ma1e s: L = 4.95+0.677-CW; p<.0001, r 2=98.4%, n=390 (4.2.4) Females: S e c t i o n 4.2 Page 28 100 -1 o UJ h- 80 H CO 60 40 O 20 cr UJ 0_ 0 o CM II c I S.EJ_ n = 50-I o O CM OJ CM ro II II II c c c X o CVJ II c O CM n c « r-CM O O A c T 82.5 92.5 102.5 112.5 122.5 CARAPACE WIDTH ( ± 2 . 5 m m ) F i g u r e 4.3.1. The percent of female C. magister inseminated as a f u n c t i o n of carapace width. F i g u r e 4.3.1 Page 29 4.4 MATING PAIRS Twenty-one (21) mat ing p a i r s of C . magi s t e r were measured between A p r i l 1985 and September 1986. These were supplemented by 97 mat ing p a i r s measured by T . H . B u t l e r (unpub. d a t a ) i n Dixon E n t r a n c e d u r i n g the 1950 ' s . F i g u r e 4 .4 .1 p r e s e n t s a s c a t t e r p l o t of male v e r s u s female carapace widths for mat ing p a i r s . As suggested by these d a t a , the l i n e s r e p r e s e n t l i m i t s of male (MCW) and female (FCW) carapace w i d t h combinat ions a p p a r e n t l y n e c e s s a r y for a mat ing embrace to o c c u r . Males are c o n s i d e r e d f u n c t i o n a l l y mature near 130 ram CW and females are c o n s i d e r e d mature near 70 mm CW ( B u t l e r 1960) . S i z e f r e q u e n c y d i s t r i b u t i o n s from B u t l e r (1961) and t h i s study ( F i g . 4 . 6 . 1 , page 37) suggest t h a t F i g . 4 .4 .1 r e p r e s e n t s mating p r e f e r e n c e s , not r e s t r i c t e d a v a i l a b i l i t y of f e m a l e s . Upper l i n e : FCW = 165 .0 • {1 . 0 - e x p [ - 0 . 0 4 • ( M C W - 1 0 5 . 0 ) ] } ( 4 . 4 . 1 ) Lower 1ine : FCW = 70.0+exp[0 .045-(MCW-130.0)] ( 4 . 4 . 2 ) S e c t i o n 4.3 Page 3 0 6 0 -\ 1 1 1 1 1 1 1 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 2 0 0 M A L E W I D T H (mm) Figure 4 .4 .1 . Carapace widths of C. magi ster mating p a i r s . The l ines (Eqns. 4.4.1 and 2) define the apparent l i m i t s in carapace widths required for a mating embrace. C i r c l e s represent data from Butler (unpub. data) , squares represent data from this study. Figure 4.4.1 Page 31 4.5 MOULT INCREMENTS R e l a t i o n s h i p s between carapace w i d t h and moult increments -a t - s i z e for male and female C . magi s t e r were o b t a i n e d from p r e -and p o s t - m o u l t carapace w i d t h measurements. The number of r e c o r d s i s smal l (76 for m a l e s , 7 for f e m a l e s ) , and w i t h i n a l i m i t e d p r e - m o u l t carapace w i d t h r a n g e , so they were supplemented w i t h e q u i v a l e n t da ta from four o ther p u b l i s h e d s o u r c e s . Because B u t l e r (1961) summarized moult i n c r e m e n t s - a t - s i z e for Dixon E n t r a n c e by 5 mm CW i n t e r v a l s , they are r e a n a l y s e d u s i n g r e g r e s s i o n a n a l y s i s . From C a l i f o r n i a , C o l l i e r (1983) and Warner (1987 ) p r o v i d e moult i n c r e m e n t s - a t - s i z e for m a l e s , and Diamond (1983 ) p r o v i d e s moult increment s -a t - s i ze for- f emales . The r e g r e s s i o n a n a l y s e s (SAS I n s t i t u t e I n c . 1985) for these data are p r e s e n t e d i n T a b l e s 4 .5 .1 and 2, f or males and f emale s , respe ct i v e l y . A n a l y s i s of c o v a r i a n c e i n d i c a t e d s i g n i f i c a n t (p<.05) d i f f e r e n c e s between the r e g r e s s i o n models for the d i f f e r e n t male and female d a t a s e t s . However, for two reasons t h i s i s not c o n s i d e r e d s u f f i c i e n t to r e j e c t the two models based on a l l male ( E q n . 4 . 5 . 1 ) and a l l female ( E q n . 4 . 5 . 2 ) d a t a combined ( F i g s . 4 .5 .1 and 2 ) . Authors used d i f f e r e n t measuring t e c h n i q u e s , and the maximum d i f f e r e n c e s between the model p r e d i c t i o n s for the i n d i v i d u a l d a t a s e t s , and those of the combined da ta s e t s , are <2 mm, and o n l y at the low extreme of the range sampled . Sect i on 4.4 Page 3 2 Table 4 . 5 . 1 . L i n e a r r e g r e s s i o n models for male C . magi s t e r moult i n c r e m e n t s - a t - s i z e for four da ta sets c o l l e c t e d from B r i t i s h Columbia ( B . C . ) and C a l i f o r n i a ( C a l . ) . Model equat i o n a n E v2{% ) Region Source I = 19 . 72+0.059-CW 277 < .0001 11.8 B.C . B u t l e r (1961) I = 15. 78 + 0 .078-CW 72 .0090 9.4 C a l . C o l l i e r (1983) I = 16 . 50+0.078-CW 19 .0794 1 .7 C a l . Warner (1987) I = 21 . 19+0.046-CW 76 .1751 2.5 B.C . T h i s study-I = 18 . 07 + 0 .069-CW 444 < .0001 11 .3 A l l d a t a s e t s b ( E q n . 4 . 5 . 1 ) I i s the moult i n c r e m e n t - a t - s i z e (mm). CW i s the p r e - m o u l t carapace w i d t h (mm). The s t a n d a r d d e v i a t i o n of the e s t i m a t e for the i n t e r c e p t i s 1 .26, for the s l o p e , 0 .009 . Table 4 . 5 . 2 . L i n e a r r e g r e s s i o n models f o r female C . magi s t e r moult i n c r e m e n t s - a t - s i z e for t h r e e da ta se ts c o l l e c t e d from B r i t i s h Co lumbia ( B . C . ) and C a l i f o r n i a ( C a l . ) . Model equat i o n a n E r2 (%) Region Source I = 28. 63 - 0 .100-CW 44 .0006 24 .6 B.C . B u t l e r (1961 ) I = 32. 11 - 0 .13 5- CW 277 < .0001 43 .5 C a l . Diamond (1983 ) I = 27. 77-0.105-CW 7 .0567 54 .9 B.C . T h i s s tudy I = 32. 3 5 - 0 .13 6•CW 328 < .0001 46.0 A l l d a t a s e t s b ( E q n . 4 . 5 . 2 ) a I i s the moult i n c r e m e n t - a t - s i z e (mm). CW i s the p r e - m o u l t carapace w i d t h (mm). b The s t a n d a r d d e v i a t i o n of the e s t i m a t e for the i n t e r c e p t i s 1 .076, for the s l o p e , 0 .008 . S e c t i o n 4.5 Page 3 3 F i g u r e 4 . 5 . 1 . Male C . magi s t e r moult increments as a f u n c t i o n of p r e - m o u l t carapace w i d t h . The p l o t uses data from B r i t i s h Columbia and C a l i f o r n i a . Data from t h i s s tudy are r e p r e s e n t e d by s q u a r e s . F i g u r e 4 .5 .1 Page 34 30 - i F i g u r e 4 . 5 . 2 . Female C . magi s t e r moult increments as a f u n c t i o n of p r e - m o u l t carapace w i d t h . The p l o t uses da ta from B r i t i s h Columbia and C a l i f o r n i a . Data from t h i s s tudy are r e p r e s e n t e d by s q u a r e s . F i g u r e 4 . 5 . 2 Page 35 4.6 GROWTH I n s t a r mean s i z e s and s t a n d a r d d e v i a t i o n s for C . magi s t e r were de termined from s i z e f requency a n a l y s e s of the carapace widths of crabs caught i n beam t r a w l samples . To i n c r e a s e the sample s i z e , and thus the power of the s i z e f r e q u e n c y a n a l y s e s , a l l da ta from crabs caught i n beam t r a w l s from June 1985 u n t i l September 1986 were combined to c r e a t e s i n g l e d i s t r i b u t i o n s (1 mm CW i n t e r v a l ) for each sex. The d i s t r i b u t i o n s are summarized by 5 mm CW i n t e r v a l s i n F i g . 4 . 6 . 1 . Cancer magi s t e r grows by m o u l t i n g from one i n s t a r to a l a r g e r i n s t a r . The s i z e d i s t r i b u t i o n of crabs w i t h i n any i n s t a r shows n a t u r a l v a r i a b i l i t y and i t i s g e n e r a l l y presumed that i n s t a r s are n o r m a l l y d i s t r i b u t e d and can be d e s c r i b e d by a mean and s t a n d a r d d e v i a t i o n ( e . g . 155.0+11.2 mm CW). S ince C . magi s t e r grows d i s c o n t i n u o u s l y by i n c r e m e n t s , w i t h one i n s t a r decomposing and s u b s e q u e n t l y forming a new i n s t a r at a l a r g e r s i z e , combining samples taken at d i f f e r e n t t imes s h o u l d not confound these normal d i s t r i b u t i o n s . Only crabs >80 mm CW were used because B u t l e r (1961) and C o l l i e r (1983) show tha t the r e l a t i o n s h i p between the s i z e of a moult increment and carapace width i s n o n l i n e a r when c r a b s <80 mm CW are i n c l u d e d . Data from crabs c o l l e c t e d i n t r a p s were not used to ana lyze growth because the s i z e f requency d i s t r i b u t i o n s o b t a i n e d from t r a p samples were s t r o n g l y b i a s e d by d i f f e r e n c e s i n the soak time tha t t r a p samples e x p e r i e n c e d ( e . g . see S e c t i o n 4 . 7 . 3 ) . S e c t i o n 4.6 Page 3 6 l O - i 8 -4-S 2-°- 0 MALE n » 3307 — LEGAL SIZE 1 ( > 155mm ) LThru >-O z UJ D O UJ I2-| 10-8 -4-2-FEMALE n - 1649 1 2.5 52.5 102.5 152.5 202.5 CARAPACE WIDTH (±2.5mm) F i g u r e 4 . 6 . 1 . S i z e f requency d i s t r i b u t i o n s for a l l male and female C . m a g i s t e r c o l l e c t e d i n beam t r a w l samples from June 1985 u n t i l September 1986. F i g u r e 4 .6 .1 Page 3 7 The s i z e f requency a n a l y s e s were based on the methodology of Schnute and F o u r n i e r (1980) , and i n c l u d e the l i n e a r e q u a t i o n s for male and female growth i n c r e m e n t s - a t - s i z e (Eqns . 4 .5 .1 and 2 in T a b l e s 4 .5 .1 and 2, page 3 3 ) . The s tandard d e v i a t i o n (D) of an i n s t a r mode was modeled as a f u n c t i o n of the c o n s e c u t i v e i n s t a r number (N) for modes r e c o g n i z e d by the model , where ' d ' i s the s t a n d a r d d e v i a t i o n f o r N=l . Males : D = d• 1 . O e S ^ ' 1 ) (4 .6 .1 ) Females: D = d - 0 . 8 6 4 ( N ' 1 > ( 4 . 6 . 2 ) The cons tants of 1 .069, for males , and 0.864, f o r f e m a l e s , are equal to the slope+1 i n E q n s . 4 .5 .1 and 2, and presume t h a t the s t a n d a r d d e v i a t i o n s for p a r t i c u l a r i n s t a r s v a r y w i t h the moult i n c r e m e n t - a t - s i z e . These e q u a t i o n s p r o v i d e d the most s u i t a b l e r e s u l t s of those a s s e s s e d , and they f a c i l i t a t e d easy s i m u l a t i o n of i n s t a r growth i n the y i e l d - and e g g s - p e r - r e c r u i t model (Sec t ion 5 ) . For each a n a l y s i s t h e r e i s one unknown parameter i n the growth e q u a t i o n ( i . e . the mean carapace w i d t h for the f i r s t i n s t a r r e c o g n i z e d by the s i z e frequency mode l ) , and one unknown parameter i n the e q u a t i o n s r e l a t i n g s tandard d e v i a t i o n to i n s t a r number ( i . e . the s t a n d a r d d e v i a t i o n for N=l ) . Subsequent i n s t a r s are d e f i n e d i n r e l a t i o n to the f i r s t i n s t a r by the growth and s t a n d a r d d e v i a t i o n e q u a t i o n s . A d d i t i o n a l parameters e s t i m a t e the S e c t i o n 4.6 Page 38 p r o p o r t i o n s - a t - a g e for each i n s t a r r e c o g n i z e d by the mode l . The s i z e f r e q u e n c y a n a l y s i s for males i n c l u d e d an a d d i t i o n a l parameter measur ing s i z e - s p e c i f i c e x p l o i t a t i o n of l e g a l - s i z e d males . The p r o b a b i l i t i e s of males between 152-156 mm b e i n g l e g a l s i z e are l i s t e d i n S e c t i o n 4 . 2 . Parameter e s t imates were o b t a i n e d us ing the SIMPLEX n o n l i n e a r e s t i m a t i o n package ( M i t t e r t r e i n e r and Schnute 1985) . A maximum l i k e l i h o o d o b j e c t i v e f u n c t i o n , the s e p a r a t i o n s t a t i s t i c ' A ' of Schnute and F o u r n i e r ( 1980 ), was used to e v a l u a t e the parameter e s t i m a t e s . Male and female i n s t a r s de termined by the s i z e f r e q u e n c y a n a l y s e s are d e f i n e d i n T a b l e s 4 .6 .1 and 2. S u b s e q u e n t l y , the r e l a t i v e p r o p o r t i o n s of male and female i n s t a r s w i t h i n a t ime s e r i e s of beam t r a w l samples ( T a b l e s 4 .6 .3 and 4) were d e t e r m i n e d from s i z e f requency a n a l y s e s u s i n g E q n s . 4 .5 .1 and 2 and E q n s . 4 .6 .1 and 2 to d e f i n e the means and s t a n d a r d d e v i a t i o n s of the i n s t a r s , r e s p e c t i v e l y . The parameter e s t imates for ' d ' i n E q n s . 4 .6 .1 and 2 were taken from T a b l e s 4 . 6 . 1 and 2. The 102.9 mm male i n s t a r dominated the beam t r a w l samples from Ju ly -December 1985, then moulted i n t o the 128.0 mm i n s t a r by l a t e s p r i n g 1986. The m o u l t i n g of t h i s i n s t a r i n t o the 155.0 mm i n s t a r throughout the remainder of 1986 was a s s e s s e d by the m a r k - r e c o v e r y program ( S e c t i o n 4 . 1 3 ) . The 100.7 mm female i n s t a r p r e s e n t from June - September 1985 moulted i n t o the 119.4 mm i n s t a r by J a n u a r y 1986. T h i s i n s t a r moul ted i n t o the 135.5 mm i n s t a r i n summer 1986, s u g g e s t i n g females t h i s s i z e moult o n l y once a n n u a l l y . S i n c e females mate o n l y f o l l o w i n g t h e i r moult ( B u t l e r S e c t i o n 4.6 Page 39 1960) , t h i s suggests peak mat ing a c t i v i t y occurs d u r i n g summer. Few males or females 80-120 mm CW were presen t d u r i n g summer 1986. Crabs t h i s s i z e are two years o l d (post - s e t t 1ement) ( B u t l e r 1961, Stevens and Armstrong 1984) s u g g e s t i n g there was e i t h e r l i t t l e l a r v a l s e t t l ement or s u r v i v a l i n 1984. T a b l e 4 . 6 . 1 . Mean and s t a n d a r d d e v i a t i o n s (SD, sd) for carapace w id ths d e f i n i n g i n s t a r s of male C . mag i s t er >80 mm CW. I n s t a r Mean SD P r o p o r t i o n 5 E s t imate sd E s t imate sd 1 79.3 0.3 9.2 0.2 0.071 2 102.9 - 9.8 - 0.295 3 128.0 - 10.5 - 0.445 4 155.0 - 11.2 - 0.188 5 b 183.8 - . 12 .0 a The p r o p o r t i o n of males i n the combined beam t r a w l samples c o n t r i b u t e d by each i n s t a r . b Determined by e x t r a p o l a t i o n . Tab le 4 . 6 . 2 . Mean and s t a n d a r d d e v i a t i o n s (SD, sd) f o r carapace w id ths d e f i n i n g i n s t a r s of female C . magi s t er >80 mm CW. I n s t a r Mean E s t i m a t e sd SD E s t imate sd Propor t i o n ' 1 2 3 4 5 6 b 79 100 119 135 149 161 4 . 6 14.8 12.8 11 .0 9 .5 8.2 7.1 2.6 0 . 001 0 .386 0 . 529 0 . 067 0 . 016 a The p r o p o r t i o n of females i n the combined beam t r a w l samples c o n t r i b u t e d by each i n s t a r . b Determined by e x t r a p o l a t i o n . Sect i on 4 .6 Page 4 0 T a b l e 4 . 6 . 3 . The r e l a t i v e p r o p o r t i o n s of male C . magi s t e r >80 mm CW w i t h i n c o n s e c u t i v e i n s t a r s for a t ime s e r i e s of beam t r a w l samples . The va lue for each date i n c l u d e s a l l males c a p t u r e d w i t h i n two weeks of tha t d a t e . The dominant i n s t a r i s h i g h l i g h t e d by an a s t e r i s k . I n s t a r mean carapace w i d t h Date Sample s i z e (mm) 79 .3 102 .9 128 .0 155.0 21 Jun 1985 97 0 . 42* 0 .23 0 . 08 0.26 11 J u l 1985 255 0 . 15 0 .73* 0 . 02 0.10 14 Aug 1985 147 0 . 14 0 .69* 0 . 04 0.13 11 Sep 1985 115 0 . 00 0 .84* 0 . 00 0.16 16 Oct 1985 290 0 . 00 0.64* 0 . 35 0 .01 4 Dec 1985 143 0 . 04 0 .48* 0 . 37 0.10 8 Jan 1986 . 202 0 . 02 0.41 0 . 56* 0 .00 4 Feb 1986 245 0 . 01 0 .24 0 . 42* 0.33 5 Mar 1986 581 0 . 00 0.10 0 . 73* 0.16 8 Apr 1986 280 0 . 02 0 .08 0 . 62* 0.27 7 May 1986 318 0 . 01 0.11 0 . 61* 0.27 4 Jun 1986 199. 0 . 03 0 .21 0 . 71* 0 .06 11 J u l 1986 41 0 . 00 0 .21 0 . 50* 0.28 6 Aug 1986 27 0 . 00 0.13 0 . 19 0 .68* 9 Sep 1986 32 0 . 02 0 .05 0 . 18 0 .75* Sect i on 4.6 Page 41 Table 4 . 6 . 4 . The r e l a t i v e p r o p o r t i o n s of female C . magi s t e r >80 mm CW w i t h i n c o n s e c u t i v e i n s t a r s for a t ime s e r i e s of beam t r a w l samples . The va lue for each date i n c l u d e s a l l females c a p t u r e d w i t h i n two weeks of t h a t d a t e . The dominant i n s t a r i s h i g h l i g h t e d by an a s t e r i s k . I n s t a r mean carapace w i d t h Date Sample s i z e (mm) 79 .1 100 . 7 119 .4 135 • .5 149 .4 21 Jun 1985 76 0 . 24 0 . 53* 0 . 14 0 . 09 0 . 00 11 J u l 1985 226 0 . 00 0 . 83* 0 . 14 0 . 00 0 . 02 14 Aug 1985 167 0 . 00 0 . 97* 0 . 00 0 . 02 0 . 01 11 Sep 1985 130 0 . 00 0 . 66* 0 . 32 0 . 01 0 . 00 16 Oct 1985 173 0 . 01 0 . 28 0 . 71* 0 . 00 0 . 00 4 Dec 1985 119 0 . 14 0 . 13 0 . 73* 0 . 00 0 . 00 8 Jan 1986 95 0 . 00 0 . 01 0 . 99* 0 . 00 0 . 00 4 Feb 1986 62 0 . 05 0 . 02 0 . 90* 0 . 03 0 . 0 0 5 Mar 1986 56 0 . 01 0 . 00 0 . 70* 0 . 30 0 . 00 8 Apr 1986 35 0 . 05 0 . 00 0 . 95* 0 . 00 0 . 00 7 May 1986 77 0 . 00 0 . 00 0 . 69* 0 . 31 0 . 00 4 Jun 1986 38 0 . 08 0 . 00 0 . 92* 0 . 00 0 . 01 11 J u l 1986 20 0 . 05 0 . 00 0 . 55* 0 . 40 0 . 00 6 Aug 1986 11 0 . 00 0 . 12 0 . 77* 0 . 11 0 . 00 9 Sep 1986 177 0 . 00 0 . 01 0 . 05 0 . 53* 0 . 40 S e c t i o n 4.6 Page 42 4.7 TRAP PERFORMANCE EXPERIMENTS 4.7.1 CATCH RATES OF TRAPS IN GRIDS A n a l y s i s of v a r i a n c e compared (1) the number of C . magi s t e r caught i n 16 per imeter and nine i n t e r i o r t r a p s w i t h i n two 5 by 5 g r i d s i n the two bays i n upper Lemmens I n l e t , and (2) the mean c a t c h r a t e s for each g r i d . No s i g n i f i c a n t d i f f e r e n c e s w i t h i n or between g r i d s were d e t e c t e d ( T a b l e 4 . 7 . 1 . 1 ) . Kolmogorov-Smirnov t e s t s (Soka l and Rohl f 1981) c o u l d not d e t e c t t h a t (1) the d i s t r i b u t i o n of the number o f crabs per t r a p d e v i a t e d s i g n i f i c a n t l y ( p > . l ) from a normal d i s t r i b u t i o n , and (2) the d i s t r i b u t i o n of the number of crabs per t r a p was s i g n i f i c a n t l y ( p > . l ) d i f f e r e n t for i n t e r i o r v e r s u s per imeter t r a p s i n e i t h e r g r i d . T h e r e f o r e , i n t e r i o r and p e r i m e t e r t r a p s , and the t r a p s of each g r i d , were c o n s i d e r e d e q u i v a l e n t sampl ing u n i t s . Tab le 4 . 7 . 1 . 1 . Comparison of the mean number of C . magi s t e r caught per t r a p for 16 p e r i m e t e r versus nine i n t e r i o r t r a p s i n two 5 by 5 g r i d s , and between a l l t r a p s in each g r i d . In ter i o r Per imeter E a Mean SD Ranqe Mean SD Ranae G r i d G r i d 1 2 5 .7 6 .9 1 .6 2 .4 5-10 3-10 6 . 5 6 . 5 2 . 7 3 . 3 3-14 0-12 > .1 > .1 Gr i d 1 G r i d 2 G r i d vs 1 6 . 2 2 .4 3-10 6 . 6 2 .9 0-14 > .1 G r i d 2 a The p r o b a b i l i t y t h a t the above r e s u l t s are o b t a i n e d g i v e n t h e r e i s no d i f f e r e n c e i n c a t c h r a t e for p e r i m e t e r and i n t e r i o r t r a p s , and between t r a p s i n G r i d 1 and G r i d 2. S e c t i o n 4 .7 Page 43 4.7.2 ESCAPE OF CRABS FROM TRAPS The p e r c e n t of t a g g e d male C. magi s t e r r e t a i n e d w i t h i n Trap A ( ' r e s e a r c h ' t r a p s ) f o r 24 h i s shown f o r 5 mm i n t e r v a l s r a n g i n g from 135-170 mm CW i n F i g . 4.7.2.1. Crabs 120-135 and 170-190 mm CW were combined i n t o l a r g e r i n t e r v a l s of 15 and 20 mm, r e s p e c t i v e l y , because t h e r e were no apparent d i f f e r e n c e s i n r e t e n t i o n over these s i z e r a n g e s . Traps are not e f f e c t i v e i n r e t a i n i n g crabs <135 mm CW because t h e y e a s i l y e n t e r and e x i t t r a p s t h r o u g h the mesh and e n t r a n c e s . Between 135-170 mm CW i n c r e a s i n g p e r c e n t r e t e n t i o n (P) w i t h carapace w i d t h (CW, mm) i s d e s c r i b e d by the f o l l o w i n g l i n e a r e q u a t i o n e s t i m a t e d by a w e i g h t e d l e a s t - squares r e g r e s s i o n , i . e . the d e v i a t i o n s of the p r e d i c t e d and measured d a t a p a i r s ( P , CW) were d i v i d e d by the s t a n d a r d d e v i a t i o n s of P from F i g . 4.7.2.1 (SAS I n s t i t u t e I n c . 1985 ) . P = 2.2432-CW-2.7797 (4.7.2.1) The p e r c e n t of males of d i f f e r e n t s i z e s r e t a i n e d f o r 24 h i n Traps B-D was e s t i m a t e d by d e t e r m i n i n g t h e i r a b i l i t y t o r e t a i n c r a b s r e l a t i v e t o Trap A. F i g u r e 4.7.2.2 shows s i z e f r e q u e n c y d i s t r i b u t i o n s f o r c a t c h e s by Traps A-D. Because b o t h males and females were caught, the carapace w i d t h s f o r females were e x p r e s s e d as m a l e - e q u i v a l e n t carapace w i d t h s f o r the same body l e n g t h s , u s i n g Eqns. 4.2.4 and 5 (page 28). S i n c e r e t e n t i o n i s S e c t i o n 4.7.2 Page 4 4 d e t e r m i n e d l a r g e l y by the a b i l i t y of a crab to walk sideways out an escape p o r t , the c r i t i c a l d imens ion in t h i s r e g a r d i s body l e n g t h . There were no apparent d i f f e r e n c e s in r e t e n t i o n of crabs among Traps A-D for crabs >155 mm CW, so the p e r c e n t r e t a i n e d by T r a p A i s presumed to a p p l y to Traps B-D . For T r a p B, t h i s p r e s u m p t i o n i s a p p a r e n t l y v a l i d for crabs >145 mm CW. Carapace w id ths of 145 and 155 mm c o r r e s p o n d to body l e n g t h s of 103 and 110 mm, r e s p e c t i v e l y ( from E q n . 4 . 2 . 4 , page 28) . These body l e n g t h s are c l o s e to the escape p o r t d iameters for Traps B ( » 1 0 3 mm) and C-D ( « 1 0 9 mm), r e s p e c t i v e l y (see S e c t i o n 3 . 7 . 1 ) , t h e r e f o r e the poorer r e t e n t i o n of crabs s m a l l e r than 155 mm and 145 mm CW for Traps C - D , and T r a p B, r e s p e c t i v e l y , suppor t s the c o n t e n t i o n t h a t r e t e n t i o n c a p a b i l i t i e s of t r a p s are l a r g e l y d e t e r m i n e d by escape p o r t d i a m e t e r . For crabs sm a l l e r than 155 mm, for Traps C - D , and s m a l l e r than 145 mm, for Trap B, the p e r c e n t r e t a i n e d i n Traps B-D i s d e t e r m i n e d by s i m u l t a n e o u s l y and i t e r a t i v e l y s o l v i n g E q n . 4 . 7 . 2 . 2 (below) for Xj^  of Traps B-D when the r a t i o of Q f o r Traps B-D r e l a t i v e to Q for Trap A , a f t e r a one day soak (T = l ) , i s d e t e r m i n e d from Table 4 . 7 . 2 . 1 . The d a i l y e n t r y r a t e (U) i s assumed to be the same for a l l t r a p t y p e s , and X^ for T r a p A i s taken from F i g . 4 . 7 . 2 . 1 . (See R i c k e r (1975) for the d e r i v a t i o n of E q n . 4 . 7 . 2 . 2 for an ana logous p r o b l e m ) . S e c t i o n 4 .7 .2 Page 45 Q = <U*Xi ) • [1 .0-exp( - X i - T ) ] ( 4 . 7 . 2 . 2 ) where: Q i s the number of crabs i n a t r a p a f t e r T days U i s the d a i l y e n t r y r a t e of crabs i n t o a t r a p X^ i s the - l n ( d a i l y p r o b a b i l i t y of a c r a b i n carapace i n t e r v a l i b e i n g r e t a i n e d by a t r a p ) R e l a t i v e r e t e n t i o n ( r a t i o of Q ' s , Table 4 . 7 . 2 . 1 ) i s d e t e r m i n e d by comparing the abundance of crabs i n Traps B-D r e l a t i v e to T r a p A . For example, the percent of males <145 mm CW r e t a i n e d i n Trap B for 24 h i s e s t i m a t e d as 0.220 t imes the p e r c e n t de termined for T r a p A . T a b l e 4 . 7 . 2 . 2 p r e s e n t s r e t e n t i o n e s t i m a t e s for males 120-170+ mm CW for Traps A - D , e x p r e s s e d as p r o b a b i l i t i e s . It i s noteworthy i n F i g . 4 . 7 . 2 . 2 t h a t Trap C , w i t h one 109 mm escape p o r t , a p p a r e n t l y r e t a i n s s m a l l e r crabs more e f f e c t i v e l y than Trap B, w i t h one 103 mm escape p o r t , perhaps r e f l e c t i n g e a s i e r e n t r y i n t o T r a p C t h rou gh the l a r g e r escape p o r t . One can presume t h a t for Traps B-D the r e l a t i v e r e t e n t i o n e s t i m a t e s are b i a s e d to some degree by smal l d i f f e r e n c e s i n e n t r y r a t e s , and perhaps a l s o by a g o n i s t i c i n t e r a c t i o n s among crabs (see S e c t i o n 4 . 7 . 3 ) . S e c t i o n 4 .7 .2 Page 4 6 T a b l e 4 . 7 . 2 . 1 . The r e l a t i v e r e t e n t i o n of crabs <155 mm CW, for Traps C - D , and crabs <145 mm CW, for Trap B, r e l a t i v e to Trap A . The r e l a t i v e r e t e n t i o n for a t r a p type i s the number of crabs caught by t h a t t r a p type d i v i d e d by the number caught by T r a p A a f t e r e q u i v a l e n t one day soaks . For T r a p A n = 536 for crabs <155 mm CW, and n=322 for crabs <145 mm CW. T r a p n R e l a t i v e r e t e n t i on S t a n d a r d e r r o r B 71 0.220 0.023 C 164 0.306 0.020 D 87 0.162 0.016 T a b l e 4 . 7 . 2 . 2 . The p r o b a b i l i t i e s of male C . magi s t e r be ing r e t a i n e d by T r a p s A - D for 24 h . Carapace w i d t h (mm) T r a p A B C D 120-125 .130 < .001 < .001 < .001 125-130 .130 < .001 < .001 < .001 130-135 .192 < .001 < .001 < .001 135-140 .304 < . 001 < .001 < .001 140-145 .416 < .001 .007 < .001 145-150 .529 .529 .012 < .001 150-155 .641 .641 .019 < .001 155-160 . 753 .753 .753 .753 160-165 .866 .866 .866 .866 165-170 .978 .978 .978 .978 >170 .992 .992 .992 .992 S e c t i o n 4 . 7 . 2 Page 47 100 - i UJ 80 < ti 6 0 t r !_ 4 0 -I—n = 126—1 UJ O or UJ 20 -0 2 S.E. I L - n = 69-1 M i ro sl- CO ii II c c X X I T 122.5 132.5 142.5 152.5 C A R A P A C E W I D T H X T 162.5 172.5 (±2.5 mm) 182.5 Figure 4.7.2.1. The percent of male C. magister retained by Trap A for 24 h, as a function of carapace width. Figure 4.7.2.1 Page 48 in X) O o o \-d> X I E C o UJ o UJ u_ 60 n 40 20 0 2 109mm ESCAPE PORTS T R A P T Y P E D nn„. 60-i 40 20 0 120 10  80 60 40 20 0 120 10  80 60 40 20 0 I 109mm ESCAPE PORT T R A P T Y P E C nDND ClrUr I I03mm ESCAPE PORT T R A P T Y P E B • r ^ n r - i n f l NO ESCAPE PORTS T R A P T Y P E A „ r i m 1 ~ 1 — 162.5 187.5 87.5 12-5 137.5 C A R A P A C E WIDTH ( ± 2 . 5 m m ) F i g u r e 4 . 7 . 2 . 2 . S i z e f r e q u e n c y d i s t r i b u t i o n s of C . mag i s ter caught i n Traps A - D . Female carapace widths are e x p r e s s e d as m a l e - e q u i v a l e n t carapace w id ths for the same body l e n g t h s . F i g u r e 4 . 7 . 2 . 2 Page 49 4 . 7 . 3 S O A K T I M E A N D B A I T E F F E C T S P r e v i o u s workers have noted that crab t r a p s s a t u r a t e , i . e . a t t a i n a s t a b l e d e n s i t y of crabs a f t e r an adequate soak t ime as a r e s u l t of a ba lance of e n t r y and e x i t r a t e s (Bennet t 1974, M i l l e r 1978, 1979, 1980). A l s o , from t r a p p i n g exper iments i t was l e a r n e d that as crabs became more abundant in t r a p s the e n t r y r a t e of crabs d e c r e a s e d . Exper iments w i t h C . p r o d u c t u s and C . magi s t e r showed that t r a p s h a u l e d more o f t en caught more crabs d e s p i t e the b a i t not b e i n g changed for the d u r a t i o n of the experiment ( M i l l e r 1979) . M i l l e r (1978) o b s e r v e d that C . productus were l e s s l i k e l y to enter t r a p s a l r e a d y o c c u p i e d by c r a b s . The experiments of M i l l e r and Bennet t , and the d i r e c t o b s e r v a t i o n s by M i l l e r (1978) of C . productus b e h a v i o r , i n d i c a t e d tha t crabs w i t h i n t r a p s c o m p e t i t i v e l y i n h i b i t e d the e n t r y of other crabs thr ough a g o n i s t i c e n c o u n t e r s . The soak time exper iments were des igned t o emphasize the e f f e c t of C . magi s t e r i n d i v i d u a l s w i t h i n a t r a p i n h i b i t i n g the e n t r y of more i n d i v i d u a l s . These a g o n i s t i c e n c o u n t e r s , when m o d i f i e d by d i f f e r e n c e s i n the a b i l i t y of a t r a p to r e t a i n crabs of d i f f e r e n t s i z e s , p r o d u c e d d i f f e r e n t s i z e f r e q u e n c y d i s t r i b u t i o n s for soak t imes of 1, 2, 5, 10 and 20 d a y s . In F i g . 4 . 7 . 3 . 2 i t can be seen how the s m a l l e r c r a b s , w h i c h e n t e r e d the t r a p s e a r l y , leave and are kept out presumably due to i n t i m i d a t i o n by l a r g e r crabs which become more abundant over t i m e . It i s p o s s i b l e t h a t the r e d u c t i o n in the abundance of smal l crabs i n t r a p s over t ime i s due to p r e d a t i o n by l a r g e r S e c t i o n 4 .7 .3 Page 50 c r a b s , but there i s no d i r e c t ev idence of t h i s . The b a i t - e f f e c t i v e n e s s exper iments were des igned to emphasize the decrease over time in the a b i l i t y of b a i t to a t t r a c t c r a b s . The r e s u l t s of changes in b a i t e f f e c t i v e n e s s were not as apparent as the soak time e f f e c t s (see F i g . 4 . 7 . 3 . 6 ) , p a r t i c u l a r l y for s m a l l e r c r a b s , because of o ther dynamic i n t e r a c t i o n s , e . g . a g o n i s t i c i n t e r a c t i o n s , s i z e - d e p e n d e n t r e t e n t i o n r a t e s , and c o n s i d e r a b l e v a r i a b i l i t y i n the d a t a . A l t h o u g h executed as two separate t r a p p i n g exper iments d e s i g n e d to emphasize a g o n i s t i c i n t e r a c t i o n s and changes i n b a i t e f f e c t i v e n e s s over time for a s i n g l e p o p u l a t i o n , b o t h exper iments were i n f l u e n c e d by b o t h p r o c e s s e s . T h e r e f o r e , assuming no i n t e r a c t i o n between these p r o c e s s e s , one would expect the parameter e s t imates for the e q u a t i o n s d e s c r i b i n g these two p r o c e s s e s to be the same for b o t h e x p e r i m e n t s . Assuming t h i s to be t r u e , a dynamic model was d e v e l o p e d to s imula te the e n t r y and e x i t of crabs w i t h i n the combined set of t r a p s used i n each e x p e r i m e n t . However, t h i s a s sumpt ion i s not s t r i c t l y t r u e s i n c e Kolmogorov-Smirnov t e s t s ( S o k a l and Rohlf 1981) i n d i c a t e d s i g n i f i c a n t l y (a=.01) d i f f e r e n t s i z e frequency d i s t r i b u t i o n s between 24 h soaks of 16 t r a p s i n the b a i t e f f e c t i v e n e s s experiment and 20 t raps i n the soak t ime exper iment , f o r b o t h the 1985 and 1986 experiments ( F i g . 4 . 7 . 3 . 1 ) . Note tha t the magnitude of the d i f f e r e n c e s are smal l (D=.20 i n 1985 and D=.13 i n 1986 exper iments ) and not unexpec ted c o n s i d e r i n g the n a t u r a l p a t c h i n e s s of animal d i s t r i b u t i o n s . S e c t i o n 4 .7 .3 Page 51 The dynamic model compared the p r e d i c t e d and observed d e n s i t i e s and s i z e f requency d i s t r i b u t i o n s w i t h i n t r a p s , the p r e d i c t e d number of crabs i n any t r a p be ing a f u n c t i o n of e n t r y and e x i t r a t e s , a g o n i s t i c i n t e r a c t i o n s and changes i n b a i t e f f e c t i v e n e s s over t i m e . In a d d i t i o n to the unknown parameters i n the f o l l o w i n g e q u a t i o n s d e s c r i b i n g a g o n i s t i c b e h a v i o r and changes i n b a i t e f f e c t i v e n e s s , a v e c t o r of parameters r e p r e s e n t s the unmodi f i ed d a i l y e n t r y r a t e s of crabs i n t o a t r a p for each of twenty ( i n 1985) and e i g h t e e n ( i n 1986) 5 mm CW i n t e r v a l s between 90-200 mm CW. For any 5 mm CW i n t e r v a l t h i s r a t e i s d e f i n e d as the number of crabs which would enter a t r a p each day i f b a i t e f f e c t i v e n e s s d i d not decrease over t i m e , and crabs w i t h i n a t r a p have no e f f e c t on the e n t r y r a t e of c r a b s . In p r a c t i c e t h i s e n t r y r a t e cannot be a c h i e v e d for any soak time because b a i t d e t e r i o r a t i o n and a g o n i s t i c i n t e r a c t i o n s b e g i n as soon as a t r a p i s p l a c e d i n the water . T h e r e f o r e , t h i s v e c t o r i s r e f e r r e d to as a v e c t o r o f ' v i r t u a l e n t r y r a t e s ' . The g e n e r a l e q u a t i o n below (Eqn . 4 . 7 . 3 . 1 ) d e s c r i b e s the net d a i l y change i n the number of crabs i n a t r a p . V e r s i o n s of t h i s g e n e r a l e q u a t i o n presuming (1) no a g o n i s t i c e f f e c t s or changes i n b a i t e f f e c t i v e n e s s over t i m e , (2) a g o n i s t i c e f f e c t s a l o n e , (3) changes i n b a i t e f f e c t i v e n e s s a l o n e , and (4) both of these p r o c e s s e s o p e r a t i n g , were a p p l i e d to the data from b o t h the 1985 and 1986 e x p e r i m e n t s . These v a r i a n t s of the dynamic model s i m u l a t e d the e n t r y and e x i t of crabs i n t o and out of t r a p s for the d u r a t i o n of the soak time and b a i t - e f f e c t i v e n e s s e x p e r i m e n t s . S e c t i o n 4 . 7 . 3 Page 5 2 As ment ioned above , the v e c t o r of v i r t u a l e n t r y r a t e s i s an unknown, but the ins tantaneous e x i t r a t e s ( X j ) for p a r t i c u l a r carapace w i d t h i n t e r v a l s ( i ) are de termined from the 24 h r e t e n t i o n p r o b a b i l i t i e s for Trap A from Table 4 . 7 . 2 . 2 (page 47) . As f u r t h e r e x p l a i n e d in S e c t i o n 4 . 7 . 2 , female carapace widths are c o n v e r t e d to m a l e - e q u i v a l e n t carapace widths for the same body l e n g t h s , s i n c e body l e n g t h i s the important body d imens ion d e t e r m i n i n g a crabs a b i l i t y to escape a t r a p . d Q i / d t = V i • R 2 - ( X i • Q i ) ( 4 . 7 . 3 . 1 ) where: Qi i s the number of crabs i n carapace i n t e r v a l i i n a t r a p t i s t ime the i n t e r v a l i n days V i i s the d a i l y v i r t u a l e n t r y r a t e i n t o a t r a p for a c r a b i n carapace i n t e r v a l i X i i s the - l n ( d a i l y p r o b a b i l i t y of a c r a b i n carapace i n t e r v a l i b e i n g r e t a i n e d by a t r a p ) from Tab le 4 . 7 . 2 . 2 (page 47) Rl the r e l a t i v e e f f e c t of a g o n i s t i c i n t e r a c t i o n s ( from E q n . 4 . 7 . 3 . 3 ) R 2 the r e l a t i v e e f f e c t of changes i n b a i t e f f e c t i v e n e s s ( from E q n . 4 . 7 . 3 . 5 ) I f one assumes that b a i t e f f e c t i v e n e s s does not change over t i m e , and t h e r e are no a g o n i s t i c i n t e r a c t i o n s among crabs near t r a p s , then R 1 =1.0 and R 2 = 1 . 0 . T h e r e f o r e , E q n . 4 . 7 . 3 . 1 can be i n t e g r a t e d from t=0 to T to y i e l d E q n . 4 . 7 . 3 . 2 (see R i c k e r 1975, page 14, f or an analogous d e r i v a t i o n ) . A l t e r n a t i v e l y , these two v a r i a b l e s v a r y from 0 .0 -1 .0 d e c r e a s i n g the v i r t u a l e n t r y r a t e ( V i ) as a r e s u l t of a g o n i s t i c i n t e r a c t i o n s ( E q n . 4 . 7 . 3 . 3 ) and changes i n b a i t e f f e c t i v e n e s s ( E q n . 4 . 7 . 3 . 5 ) , r e s p e c t i v e l y . When R3/I or R 2<1 then Eqn. 4 . 7 . 3 . 1 cannot be e a s i l y i n t e g r a t e d , so S e c t i o n 4 . 7 . 3 Page 53 the e n t r y and e x i t r a t e s are i n t e g r a t e d over time to p r e d i c t the number of crabs i n a t r a p at any time u s i n g the Runge-Kutta method of n u m e r i c a l i n t e g r a t i o n (Boyce and D i P r i m a 1977) . Qi = ( V i ^ X i )• [1 . 0 - e x p ( - X i - T ) ] ( 4 . 7 . 3 . 2 ) where: Qi i s the number of crabs i n carapace i n t e r v a l i i n a t r a p a f t e r T days V i i s the d a i l y v i r t u a l e n t r y r a t e i n t o a t r a p f o r a c r a b i n carapace i n t e r v a l i X i i s the - l n ( d a i l y p r o b a b i l i t y of a c r a b i n carapace i n t e r v a l i b e i n g r e t a i n e d by a t r a p ) from T a b l e 4 . 7 . 2 . 2 (page 47) The e q u a t i o n used to d e s c r i b e the e f f e c t i v e n e s s of crabs w i t h i n a t r a p r e d u c i n g the v i r t u a l e n t r y r a t e of crabs i s i n t r o d u c e d be low. E q u a t i o n 4 . 7 . 3 . 3 was f o r m u l a t e d based on the r e s u l t s of c o m p e t i t i o n exper iments by S c r i v e n e r (1971) w i t h the American l o b s t e r (Homarus amer i canus MiIne-Edwards ). He determined t h a t even smal l d i f f e r e n c e s i n the r e l a t i v e s i z e s of two c o n t e s t i n g i n d i v i d u a l s n e a r l y a s s u r e d the l a r g e r i n d i v i d u a l of w i n n i n g the c o n t e s t . For example, a l e g a l - s i z e d l o b s t e r w i t h a carapace l e n g t h 5% l a r g e r than i t s c o m p e t i t o r won *90% of e n c o u n t e r s , i . e . the l o s e r backed away. The o b s e r v a t i o n s of M i l l e r (1978 ) suggest s i m i l a r b e h a v i o r f o r C . p r o d u c t u s . Crab d r y weight was used as a measure of a c r a b ' s c o m p e t i t i v e a b i l i t y . U s i n g weight presumes tha t competing i n d i v i d u a l s p e r c e i v e a c o m p e t i t o r ' s t h r e e - d i m e n s i o n a l s i z e , or a f e a t u r e r e l a t e d to o v e r a l l s i z e , such as claw s i z e ( S c r i v e n e r 1971, Atema and Cobb 1980 ). In the s p e c i a l case of a g o n i s t i c i n t e r a c t i o n s between crabs w i t h i n a t r a p and one a t t e m p t i n g to S e c t i o n 4 . 7 . 3 Page 54 enter that t r a p , the weight of crabs w i t h i n a t r a p i s a proxy for the comparat ive c o m p e t i t i v e a b i l i t y of a t r a p f u l l of c r a b s . A l t h o u g h E q n . 4 . 7 . 3 . 3 i s l i k e l y an imperfect r e p r e s e n t a t i o n of r e l a t i v e c o m p e t i t i v e n e s s , o ther one and two parameter models based on numbers a n d / o r weight as a measure of r e l a t i v e c o m p e t i t i v e a b i l i t y were l e s s capable of d e s c r i b i n g the d a t a . R% = e x p [ - e • ( W * W i ) f ] ( 4 . 7 . 3 . 3 ) where: R^ i s the r e l a t i v e e n t r y r a t e i n t o a t r a p for a c r a b of weight w W i s the t o t a l weight of crabs i n a t r a p w^ i s the weight of a crab i n carapace i n t e r v a l i a t t e m p t i n g to enter a t r a p e i s the i n s t a n t a n e o u s r a t e of d e c r e a s e i n the e n t r y r a t e of a crab as a f u n c t i o n of the 'weight e f f e c t ' r a t i o (w>w^ ) f a l l ows the 'weight e f f e c t ' r a t i o (W-rWj ) t o assume a n o n l i n e a r form Dry weight (w, g) f o r males and females was d e t e r m i n e d from i t s r e l a t i o n s h i p to carapace w i d t h (CW, mm) as d e f i n e d by Stevens and Armstrong (1984) ( E q n . 4 . 7 . 3 . 4 ) . ln(w) = -9 .36+2 .832• ln (CW) ( 4 . 7 . 3 . 4 ) The e q u a t i o n chosen to d e s c r i b e changes i n b a i t e f f e c t i v e n e s s over time i s as f o l l o w s . E q u a t i o n 4 . 7 . 3 . 5 assumes a base r a t e at which crabs are a t t r a c t e d to t r a p s i n the absence of b a i t p l u s a complementary component which has a maximum a b i l i t y to a t t r a c t crabs at T=0 and which d e c l i n e s e x p o n e n t i a l l y w i t h t i m e . S e c t i o n 4 . 7 . 3 Page 5 5 R 2 = g + [ d . 0 - g ) - e x p ( - h - T ) ] ( 4 . 7 . 3 . 5 ) where: R2 i s the r e l a t i v e e n t r y ra te of crabs i n t o a t r a p T i s the age of the b a i t ( i n d a y s ) g i s the base r e l a t i v e e n t r y r a t e of crabs i n t o a t r a p when t h e r e i s no b a i t h i s the d a i l y i n s t a n t a n e o u s r a t e of decrease i n b a i t e f f e c t i v e n e s s Separate parameter e s t i m a t e s were obta ined for the 1985 and 1986 experiments u s i n g the SIMPLEX n o n l i n e a r e s t i m a t i o n package ( M i t t e r t r e i n e r and Schnute 1985) . A maximum l i k e l i h o o d o b j e c t i v e f u n c t i o n , the s e p a r a t i o n s t a t i s t i c ' A ' of Schnute and F o u r n i e r (1980) , was used to e v a l u a t e the parameter e s t i m a t e s . The A k a i k e i n f o r m a t i o n c r i t e r i o n (AIC) ( A k a i k e 1974) , which e q u a l s A p l u s twice the number of model p a r a m e t e r s , was used to judge o v e r a l l model per formance , a lower v a l u e i n d i c a t i n g a more s u i t a b l e model . Table 4 . 7 . 3 . 1 l i s t s A and AIC for the four v a r i a n t s of the g e n e r a l model . In both 1985 and 1986 Model ' 4 ' , wh ich i n c l u d e s both b a i t - e f f e e t i v e n e s s and a g o n i s t i c p r o c e s s e s , o u t p e r f o r m e d a l l o ther models . For the 1985 exper iments a g o n i s t i c i n t e r a c t i o n s were c l e a r l y dominant over changes i n b a i t e f f e c t i v e n e s s . For both the 1985 and 1986 exper iments the a g o n i s t i c - i n t e r a c t ions and b a i t - e f f e e t i v e n e s s equat ions e x p l a i n c o n s i d e r a b l e v a r i a b i l i t y i n the d e n s i t y and s i z e f r e q u e n c y d i s t r i b u t i o n of crabs among the e x p e r i m e n t a l t r e a t m e n t s . These s a t i s f a c t o r y r e s u l t s suggest the s t r u c t u r e of Eqns . 4 . 7 . 3 . 3 and 5 approximate the f u n c t i o n a l r e l a t i o n s h i p s for the dynamic p r o c e s s e s they attempt to s i m u l a t e . S e c t i o n 4 .7 .3 Page 56 The s t r u c t u r e of the s t a n d a r d i z a t i o n model p r e c l u d e d e s t i m a t i o n of conf idence i n t e r v a l s for the parameter e s t imates of Eqns . 4 . 7 . 3 . 3 and 5, and the v i r t u a l e n t r y r a t e s . The a p p l i c a t i o n of approximate a n a l y t i c a l t e chn iques ( M i t t e r t r e i n e r and Schnute 1985) was f r u s t r a t e d by problems w i t h m a t r i x i n v e r s i o n . Use of the b o o t s t r a p r e s a m p l i n g method ( E f r o n 1982) , was p r o h i b i t e d by a lack of computer p r o c e s s i n g t i m e . Table 4 . 7 . 3 . 1 . Comparison of d i f f e r e n t models e x p l a i n i n g d e n s i t i e s and s i z e f requency d i s t r i b u t i o n s of C . magi s t e r in sets of t r a p s which e x p e r i e n c e d d i f f e r e n t soak t imes and b a i t ages d u r i n g e q u i v a l e n t exper iments i n 1985 and 1986. The o b j e c t i v e f u n c t i o n (A) i s the s e p a r a t i o n s t a t i s t i c of Schnute and F o u r n i e r (1980) . P i s the number of parameters i n the model . AIC (see t e x t ) measures model p e r f o r m a n c e , the lower the va lue the more s u i t a b l e the model . 1985 1986 Model A P AIC A P AIC 1. Constant e n t r y r a t e s 3 657 20 697 736 18 772 2 . Agon i s t i c - i n t e r a c t i o n s b 433 22 477 549 20 589 3 . B a i t - e f f e c t i v e n e s s c 601 22 645 545 20 585 4 . 2 and 3 a b o v e d 422 24 470 469 22 513 T h i s model expects 5 mm CW i n t e r v a l . a s y m p t o t i c a l l y (Eq T h i s model expects d i s t r i b u t i o n s over T h i s model expects d i s t r i b u t i o n s over T h i s model expects d i s t r i b u t i o n s over and R2<1 .0 ) . the same e n t r y r a t e over time for each The number o f crabs i n a t r a p i n c r e a s e s n . 4 . 7 . 3 . 1 w i t h R 1 =1.0 and R 2 = 1 . 0 ) . d i f f e r e n t e n t r y r a t e s and s i z e f r e q u e n c y time ( E q n s . 4 . 7 . 3 . 1 and 3, R 2 = 1 . 0 , R 1 <1 .0 ) d i f f e r e n t e n t r y r a t e s and s i z e f r e q u e n c y t ime ( E q n s . 4 . 7 . 3 . 1 and 5, R 1 = 1 . 0 , R 2 < 1 . 0 ) d i f f e r e n t e n t r y r a t e s and s i z e f r e q u e n c y t ime ( E q n s . 4 . 7 . 3 . 1 , 3 and 5, R 1 <1.0 S e c t i o n 4 . 7 . 3 Page 57 D i f f e r e n c e s i n the parameter e s t imates for the a g o n i s t i c -i n t e r a c t i o n s e q u a t i o n ( E q n . 4 . 7 . 3 . 3 , F i g . 4 . 7 . 3 . 3 ) for the i985 and 1986 exper iments may r e f l e c t d i f f e r e n c e s i n the s i z e f requency d i s t r i b u t i o n s of the crab p o p u l a t i o n s for 1985 and 1986. E q u a t i o n 4 . 7 . 3 . 3 cannot account for s i z e - d e p e n d e n t b i a s e s i n the r e l a t i v e c o m p e t i t i v e n e s s of C . magi s t e r i n d i v i d u a l s , so the h i g h e r d e n s i t y of s m a l l e r c r a b s i n the 1985 exper iments might be expected to produce parameter e s t imates d i f f e r e n t from those o b t a i n e d for the 1986 e x p e r i m e n t s . F o r t y - f o u r p e r c e n t (44%) of the 1602 crabs c a p t u r e d i n the 1985 experiments were <130 mm CW, compared to o n l y 15% of the 2220 crabs c a p t u r e d i n the 1986 e x p e r i m e n t s . As e x p l a i n e d i n S e c t i o n 4 . 7 . 2 , t r a p s are i n e f f e c t i v e i n r e t a i n i n g crabs <135 mm CW. Thus , the d i f f e r e n c e i n the parameter e s t imates for t h i s model may a l s o r e f l e c t poor e s t i m a t e s of c r a b r e t e n t i o n p r o b a b i l i t i e s for these c r a b s . D i f f e r e n t parameter e s t i m a t e s for the b a i t - e f f e e t i v e n e s s e q u a t i o n ( E q n . 4 . 7 . 3 . 5 , F i g . 4 . 7 . 3 . 4 ) between 1985 and 1986 may be due to h a b i t a t d i f f e r e n c e s . The 1985 experiments were per formed i n 12 m deep, calm water i n upper Lemmens I n l e t , whereas the 1986 exper iments were performed i n 8 m deep water w i t h s t r o n g t i d a l c u r r e n t s near Ind ian I s l a n d . B a i t e f f e c t i v e n e s s p r o b a b l y d i m i n i s h e d l e s s r a p i d l y near Ind ian I s l a n d because of g r e a t e r f l u s h i n g of the b a i t and a more e x t e n s i v e odour t r a i l . In c o n t r a s t , i n upper Lemmens I n l e t , once the l i q u i d content of the b a i t d i s s i p a t e d a f t e r a one or two day soak t h e r e was l i t t l e c u r r e n t to produce an e f f e c t i v e odour t r a i l . S e c t i o n 4 . 7 . 3 Page 58 F u r t h e r , the sm a l l e r crabs p r e s e n t i n 1985 may have been a t t r a c t e d to t r a p s as a r e f u g e , t h e r e b y c a u s i n g a h i g h c a t c h ra te in the absence of b a i t . F i g u r e 4 . 7 . 3 . 5 p r e s e n t s response s u r f a c e p l o t s of the p r e d i c t e d numbers of crabs i n each 5 mm CW i n t e r v a l w i t h i n a 20 t r a p set as a f u n c t i o n of soak t i m e . The r e d u c t i o n i n e n t r y r a t e s , and i n the number of s m a l l e r crabs i n the t r a p s , over time i s e v i d e n t for both the 1985 and 1986 e x p e r i m e n t s . The v i r t u a l e n t r y r a t e f o r any 5 mm CW i n t e r v a l i s the s l o p e , at t ime = z e r o , of the number of crabs as a f u n c t i o n of t i m e . The p r e d i c t e d and observed s i z e frequency d i s t r i b u t i o n s for the 1, 2, 5, 10 and 20 day soak t ime t r i a l s are compared i n F i g . 4 . 7 . 3 . 2 . F i g u r e 4 . 7 . 3 . 6 p r e s e n t s response s u r f a c e p l o t s comparing the p r e d i c t e d and observed numbers of crabs i n each 5 mm CW i n t e r v a l w i t h i n a 16 t r a p set r e p r e s e n t i n g b a i t ages (at the t ime b a i t i s p l a c e d i n a t r a p ) from zero to e igh t d a y s . The observed s i z e f requency d i s t r i b u t i o n for the n i n t h day was o b t a i n e d w i t h no b a i t i n the t r a p s . The decrease i n b a i t e f f e c t i v e n e s s over t ime , as shown i n F i g . 4 . 7 . 3 . 4 , does not appear as d r a m a t i c a l l y i n F i g . 4 . 7 . 3 . 6 because of the confound ing e f f e c t s of a g o n i s t i c i n t e r a c t i o n s and escapement. R e s i d u a l s are not randomly d i s t r i b u t e d above and below the p lane of the response s u r f a c e i n F i g s . 4 . 7 . 3 . 2 and 6. There are s e v e r a l p o s s i b l e r e a s o n s . It may (1) r e f l e c t poor e s t i m a t e s of crab r e t e n t i o n p r o b a b i l i t i e s f or p a r t i c u l a r carapace width S e c t i o n 4 . 7 . 3 Page 59 i n t e r v a l s , (2) r e f l e c t the i n f l u e n c e of t i d e s , c u r r e n t s or other i n t e r v e n t i o n s , (3) i n d i c a t e imperfec t u n d e r s t a n d i n g of a g o n i s t i c -i n t e r a c t i o n s and b a i t - e f f e e t i v e n e s s p r o c e s s e s , and (4) i n d i c a t e the presence of u n i d e n t i f i e d p r o c e s s e s . In p a r t i c u l a r , the t h e o r e t i c a l s u i t a b i l i t y of the a g o n i s t i c - i n t e r a c t ions e q u a t i o n i s d i f f i c u l t to e v a l u a t e s i n c e l i t t l e i s known about the dynamics of such i n t e r a c t i o n s . The s i z e f r e q u e n c y d i s t r i b u t i o n s , and abundance of l e g a l - s i z e d male s , were more t y p i c a l of commercial t r a p s i n the Ind ian I s l a n d exper iments than in the upper Lemmens I n l e t exper iments . T h u s , the 1986 experiments were c o n s i d e r e d to p r o v i d e b e t t e r parameter e s t i m a t e s for the e q u a t i o n s mode l ing the dynamic i n t e r a c t i o n s between crabs and commercia l t r a p s . A l though the g e n e r a l model i n c l u d i n g both the a g o n i s t i c -i n t e r a c t i o n s and changes i n b a i t e f f e c t i v e n e s s e q u a t i o n s i s i m p e r f e c t , the 1986 parameter es t imates for t h i s model were used when s t a n d a r d i z i n g commercia l samples to reduce b i a s i n t r o d u c e d by d i f f e r e n t soak t imes and t r a p t y p e s . Another r e s u l t of d i f f e r e n t soak t imes was d i f f e r e n t p r o p o r t i o n s of h a r d - and s o f t - s h e l l e d crabs w i t h i n t r a p s . L e g a l - s i z e d males are s o f t - s h e l l e d for the f i r s t few months f o l l o w i n g a moult (see T a b l e 4 . 1 0 . 1 , page 80 ) , and d u r i n g t h i s p e r i o d they enter t r a p s , but are v u l n e r a b l e i n c o n t e s t s w i t h h a r d c r a b s . F i g u r e 4 . 7 . 3 . 7 suggests s o f t - s h e l l e d crabs may not r e a d i l y enter or s u r v i v e i n t r a p s c o n t a i n i n g h a r d - s h e l l e d c r a b s . S e c t i o n 4 .7 .3 Page 60 c CD O i_ CD CX o "2 LLl ZD o UJ cr u_ 2 0 - i 10 -0 BE 1985 n = l40 2 0 - i 10 0 1 — I — I I ST 1985 ,-, n = l70 nilOILn i i i i—r E l 1 I I on DflilD n T — i — i — r 20 - i 1 0 -o- i—r 2 0 - | BE 1986 n = 194 OIMQ I i i i i r i r io o ST 1986 n = 223 DDII n r i n - . i—i—i—r—i—i—i—i i i n 82.5 102.5 122.5 142.5 162.5 182.5 CARAPACE WIDTH (±2.5mm) F i g u r e 4 . 7 . 3 . 1 . Comparison of s i z e f requency d i s t r i b u t i o n s of C . magi s t e r i n t r a p s soaked 24 h i n the soak t ime ( S T , 20 t r a p s ) and b a i t e f f e c t i v e n e s s ( B E , 16 t r a p s ) exper iments i n 1985 and 1986. Female carapace widths are e x p r e s s e d as male-e q u i v a l e n t carapace widths for the same body l e n g t h s . F i g u r e 4 . 7 . 3 . 1 Page 61 1985 1986 40 30 20 10 0 40 30 20 i 10 « 0 v 40 Q. ~ 30 20 • 10 UJ § o. LU 40 tr ^ 30 20 10 0-40 30 20 10 • 0 I DAY SOAK n « 170 Mia i r 2 DAY SOAK n * 17 M B T——r 5 DAY SOAK n = 19 I i i r 10 DAY SOAK n = 145 i i r 20 DAY SOAK n = 154 .n£8a*_ I DAY SOAK n » 23 "i 1 1 1 i • 2 DAY SOAK n = 194 10 DAY SOAK n = 205 i r 20 DAY SOAK n = 209 T T T 87.5 12.5 137.5 162.5 187.5 87.5 12-5 137.5 162.5 187-5 CARAPACE WIDTH (±2.5mm) F i g u r e 4 . 7 . 3 . 2 . S i z e f requency d i s t r i b u t i o n s of C . magi s t e r for se ts of 20 type A t r a p s w i t h d i f f e r e n t soak t imes from e q u i v a l e n t exper iments i n 1985 and 1986. S o l i d c i r c l e s p r o f i l e p r e d i c t e d s i z e f requency d i s t r i b u t i o n s u s i n g Model '4 ' (Tab le 4 . 7 . 3 . 1 ) . Female carapace widths are e x p r e s s e d as male-e q u i v a l e n t carapace widths for the same body l e n g t h s . F i g u r e 4 . 7 . 3 . 2 Page 62 0 5 10 15 20 25 30 W E I G H T R A T I O F i g u r e 4 . 7 . 3 . 3 . The r e l a t i v e r a t e at which C . magi s t e r en ter T r a p A, as a f u n c t i o n of the r a t i o between the weight of crabs i n a t r a p , and the weight o f the crab a t t e m p t i n g to enter the t r a p . T h i s p l o t uses the bes t parameter e s t i m a t e s for E q n . 4 . 7 . 3 . 3 from Model '4 ' ( T a b l e 4 . 7 . 3 . 1 ) . F i g u r e 4 . 7 . 3 . 3 Page 63 r -U UJ U_ U_ LLl 5 ° - 6 H 00 UJ > UJ o r 0 .8 -0 . 4 -0 . 2 -0 . 0 0 1985 EXPERIMENTS Y = 0 . 6 6 9 + ( 1 . 0 - 0 . 6 6 9 ) - e _ l -25 -x 1986 EXPERIMENTS Y = 0 . 4 9 3 + ( 1 . 0 - 0 . 4 9 3 ) • e"0.405-x n 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 B A I T A G E (days) Figure 4 . 7 . 3 . 4 . The r e l a t i v e entry rate of C . magister into Trap A as a function of bait age. This plot uses the best parameter estimates for Eqn. 4 . 7 . 3 . 5 from Model ' 4 ' (Table 4 .7 .3 .1 ) . Figure 4 . 7 . 3 . 4 Page 64 CARAPACE WIDTH (±2.5mm) F i g u r e 4 . 7 . 3 . 5 . Response s u r f a c e of the p r e d i c t e d changes i n the s i z e f requency d i s t r i b u t i o n of C . magi s t e r w i t h i n 20 type A t r a p s , as a f u n c t i o n of t i m e . These r e s u l t s use the best parameter e s t i m a t e s for E q n s . 4 . 7 . 3 . 3 and 5 from Model '4 ' (Tab le 4 . 7 . 3 . 1 ) . Female carapace w id ths are e x p r e s s e d as male-e q u i v a l e n t carapace widths for the same body l e n g t h s . F i g u r e 4 . 7 . 3 . 5 Page 65 CARAPACE WIDTH (±2.5mm) 1986 CARAPACE WIDTH (±2.5mm) F i g u r e 4.7.3.6. Response s u r f a c e of the p r e d i c t e d s i z e f requency d i s t r i b u t i o n s of C. magi s t e r w i t h i n 10 s e t s of 16 type A t r a p s . Each set used b a i t r a n g i n g i n age from zero to e i g h t d a y s , soaked for one day . The b a i t was removed for the n i n t h day . The v e r t i c a l l i n e s show the observed d a t a for a p a r t i c u l a r c o m b i n a t i o n of b a i t age and carapace w i d t h , f or d i f f e r e n c e s g r e a t e r than one. These r e s u l t s use the best parameter e s t imates for Eqns . 4.7.3.3 and 5 from Nodel '4' ( T a b l e 4 . 7 . 3 . 1 ) . Female carapace widths are expres sed as m a l e - e q u i v a l e n t carapace widths for the "same body l engths . F i g u r e 4.7 .3.6 Page 66 22 50 - i \~ 40 u_ O CO S . D . -z. UJ or UJ 30 -20 10 -0 0 2d \ 3 9 I 60 \ 62 ~~\ 1 r~ 5 10 15 S O A K T I M E (days) 20 F i g u r e 4.7.3.7. The p e r c e n t of s o f t - s h e 11ed l e g a l - s i z e d male C . mag i s t er i n T r a p A , as a f u n c t i o n of soak t i m e . These r e s u l t s were o b t a i n e d from the soak time experiment performed near Ind ian I s l a n d (H; F i g . 2 . 1 , page 9) i n 1986. Above the S . D . bars i s the number of l e g a l - s i z e d males caught i n 20 t r a p s . F i g u r e 4.7.3.7 Page 67 4.8 TRAP DISTRIBUTION F i g u r e 4 . 8 . 1 b p r e s e n t s time s e r i e s p r o f i l e s f or the number of t r a p s f i s h e d at s p e c i f i c s i t e s throughout the main s tudy a r e a . F i g u r e 4 . 8 . 1 a compares the number of t r a p s f i s h e d i n Lemmens I n l e t as de termined (1) by c o u n t i n g the t r a p buoys a n d , (2) from i n t e r v i e w s w i t h the f i s h e r m e n . The s i m i l a r i t y of the assessments suggests the time s e r i e s p r o f i l e s i n F i g . 4 . 8 . 1 b are an a c c u r a t e documentat ion of t r a p d i s t r i b u t i o n s . S e c t i o n 4 .7 .3 Page 68 cn Q-< cr o cr LU CD 1000-1 800 600-400-200 • TRAP COUNT • INTERVIEWS WITH FISHERMEN o-h—T i — i — I — i — i i—i—r i—r—i—r 2000 -j 1600 -1200-800 -4 0 0 -• STUDY SITE (excluding o,a,• ) o LEMMENS INLET ( A- D) A INDIAN ISLAND (H) • BROWNING PASSAGE • ELSEWHERE ' l G ) ! i I r M J J A S O N D l J F M A M J J A S O N 1985 1986 DATE F i g u r e 4 . 8 . 1 . (A) Time s e r i e s comparison of the number of t r a p buoys counted i n Lemmens I n l e t , and the number of t r a p s e s t i m a t e d by i n t e r v i e w i n g f i s h e r m e n . (B) Time s e r i e s of the number of t r a p s e s t i m a t e d by i n t e r v i e w i n g f i s h e r m e n . The ' E l s e w h e r e ' c a t e g o r y i n c l u d e s t r a p s f i s h e d o u t s i d e the s tudy area i n S t a t i s t i c a l Area 24 by f i shermen who a l s o f i s h i n the s tudy a r e a . The c a p i t a l l e t t e r s i n parentheses i d e n t i f y these areas i n F i g . 2.1 (page 9 ) . F i g u r e 4 .8 .1 Page 69 4 . 9 COMMERCIAL EXPLOITATION OF MALES I d e f i n e the degree of e x p l o i t a t i o n of l e g a l - s i z e d males as the p r o p o r t i o n of males m i s s i n g from the 155.0+11.2 mm i n s t a r . T h i s p r o p o r t i o n was e s t i m a t e d u s i n g a s i z e f requency a n a l y s i s which measured the p r o p o r t i o n of males m i s s i n g from the 155.0 mm i n s t a r , as d e s c r i b e d d i a g r a m m a t i c a l 1 y i n F i g . 4 . 9 . 1 . The i n f l u e n c e of the 183.8 mm i n s t a r i s unimportant because of low s u r v i v o r s h i p to t h i s i n s t a r ( S e c t i o n 4 . 1 3 ) . As e v i d e n t i n F i g . 4 . 9 . 1 , there i s l i t t l e o v e r l a p between the 155.0 mm and the next s m a l l e r 128.0+10.5 mm i n s t a r , w i t h the 155.0 mm i n s t a r r e m a i n i n g r e l a t i v e l y d i s t i n c t even when c o n s i d e r a b l y lower i n abundance than the 128.0 mm i n s t a r . N e v e r t h e l e s s , to reduce the i n f l u e n c e of s m a l l e r i n s t a r s , whose abundance i s l e s s c o n f i d e n t l y measured, the s i z e f requency a n a l y s e s were performed on a subset of the d i s t r i b u t i o n s >145 mm CW. S ince males c o n t i n u a l l y moult i n t o t h i s i n s t a r , which I d e f i n e by s i z e and not by c o h o r t , the p r o p o r t i o n e x p l o i t e d measures the d i f f e r e n c e between r e c r u i t m e n t and e x p l o i t a t i o n . Before p e r f o r m i n g the s i z e f requency a n a l y s e s measur ing e x p l o i t a t i o n of the 155.0 mm i n s t a r , the s i z e f requency d i s t r i b u t i o n s were s t a n d a r d i z e d to min imize b i a s i n t r o d u c e d by d i f f e r e n t soak t i m e s . T h i s was done u s i n g the r e s u l t s from the model which a n a l y z e d the soak time and b a i t - e f f e c t i v e n e s s exper iments ( S e c t i o n 4 . 7 . 3 ) . The parameter e s t imates for Eqns . 4 . 7 . 3 . 3 and 5 (pages 55 and 56) o b t a i n e d for the 1986 exper iments near I n d i a n I s l a n d were u s e d . The unknown parameters are the S e c t i o n 4.9 Page 70 ' v i r t u a l e n t r y r a t e s ' for each 5 mm CW i n t e r v a l . The v e c t o r of c r a b r e t e n t i o n p r o b a b i l i t i e s ( f o r each 5 ram CW i n t e r v a l ) a p p r o p r i a t e for each t r a p type ( T a b l e 4 . 7 . 2 . 2 , page 47) was used to e s t imate the escapement of crabs from t r a p s . The s t a n d a r d i z a t i o n model s i m u l a t e d the e n t r y and e x i t of crabs i n t o the set of t r a p s c o m p r i s i n g the commercial sample . The accepted e s t i m a t e s for the v e c t o r of v i r t u a l e n t r y r a t e s were those which y i e l d e d the s i z e frequency d i s t r i b u t i o n , a f t e r the a p p r o p r i a t e soak t i m e , which most c l o s e l y resembled that of the commercial sample . As i n the a n a l y s i s of the soak time and b a i t e f f e c t i v e n e s s e x p e r i m e n t s , the s e p a r a t i o n s t a t i s t i c ' A ' of Schnute and F o u r n i e r (1980) , was used to e v a l u a t e the parameter est i m a t e s . F i g u r e 4 .9 .2 p l o t s the percent of l e g a l - s i z e d male C . magi s t e r taken by the f i s h e r y for dates from A p r i l 1985 u n t i l August 1986. E x p l o i t a t i o n i n c r e a s e d r a p i d l y i n s p r i n g 1985 and remained at 60-90%. In upper Lemmens I n l e t , a poorer crab h a b i t a t , e x p l o i t a t i o n was near 100%. T h i s r a p i d i n c r e a s e i n e x p l o i t a t i o n suggests h a r v e s t i n g of a p r e v i o u s l y u n a v a i l a b l e 155.0 mm i n s t a r abundant i n 1985 and 1986. The number of t r a p s i n c r e a s e d s t e a d i l y u n t i l summer 1986 ( F i g . 4 . 8 . 1 b , page 69) i n response to f i s h i n g s u c c e s s . I f the 1985 and 1986 155.0 mm i n s t a r s were indeed more abundant than i n the i m m e d i a t e l y p r e c e d i n g y e a r s , one would expect an i n c r e a s e i n abundance of s u b l e g a l - s i z e d males i n the 155.0 mm i n s t a r over t h i s p e r i o d . F i g u r e 4 .9 .3 shows that the Sect i on 4.9 Page 71 v i r t u a l e n t r y r a t e s for males 145-155 mm CW a p p r o x i m a t e l y d o u b l e d . Because of h i g h n a t u r a l m o r t a l i t y ( S e c t i o n 4 . 1 3 ) , the r e c r u i t m e n t r a t e over t h i s p e r i o d was p r o b a b l y much g r e a t e r , s u g g e s t i n g there may have been l a r v a l s e t t l ement i n t h i s area i n 1982 and 1983, but not i n . 1981 . F i g u r e 4 .9 .4 shows that f i s h i n g success ( the number of l e g a l - s i z e d males caught per 100 t r a p s per soak day) i n Lemmens I n l e t i n c r e a s e d d u r i n g s p r i n g and summer and was poor i n w i n t e r . O u t s i d e Lemmens I n l e t f i s h i n g success remained r e l a t i v e l y cons tant throughout the y e a r . The p a t t e r n observed i n Lemmens I n l e t p r o b a b l y r e f l e c t s r e l a t i v e abundance s i n c e e x p l o i t a t i o n r a t e s there were h i g h , i . e . a h i g h t r a p d e n s i t y ( F i g . 4 . 8 . 1 , page 69) and shor t (1-2 days) soak t i m e s . A s i m i l a r seasona l p a t t e r n of abundance i s suggested by the s t a n d a r d i z e d da ta i n F i g . 4 . 9 . 5 . In c o n t r a s t , the absence of a s easona l p a t t e r n s i m i l a r to that observed , i n Lemmens I n l e t ( F i g . 4 . 9 . 4 ) o u t s i d e of Lemmens I n l e t i s p r o b a b l y due to the r e l a t i o n s h i p between abundance and ca tch r a t e b e i n g d i s g u i s e d by lower e f f o r t , i . e . a lower t r a p d e n s i t y ( F i g . 4 . 8 . 1 ) and longer ( o f t e n at l e a s t a week) soak times.-For reasons e x p l a i n e d above, the h i g h c a t c h r a t e near Indian I s l a n d i n s p r i n g 1986 i s thought to r e s u l t from r e c r u i t m e n t to the f i s h e r y of the 1983 y e a r - c l a s s which may have s e t t l e d on adjacent m u d f l a t s . E f f o r t i n c r e a s e d near I n d i a n I s l a n d about t h i s time ( F i g . 4 . 8 . 1 b , page 69) i n response to the i n c r e a s e d c a t c h r a t e . Sect i on 4.9 Page 72 L E G A L SIZE C A R A P A C E W I D T H (mm) F i g u r e 4 . 9 . 1 . Diagram e x p l a i n i n g how the degree of e x p l o i t a t i o n of male C . m a g i s t e r i n the 155.0+11.2 mm i n s t a r was e s t i m a t e d . The p r o p o r t i o n e x p l o i t e d (A+[A+B]) was de termined by-s i z e f requency a n a l y s i s . F i g u r e 4 .9 .1 Page 73 Q UJ O 100 - i 80 -Sc 60 UJ <D®® ®S).®.®®®®(5) ® UJ o or UJ Q_ 40 -20 -• ® T R A P T Y P E A • ® T R A P T Y P E B o --—i—l—i—I—l—l—I—I—I—I—I—l—l—l—l—I—l—l—f A M J J A S O N D ' J F M A M J J A S 19 8 5 1 9 8 6 D A T E F i g u r e 4.9.2. The p e r c e n t of l e g a l - s i z e d male C. magi s t e r removed from the 155.0 mm i n s t a r by f i s h i n g , as de termined by s i z e f r e q u e n c y a n a l y s i s of t r a p samples . The e n c i r c l e d data p o i n t s are f o r upper Lemmens I n l e t . The remainder are for the r e s t of the s tudy a r e a . F i g u r e 4.9.2 Page 74 • TRAP TYPE A • TRAP TYPE B l—I—I—i—l—l—I—l—l—I—l—l—l—I—I—I—I—I—I A M J J A S O N D ' j F M A M J J A S 1985 1986 DATE F i g u r e 4 . 9 . 3 . L i n e a r r e g r e s s i o n of v i r t u a l e n t r y r a t e s of male C . magi s t e r 145-155 mm CW i n t o t r a p s over t i m e . Data from upper Lemmens I n l e t , a poor c r a b h a b i t a t , are not i n c l u d e d i n t h i s p l o t . F i g u r e 4 .9 .3 Page 75 CO CL D O O QJ h-< or x o i -< o 2 0 0 - i 1 0 0 -• STUDY AREA (excluding A-D.H) • INDIAN ISLAND (H) 0 i—i—i—i—i—i—i—i—r T— i — i — i — i — i — i — i— I 2 0 0 - i 1 0 0 -UPPER LEMMENS INLET (A) MIDDLE 8 LOWER LEMMENS INLET i — i — i — r A M J J A S O N D l J F M A M J J A S 1 9 8 5 1986 D A T E Figure 4.9.4. Time series of commercial catch rates of lega l - s i z e d male C. magi ster. The capit a l l e t t e r s in parentheses i d e n t i f y these areas in F i g . 2.1 (page 9). Figure 4.9.4 Page 76 I to Q. D O O UJ h -< or >-rr UJ _ i < Z> i -> 250 200 H 150 H 100 50 0 • T R A P T Y P E A • T R A P T Y P E B A T R A P T Y P E D A • A A A A • A 1 I I I I I I 1 1 1 1 1 1 1 1 1 1 1 1 A M J J A S O N D ' j F M A M J J A S 1 9 8 5 1 9 8 6 DATE F i g u r e 4 .9 .5 . V i r t u a l e n t r y r a t e s of l e g a l - s i z e d male C. magister i n t o t r a p s over time. Data from upper Lemmens I n l e t , a poor crab h a b i t a t , are not i n c l u d e d i n t h i s p l o t . F i g u r e 4.9.5 Page 77 4.10 MALE MATING ACTIVITY F i g u r e 4 .10 .1 p r o f i l e s the percent o c c u r r e n c e of mat ing marks ( B u t l e r 1960 ) on the claws of males for 5 mm i n t e r v a l s r a n g i n g from 120-190 mm CW. Mat ing marks are caused by a male embracing a female and i n d i c a t e involvement i n m a t i n g . They occur w i t h i n c r e a s i n g f requency above *120 mm CW as males approach l e g a l s i z e , then l e s s f r e q u e n t l y for l e g a l - s i z e d males . Note that because the samples i n c l u d e males c o l l e c t e d a f t e r d i f f e r e n t p e r i o d s of time i n an i n s t a r , the p e r c e n t of males w i t h mating marks i s not a measure of the number of males i n a p a r t i c u l a r carapace w i d t h i n t e r v a l tha t w i l l e v e n t u a l l y mate. The d i s t r i b u t i o n of mat ing a c t i v i t y for carapace w i d t h i n t e r v a l s below l e g a l s i z e approx imates the normal d i s t r i b u t i o n of the 155.0+11.2 mm i n s t a r (see F i g . 4 . 9 . 1 , page 73 ) . S i n c e males in l a r g e r i n s t a r s are r a r e ( S e c t i o n 4 . 1 3 ) , the mat ing marks are p r e d o m i n a t e l y on males i n the 155.0 mm i n s t a r , s u g g e s t i n g that t h i s i n s t a r i s r e s p o n s i b l e for most mating a c t i v i t y . F i g u r e 4 .10 .2 compares the r e l a t i v e mat ing a c t i v i t y of s u b l e g a l - and l e g a l - s i z e d males from J u l y 1985 u n t i l August 1986. S ince mat ing marks occur i n f r e g u e n t l y on males <140 mm CW, the s u b l e g a l c a t e g o r y i n c l u d e s males 140-154 mm CW. To compare the mating a c t i v i t y of l e g a l - and s u b l e g a l - s i z e d m a l e s , a time s e r i e s of mat ing r a t i o s was o b t a i n e d by d i v i d i n g the p e r c e n t occurrence of mat ing marks on s u b l e g a l - s i z e d males by t h e i r percent o c c u r r e n c e on l e g a l - s i z e d m a l e s . An i n t e r v e n t i o n model (Noakes 1986) , u s i n g the M c L e o d - H i p e l a l g o r i t h m ( H i p e l and McLeod 1987), S e c t i o n 4.10 Page 78 r e v e a l e d no s i g n i f i c a n t a u t o c o r r e l a t i o n s in the t ime s e r i e s when comparing 1985 and 1986 mat ing r a t i o s ( F i g . 4 . 1 0 . 3 ) . T h e r e f o r e , a s t u d e n t ' s T - t e s t (Soka l and R o h l f 1981) was used to conc lude tha t the mean r a t i o for 1986 was *29% (p<.001) of the 1985 r a t i o . T h i s suggests lower mat ing a c t i v i t y by l e g a l - s i z e d males i n 1986, when e f f o r t ( F i g . 4 . 8 . 1 b , page 69) ar.d e x p l o i t a t i o n ( F i g . 4 . 9 . 2 , page 74) were h i g h e r . A h i g h e x p l o i t a t i o n r a t e means most males caught are s o f t - s h e 11ed. W i t h F = 5 .11-6 .90 and M = 3 .48 -4 .48 (from S e c t i o n 4 . 1 3 ) , o n l y 6-12% of l e g a l - s i z e d males s u r v i v e 90 d a y s , near the t ime needed for t h e i r s h e l l to h a r d e n b e f o r e they can mate ( T a b l e 4 . 1 0 . 1 ) . T h i s a n a l y s i s c o r r o b o r a t e s F i g . 4 .10 .2 which shows that mat ing marks g e n e r a l l y o c c u r r e d on <10% of l e g a l - s i z e d males i n 1986. C o v a r i a t i o n of the t ime s e r i e s for mat ing marks and hardness i s ev ident F i g . 4 . 1 0 . 2 . The i m p l i c a t i o n i s tha t e x p l o i t a t i o n r a t e s can be h i g h enough to markedly reduce the o p p o r t u n i t y f o r l e g a l - s i z e d males t o mate. The h i g h r a t i o of mat ing a c t i v i t y i n Kay 1986 ( F i g . 4 . 1 0 . 3 ) i s not t y p i c a l f or the s tudy a r e a , so was not i n c l u d e d when comparing 1985 and 1986. Most o f these crabs were h a r d - s h e 11ed, and from t h e i r s h e l l c o n d i t i o n , had not moulted r e c e n t l y . These c r a b s , w i t h an e s t i m a t e d age o f at l e a s t four y e a r s , b r i e f l y appeared in s h a l l o w water near the open coast ( F ; F i g . 2 . 1 , page 9 ) , p o s s i b l y from nearby d e e p e r , more s h e l t e r e d , h a b i t a t where they w i n t e r e d . They do not r e f l e c t the m o u l t i n g and mating a c t i v i t y of the l o c a l s h a l l o w water p o p u l a t i o n . S i m i l a r movement was observed for s m a l l ( f i r s t - y e a r ) crabs ( S e c t i o n 4 . 1 1 ) . S e c t i o n 4.10 Page 79 T a b l e 4 . 1 0 . 1 . The p e r c e n t of male C . magi s t e r , tagged when s o f t - s h e 11ed, which were h a r d - s h e l l e d when r e c o v e r e d . The r e s u l t s are r e p o r t e d for 30 day i n t e r v a l s of t i m e - a t - l a r g e . The carapace w id ths of r e c o v e r e d males were a p p r o x i m a t e l y n o r m a l l y d i s t r i b u t e d (153.4+6.0 mm) and ranged from 135-173 mm. T i m e - a t - l a r g e (d ) Sample s i z e P e r c e n t h a r d - s h e l i e d 1-30 31 32.3+ 8 . 4 a 31-60 20 6 0 . 0 ± 1 1 . 0 . 61-90 23 91 .3+ 5.9 >90 56 100.0 a 1 S . E . o f the e s t i m a t e . S e c t i o n 4.10 Page 80 CO cr < X t h-UJ o rr UJ o_ 5 0 -. 4 0 -3 0 -2 0 1 0 0 S.E o C D II O in ii c — CO CO r o n n c c 1 2 2 . 5 1 3 2 . 5 1 4 2 . 5 1 5 2 . 5 1 6 2 . 5 1 7 2 . 5 1 8 2 . 5 CARAPACE WIDTH (± 2.5mm ) Figure 4.10.1. The percent of male C. magister with mating marks (Butler 1960) as a function of carapace width. The minimum legal size l i m i t i s ==154 mm CW. Figure 4.10.1 Page 81 100 - i 80 -60 -U J (J rr U J D _ 40 20 Hard shell Legal-sized males.with mating marks Sublegal-sized males with mating marks 33 1 1—I 1—I 1 1—I 1 1 1 I 1 I 1 I 1 1—I A M J J A S O N D I J F M A M J J A S I 9 8 5 D A T E 1986 F i g u r e 4 . 1 0 . 2 . T i m e s e r i e s o f t h e p e r c e n t o f h a r d - s h e l l e d l e g a l - s i z e d (>154 mm CW) m a l e , l e g a l - s i z e d m a l e w i t h m a t i n g m a r k s ( B u t l e r 1 9 6 0 ) , a n d s u b l e g a l - s i z e d ( 1 4 0 - 1 5 4 mm CW) m a l e C . m a g i s t e r w i t h m a t i n g m a r k s . E x c e p t w h e r e n o t e d , a l l s a m p l e s i z e s a r e >100 c r a b s . F i g u r e 4 . 1 0 . 2 P a g e 82 I-< rr 0.5-1 0 . 4 -1985 M E A N = 0 . 3 -0.2 -0.1 -1986 M E A N = . 0 9 6 0 .0 - -—i—|—i—i—i—\—i—i— r A M J J A S O N D l j F M A M J J A S 1985 1986 D A T E F i g u r e 4 . 1 0 . 3 . Time s e r i e s i n d i c a t i n g t h a t the r e l a t i v e l e v e l of mat ing a c t i v i t y by l e g a l - s i z e d male C . magi s t e r i n 1986 was =*29% of the l e v e l i n 1985. The s u b l e g a l : 1 ega l mat ing r a t i o i s o b t a i n e d by d i v i d i n g the p e r c e n t of l e g a l - s i z e d males w i t h mat ing marks by the p e r c e n t of s u b l e g a l - s i z e d males w i t h mat ing marks . The r a t i o for May 1986 was e x c l u d e d from the comparison for reasons g i v e n i n the t e x t . F i g u r e 4 .10 .3 Page 83 4.11 SPATIAL AND TEMPORAL DISTRIBUTIONS Beam trawl surveys in 1985 and 1986 co l l ec t ed few small C. magi ster except in the se lected locations considered below. In 46 beam trawl samples, one year o ld ( « 4 0 - 7 5 mm CW) and two year old (*75-145 mm CW) crabs (Butler 1961, Stevens and Armstrong 1984) were found at dens i t ies general ly less than 10 i n d - h a " 1 . Where higher dens i t i es were found, there were important seasonal d i f ferences , and di f ferences in the r e l a t i v e proport ions of males and females. Note that beam trawls are not 100% e f f i c i e n t , so reported dens i t i e s are only an index of abundance. A peak in abundance of male and female one year o ld crabs on the shallow sand bottom of an exposed shore occurred in summer 1985 ( F i g . 4 .11.1b) . Their occurrence is suspected to be the resu l t of movement into shallower water (E; F i g . 2 .1 , page 9) of the 1984 year-c lass which s e t t l e d on the outer coast . Abundance decl ined q u i c k l y , but some may have moved to the entrance of Lemmens Inlet by December 1985 ( F i g . 4.11.1a). S imi lar movement of larger crabs into shallow water is described in Sect ion 4.10. In upper Lemmens Inlet the dens i t ies of two year o ld males and females were i n i t i a l l y low in summer 1985 and dec l ined through 1986 ( F i g . 4 .11.2a) . This cohort was abundant elsewhere suggesting upper Lemmens Inlet is poor crab h a b i t a t . The highest densi ty of males was observed in middle Lemmens Inlet ( F i g . 4 .11.2b) . During autumn 1985 and the subsequent winter, male dens i t i e s s t e a d i l y increased to >1200 ind-ha"*. Section 4.11 Page 84 Toward the mouth of Lemmens I n l e t male d e n s i t i e s g e n e r a l l y d e c l i n e d ( F i g . 4 . 1 1 . 2 c , d ) . Because d e n s i t i e s of two to three year o l d males e lsewhere were c o n s i s t e n t l y low, the i n c r e a s e i n the number of males i n middle Lemmens I n l e t c o u l d be due to movement away from exposed s h a l l o w water d u r i n g w i n t e r . They may have c o n c e n t r a t e d i n middle Lemmens I n l e t because of poor h a b i t a t f u r t h e r up the i n l e t . The h i g h d e n s i t y of males i n middle Lemmens I n l e t decreased r a p i d l y d u r i n g l a t e s p r i n g 1986. Most males were i n the 128.0 mm i n s t a r ( T a b l e 4 . 6 . 3 , page 41) and moulted to l e g a l s i z e i n 1986, a f t e r which they were soon caught in an intense f i s h e r y . F i g u r e 4 . 8 . 1 b (page 69) suggests tha t 25-35% of the f i s h i n g e f f o r t , i n the s tudy area was c o n c e n t r a t e d i n Lemmens I n l e t d u r i n g s p r i n g 1986. Males began to enter the f i s h e r y about t h r e e y e a r s a f t e r l a r v a l s e t t l ement ( i n s p r i n g 1986) , and c o n t i n u e d t o moult, t o l e g a l s i z e for the next 6-9 months (see F i g . 4 . 1 3 . 3 , page 105) . A h i g h d e n s i t y of two year o l d females was observed i n the narrow channel at the lower end of Lemmens I n l e t i n June 1985 ( F i g . 4 . 1 1 . 2 c ) . D e n s i t y d e c l i n e d a f t e r t h i s d a t e , but i n c r e a s e d d u r i n g autumn i n the e n t r a n c e to Lemmens I n l e t ( F i g . 4 .11;2d) 0 . 5 - 1 . 0 km seaward of the narrow c h a n n e l . Female d e n s i t y f u r t h e r up Lemmens I n l e t c o n t i n u e d to d e c l i n e s u g g e s t i n g seaward movement. The i n c r e a s e i n female abundance i n September 1986 where the main channel out of the s tudy area meets the open coast Sect i o n 4.11 Page 85 ( F i g . 4 . 1 1 . 1 c ) a l s o suggests seaward movement of f emale s . These females were three years o l d and were m a i n l y i n the 135.5 and 149.4 mm i n s t a r s (Tab le 4 . 6 . 4 , page 42) . D e s p i t e the h i g h d e n s i t y of females i n the channel at the mouth of Lemmens I n l e t d u r i n g summer 1985 ( F i g . 4.11 .2c) i t appears t h a t a l l females t h a t moul ted to the next i n s t a r were mated ( F i g . 4 . 3 . 1 , page 29) . Most of the data for the s m a l l e r females i n F i g . 4 . 3 . 1 , which documents the percent of females i n s e m i n a t e d as a f u n c t i o n of carapace w i d t h , were o b t a i n e d from crabs c o l l e c t e d near t h i s l o c a t i o n . The r e l a t i v e abundance of l a r g e r females i n the s tudy a r e a was a s s e s s e d by t r a p s a m p l i n g . Females were most abundant i n s p r i n g ( F i g . 4 . 1 1 . 3 ) perhaps because they forage more a c t i v e l y a f t e r a w i n t e r of i n c u b a t i n g eggs . The h i g h e s t o b s e r v e d abundance of females i n s p r i n g 1985 and 1986 was in the main channel out of the s tudy a r e a ( T a b l e 4.11.1) where the h i g h abundances of the 135.5 and 149.4 mm i n s t a r s were c o l l e c t e d i n beam t r a w l s i n September 1986. T a b l e 4.11.1 r e p o r t s on. females >145 mm CW m a i n l y r e p r e s e n t i n g i n s t a r s four and f i v e y e a r s o l d . Females t h i s s i z e have a h i g h m o r t a l i t y r a t e (M>2.0, Hankin et a l . 1985 ) , so the lower c a t c h r a t e s i n 1986 may i n d i c a t e a weak 1981 y e a r - c l a s s , as i n t e r p r e t e d from F i g . 4 . 9 . 3 (page 7 5 ) . The r e l a t i v e l y h i g h d e n s i t i e s of male and female C. magi s t e r c o l l e c t e d i n beam t r a w l samples near I n d i a n I s l a n d ( T a b l e 4 . 1 1 . 2 ) may have r e s u l t e d from a l a r v a l s e t t l ement on nearby m u d f l a t s i n S e c t i o n 4.11 Page 86 1983. In c o n t r a s t to Lemmens I n l e t , near I n d i a n I s l a n d male d e n s i t y d e c r e a s e d r e l a t i v e to female d e n s i t y from 1985 to 1986. Females may p r e f e r an open coast h a b i t a t , but deep water s u r r o u n d i n g I n d i a n I s l a n d may prevent easy a c c e s s to Browning Passage , t h e r e b y c o n f i n i n g them to the Ind ian I s l a n d a r e a . T a b l e s 4 .11 .3 and 4 summarize tag r e l e a s e s and r e c o v e r i e s of male and female C. magi s t e r . r e s p e c t i v e l y . Most male and female r e c o v e r i e s o c c u r r e d near where they were t a g g e d . The on ly s u g g e s t i o n of d i r e c t i o n a l movement i s the l a r g e number of r e c o v e r i e s of males , tagged i n the poor h a b i t a t o f upper Lemmens I n l e t , lower down the i n l e t . However, t h i s p r o b a b l y a l s o r e s u l t s from o n l y 2.8% of f i s h i n g e f f o r t b e i n g i n upper Lemmens I n l e t . Only two male , and no female , r e c o v e r i e s were from o u t s i d e the main study a r e a d e s p i t e a l a r g e number of t r a p s f i s h e d ' e l s e w h e r e ' by l o c a l f i shermen ( F i g . 4 . 8 . 1 b , page 69 ) , sugges t ing l i t t l e movement of crabs from the s tudy a r e a . S i m i l a r l y , male and female movement near I n d i a n I s l a n d i s r e s t r i c t e d , as p r e v i o u s l y s u r m i s e d , w i t h 35 of 41 males , and 20 of 21 females , r e c o v e r e d near where they were t a g g e d . His tograms of mean d i s t a n c e s moved a l s o i n d i c a t e l i m i t e d movement ( F i g . 4 . 1 1 . 4 ) . Males and females moved (net d i s t a n c e ) , on average , l e s s than 30 and 20 m per day , r e s p e c t i v e l y . A s imple t w o - d i m e n s i o n a l random d i s p e r s i o n model e s t i m a t e d that the h i s t o g r a m of mean d i s t a n c e s moved by males ( F i g . 4 . 1 1 . 4 ) c o u l d be e x p l a i n e d by a p o p u l a t i o n whose gros s movement r a t e s ( i n m-d" 1 ) are d e s c r i b e d by the f o l l o w i n g l o g - n o r m a l d i s t r i b u t i o n . S e c t i o n 4.11 Page 8 7 G = 2 8 0 - e x p ( l . 1 - v ) (4.11 .1 ) where: G i s a p o i n t on the d i s t r i b u t i o n of d a i l y movement r a t e s (m-d" 1) v i s a random normal d e v i a t e w i t h a mean of 0 and a s t a n d a r d d e v i a t i o n of 1 A p p r o x i m a t e l y 22% of males whose movement i s d e s c r i b e d by the above d i s t r i b u t i o n of movement r a t e s would t r a v e l more than 10 km from t h e i r p o i n t of r e l e a s e a f t e r one year i n an unbounded environment, assuming no m o r t a l i t y . Because of g e o g r a p h i c a l and h a b i t a t b o u n d a r i e s , and h i g h m o r t a l i t y , the p e r c e n t l e a v i n g the st u d y a r e a i s l i k e l y much lo w e r . Table 4.11.1. Abundance of female C . magi s t e r >145 mm CW i n commercial t r a p s i n May and June of 1985 and 1986. Area Sampled Female abundance (n • 1 0 0 • t r a p " 1 • s o a k d a y " 1 ) '. 'J 1985 1986 Upper Lemmens I n l e t (A; F i g . 2.1) 7 13 Lemmens I n l e t (B-D; F i g . 2.1) 15 8 Browning Passage ( G ; F i g . 2.1) 22 4 Near I n d i a n l i s ! a n d (H; F i g . 2.1) 10 36 Main channel ( F ; F i g . 2.1) 429 138 Table 4.11.2-. D e n s i t i e s of two t o t h r e e year o l d («=75-145 mm CW) C . "irnag i s t e r from beam t r a w l samples near I n d i a n I s l a n d . ,;: Date ">. Dens i t y ( n • h a " 1 ) • Male Female 20 Jun 198!5 155 117 1-7 Oct 1985 9 6 172 8 May 1986 70 99 S e c t i o n 4.11 Page 88 T a b l e 4 . 1 1 . 3 . Summary of tag r e c o v e r i e s , by l o c a t i o n , of s u b l e g a l - and l e g a l - s i z e d male C . mag i s ter between A p r i l 1985 and August 1986. The number of t r a p h a u l s was determined by i n t e r v i e w i n g f i s h e r m e n . Only r e c o r d s from f i shermen whose e f f o r t was known are r e p o r t e d . Except where n o t e d , r e c o v e r i e s were from w i t h i n the s tudy a r e a as d e f i n e d i n F i g . 2.1 (page 9 ) . L o c a t i o n where crabs were T r a p hau l s Number Number of r e c o v e r i e s 9  (Mean d a y s - a t - l a r g e ) tagged n Tagged Toward Toward Toward Where Up Down Open Browning I n d i a n tagged I n l e t I n l e t Ocean Passage Is l a n d T o t a l Upper Lemmens I n l e t 2234 ( 2 .8 ) 1686 116 - 189 l c - - 306 (A; F i g . 2 .1 ) (93 ) (157) ( 545 ) M i d d l e Lemmens I n l e t 8655 (11 .0) 1653 132 68 263 - - 463 (B; F i g . 2 . 1 ) (116 ) (132 ) (170) 3 4 d Lower Lemmens I n l e t 16165 ( 20 .5 ) 595 86 17 - 7 - 144 ( C D ; F i g . 2 .1) (118 ) (143 ) (156 ) (102) Browning Passage 1053 ( 1 .3 ) 85 7 14 - 4 - 0 25 (G; F i g . 2.1 ) (173 ) (125 ) ( 219 ) Near Ind ian I s l a n d 9606 (12 , .2 ) 166 35 - - - 6 - 41 (H; F i g . 2.1 ) (154 ) (124 ) Rest of s tudy a r e a 25294 (32 , .1 ) 215 63 2 - - 2 - 67 ( F i g . 2 .1) (151 ) (166 ) (135) Elsewherek 15729 ( 20 , .0) 0 T o t a l 78736 4400 - - - - - - 1046 a These areas are expressed r e l a t i v e to the a r e a where the crabs were t a g g e d . A dash ( - ) i n d i c a t e s an i n v a l i d ca tegory for a s s e s s i n g tag r e c o v e r i e s i n t h i s manner, not zero (0) r ecover i e s . b O u t s i d e the s tudy area but s t i l l in SA 24. c Recovered o u t s i d e the study a r e a . d One male r e c o v e r e d ou t s ide the s tudy a r e a a f t e r 370 days a t l a r g e . S e c t i o n 4.11 Page 89 Table 4 . 1 1 . 4 . Summary of tag r e c o v e r i e s , by l o c a t i o n , of female C . magi s t e r between A p r i l 1985 and August 1986. The number of t r a p hau l s was de termined by i n t e r v i e w i n g f i s h e r m e n . Only r e c o r d s from f i shermen whose e f f o r t was known are r e p o r t e d . A l l r e c o v e r i e s were from w i t h i n the s tudy a r e a as d e f i n e d i n F i g . 2.1 (page 9 ) . L o c a t i o n where crabs were Trap h a u l s Number Number of r e c o v e r i e s 3  (Mean d a y s - a t - l a r g e ) tagged n ( X ) Tagged Toward Toward Toward Where Up Down Open Br owning Ind ian tagged I n l e t I n l e t Ocean Passage I s l a n d T o t a l Upper Lemmens I n l e t 2234 ( 2 .8 ) 495 6 - 11 - - - 17 (A; F i g . 2 .1 ) (125 ) (112 ) M i d d l e Lemmens In l e t 8655 (11 .0 ) 540 13 4 14 - - - 31 (B; F i g . 2 .1 ) (97) ( 56 ) (179 ) Lower Lemmens I n l e t 16165 (20 .5) 334 6 2 - 4 0 - 12 ( C , D ; F i g . 2 .1) (96 ) (91 ) (197) Browning Passage 1053 (1 .3 ) 12 0 1 - 0 - 0 1 (G; F i g . 2 .1 ) (68 ) Near Ind ian I s l a n d 9606 (12 .2 ) 147 20 - - - 1 - 21 (H; F i g . 2 .1 ) (283 ) ( 518 ) Rest of s tudy a r e a 25294 (32 .1 ) 635 41 1 - - 1 - 43 ( F i g . 2 .1) ( 230 ) (40 ) (57) Elsewhere* 5 15729 (20 .0 ) 0 T o t a l 78736 2163 - - - - - - 125 a These areas are expressed r e l a t i v e to the a r e a where the crabs were t a g g e d . A dash ( - ) i n d i c a t e s an i n v a l i d ca tegory for a s s e s s i n g tag r e c o v e r i e s i n t h i s manner, not zero (0) r e c o v e r i e s . b Out s ide the s tudy area but s t i l l i n SA 24. S e c t i o n 4.11 Page 9 0 (45-75mm CW) 300 - i ENTRANCE TO LEMMENS INLET (D) ~ 0 A 1—r 300 -j >-h-co -z. U J Q m < rr o 0 i T — i — i i—r SHALLOW SAND BOTTOM (E l i i i r B l — r i—i—i i r T i r 600 300 0 (75 - l45mm C W ) MAIN CHANNEL (F) > M A L E • F E M A L E c _ i l l I—f I I M J J A S O N D I J F M A M J J A S 1985 1986 D A T E F i g u r e 4.11.1. Time s e r i e s of d e n s i t i e s f o r one year o l d (»40-75 mm CW) male and female C. magi s t e r i n the entrance to Lemmens I n l e t ( A), and on the shallow sand bottom of an exposed shore ( B). Time s e r i e s of d e n s i t i e s of two to three year o l d (»75-145 mm CW) male and female C. magi s t e r i n the main channel out t o sea ( C ) . The c a p i t a l l e t t e r s i n parentheses i d e n t i f y these areas i n F i g . 2.1 (page 9). F i g u r e 4.11.1 Page 91 3 0 0 1500 -1 1 2 0 0 -~ 9 0 0 -6 0 0 ' 3 0 0 -U P P E R L E M M E N S INLET (A) C O i — i — i — i — i — r ^ M I D D L E L E M M E N S I N L E T ( B ) i f i i i i r • MALE • FEMALE (75-145mm CW) B T 1 1—I 1—I 1 1 1 1 1 1—I 1 I I I I L O W E R L E M M E N S I N L E T ( C ) i—i—i—i—i—i—i—|—i—i—i i—i—m I—I 6 O O - 1 E N T R A N C E TO L E M M E N S I N L E T ( D ) 3 0 0 DATE Figure 4.11.2. Time series of densities for two to three year old (=75-145 mm CW) male and female C. magi ster in Lemmens Inlet. The c a p i t a l l e t t e r s in parentheses i d e n t i f y these areas in F i g . 2.1 (page 9 ) . Figure 4.11.2 Page 9 2 1 9 8 5 1986 D A T E F i g u r e 4 . 1 1 . 3 . Time s e r i e s comparison of two i n d i c e s of abundance for female C . magi s t e r (>145 mm CW) i n the s tudy a r e a , but e x c l u d i n g Lemmens I n l e t , Browning Passage , and near I n d i a n I s l a n d , where female d e n s i t i e s were g e n e r a l l y low ( T a b l e 4 . 1 1 . 1 ) . ' V i r t u a l e n t r y r a t e s ' were e s t i m a t e d as i n S e c t i o n 4 . 9 . F i g u r e 4 .11 .3 Page 93 c o 4 0 -3 0 -2 0 -1 0 -0 M A L E n = 1 2 4 5 D o n n r-i r-i >- 5 0 n (J z LU 4 0 -Z> O w 30H r r Li_ 20 I O H o F E M A L E n = 130 on n i " 1 1 " i " " ' T ^ ^ T ^ 1 1 l —\— 25 55 85 115 145 175 D I S T A N C E M O V E D ( ^ m - d " 1 ) 205 F i g u r e 4.11.4. Frequency d i s t r i b u t i o n s of mean d a i l y movement r a t e s f o r male and female C. magister . Crabs were rec o v e r e d a f t e r a mean of »150 days-at - l a r g e . F i g u r e 4.11.4 Page 94 4.12 TAG RETENTION AND TAG INDUCED MORTALITY Tag r e t e n t i o n was e s t i m a t e d from r e c o v e r i e s of 850 double t a g g e d s u b l e g a l - s i z e d males r e l e a s e d i n s p r i n g 1 9 8 6 . Tag r e t e n t i o n was a n a l y z e d s e p a r a t e l y f o r males t h a t m o u l t e d , and those t h a t d i d not moult, b e f o r e b e i n g r e c o v e r e d . The number of males r e c o v e r e d t h a t d i d not moult and r e t a i n e d b o t h or one t a g was 59 and 4 , r e s p e c t i v e l y , f o r a r e t e n t i o n r a t e of 9 6 . 8 % . The mean and median t i m e s - a t - l a r g e f o r these males were 83 and 69 days, r e s p e c t i v e l y . Number of double tagged c r a b s r e c o v e r e d : 63 E x p e c t e d number of t a g s : 6 3 - 2 = 126 Observed number of t a g s : ( 5 9 - 2 ) + 4 = 122 P e r c e n t r e t e n t i o n : (122+ 126 ) •100 = 9 6 . 8 The number of males r e c o v e r e d t h a t r e t a i n e d b o t h or one t a g t h r o u g h a moult was 64 and 1 , r e s p e c t i v e l y , f o r a r e t e n t i o n r a t e of 99 . 2%. Number of double t a g g e d c r a b s r e c o v e r e d : 65 E x p e c t e d number of t a g s : 6 5 - 2 = 1 3 0 Observed number of t a g s : ( 6 4 - 2 ) + l = 129 P e r c e n t r e t e n t i o n : (129+ 130 ) •100 = 9 9 . 2 Because the t a g r e t e n t i o n r a t e i s a p p a r e n t l y h i g h , t a g l o s s was assumed t o be n e g l i g i b l e i n m o r t a l i t y e s t i m a t e s ( S e c t i o n 4 . 1 3 ) . I n f o r m a l o b s e r v a t i o n s of t a g g e d and untagged C. m a g i s t e r h e l d i n t a n k s at the P a c i f i c B i o l o g i c a l S t a t i o n f o r s e v e r a l months d i d not i n d i c a t e a h i g h e r m o r t a l i t y r a t e due t o a crab h a v i n g been tagged. S e c t i o n 4 . 1 2 Page 95 4.13 FISHING AND NATURAL MORTALITY OF MALES The mark - r e c o v e r y program p r o v i d e d e s t imates of f i s h i n g and n a t u r a l m o r t a l i t y for male C . magi s t e r . (No e s t i m a t e s were made of female n a t u r a l m o r t a l i t y because an i n s u f f i c i e n t number was tagged and r e c o v e r e d ) . The l o g a r i t h m s of the number of r e c o v e r i e s of males tagged , r e l e a s e d and r e c o v e r e d when s u b l e g a l s i z e (145-155 mm CW) are p l o t t e d for c o n s e c u t i v e one month i n t e r v a l s i n F i g . 4 . 1 3 . 1 . These r e s u l t s were o b t a i n e d from the four f i shermen and m y s e l f , who r e c o r d e d a l l o c c u r r e n c e s of s u b l e g a l - s i z e d males i n t h e i r t r a p s , then r e l e a s e d them. The e f f o r t of a l l four f i shermen was c o n s i s t e n t over the s tudy per i o d . The annua l ins tantaneous r a t e of d i s a p p e a r a n c e of these males i s the n e g a t i v e s lope of the l i n e a r r e l a t i o n s h i p (SAS I n s t i t u t e I n c . 1985) i n F i g . 4 .13 .1 (Tab le 4 . 1 3 . 1 ) t imes 365 days (=3.48, 95% C . I . i s 2 . 90 -4 .06 ) ( G u l l a n d 1983) . S ince movement from the s tudy area ( S e c t i o n 4 . 1 1 ) , t a g l o s s and tag induced m o r t a l i t y ( S e c t i o n 4 .12) seem to be smal l c o n t r i b u t o r s to the d i s a p p e a r a n c e of tagged crabs , t h i s r a t e m a i n l y measures the combinat ion of M (the annual in s tantaneous r a t e of n a t u r a l m o r t a l i t y ) and the i n s t a n t a n e o u s r a t e of m o u l t i n g i n t o l e g a l s i z e . The s lope of F i g . 4 .13 .1 can be c o n s i d e r e d a maximum es t imate of M w h i l e these males remain i n t h i s same i n s t a r . A q u a d r a t i c curve a p p l i e d to the d a t a i n F i g . 4 .13 .1 (Tab le 4 . 1 3 . 2 ) suggests t h a t the r a t e of d i s a p p e a r a n c e of these males i n c r e a s e s as the t ime w i t h i n an i n s t a r i n c r e a s e s . S e c t i o n 4.13 Page 9 6 Table 4 . 1 3 . 1 . S t a t i s t i c s of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13 .1 from which the annual i n s t a n t a n e o u s r a t e of d i s a p p e a r a n c e of s u b l e g a l - s i z e d ( 145-155 mm CW) male C . mag i s t e r was e s t i m a t e d . The r e l a t i o n s h i p has the form Y = a+b-X; where Y i s the l o g a r i t h m of the number of r e c o v e r i e s w i t h i n c o n s e c u t i v e one month i n t e r v a l s , and X i s the t i m e - a t - l a r g e i n d a y s . Parameter E s t imate S tandard e r r o r a 5.99 0.25 b - 9 . 5 4 E - 3 0 .81E-3 Tab le 4 . 1 3 . 2 . S t a t i s t i c s of the q u a d r a t i c r e l a t i o n s h i p i n F i g . 4 .13 .1 which suggests the m o r t a l i t y r a t e may i n c r e a s e as the t i m e - a t - l a r g e for s u b l e g a l - s i z e d (145-155 mm CW) male C . magi s t e r i n c r e a s e s . The r e l a t i o n s h i p has the form Y = a + b - X + c - X 2 ; where Y i s the l o g a r i t h m of the number o f r e c o v e r i e s w i t h i n c o n s e c u t i v e one month i n t e r v a l s , and X i s the t i m e - a t - l a r g e i n d a y s . Parameter E s t imate S t a n d a r d e r r o r a 4.92 0.40 b 3 . 6 5 E - 5 a 316 . 0 E - 5 .. c - 1 . 6 7 E - 5 0 .54E-5 a Not s i g n i f i c a n t l y d i f f e r e n t from b=0.0 . F i g u r e 4 .13 .2 p l o t s the r e c o v e r y of 182 male s , l e g a l s i z e when tagged and r e l e a s e d (n=341), f or c o n s e c u t i v e 15 day i n t e r v a l s , for a t o t a l r e c o v e r y of 53.4% from a l l f i s h e r m e n . The t o t a l annual ins tantaneous r a t e of d i s a p p e a r a n c e of l e g a l - s i z e d males ( Z ) i s the nega t ive s lope of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13 .2 ( T a b l e 4 . 1 3 . 3 ) t imes 365 days (=9.23, 95% C . I . i s 7 . 23 -11 .23 ) ( G u l l a n d 1983, p . 110, E q n . 4 . 3 3 ) . A p r o v i s i o n a l and minimum es t imate of the annual i n s t a n t a n e o u s r a t e of f i s h i n g Sect i o n 4.13 Page 9 7 m o r t a l i t y ( F ) i s 4.95 (=9 .23 -0 .534 ) . T h e r e f o r e , an annual in s tantaneous r a t e of 4.29 accounts for the lack of r e c o v e r i e s for a l l o ther r e a s o n s . A g a i n , s ince there i s no s i g n i f i c a n t movement of tagged crabs from the s tudy area over t h i s t i m e , or tag lo s s or tag induced m o r t a l i t y , these tags were p r o b a b l y not r e c o v e r e d because of (1) n a t u r a l m o r t a l i t y , and (2) they were missed by , or I d i d not o b t a i n the tags from the f i s h e r m e n . Tab le 4 . 1 3 . 3 . S t a t i s t i c s of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13 .2 from which the annual i n s t a n t a n e o u s r a t e of d i s a p p e a r a n c e (Z) of l e g a l - s i z e d male C . magi s t e r was e s t i m a t e d . The r e l a t i o n s h i p has the form Y = a+b-X; where Y i s the l o g a r i t h m of the number of r e c o v e r i e s w i t h i n c o n s e c u t i v e 15 day i n t e r v a l s , and X i s the t i m e - a t - l a r g e i n d a y s . Parameter E s t imate S t a n d a r d e r r o r a 4.23 0.27 b - 2 . 5 3 E - 2 0 .28E-2 From r e c o v e r i e s of males , 125-155 mm CW when t a g g e d , and l e g a l s i z e when r e c o v e r e d , a seasonal p r o f i l e of m o u l t i n g i n t o l e g a l s i z e was o b t a i n e d ( F i g . 4 . 1 3 . 3 ) . From the r e v i s e d e s t imate of F ( 5 . 1 1 - 6 . 9 0 ) below, the time to a 50% e x p e c t a t i o n of r e c o v e r y for a l e g a l - s i z e d male i s 37-50 d ays . S ince F i g . 4 . 1 3 . 3 b covers a t ime p e r i o d much g r e a t e r than t h i s , i t c l o s e l y resembles the s e a s o n a l i t y of m o u l t i n g of s u b l e g a l - s i z e d males 125-155 mm CW i n t o l e g a l s i z e . M o u l t i n g occurs a l l y e a r , but m o s t l y i n summer. F i g u r e 4 .13 .3 shows t h a t s u r v i v o r s h i p to the next i n s t a r decreases w i t h s i z e , w i t h a s m a l l e r p e r c e n t of crabs 140-155 mm S e c t i o n 4.13 Page 9 8 CW a t t a i n i n g l e g a l s i z e than those 125-140 mm CW. T h i s seems not to be a r e s u l t of i n s u f f i c i e n t i n t e r m o u l t time for the l a r g e r c r a b s . Most tagged crabs were moni tored for 400-600 d a y s , and n e a r l y a l l m o u l t i n g was observed a f t e r l e s s than 400 days at l a r g e ( F i g . 4 . 1 3 . 4 , Table 4 . 1 3 . 4 ) . The annual i n s t a n t a n e o u s r a t e of d i s a p p e a r a n c e for males 145-155 mm CW of 3.48 ( F i g . 4 . 1 3 . 1 , T a b l e 4 . 1 3 . 1 ) a l s o suggests t h i s s ince <3% of these crabs were p r e s e n t at t h i s s i z e a f t e r 400 days at l a r g e . F i g u r e 4 .13 .4 shows a t r e n d toward a longer i n t e r m o u l t p e r i o d w i t h i n c r e a s i n g s i z e . The l e n g t h of the i n t e r m o u l t p e r i o d cannot be p r e c i s e l y de termined from t h i s r e l a t i o n s h i p because i t i s not known how long a f t e r m o u l t i n g crabs were tagged , t h e r e f o r e F i g . 4 .13 .4 p r o v i d e s o n l y a minimum es t imate of the l e n g t h of the i n t e r m o u l t per i o d . Table 4 . 1 3 . 4 . S t a t i s t i c s of the l i n e a r r e l a t i o n s h i p i n F i g . 4 .13 .4 e s t i m a t i n g the mean t i m e - a t - l a r g e for r e c o v e r e d tagged s u b l e g a l - s i z e d male C . magi s t e r . The r e l a t i o n s h i p has the form Y = a+b-X; where Y i s the time to r e c o v e r y ( i n d a y s ) , and X i s the p r e - m o u l t carapace w i d t h . Parameter E s t imate S tandard e r r o r a -628.4 113.0 b 6.22 0.81 The percent of s u b l e g a l - s i z e d males expected to s u r v i v e to l e g a l s i z e . i s e s t i m a t e d from the number of r e c o v e r e d tagged l e g a l - s i z e d males that were tagged when s u b l e g a l s i z e (Tab le 4 . 1 3 . 5 ) . C a l c u l a t i o n of m o r t a l i t y from these da ta i s somewhat S e c t i o n 4.13 Page 99 h i n d e r e d by an u n c e r t a i n e s t i m a t e of the p r o p o r t i o n of tagged l e g a l - s i z e d males caught t h a t I o b s e r v e d . I w i l l r e f e r to t h i s p r o p o r t i o n as c o m p l i a n c e . S i n c e 0.534 of the 341 l e g a l - s i z e d males tagged and r e l e a s e d were r e c o v e r e d ( F i g . 4 . 1 3 . 2 ) , t h i s r e p r e s e n t s a minimum e s t i m a t e of c o m p l i a n c e . T h i s e s t i m a t e can be r e v i s e d as e x p l a i n e d be low. From c a t e g o r i e s 145-150 and 150-155 mm CW from T a b l e 4 . 1 3 . 5 , which are composed of males c l o s e to l e g a l s i z e w i t h i n the 155.0 mm i n s t a r , M can be p r o v i s i o n a l l y e s t imated at 4.48 ( i . e . the n e g a t i v e log of the p r o p o r t i o n r e c o v e r e d , a d j u s t e d for the t i m e - a t - l a r g e ) . M = - ln(53*2246 )•( 365-305 ) ( 4 .13 .1 ) A r e v i s e d e s t imate of M, i n c o r p o r a t i n g an adjustment for compl iance ( C ) , i s : M = 4.48 + l n ( C ) ( 4 . 1 3 . 2 ) From F i g . 4 .13 .2 and T a b l e 4 . 1 3 . 3 , which document the r e c o v e r y of males t a g g e d , r e l e a s e d and r e c o v e r e d when l e g a l s i z e , and i n the 155.0 mm i n s t a r : Z = 9 .23 + 1 .02 ( 4 .13 .3 ) F = ( 0 .534*C ) -Z ( 4 . 1 3 . 4 ) M = Z - F ( 4 . 1 3 . 5 ) there f o r e , M = Z - ( 0 .534-C ) -Z ( 4 . 1 3 . 6 ) S e c t i o n 4.13 Page 100 If one assumes that M and C are the same for both a n a l y s e s , an e s t imate of C can be o b t a i n e d by s o l v i n g Eqns . 4 .13.2 and 6 s i m u l t a n e o u s l y for a s i n g l e e s t imate of M. W i t h i n the 95% conf idence l i m i t s of Z ( 7 . 2 3 - 1 1 . 2 3 ) , for Z<9.59 no c o r r e s p o n d i n g e s t imate of M i s o b t a i n a b l e because C must, but o b v i o u s l y cannot , exceed 1 .0 . For Z=11.23, C i s e s t i m a t e d at 0 .869 , and M at 4 . 3 3 . The range of M for C r a n g i n g from 0 .869-1 .00 i s 4.33 - 4 . 4 8 . The e q u i v a l e n t range for F i s 5 . 1 1 - 6 . 9 0 . In c o n s i d e r a t i o n of the c l o s e m o n i t o r i n g of t h i s f i s h e r y , I accept the lower compl iance e s t imate of 0.869 as p l a u s i b l e . T a b l e 4 .13 .5 r e p o r t s e s t i m a t e s of M for 5 mm CW i n t e r v a l s from 125-155 mm assuming the more c o n s e r v a t i v e e s t imate of compl iance of 0 .869. As was apparent i n F i g . 4 . 1 3 . 3 , the r e s u l t s suggest s i z e - d e p e n d e n t m o r t a l i t y , l a r g e r crabs h a v i n g the lower s u r v i v o r s h i p . The e s t imate of M=4.33-4.48 for crabs 145-155 mm CW i s h i g h e r than the maximum e s t i m a t e of M=3.48, for e s s e n t i a l l y the same s i z e r a n g e , o b t a i n e d from F i g . 4 . 1 3 . 1 . S ince the l a t t e r e s t imate a p p l i e s on ly to males s t i l l s u b l e g a l s i z e , the bes t e x p l a n a t i o n for t h i s d i s c r e p a n c y i s a h i g h e r m o r t a l i t y r a t e for males d u r i n g , or whi l e s o f t - s h e l l e d f o l l o w i n g , the moult to l e g a l s i z e . I f t h i s i s the c o r r e c t e x p l a n a t i o n then the above assumption t h a t the e s t i m a t e s o f M s h o u l d be s i m i l a r f o r the a n a l y s e s based on the data i n T a b l e s 4 .13 .3 and 5 i s not s t r i c t l y t r u e . T h u s , f i s h i n g m o r t a l i t y ( F ) may be underes t imated and M may be o v e r e s t i m a t e d . Sect i on 4.13 Page 101 No exper iments were a t tempted to d i s t i n g u i s h between (1) the d i s a p p e a r a n c e of sublega1 - s i z e d males due to m o u l t i n g to l e g a l s i z e and d i s a p p e a r a n c e due to m o r t a l i t y i n F i g . 4 . 1 3 . 1 , and (2) between p r e - and immediate ly p o s t - m o u l t m o r t a l i t y i n Table 4 . 1 3 . 5 , so the d i s c r e p a n c i e s in the e s t imates of M cannot be f u r t h e r r e s o l v e d . However, one can conclude t h a t the more the d i s a p p e a r a n c e of s u b l e g a l males i n F i g . 4 .13 .1 i s a t t r i b u t a b l e to m o u l t i n g , the g r e a t e r the m o u l t , or p o s t - m o u l t , m o r t a l i t y . S i z e f requency a n a l y s i s on t r a p sampled males for each f i s h e r y , i n c l u d i n g the l i g h t l y f i s h e d H o l b e r g I n l e t f i s h e r y , c o u l d not d e t e c t an 183.8 mm i n s t a r . T h i s i s c o n s i s t e n t w i t h the mark - r e c o v e r y r e s u l t s p r e s e n t e d i n t h i s s e c t i o n which i n d i c a t e low s u r v i v o r s h i p from the 155.0 mm to the 183.8 mm i n s t a r . Table 4 . 1 3 . 5 . Summary of s u r v i v o r s h i p to l e g a l s i z e of male C . magi s t e r which were tagged when s u b l e g a l s i z e , and r e c o v e r e d when l e g a l s i z e , f or 5 mm i n t e r v a l s from 125-155 mm CW. Pre -moul t Per cent Mean carapace s u r v i v i n g days Instantaneous width Number Recover ie s to l e g a l at annual (mm) tagged n <* ) s i z e a l a r g e 1 3 m o r t a l i t y 125-130 168 20 11 .9 32 .1 165 2 .87 130-135 310 50 16.1 24.0 196 2.96 135-140 366 52 14 .2 19 . 2 227 2.91 140-145 499 35 7.0 9.5 258 3 .56 145-150 1027 28 2 .7 3 .7 289 4.37 150-155 1219 25 2.1 2.8 320 4.27 a C a l c u l a t e d by m u l t i p l y i n g the p e r c e n t r e c o v e r e d i n each 5 mm CW i n t e r v a l by 1.15 to compensate for the more c o n s e r v a t i v e e s t imate of o n l y 86.9% of tagged l e g a l - s i z e d crabs landed b e i n g o b s e r v e d . The p e r c e n t r e c o v e r e d i n i n t e r v a l s 125-130 and 130-135 mm CW was f u r t h e r m u l t i p l i e d by 2.0 and 1 . 1 , r e s p e c t i v e l y , because o n l y 50% and 90% of crabs t h i s s i z e are expected to a t t a i n l e g a l s i z e w i t h t h e i r next m o u l t . b From r e g r e s s i o n parameters of F i g . 4 .13 .4 (Y = - 628 . 4+ 6 . 22•X ). S e c t i o n 4.13 Page 102 F i g u r e 4 . 1 3 . 1 . L i n e a r and q u a d r a t i c r e g r e s s i o n s of r e c o v e r i e s over time for tagged male C . magi s t e r r e l e a s e d and r e c o v e r e d as s u b l e g a l - s i z e d crabs 145-155 mm CW. Most t a g g i n g was done from M a y - J u l y 1985. The open c i r c l e s were not i n c l u d e d i n the r e g r e s s i o n a n a l y s e s because f i shermen were not w e l l p r e p a r e d f o r the m a r k - r e c o v e r y program at t h i s t i m e . F i g u r e 4 .13 .1 Page 103 F i g u r e 4 . 1 3 . 2 . L i n e a r r e g r e s s i o n of r e c o v e r i e s over time for 341 tagged male C . magi s t e r r e l e a s e d and r e c o v e r e d as l e g a l - s i z e d c r a b s , m o s t l y i n s p r i n g 1986. F i g u r e 4 .13 .2 Page 104 c a> o a> CL o z IxJ ZD O UJ cr u_ 50 - i 40-30-20 10' 0 50-40-30-20-10' 0 R E L E A S E S OF S U B L EG A L - S I Z E D M A L E S n ( 1 2 5 - 1 4 0 m m ) = 8 4 4 ( 2 3 . 5 % ) n ( 1 4 0 - 1 5 5 m m ) = 2 7 4 5 ( 7 6 . 5 % ) • 125 - 140 mm " T T ^ T T I i T i S T i T • 140 - 155 mm i—i—i—rn—r RECOVERIES OF L E G A L - S I Z E D M A L E S n ( 1 2 5 - 1 4 0 m m ) = 127 ( 5 8 . 8 % ) n ( I 4 0 - I 5 5 m m ) = 8 9 ( 4 1 . 2 % ) I i I I T A M J J A S O N D J J F M A M J J A S 0 N DjJ F 1 9 8 5 1 9 8 6 1987 D A T E F i g u r e 4 . 1 3 . 3 . (A) Frequency d i s t r i b u t i o n of r e l e a s e dates of s u b l e g a l - s i z e d male C . magi s t e r . (B) Frequency d i s t r i b u t i o n of r e c o v e r y dates for those crabs r e l e a s e d i n (A) and r e c o v e r e d as l e g a l - s i z e d c r a b s . F i g u r e 4 .13 .3 Page 105 _ 6 0 0 - i CO •5 500 H UJ 4 0 0 -(3 or ^ 300 -1 < 200 H I UJ S 100 -I 0 n = 216 p < . 0 0 0 l r2 = 2 1 . 4 % • • • • I # • • • • • • • • • ••• • 9 T T 135 ~ I — 140 125 130 5 0 145 150 P R E - M O U L T C A R A P A C E W I D T H ( m m ) ~1 155 F i g u r e 4 . 1 3 . 4 . L i n e a r r e g r e s s i o n of t i m e - a t - l a r g e for male C . magi s t e r . tagged and r e l e a s e d when s u b l e g a l s i z e and r e c o v e r e d when l e g a l s i z e , on p r e - m o u l t carapace w i d t h . F i g u r e 4 .13 .4 Page 106 4.14 FISHING INTENSITY AND FEMALE CATCH CURVES IN SELECTED FISHERIES Table 4 .14 .1 compares f i s h i n g i n t e n s i t y i n four r e g i o n a l f i s h e r i e s as d e f i n e d by S t a t i s t i c a l A r e a . These s t a t i s t i c a l areas do not d i f f e r markedly i n a r e a . The q u a n t i t y of males l a n d e d , the number of days f i s h e d , the number of v e s s e l s f i s h i n g , and the number of sa l e s i n these r e g i o n a l f i s h e r i e s are r e l a t i v e i n d i c a t o r s of f i s h i n g e f f o r t . The degree of e x p l o i t a t i o n and the v i r t u a l e n t r y r a t e of l e g a l - s i z e d males are i n d i c a t o r s of f i s h i n g impact . These impacts were de termined as i n S e c t i o n 4 . 9 . The F r a s e r d e l t a f i s h e r y appears h e a v i l y e x p l o i t e d , w h i l e the H o l b e r g I n l e t f i s h e r y i s l i g h t l y e x p l o i t e d . Two other f i s h e r i e s , near T o f i n o and i n Dixon E n t r a n c e e x p e r i e n c e i n t e r m e d i a t e f i s h i n g i n t e n s i t y , except that t h i s s tudy shows that s i n c e 1985 the C . magi s t e r p o p u l a t i o n near T o f i n o has e x p e r i e n c e d heavy f i s h i n g . D e s p i t e females not b e i n g f i s h e d , the c a t c h curves ( R i c k e r 1975) for females caught by these f i s h e r i e s ( F i g . 4 . 1 4 . 1 ) suggest a lower s u r v i v o r s h i p to l a r g e r i n s t a r s i n the more h e a v i l y f i s h e d p o p u l a t i o n s . The ca tch curve ' for each f i s h e r y combines commercial samples from the two c o n s e c u t i v e years when each of these f i s h e r i e s were sampled. Combining samples from c o n s e c u t i v e years was suggested by R i c k e r (1975) to reduce the i n f l u e n c e of a p o s s i b l y dominant a g e - c l a s s . P r i o r to p l o t t i n g the c a t c h curves the samples were s t a n d a r d i z e d to o b t a i n v i r t u a l e n t r y r a t e s as i n S e c t i o n 4 . 9 . S u r v i v o r s h i p of females to l a r g e r i n s t a r s i n the S e c t i o n 4 .14 Page 107 h e a v i l y f i s h e d F r a s e r d e l t a f i s h e r y i s much lower than that for the l i g h t l y f i s h e d H o l b e r g I n l e t f i s h e r y , whi l e the c a t c h curves for the other two r e g i o n s are i n t e r m e d i a t e . It i s u n l i k e l y tha t the absence of l a r g e females i n the i n t e n s e l y e x p l o i t e d F r a s e r d e l t a f i s h e r y r e s u l t s from l e g a l - s i z e d females h a v i n g been h a r v e s t e d because the s i z e f requency d i s t r i b u t i o n s do not show a d i s c o n t i n u o u s decrease i n abundance at l e g a l s i z e . It a l s o seems u n l i k e l y t h i s p a t t e r n r e s u l t s from i n c r e a s e d m o r t a l i t y due to t r a p p i n g and e x c e s s i v e h a n d l i n g i n an i n t e n s i v e f i s h e r y . M o r t a l l y i n j u r e d or dead crabs were seldom seen i n t r a p s or t r a w l s d u r i n g t h i s s t u d y . When such crabs were encountered they were w e l l r e p r e s e n t e d by connected body p a r t s , i n c l u d i n g the c a r a p a c e , s u g g e s t i n g l i t t l e unseen m o r t a l i t y occurs w i t h i n t r a p s . I f m o r t a l i t y i n t r a p s i s low, d e s p i t e the a r t i f i c i a l l y h i g h d e n s i t y of crabs i n t r a p s , then t r a p p i n g and h a n d l i n g induced m o r t a l i t y o u t s i d e t r a p s would be expec ted to be lower . Thus , there i s no d i r e c t ev idence to suggest tha t lower s u r v i v o r s h i p of females i n i n t e n s e m a l e - o n l y f i s h e r i e s i s due to t r a p p i n g and h a n d l i n g . S ince females moult and mate i n the company of a l a r g e r male , many of whom may have been removed i n a h e a v i l y f i s h e d p o p u l a t i o n , i t i s c o n c e i v a b l e t h a t females may not a c h i e v e l a r g e r i n s t a r s i n h e a v i l y f i s h e d p o p u l a t i o n s because of a lack of l e g a l - s i z e d males for mat ing p a r t n e r s . The f o l l o w i n g s e c t i o n e l a b o r a t e s on t h i s p o s s i b i l i t y , and i t s p o t e n t i a l consequences for p o p u l a t i o n egg p r o d u c t i o n . S e c t i o n 4.14 Page 108 Table 4 . 1 4 . 1 . Comparisons among d i f f e r e n t measures of f i s h i n g e f f o r t , and f i s h i n g impact , on male C . magi s t e r p o p u l a t i o n s i n four r e g i o n a l f i s h e r i e s d e f i n e d by S t a t i s t i c a l Area ( S A ) . The s t a t i s t i c a l areas do not d i f f e r markedly i n a r e a . Annual f i s h i n g s t a t i s t i c s i n c l u d e the m e t r i c tonnes landed ( t ) and the number of days f i s h i n g (DF) . Annual f i s h i n q s t a t i s t i c s Degree V i r t u a l Number Number 1983 1984 1985 of e n t r y o f of Region e x p l o i t a t i o n 3 r a t e " v e s s e l s 0 s a l e s c t DF t DF t. DJL H o l b e r g I n l e t (SA 27 ) 1 7 d 641 10 37 3 73 5 116 5 185 Dixon E n t r a n c e (SA 1 ) 4 5 e 84 25 135 136 394 146 457 160 474 Near T o f i n o (SA 24 ) * 7 5 f 103 27 434 136 1869 110 1228 152 1391 F r a s e r d e l t a (SA 29) 869 49 119 1307 274 2341 341 3636 353 3662 B r i t i s h Co lumbia T o t a l - - - - 959 12987 1155 15731 1165 16851 a The percent of the l e g a l - s i z e d males i n the 155.0 mm i n s t a r taken by the f i s h e r y near the end of the season. See S e c t i o n 4.9 for an e x p l a n a t i o n of t h i s e s t i m a t e . b The number of l e g a l - s i z e d male crabs tha t would enter 100 t r a p s i f the e n t r y r a t e was not reduced (1) by crabs w i t h i n t r a p s i n h i b i t i n g the e n t r y of more c r a b s , and (2) changes in b a i t e f f e c t i v e n e s s . See S e c t i o n 4.7 for a more complete e x p l a n a t i o n . c In 1984. d In December 1984. e Mean of October 1983 and 1984. f From F i g u r e 4 . 9 . 2 . <? Mean of October 1984 and 1985. S e c t i o n 4.14 Page 109 TLX1 2 • A R E A 2 7 (Holberg Inlet) 142.5 152.5 162.5 172.5 182.5 192.5 C A R A P A C E W I D T H ( - 2 . 5 m m ) F i g u r e 4 . 1 4 . 1 . Comparison of c a t c h curves ( R i c k e r 1975) for females from four r e g i o n a l C . magi s t e r f i s h e r i e s d e f i n e d by-S t a t i s t i c a l A r e a i n B r i t i s h C o l u m b i a . F i g u r e 4 .14 .1 Page 110 5 Y I E L D - AND EGGS-PER-RECRUIT MODEL 5.1 DEVELOPMENT T h i s s e c t i o n e v a l u a t e s t r a d e - o f f s i n C . magi s t e r y i e l d - and e g g s - p e r - r e c r u i t r e s u l t i n g from a l t e r i n g the minimum l e g a l s i z e l i m i t for m a l e s . Model s t r u c t u r e and e s t imates for c r i t i c a l p o p u l a t i o n v a r i a b l e s ( e . g . growth and m o r t a l i t y ) are based on i n f o r m a t i o n o b t a i n e d in t h i s s tudy supplemented by i n f o r m a t i o n on female g r o w t h , m o r t a l i t y and f e c u n d i t y from Hankin et a l . (1985) . R e l a t i v e y i e l d - p e r - r e c r u i t was de termined by a c c o u n t i n g the p r e d i c t e d c a t c h of males , by w e i g h t , for d i f f e r e n t minimum l e g a l s i z e l i m i t s . Dry weight was d e t e r m i n e d from carapace w i d t h u s i n g E q n . 4 . 7 . 3 . 4 (page 55) . As recommended by Caddy (1986) , the y i e l d - p e r - r e c r u i t a n a l y s i s i s based on moult i n c r e m e n t s - a t - s i z e , moult f requency and moult p r o b a b i l i t i e s , acknowledg ing d i s c o n t i n u o u s growth . Some workers have used a von B e r t a l a n f f y growth model for c r u s t a c e a n s when i n s t a r s were not e a s i l y d i s t i n g u i s h e d and a cont inuous growth model seemed an a p p r o p r i a t e s i m p l i f i c a t i o n . W i t h C . magi s t e r h a v i n g few moults and l a r g e moult i n c r e m e n t s - a t - s i z e f o r the s i z e s r e l e v a n t to t h i s a n a l y s i s , t h i s would not have been a p p r o p r i a t e . The d e t e r m i n a t i o n of y i e l d - and e g g s - p e r - r e c r u i t i s e x p l a i n e d i n the f o l l o w i n g p a r a g r a p h s . The model i n c l u d e s the 1 0 2 . 9 , 128 .0 , 155.0 and 183.8 mm male , and the 100 .7 , 119 .4 , 1 3 5 . 5 , 149.4 and 161.4 mm female , i n s t a r s d e f i n e d by the s i z e f r e q u e n c y a n a l y s e s i n S e c t i o n 4 . 6 . S e c t i o n 5 Page 111 The s m a l l e s t male and female i n s t a r s are dominant i n summer two years a f t e r s e t t l e m e n t . Moult t i m i n g , and the time when p a r t i c u l a r i n s t a r s dominate ( T a b l e 5 . 1 . 1 ) , are e s t i m a t e d from T a b l e s 4 .6 .3 and 4 (pages 41 and 42) , and F i g . 4 .13 .3 (page 105) . A l l i n d i v i d u a l s i n male and female i n s t a r s for each a g e - c l a s s are a c c o u n t e d . For females an a d d i t i o n a l four v e c t o r s account i n d i v i d u a l s i n each a g e - c l a s s which f a i l e d to moult for 1-4 y e a r s . Male and female growth was modeled by c r e a t i n g a normal s i z e d i s t r i b u t i o n of 1 mm CW i n t e r v a l s for the s m a l l e s t i n s t a r s i n Table 5 . 1 . 1 , then i n c r e m e n t i n g t h i s d i s t r i b u t i o n by a p p l y i n g Eqns . 4 .5 .1 and 2 (moult i n c r ement s -a t - s i ze , page 33) for males and f emales , r e s p e c t i v e l y . Table 5 . 1 . 1 . The mean and s t a n d a r d d e v i a t i o n (mm) of age and time of year when they are n e a r l y f u l l y formed. Males become s e x u a l l y ac t i ve i n the 155 .0 mm i n s t a r • Date Male i n s t a r s Female i n s t a r s Winter Age 2 Spr ing Summer 102 .9+ 9.8 100 .7 + 12 .8 Autumn 119 .4 + 11 .0 egg p r o d u c i n g females Winter from Age 3 Spr ing 128 .0+10.5 t h i s Summer i n s t a r Autumn 155 .0 + 11 .2 135.5+ 9.5 on Winter assumes females i n Age 4 Spr ing 135 . 5 to 161 .4 mm Summer i n s t a r s n o r m a l l y Autumn 183 . 8 ± 1 2 .0 149 .4+ 8.2 moult a n n u a l l y Winter H assumes males Age 5 Spr ing n t h i s s i z e Summer II do not Autumn n 161 .4+ 7.1 moult a n n u a l l y Sect i on 5.1 Page 112 Annual m o r t a l i t y r a t e s are a p p l i e d to the i n s t a r s i n Table 5 .1 .1 to determine the numbers-at -age for males and females . Annual in s tantaneous n a t u r a l m o r t a l i t y (M) e s t i m a t e s for males were de termined i n t h i s s t u d y . Female m o r t a l i t y e s t i m a t e s are from Hankin et a l . (1985 ), who e s t imated M at 0 . 7 - 2 . 5 , M i n c r e a s i n g w i t h i n c r e a s i n g carapace widths for females >125 mm. A c o n s i d e r a t i o n of t h e i r m a r k - r e c o v e r y methodology suggests M=0.7 i s an underes t imate because commercial t r a p s do not e f f e c t i v e l y r e t a i n smal l c r a b s . As the s m a l l e r tagged crabs moult to l a r g e r s i z e s t h e i r occurrence i n t r a p s i n c r e a s e s , thus m i s r e p r e s e n t i n g r e l a t i v e abundance. Because of v a r i a b i l i t y i n the m o r t a l i t y e s t i m a t e s , I r e p o r t y i e l d - and e g g s - p e r - r e c r u i t r e s u l t s for annual m o r t a l i t y e s t imates of 1 .0 , 2.5 and 4 . 0 . M o r t a l i t y r a t e s are assumed constant for a l l s i z e s and ages . C o n s i d e r i n g the h i g h m o r t a l i t y e s t i m a t e s , c o h o r t s are f o l l o w e d to v i r t u a l e x t i n c t i o n . As suggested by the s i z e frequency d i s t r i b u t i o n of the o c c u r r e n c e of mating marks ( F i g . 4 . 1 0 . 1 , page 8 1 ) , males are not c o n s i d e r e d s e x u a l l y mature u n t i l they a t t a i n the 155.0 mm i n s t a r . B u t l e r (1960) suggests males are mature at 100-110 mm CW, but mat ing marks on males t h i s s i z e were r a r e . Males t h i s s i z e would have d i f f i c u l t l y f i n d i n g mature females of a s i z e that they cou ld embrace s i n c e F i g . 4 .4 .1 (page 31) suggests males must mate w i t h a female c o n s i d e r a b l e s m a l l e r than themse lves . Most males become Sect i o n 5.1 Page 113 f u n c t i o n a l l y mature a f t e r a t t a i n i n g 13C mm CW. T h i s i s c o n s i s t e n t w i t h t h e i r becoming f u n c t i o n a l l y mature upon a t t a i n i n g the 155.0 mm i n s t a r . S ince one male can a p p a r e n t l y mate w i t h s e v e r a l females i n one summer season ( B u t l e r 1 9 6 0 ) , an e s t imate of the maximum number of females mated by each male i s r e q u i r e d ( F : M mat ing r a t i o ) . Such e s t imates e l u s i v e s i n c e n a t u r a l b e h a v i o r cannot be r e p l i c a t e d i n the l a b o r a t o r y , and o b s e r v a t i o n s of i n d i v i d u a l males i n nature , for a mat ing season are not p o s s i b l e . In a one week p e r i o d I observed a male mate s u c c e s s f u l l y w i t h two females i n a l a b o r a t o r y t a n k . Snow and N e i l s e n (1966) r e p o r t t h a t mat ing r e q u i r e d 10 days for the p a i r they o b s e r v e d . Over a mat ing season the F:M mat ing r a t i o i s p o t e n t i a l l y l a r g e . In c o n s i d e r a t i o n of the u n c e r t a i n t y in such e s t i m a t e s , I r e p o r t eggs-per.-r e c r u i t r e s u l t s f o r maximum F:M mat ing r a t i o s of 5, 10 and 20:1. S ince t h e r e are no data to d e v e l o p a f u n c t i o n a l response r e l a t i o n s h i p between the F:M mat ing , r a t i o and female d e n s i t y , I must assume t h a t the maximum nueber of females tha t can be mated by a male i s not m o d i f i e d by female d e n s i t y . It i s reasonable to expect t h a t at any female d e n s i t y males would attempt to maximize t h e i r e v o l u t i o n a r y f i t n e s s by m a x i m i z i n g the number of females w i t h w h i c h t h e y mate. For females the 100.7 mm i n s t a r i s c o n s i d e r e d the f i r s t s e x u a l l y mature i n s t a r . F u r t h e r moults r e q u i r e a female to have a male p a r t n e r . As r e p o r t e d i n F i g . 4.3.1 (page 2 9 ) , no s e x u a l l y S e c t i o n 5.1 Page 114 mature females were found wi thout sperm packs i n d i c a t i n g that females do not a t t a i n l a r g e r s i z e s without h a v i n g mated. P.W. W i l d ( c i t e d i n Hankin et a l . 1985 ) and G . S . Jamieson ( p e r s . comm.) have both observed females m o u l t i n g in the absence of ma le s , but t h i s i s not n e c e s s a r i l y t y p i c a l for f e m a l e s . The data of Hankin et a l . ( 1985 ) , and the female ca tch curves i n S e c t i o n 4 .14 , suggest t h i s i s not the case for females >145 mm CW. Hankin et a l . (1985) r e p o r t that annua l m o u l t i n g p r o b a b i l i t i e s f or females i n c e n t r a l C a l i f o r n i a d e c l i n e p r e c i p i t o u s l y from near 1 .0 , for a female 130 mm CW, to near 0 .0 , for a female 145 mm CW. Females 140 mm CW and l a r g e r r e q u i r e a male at l e a s t 155 mm CW for a mat ing p a r t n e r ( F i g . 4 . 4 . 1 , page 31) , so a p o s s i b l e e x p l a n a t i o n for females not m o u l t i n g to l a r g e r i n s t a r s i s a lack of l e g a l - s i z e d males . C a l i f o r n i a f i s h e r i e s remove a l a r g e p o r t i o n of l e g a l - s i z e d males each year (Methot and B o t s f o r d 1982) . The lower s u r v i v o r s h i p of females to l a r g e r i n s t a r s i n h e a v i l y e x p l o i t e d C . magi s t e r p o p u l a t i o n s i n B r i t i s h Columbia ( S e c t i o n 4 .14) a l s o suggests a lack of mat ing and m o u l t i n g for l a r g e r f e m a l e s . S u b s t a n t i a t i n g t h i s i s the c o n c l u s i o n tha t e x p l o i t a t i o n r a t e s o f l e g a l - s i z e d males can be h i g h enough to markedly reduce t h e i r mating p o t e n t i a l ( F i g . 4 . 1 0 . 3 , page 83 ). The p r o p o r t i o n of females i n each 1 mm CW i n t e r v a l m o u l t i n g each year was de termined as f o l l o w s . A l l males i n the 120-121 mm CW i n t e r v a l w i t h i n e i t h e r the 155.0 or 183.8 mm i n s t a r s were d i s t r i b u t e d p r o p o r t i o n a t e l y among females a v a i l a b l e for mating S e c t i o n 5.1 Page 115 w i t h i n the carapace width l i m i t s d e f i n e d in F i g . 4 .4 .1 (page 31) . T h i s was r e p e a t e d for a l l 1 mm CW i n t e r v a l s >121 mm CW. The r e s u l t s for each 1 mm CW i n t e r v a l were then m u l t i p l i e d by the F:M mating r a t i o to d e f i n e the p o t e n t i a l number of females mated for each i n t e r v a l . The p r o p o r t i o n of females mated i n each 1 mm CW i n t e r v a l i s the p o t e n t i a l number of females mated d i v i d e d by the t o t a l number of females a v a i l a b l e , to a maximum of 1 .0 . Hankin et a l . (1985 ) show tha t w i n t e r egg p r o d u c t i o n by females which d i d not mate and moult i n the c u r r e n t season i s lower than f o r females which d i d mate and moul t . T h e i r d a t a are q u a l i t a t i v e , and do not d e f i n e a r e l a t i o n s h i p between egg p r o d u c t i o n and the number of y e a r s s ince a female mated and m o u l t e d . T h e r e f o r e , t h i s model e v a l u a t e s egg p r o d u c t i o n for extreme e s t i m a t e s of the annual r a t e of decrease i n egg p r o d u c t i o n by females which f a i l t o undergo an annual m o u l t . The r a t e s e v a l u a t e d were 1.0 ( i . e . no d e c r e a s e ) and 0.0 t imes the egg p r o d u c t i o n f o r the p r e v i o u s y e a r . Female f e c u n d i t y ( E ) as a f u n c t i o n of carapace w i d t h (CW, mm) was e s t i m a t e d u s i n g the f o l l o w i n g r e l a t i o n s h i p from Hankin et a l . (1985 ) . E = -593000+9670•CW ( 5 . 1 . 1 ) To be c o n s i s t e n t w i t h the minimum s i z e of females observed w i t h eggs i n t h i s s tudy o n l y females >100 mm CW w i t h i n i n s t a r s l a r g e r than the 100.7 mm i n s t a r produced eggs. T h i s i s Sect i o n 5.1 Page 116 e q u i v a l e n t to a p r e - m o u l t carapace w i d t h of 78 ram (from Eqn. 4 . 5 . 2 , page 33) , c l o s e to the s m a l l e s t s i z e of female observed in a mat ing embrace . 5.2 RESULTS F i g u r e 5 .2 .1 i n d i c a t e s that a F :M mat ing r a t i o of =10-15:1 a s s u r e s near maximum p o p u l a t i o n egg p r o d u c t i o n when M=2.5. These r e s u l t s a l s o p r o v i d e some i n s i g h t for e v a l u a t i n g e s t imates of M. For example, f or M=4.0, an e x t r e m e l y h i g h F : M mating r a t i o (=60:1) would be r e q u i r e d for males to mate a l l f e m a l e s . At such a h i g h m o r t a l i t y r a t e , then c o n s i d e r i n g the t ime i n v o l v e d in m a t i n g , a mean F:M mating r a t i o of 60:1 for the male p o p u l a t i o n c o u l d not be a c h i e v e d because of shor t l i f e e x p e c t a n c i e s . This would seem to i n d i c a t e that M=4.0 i s u n l i k e l y for mature C . magi s t e r , s i n c e no mature females were ever o b s e r v e d that had not been mated. A l t e r n a t i v e l y , f or M=1.0, a F : M mat ing r a t i o as low as 3:1 i s s u f f i c i e n t to ensure a l l females are mated. Since s u b l e g a l - s i z e d males w i t h e x t e n s i v e and deep s c a r s on the c h e l i p e d s (mat ing marks) were common i n t h i s s tudy and in B u t l e r ' s (1960) s t u d y , one would surmise t h a t many more than t h r e e females were mated by these m a l e s . C o n s e q u e n t l y , a maximum F : M mat ing r a t i o of =10-15:1 w i t h M=2.5 seem the more p l a u s i b l e e s t i m a t e s for these p r o c e s s e s . I f M=2.87-4.48 (as e s t i m a t e d i n S e c t i o n 4.13 of t h i s study) i s an a c c u r a t e annual e s t i m a t e , then m o r t a l i t y r a t e s must be lower d u r i n g the time of year when males are r e p r o d u c t i vely S e c t i o n 5.1 Page 117 F i g u r e 5 . 2 . 1 . R e l a t i v e egg p r o d u c t i o n by C. mag i s t er p o p u l a t i o n s as a f u n c t i o n of the F:M mat ing r a t i o , and for three e s t i m a t e s of M. These r e s u l t s are not n o t i c e a b l y s e n s i t i v e to the annual r a t e of decrease i n egg p r o d u c t i o n by females who f a i l to mate and moult i n p r e v i o u s y e a r s . F i g u r e 5 .2 .1 Page 120 FISHING M O R T A L I T Y ( F ) Figure 5 .2 .2 . Y i e l d - p e r - r e c r u i t (YPR) for increasing f i s h i n g m o r t a l i t y ( F ) . The re su l t s are reported r e l a t i v e to F=<». Figure 5.2.2 Page 121 LEGAL CARAPACE WIDTH (mm) F i g u r e 5 . 2 . 3 . Y i e l d - p e r - r e c r u i t i s r e p o r t e d r e l a t i v e to 1.0 at 165 ram CW ( S - S ) . E g g s - p e r - r e c r u i t are r e p o r t e d r e l a t i v e to an u n f i s h e d p o p u l a t i o n . The b r e a d t h of the r e l a t i o n s h i p s i n d i c a t e the range when the annual decrease i n egg p r o d u c t i o n by females t h a t d i d not mate and moult i n p r e v i o u s y e a r s i s v a r i e d from 0 . 0 - 1 . 0 t imes the egg p r o d u c t i o n of the p r e v i o u s y e a r . Both n o t c h - t o - n o t c h (N-N) and s p i n e - t o - s p i n e ( S - S ) carapace w i d t h s , and the c u r r e n t Canadian (C) and American (A) l e g a l s i z e s , are n o t e d . F i g u r e 5 .2 .3 Page 122 6 DISCUSSION 6.1 TRAP PERFORMANCE EXPERIMENTS Caddy (1979) o u t l i n e s many f a c t o r s to be c o n s i d e r e d when u s i n g t r a p sampling data as an index of p o p u l a t i o n abundance. These i n c l u d e changes i n b a i t e f f e c t i v e n e s s , a c c e s s i b i l i t y of the t r a p to the t a r g e t s p e c i e s , t r a p d e s i g n and r e t e n t i o n c a p a b i l i t i e s , env ironmenta l f a c t o r s , and b e h a v i o r of the t a r g e t s p e c i e s . In t h i s s tudy such f a c t o r s r e s u l t e d i n the s i z e f requency d i s t r i b u t i o n and r e l a t i v e abundance of male and female C . mag i s ter i n t r a p s to v a r y over t i m e , w i t h c o r r e s p o n d i n g impacts on the i n t e r p r e t a t i o n of r e l a t i v e p o p u l a t i o n d e n s i t y . F i g u r e 4 . 7 . 3 . 5 (page 65) shows tha t as soak time i n c r e a s e s , abundance w i t h i n t r a p s i n c r e a s e s l e s s r a p i d l y and e v e n t u a l l y s t a b i l i z e s . Thus , u s i n g the mean d a i l y c a t c h r a t e as an index of p o p u l a t i o n abundance i s i n a p p r o p r i a t e i f soak t imes are not s t a n d a r d i z e d among the samples . Such problems w i t h t r a p sampl ing da ta are common for i n v e r t e b r a t e f i s h e r i e s . Bennett (1974) demonstrates a dramat ic d e c r e a s e i n c a t c h per t r a p per day w i t h i n c r e a s i n g soak t imes for Cancer pagurus L . D e c r e a s i n g c a t c h per t r a p per day has a l s o been r e p o r t e d by M i l l e r (1983) for crabs and l o b s t e r s , and B o u t i l l i e r (1986) for prawns. Even for equal soak t i m e s , i f p o p u l a t i o n d e n s i t i e s , or s i z e d i s t r i b u t i o n s , d i f f e r among the p o p u l a t i o n s sampled, then the t r a p sampling r e s u l t s may be b i a s e d . I n t e r a c t i o n s between i n d i v i d u a l s w i t h i n , and a t t e m p t i n g to e n t e r , t r a p s can s t r o n g l y S e c t i o n 6 Page 123 i n f l u e n c e the d e n s i t i e s at which e n t r y and e x i t from t r a p s are b a l a n c e d . For crabs i t seems t h a t i n t r a s p e c i f i c i n t e r a c t i o n s are a g o n i s t i c . M i l l e r (1978, 1979) demonstrated that the c a t c h r a t e of C . pr oductus was l i m i t e d by a g o n i s t i c i n t e r a c t i o n s between crabs w i t h i n a t r a p , and those t r y i n g to enter that t r a p . M i l l e r (1980 ) observed a g o n i s t i c i n t e r a c t i o n s when t r a p p i n g C . magi s t e r and C . p r o d u c t u s . By h a u l i n g and emptying one set of t r a p s more o f t e n than an e q u i v a l e n t s e t , w i t h o u t changing the b a i t , he demonstrated t h a t the t r a p s h a u l e d more o f t e n caught more c r a b s . W i l l i a m s and H i l l (1982) c o n c l u d e d tha t the presence of a crab i n a t r a p r e d u c e d the p r o b a b i l i t y of f u r t h e r c a p t u r e s of the p o r t u n i d c r a b S c y l l a s e r r a t a F o r s k a l . Munro ( 1974 ) was one of the f i r s t to improve i n f o r m a t i o n from t r a p samples . In h i s paper on the dynamic i n t e r a c t i o n s between A n t i l l e a n f i s h t r a p s and r e e f f i s h e s he r e p o r t e d that the e v e n t u a l number of f i s h i n a t r a p r e s u l t s from a b a l a n c e i n the r a t e s of e n t r y and e x i t p r o c e s s e s . These p r o c e s s e s were m o d i f i e d by b a i t e f f e c t i v e n e s s , t r a p d e s i g n and s p e c i e s b e h a v i o r . F o l l o w i n g Munro ' s theme, t h i s s tudy measured (1) changes i n b a i t e f f e c t i v e n e s s over t i m e , (2) the e f f e c t s of a g o n i s t i c i n t e r a c t i o n s among C . mag i s t er i n d i v i d u a l s i n r e d u c i n g e n t r y r a t e s i n t o a t r a p , and (3) the a b i l i t y of t r a p s to r e t a i n C . magi s t e r of d i f f e r e n t s i z e s . I n c o r p o r a t i o n of these f a c t o r s i n t o a model s i m u l a t i n g e n t r y and e x i t r a t e s i n t o and out of t r a p s was s u c c e s s f u l i n improv ing i n f o r m a t i o n from t r a p samples which e x p e r i e n c e d d i f f e r e n t soak t i m e s . Sect i on 6.1 Page 124 A l t h o u g h the s t a n d a r d i z a t i o n model improved the t r a p sampl ing d a t a , i t d i d not c o m p l e t e l y e x p l a i n the dynamic i n t e r a c t i o n s between C . magi s t e r and t r a p s . U n c e r t a i n t y about the c o r r e c t f o r m u l a t i o n for the e q u a t i o n s i m u l a t i n g a g o n i s t i c i n t e r a c t i o n s ( E q n . 4 . 7 . 3 . 3 , page 55) i s an important u n c e r t a i n t y . A l s o , env i ronmenta l c o n s i d e r a t i o n s such as t i d e s , c u r r e n t s , t e m p e r a t u r e , and seasonal changes i n dynamics were not s t u d i e d . D i f f e r e n c e s among b a i t s were not s t u d i e d , but the f i shermen whose t r a p s were sampled used geoduck clam (P . a b r u p t a ) almost e x c l u s i v e l y . Females were assumed to have the same dynamics as ma1e s . By a c c e p t i n g the r e s u l t s of the s t a n d a r d i z a t i o n model one a l s o assumes tha t the d i s t r i b u t i o n of v i r t u a l e n t r y r a t e s for crabs of d i f f e r e n t s i z e s r e f l e c t s t h e i r r e l a t i v e d e n s i t y i n the p o p u l a t i o n . I f d i f f e r e n t s i z e s of crabs move at d i f f e r e n t r a t e s , some w i l l be l e s s l i k e l y to encounter a t r a p than o t h e r s , and thus may be undersampled . For example, M i l l e r (1975) observed that immature and female Chionoece te s o p i 1 i o 0. F a b r i c u s were a g g r e g a t e d , whereas mature males were a p p a r e n t l y randomly d i s t r i b u t e d . F u r t h e r , the s t a n d a r d i z a t i o n model does not c o n s i d e r a g o n i s t i c i n t e r a c t i o n s among crabs o u t s i d e a t r a p , where s m a l l e r crabs would be expec ted to be weak c o m p e t i t o r s a g a i n s t l a r g e r c r a b s . M i l l e r (1978) observed a g o n i s t i c i n t e r a c t i o n s between i n d i v i d u a l s of C . produc tus around the o u t s i d e of a t r a p . S e c t i o n 6.1 Page 125 Another c o n s i d e r a t i o n i s tha t as soak time i n c r e a s e s , i n f o r m a t i o n on sm a l l er crabs i s l o s t ( F i g . 4 . 7 . 3 . 2 , page 62) . Thus , when the d e n s i t i e s and s i z e frequency d i s t r i b u t i o n s of samples w i t h long soak t imes are s t a n d a r d i z e d , the r e s u l t s for s m a l l e r crabs w i l l remain b i a s e d . The e s t i m a t e d weight of crabs i n the t r a p s for the s h o r t e r soak t i m e s , which i s an important v a r i a b l e i n the model , w i l l be u n d e r e s t i m a t e d because of t h i s lack of i n f o r m a t i o n . The e s t i m a t e s of the crab r e t e n t i o n p r o b a b i l i t i e s (see Table 4 . 7 . 2 . 2 on page 47 and a s s o c i a t e d t e x t ) are a l s o l e s s r e l i a b l e for s m a l l e r c r a b s , m a i n l y because t r a p s are not d e s i g n e d to r e t a i n s m a l l e r c r a b s . The above c o n s i d e r a t i o n s are not as s e r i o u s a concern for e s t i m a t i n g the v i r t u a l e n t r y r a t e s for l a r g e r c r a b s . T h i s i s because the weight of crabs w i t h i n a t r a p must exceed the weight of a crab e n t e r i n g a t r a p by at l e a s t 5 t imes b e f o r e the r e l a t i v e e n t r y r a t e of crabs i n t o a t r a p i s m o d i f i e d ( F i g . 4 . 7 . 3 . 3 , page 63) . A l s o , the r e t e n t i o n r a t e s for l a r g e r crabs are h i g h e r and more p r e c i s e l y and c o n f i d e n t l y e s t i m a t e d . S m a l l e r crabs weigh much l e s s than l a r g e r crabs and spend much l e s s t ime i n the t r a p s , so the dynamics o f the s m a l l e r crabs i s not an important f a c t o r i n f l u e n c i n g the dynamic i n t e r a c t i o n s between t r a p s and l a r g e r c r a b s . For the above r e a s o n s , the s t a n d a r d i z a t i o n model used i n t h i s study s h o u l d be used c a u t i o u s l y , p a r t i c u l a r l y when making i n f e r e n c e s about s m a l l e r c r a b s , or from samples w i t h long soak t i m e s . In t h i s s t u d y , no samples were c o n s i d e r e d when the soak S e c t i o n 6.1 Page 126 t imes were longer than 10 d ays . A l s o , for s t a n d a r d i z e d samples to which a s i z e f requency a n a l y s i s was a p p l i e d , o n l y t h a t p o r t i o n of the d i s t r i b u t i o n w e l l sampled was i n c l u d e d i n the a n a l y s i s . T h i s s t a n d a r d i z a t i o n model sh ou ld not be c o n s i d e r e d an a l t e r n a t i v e to u s i n g equal and short soak times when p o s s i b l e i f the purpose i s to measure r e l a t i v e p o p u l a t i o n d e n s i t i e s . From F i g . 4 . 7 . 3 . 5 (page 65) , which shows how the d e n s i t y and s i z e d i s t r i b u t i o n of C . magi s t e r i n t r a p s changes over t i m e , i t can be seen tha t the e n t r y r a t e s for each 5 mm CW i n t e r v a l are n e a r l y cons tant for one and two day soaks i n both the 1985 and 1986 e x p e r i m e n t s . Thus data from short soak t imes may be s a t i s f a c t o r y . One s h o u l d a l s o c o n s i d e r that development of the s t a n d a r d i z a t i o n model r e q u i r e d s e v e r a l weeks of f i e l d e x p e r i m e n t a t i o n and computer a n a l y s i s . In some c i r c u m s t a n c e s the cost of such an a n a l y s i s may not be j u s t i f i a b l e . Diamond and Hankin (1985b) compared the s e l e c t i v i t i e s of two se ts of C . magi s t e r t r a p s , one w i t h escape p o r t s , and one w i t h o u t escape p o r t s . They r e p o r t e d d i f f i c u l t i e s comparing t h e i r r e l a t i v e s e l e c t i v i t i e s because of d i f f e r e n c e s i n soak t imes which they c o u l d not c o n t r o l . Part of the d i f f i c u l t y r e s u l t s from t h e i r f u n c t i o n a l l y d e f i n i n g s e l e c t i v i t y as the c o m b i n a t i o n of s e v e r a l i n t e r a c t i n g p r o c e s s e s , e . g . e n t r y and e x i t r a t e s , changes i n b a i t e f f e c t i v e n e s s , and a g o n i s t i c i n t e r a c t i o n s . For t h i s s tudy I c o n s i d e r e d these processes s e p a r a t e l y , and i n p a r t i c u l a r , I d e f i n e s e l e c t i v i t y as the a b i l i t y o f t r a p s to S e c t i o n 6.1 Page 127 r e t a i n crabs of d i f f e r e n t s i z e s for a s p e c i f i e d l e n g t h of t i m e . T h i s d e f i n i t i o n i s more c o n s i s t e n t w i t h the d e f i n i t i o n used i n other types of f i s h e r i e s , e . g . g i l l n e t s , t r a w l s (Pope et a l . 1975) , and presumably p r o v i d e s a more c o n s i s t e n t measurement of s e l e c t i v i t y tha t i s l e s s s e n s i t i v e to f a c t o r s tha t v a r y w i t h t i m e , and subsequent ly a l t e r t r a p c o n t e n t s . The r e t e n t i o n p r o b a b i l i t i e s p r e s e n t e d i n T a b l e 4 . 7 . 2 . 2 (page 47) are s i g n i f i c a n t l y i n f l u e n c e d o n l y by the b e h a v i o r of the s p e c i e s and t r a p d e s i g n . Others have measured the a b i l i t y of t r a p s to r e t a i n C . magi s t e r , but have not p r e s e n t e d t h e i r r e s u l t s to permi t comparison w i t h the r e s u l t s of t h i s s t u d y . H i g h (1976a) and Muir et a l . ( 1984 ) present c u m u l a t i v e escapement over t i m e , not escapement r a t e s , and o n l y d i s t i n g u i s h s u b l e g a l - and l e g a l - s i z e d m a l e s . Such i n f o r m a t i o n i s u s e f u l f or e v a l u a t i n g t r a p d e s i g n s , but i s l e s s a p p l i c a b l e i n models des igned t o improve u n d e r s t a n d i n g of the dynamic i n t e r a c t i o n s between C . magi s t e r and t r a p s . 6.2 SPATIAL AND TEMPORAL DISTRIBUTIONS Smal l male C . magi s t e r appeared to r e t r e a t short d i s t a n c e s to more s h e l t e r e d h a b i t a t i n autumn and w i n t e r . T h i s was p a r t i c u l a r l y ev ident i n F i g . 4 . 1 1 . 2 b where a large c o n c e n t r a t i o n of s m a l l males g a t h e r e d i n the p r o t e c t e d waters of midd le Lemmens I n l e t . T h i s c o n c e n t r a t i o n d i s p e r s e d d u r i n g summer, a l t h o u g h the d e c r e a s e d abundance i s a l s o due to m o u l t i n g to l e g a l s i z e and S e c t i o n 6.1 Page 128 subsequent c a p t u r e by f i s h e r m e n . Others o b s e r v e d , or i n f e r r e d , s i m i l a r b e h a v i o r for C . magi s t e r . Stevens and Armstrong ( 1984 ) r e p o r t e d tha t the 1980 y e a r - c l a s s i n Grays H a r b o r , Wash ington , d i s a p p e a r e d d u r i n g the w i n t e r of i t s f i r s t y e a r , then reappeared the f o l l o w i n g s p r i n g . G o t s h a l l (1978b) observed movement of s u b l e g a l - and l e g a l - s i z e d male C . magi s t e r i n n o r t h e r n C a l i f o r n i a to deeper water i n w i n t e r , and a r e t u r n to s h a l l o w e r water . , i n s p r i n g . It i s r easonab le to surmise t h a t t h i s autumn movement i s to a v o i d rough water d u r i n g the w i n t e r . R e t u r n i n g to s h a l l o w , warmer and more p r o d u c t i v e water d u r i n g summer would c o n c e i v a b l y i n c r e a s e food a v a i l a b i l i t y . Average movement r a t e s for male C . magi s t e r of <30 m per day ( F i g . 4 . 1 1 . 4 , page 94) , seem c o n s i s t e n t w i t h the r e s u l t s of other s t u d i e s , and suggest tha t C . magi s t e r p o p u l a t i o n s remain l o c a l ( B u t l e r 1957, G o t s h a l l 1978b) . Except for the apparent seasona l changes i n h a b i t a t , which i n v o l v e movement over shor t d i s t a n c e s , no s t u d i e s suggest d i r e c t i o n a l m i g r a t o r y movements for male C . magi s t e r . However, G o t s h a l l ( 1978b) noted tha t males seem to move i n the d i r e c t i o n of p r e v a i l i n g c u r r e n t s . Bennett and Brown (1983) r e p o r t tha t most tagged male C . pagurus remained near where they were r e l e a s e d i n the E n g l i s h C h a n n e l . Females were observed to move from c o a s t a l i n l e t s , where the s u b s t r a t e ranged from mud to a mud/sand mix , to the more exposed a r e a i n the main channel i n t o the s tudy area where the bottom was m a i n l y sand or a s a n d / g r a v e l mix . W i l d (1980) s t a t e s that females must be at l e a s t p a r t i a l l y b u r i e d i n sandy s u b s t r a t e to Sect i on 6.2 Page 129 extrude and incubate eggs . Stevens and Armstrong (1984) noted that e g g - b e a r i n g females were r a r e i n Grays H a r b o r , and s p e c u l a t e d tha t most mature females l e f t the harbour to r e l e a s e t h e i r eggs i n a p r e f e r r e d env ironment . Diamond and Hankin (1985a) argue tha t mature female C . magi s t e r undergo l i m i t e d movements i n o f f s h o r e waters and suggest that females c o n s t i t u t e l o c a l i z e d p o p u l a t i o n s . In t h i s s tudy average movement r a t e s for females (<20 m per day) were l e s s than the r a t e s for males ( F i g . 4 . 1 1 . 4 , page 9 4 ) . Thus , i t appears tha t females may undergo some m i g r a t o r y movement i n order to l o c a t e s u b s t r a t e s u i t a b l e for i n c u b a t i n g eggs . They a l s o suspect tha t females r e t u r n short d i s t a n c e s to s h a l l o w e r water i n s p r i n g to mate and m o u l t . Males and females may improve mating o p p o r t u n i t i e s by c o n c e n t r a t i n g i n s h a l l o w w a t e r . S i m i l a r movement b e h a v i o r has been r e p o r t e d for o ther c r a b s . H y l a n d et a l . ( 1984 ) observed the movement of female p o r t u n i d c r a b s , S. s e r r a t a , from an e s t u a r i n e env i ronment , where they l i v e d as j u v e n i l e s , to the open ocean where they r e l e a s e d t h e i r eggs. Some females r e t u r n e d to i n s h o r e waters a f t e r the h a t c h i n g season . Bennett and Brown (1983) demonstrated tha t female C . paqurus undergo e x t e n s i v e movements, a p p a r e n t l y to h a b i t a t more s u i t a b l e for egg i n c u b a t i o n . U s i n g SCUBA, Howard (1982) observed e g g - b e a r i n g female C . pagurus congregated i n r e l a t i v e l y deep (24 m), calm w a t e r . S ince they were r a r e e l s ewhere , he Sect i on 6.2 Page 13 0 conc luded t h i s was a p r e f e r r e d h a b i t a t . D i n n e l et a l . ( 1987 ) observed female C . magi s t e r i n a s i m i l a r h a b i t a t i n Puget Sound, Wash ington , from the s u b m e r s i b l e PISCES IV. 6.3 GROWTH AND MORTALITY B u t l e r (1961) d e t e r m i n e d tha t male C . magi s t e r i n Dixon E n t r a n c e a t t a i n e d l e g a l s i z e d u r i n g t h e i r f o u r t h year a f t e r s e t t l e m e n t . U s i n g the s i z e f requency a n a l y s i s of MacDonald and P i t c h e r (1979) , Warner (1985, 1987) conc luded t h a t for the two y e a r - c l a s s e s he f o l l o w e d i n n o r t h e r n C a l i f o r n i a , 60% and 28% of each y e a r - c l a s s a t t a i n e d l e g a l s i z e (159 mm CW) d u r i n g t h e i r f o u r t h year a f t e r s e t t l e m e n t . The remainder r e c r u i t e d to the f i s h e r y d u r i n g t h e i r f i f t h y e a r . In t h i s study about 50% of male crabs that moul ted i n t o the 155.0 mm i n s t a r d u r i n g t h e i r f o u r t h year a t t a i n e d l e g a l s i z e (153.7 mm CW)." S i n c e <10% . o f s u b l e g a l - s i z e d males i n the 155.0 mm i n s t a r w i l l ever a t t a i n l e g a l s i z e due to h i g h n a t u r a l m o r t a l i t y , >90% of the y i e l d from t h i s i n s t a r i s from males i n t h e i r f o u r t h y e a r . D i f f e r e n c e s i n the s i z e frequency models between t h i s and W a r n e r ' s s tudy are p o s s i b l e reasons for d i f f e r e n t c o n c l u s i o n s about the age when males enter the f i s h e r y . Wi th growth s t r u c t u r e ( i . e . moult i n c r e m e n t s - a t - s i z e ) i n c l u d e d i n the s i z e f requency model i n t h i s s tudy (see Schnute and F o u r n i e r 1980) , the s i z e f requency a n a l y s i s w i l l tend to d e f i n e s i z e f requency modes that r e s p e c t the expec ted d i f f e r e n c e s i n i n s t a r mean s i z e s . W a r n e r ' s model d i d not i n c l u d e i n f o r m a t i o n on moult i n c r e m e n t s -S e c t i o n 6.2 Page 131 a t - s i z e , and f u r t h e r , h i s a n a l y s i s d i d not account for the e f f e c t of e x p l o i t a t i o n of l e g a l - s i z e d males on s i z e f requency d i s t r i b u t i o n s . These c o n s i d e r a t i o n s a lone may l e a d to d i f f e r e n t i n t e r p r e t a t i o n s of s i z e f r e q u e n c y i n f o r m a t i o n . N e v e r t h e l e s s , u n u s u a l l y h i g h p o p u l a t i o n abundance near T o f i n o i n 1986 (see be low, and F i g . 2 .2 , page 10) may have r e s u l t e d i n h i g h d e n s i t y - d e p e n d e n t m o r t a l i t y . T h e r e f o r e , male m o r t a l i t y r a t e s may be lower for the p o p u l a t i o n tha t Warner s t u d i e d , i n c r e a s i n g s u r v i v o r s h i p and r e c r u i t m e n t to the f i s h e r y of males o l d e r than four year s . D i f f e r e n c e s i n growth r a t e s may a l s o r e s u l t i n d i f f e r e n c e s in the ages at which males r e c r u i t to the f i s h e r y between B r i t i s h Columbia and C a l i f o r n i a . Stevens and Armstrong (1984) demonstrated that f i r s t year C . magi s t e r grew more q u i c k l y i n Grays Harbor e s t u a r y , Wash ington , than i n the a d j a c e n t open ocean where sea water t emperatures were lower . Water t emperatures i n the i n l e t s near T o f i n o were s l i g h t l y h i g h e r than a l o n g the open c o a s t , so growth r a t e s may be f a s t e r . However, i t i s e l u c i d a t i n g to note tha t there are a p p a r e n t l y no large d i f f e r e n c e s i n the moult i n c r e m e n t s - a t - s i ze f o r male C . magi s t er ( >80 mm CW) from c e n t r a l C a l i f o r n i a to the Queen C h a r l o t t e I s lands ( T a b l e 4 . 5 . 1 , page 33 ) . B u t l e r (1961) and Stevens and Armstrong (1984) d e t e r m i n e d tha t females are two years o l d when they are =100 mm CW. T h i s s tudy suggests that females i n the 135.5 mm i n s t a r are t h r e e years o l d , thus those i n the 149.4 and 161.4 mm i n s t a r s are Sect i on 6.3 Page 13 2 p r o b a b l y four and f i v e years o l d , g i v e n that they undergo an annual moul t . However, i t has been suggested in t h i s s t u d y , and by Hankin et a l . (1985 ) , tha t moults may occur l e s s f r e q u e n t l y than a n n u a l l y for females l a r g e r than =145 mm CW, p a r t i c u l a r l y i n i n t e n s i v e l y f i s h e d p o p u l a t i o n s ( S e c t i o n 4 . 1 4 ) . As was observed for males , moult i n c r e m e n t s - a t - s i z e for female C . magi s t e r vary l i t t l e from c e n t r a l C a l i f o r n i a to the Queen C h a r l o t t e I s l ands ( T a b l e 4 . 5 . 2 , page 33) . The e x p l o i t a t i o n r a t e on l e g a l - s i z e d male C . magi s t e r near T o f i n o i s h i g h (F = 5 .11 -6 .90 ), w i t h l e g a l - s i z e d males h a v i n g o n l y a 50% chance of s u r v i v i n g the f i s h e r y for more than 37-50 d ay s . Because of the i n t e n s i t y of the f i s h e r y , the seasonal p a t t e r n of f i s h i n g success i n Lemmens I n l e t ( F i g . 4 . 9 . 4 , page 76) mimics the time d i s t r i b u t i o n of m o u l t i n g i n t o l e g a l s i z e for the 128.0 mm i n s t a r ( F i g . 4 . 1 3 . 3 , page 105) . M o u l t i n g occurs over 6-9 months s u s t a i n i n g the f i s h e r y for most of the y e a r . F i g u r e 4 . 9 . 5 (page 77) , which p r e s e n t s a s e a s o n a l p r o f i l e of v i r t u a l e n t r y r a t e s of l e g a l - s i z e d males ( i . e . s t a n d a r d i z e d d a t a ) for t r a p s samples from throughout the study a r e a , shows a p a t t e r n s i m i l a r t o t h a t i n F i g . 4 . 9 . 4 . The seasona l p a t t e r n of f i s h i n g success observed w i t h i n Lemmens I n l e t ( F i g . 4 . 9 . 4 ) was not apparent o u t s i d e Lemmens I n l e t , a p p a r e n t l y because l e s s e f f o r t ( lower t r a p d e n s i t i e s and longer soak t i m e s ) d i s g u i s e d the r e l a t i o n s h i p between moult t i m i n g and c a t c h r a t e s ( n • t r a p " * - d " * ) . S e c t i o n 6.3 Page 133 High f i s h i n g m o r t a l i t y r a t e s have p r e v i o u s l y been measured for C . mag i s t er i n n o r t h e r n C a l i f o r n i a . Jow (1965) e s t i m a t e d F at 7 . 9 , based on r e c o v e r y of tagged l e g a l - s i z e d males d u r i n g the f i s h i n g season , which l a s t s about s i x months. U s i n g c a t c h - p e r -u n i t - e f f o r t d a t a , G o t s h a l l (1978a) e s t imated F to range from 1 . 1 8 - 7 . 0 0 , depending on the y e a r . S i m i l a r l y , Methot and B o t s f o r d (1982) e s t i m a t e d F to range from 0 .8 -3 .2 for the p e r i o d 1951 u n t i l 1977. N a t u r a l m o r t a l i t y for male C . magi s t e r i n the 155.0 mm i n s t a r was de termined to be h i g h . A maximum e s t i m a t e of M=3.48 was sugges ted by the d i s a p p e a r a n c e of tagged s u b l e g a l - s i z e d males over time (Tab le 4 . 1 3 . 1 , page 97 and F i g . 4 . 1 3 . 1 , page 103) . E s t i m a t e s of M r a n g i n g from 2 . 8 7 - 4 . 3 7 were suggested by the lack of r e c o v e r y of l e g a l - s i z e d males t h a t were tagged when they were s u b l e g a l s i z e (Tab le 4 . 1 3 . 5 , page 102) . An e s t i m a t e for M of 4 . 33 -4 .48 was suggested from the r e c o v e r y of males r e l e a s e d and r e c o v e r e d when l e g a l s i z e . No d e t e c t i o n of the 183.8 mm male i n s t a r i n s i z e f requency a n a l y s e s , i n c l u d i n g those per formed on the l i g h t l y f i s h e d H o l b e r g I n l e t f i s h e r y , a l s o s t r o n g l y suggests low s u r v i v o r s h i p to i n s t a r s l a r g e r than the 155.0 mm i n s t a r . T a b l e 4 .13 .5 shows t h a t males have a reduced l i k e l i h o o d to s u r v i v e to the next i n s t a r as t h e i r s i z e i n c r e a s e s . The c a t c h c u r v e s i n F i g . 4 .14 .1 (page 110) i n d i c a t e the same phenomenon for f e m a l e s . I n c r e a s i n g n a t u r a l m o r t a l i t y r a t e s w i t h i n c r e a s i n g s i z e have been observed for o ther c r a b s p e c i e s . H i l l (1975) r e p o r t s an i n c r e a s e i n the m o r t a l i t y r a t e of the p o r t u n i d c r a b , Sect i on 6.3 Page 134 S. s e r r a t a , from i t s second to t h i r d year of l i f e . As crabs become l a r g e r , and the energy r e q u i r e d to a t t a i n the next i n s t a r i n c r e a s e s , the time between moults i n c r e a s e s . C o u p l e d w i t h s h e l l d e t e r i o r a t i o n , and i n c r e a s i n g energy r e q u i r e m e n t s , the l i k e l i h o o d of these i n d i v i d u a l s a t t a i n i n g the next i n s t a r i s d e c r e a s e d . The growth and m o r t a l i t y r a t e e s t imates for males o b t a i n e d i n t h i s s tudy may have i m p l i c a t i o n s for models which have a t tempted to e x p l a i n C.. magi s t e r p o p u l a t i o n dynamics i n other f i s h e r i e s . In p a r t i c u l a r , models proposed to e x p l a i n the c y c l i c a l na ture of C . mag i s t er l a n d i n g s i n C a l i f o r n i a (see McKelvey et a l . 1980, B o t s f o r d 1984, 1986a, Methot 1986 ) have been based on male growth r a t e s s lower ( e . g . =50% of males becoming l e g a l s i z e when 5+ years o l d ) , and m o r t a l i t y r a t e s much lower (M=0.15-0.90 for immature m a l e s ) , than those p r e s e n t e d h e r e . I f the growth and m o r t a l i t y r a t e s o b t a i n e d i n t h i s s tudy for mature males can be j u s t i f i e d for immature males i n p o p u l a t i o n s a l o n g the coast of Wash ington , Oregon and C a l i f o r n i a , these models may need to be a d j u s t e d n u m e r i c a l l y , and i n some c a s e s , perhaps c o n c e p t u a l l y . C o n c e i v a b l y the h i g h m o r t a l i t y r a t e s o b t a i n e d i n t h i s s tudy are p a r t l y due to d e n s i t y - d e p e n d e n t f a c t o r s r e s u l t i n g from an u n u s u a l l y h i g h abundance of C . magi s t e r i n 1986. Cancer magi s t er l a n d i n g s for SA 24 i n 1986 were 265 t . T h i s i s the t h i r d h i g h e s t t o t a l i n the h i s t o r y of the f i s h e r y , and more than double the mean tonnage landed the p r e v i o u s 10 years (131+26 t , see F i g . 2 . 2 , page 1 0 ) . However, s i z e f r e q u e n c y a n a l y s i s on males i n S e c t i o n 6.3 Page 135 other B r i t i s h Columbia f i s h e r i e s a l s o i n d i c a t e d low s u r v i v o r s h i p of s u b l e g a l - s i z e d males from the 155.0 mm i n s t a r to the 183.8 mm i n s t a r . V a r i a t i o n i n M i s a reasonab le e x p e c t a t i o n s i n c e G o t s h a l l ( 1978b), us ing c a t c h - p e r - u n i t - e f f o r t d a t a , e s t i m a t e d M to range from 0 .88-2 .50 i n n o r t h e r n C a l i f o r n i a . However, G o t s h a l l ' s e s t imates of m o r t a l i t y and p o p u l a t i o n s i z e were not o b t a i n e d i n d e p e n d e n t l y , h i s e s t i m a t e s of p o p u l a t i o n s i z e ( L e s l i e method, see R i c k e r 1975) f a i l i n g the assumpt ion of low n a t u r a l m o r t a l i t y . For t h i s reason h i s e s t imates of M cannot be accepted w i t h c o n f i d e n c e . Male c r a b d e n s i t i e s near T o f i n o i n 1987 appear to be c o n s i d e r a b l y lower than i n 1986, as i n d i c a t e d by low p r e - r e c r u i t abundance and d e c l i n i n g f i s h i n g success ( G . S . J a m i e s o n , P a c i f i c B i o l o g i c a l S t a t i o n , Nanaimo, B . C . , p e r s . comm.). T h i s may p r o v i d e an o p p o r t u n i t y to measure the e f f e c t of d e n s i t y on m o r t a l i t y , f a c i l i t a t i n g more r e l i a b l e e x t r a p o l a t i o n s to h a b i t a t s w i t h d i f f e r e n t crab d e n s i t i e s . The l i f e h i s t o r y of C . magi s t e r . as c u r r e n t l y u n d e r s t o o d , appears t y p i c a l of r - s t r a t e g i s t s (S tearns 1976, 1977): f a s t g r o w i n g , s h o r t - l i v e d , h i g h f e c u n d i t y , e a r l y m a t u r i t y , and f l u c t u a t i n g p o p u l a t i o n s i z e s . A s s o c i a t e d w i t h these t r a i t s i s the p r e d i c t i o n of h i g h d e n s i t y - i n d e p e n d e n t m o r t a l i t y . Causes of a h i g h n a t u r a l m o r t a l i t y r a t e for C . magi s t e r are p r e s e n t l y unknown. U n l i k e many i n v e r t e b r a t e s p e c i e s whose j u v e n i l e and a d u l t s tages occupy d i f f e r e n t h a b i t a t s (Caddy 1986) , j u v e n i l e and a d u l t C . magi s t e r occur t o g e t h e r on sand, so d e n s i t y - d e p e n d e n t Sect i on 6.3 Page 136 m o r t a l i t y may be important for t h i s s p e c i e s . For example, c a n n i b a l i s m of a d u l t s on j u v e n i l e s ( B o t s f o r d and Wickham 1978) i s b e i n g i n v e s t i g a t e d as a p o s s i b l e e x p l a n a t i o n of the c y c l e s i n C a l i f o r n i a C . magi st er l a n d i n g s . F a c t o r s a s s o c i a t e d w i t h the growth , p h y s i o l o g y , and l i f e h i s t o r y of C . mag i s ter i n d i v i d u a l s are p o s s i b l e causes of d e n s i t y - i n d e p e n d e n t m o r t a l i t y . Over the course of t h i s s tudy crabs showed an obvious p r o g r e s s i o n of s h e l l d e t e r i o r a t i o n and l o s s of v i g o r as the time they spent w i t h i n an i n s t a r i n c r e a s e d . Disease i s not b e l i e v e d to be an important c o n t r i b u t o r to C . mag i s t er m o r t a l i t y near T o f i n o but p r e d a t i o n i s a p o s s i b i l i t y . The g i a n t P a c i f i c o c t o p u s , Octopus d o f l e i n i ( W u l k e r ) , an important p r e d a t o r of C . magi s t e r , i s abundant i n t h i s v i c i n i t y ( H i g h 1976b, Hartwick et a l . 1978 ). Octopus d o f l e i n i were o c c a s i o n a l l y caught i n crab t r a p s d u r i n g t h i s s t u d y . H i g h (1976a) observed 0. d o f l e i n i p r e d a t i o n on C . magi s t e r d u r i n g t r a p escapement e x p e r i m e n t s . 6.4 YIELD- AND EGGS-PER-RECRUIT Males under l e g a l s i z e i n the 155.0 mm i n s t a r (about 50% of t h i s i n s t a r ) have a low p r o b a b i l i t y (<10%) of a t t a i n i n g l e g a l s i z e at a f u t u r e d a t e . F i g u r e 5 .2 .3 (page 122) shows t h a t for M=2.5-4.0 ( s i m i l a r to the e s t imates o b t a i n e d i n S e c t i o n 4 .13) t h e r e i s a p o t e n t i a l i n c r e a s e i n y i e l d - p e r - r e c r u i t o f 2-3 f o l d r e l a t i v e to the c u r r e n t minimum l e g a l s i z e l i m i t of 165 mm CW ( s p i n e - t o - sp ine ) i f a l l males >140 mm CW ( s p i n e - t o - sp ine ) are Sect i on 6.3 Page 137 e x p l o i t e d . F u r t h e r r e d u c t i o n s i n the s i z e l i m i t a l s o suggest i n c r e a s e d y i e l d , but presume a c c u r a c y i n the model r e s u l t s below the carapace widths for which m o r t a l i t y was c o n f i d e n t l y measured. For many spec i e s y i e l d - p e r - r e c r u i t cannot be improved by r e d u c i n g the s i z e of an imals taken i n a f i s h e r y because of the r i s k of r e c r u i t m e n t - o v e r f i s h i n g (Cush ing 1973), i . e . r e d u c i n g p o p u l a t i o n egg p r o d u c t i o n below a l e v e l that can be c o n s i s t e n t l y compensated by d e n s i t y - d e p e n d e n t r e s p o n s e s , thereby r e s u l t i n g i n d e c l i n i n g abundance. For C . magi s t e r a r e l a t i o n s h i p between s tock and r e c r u i t m e n t has not been found . In f a c t , documentat ion of compensatory stock and r e c r u i t m e n t r e l a t i o n s h i p s i s r a r e for i n v e r t e b r a t e s in g e n e r a l (Hancock 1973, Caddy 1986). As Jamieson (1986) n o t e s , such r e l i a b l e r e l a t i o n s h i p s may or may not e x i s t for c e r t a i n crab s p e c i e s , and i n many cases r e l a t i o n s h i p s may be d i s g u i s e d by poor d a t a . C o n s e q u e n t l y , many i n v e r t e b r a t e f i s h e r i e s are managed by s i z e l i m i t a t i o n s which p r o t e c t r e p r o d u c t i v e f emales . Minimum l e g a l s i z e l i m i t s have been s u c c e s s f u l measures i n some f i s h e r i e s , e . g . the e a s t e r n Canad ian l o b s t e r ( H . amer i canus ) f i s h e r y , where r e g u l a t o r y measures a p p a r e n t l y p r o t e c t a s u f f i c i e n t p o r t i o n of p o p u l a t i o n egg p r o d u c t i o n (Jamieson and Caddy 1986) . The p o s s i b i l i t y of r e c r u i t m e n t - o v e r f i s h i n g for C . magi s t e r p o p u l a t i o n s has never been s e r i o u s l y c o n s i d e r e d because of the h i s t o r i c a l presumpt ion t h a t the c u r r e n t Canadian and Amer ican minimum l e g a l s i z e l i m i t s for males p r e s e r v e adequate p o p u l a t i o n egg p r o d u c t i o n ( C l e a v e r 1949, Poole and G o t s h a l l 1965, Methot S e c t i o n 6 .4 Page 138 1986) . S i n c e few females a t t a i n l e g a l s i z e , and egg b e a r i n g females of a l l observed s i z e s above the s i z e - a t - m a t u r i t y are r e l a t i v e l y common, i t has been assumed tha t t a k i n g o n l y males d i d not a f f e c t p o p u l a t i o n egg p r o d u c t i o n . In support of t h i s , B r i t i s h Columbia f i s h e r i e s show no s t r o n g ev idence of r e c r u i t m e n t - o v e r f i s h i n g . In apparent agreement w i t h t h i s a s s u m p t i o n , t h i s s tudy noted t h a t a l l mature females ( g r e a t e r than =115 mm CW) d i s s e c t e d i n the f i e l d c o n t a i n e d a p a i r of sperm p a c k s . However, the female c a t c h curves i n F i g . 4 .14 .1 (page 110) , which imply d e c r e a s i n g l i k e l i h o o d s of females a t t a i n i n g l a r g e r i n s t a r s i n the more h e a v i l y f i s h e d r e g i o n s , suggest t h a t mature females may o n l y moult when accompanied by a l a r g e r male i n a mat ing embrace. It i s t y p i c a l for female c a n c r i d crabs to mate w i t h a l a r g e r and h a r d - s h e l l e d male ( B u t l e r 1960, Snow and N e i l s e n 1966, E l n e r et a l . 1985) . F i g u r e 4 .4 .1 (page 31) , which p l o t s the r e l a t i v e s i z e s of males and females i n mat ing embraces , suggests tha t females l a r g e r than =140 mm CW may not have an o p p o r t u n i t y to mate and moult i n the more h e a v i l y f i s h e d p o p u l a t i o n s . Such a phenomenon of females m o u l t i n g o n l y when accompanied by a male i n a mating embrace i s c o n s i s t e n t w i t h the o b s e r v a t i o n tha t a l l mature females c o n t a i n e d a p a i r of sperm p a c k s . It i s no teworthy , however, that Brown and Bennett (1980) suggested tha t l a r g e female C . paqurus f a i l e d to undergo an annual moult because the presence of a p a i r of sperm packs i n h i b i t e d m o u l t i n g . One S e c t i o n 6.4 Page 139 can not i n t e r p r e t from t h e i r r e s u l t s whether the m o u l t i n g of females may have been i n h i b i t e d by the absence of males large enough to mate w i t h the l a r g e r f e m a l e s . So even though a l l females i n a h e a v i l y f i s h e d p o p u l a t i o n may have been mated, p o p u l a t i o n egg p r o d u c t i o n may s t i l l be r e d u c e d r e l a t i v e to an u n f i s h e d p o p u l a t i o n . T h i s would r e s u l t from (1) a s h i f t in the s i z e f r e q u e n c y d i s t r i b u t i o n of females to s m a l l e r s i z e s , w i t h s m a l l e r females p r o d u c i n g fewer eggs than l a r g e r females (Eqn . 5 .1 .1 on page 116 of t h i s s t u d y , which i s from Hankin et a l . 1985) , and (2) reduced f e c u n d i t y each year a female f a i l s to moul t . Both r e s u l t from a decrease i n p o t e n t i a l mat ings by the male p o p u l a t i o n . In an in tense C . magi s t e r f i s h e r y many l e g a l - s i z e d males l anded are s o f t - s h e 11ed. From a r e p r o d u c t i v e p e r s p e c t i v e , l a n d i n g a s o f t - s h e l l e d male that i s j u s t l e g a l s i z e (a t the mode of the 155.0 mm i n s t a r ) i s e q u i v a l e n t to l a n d i n g a h a r d - s h e l l e d male 128 mm CW (at the mode of the next s m a l l e r i n s t a r ) . In c o n s i d e r a t i o n of the s i z e f requency d i s t r i b u t i o n of the percent of males w i t h mating marks ( F i g . 4 . 1 0 . 1 , page 81) , i t i s l i k e l y t h a t many males w i l l have never mated b e f o r e b e i n g taken by the f i s h e r y . T h e r e f o r e , i n an h e a v i l y e x p l o i t e d r e g i o n a l f i s h e r y , v i r t u a l l y a l l mating i s by s u b l e g a l - s i z e d males i n the 155.0 mm i n s t a r . Intense f i s h i n g r e s u l t s i n the number of p o t e n t i a l matings by males b e i n g reduced by =50% r e l a t i v e to an u n f i s h e d S e c t i o n 6.4 Page 140 p o p u l a t i o n . The a c t u a l decrease i n the number of mat ings depends on how w e l l s u b l e g a l - s i z e d males compensate by mat ing more females than they would i n an u n f i s h e d p o p u l a t i o n . F i g u r e 5 .2 .1 (page 120) i n d i c a t e s tha t as the p o t e n t i a l F :M mat ing r a t i o for the male p o p u l a t i o n i n c r e a s e s above =10:1 ( f o r M=2.5) , the impact on p o p u l a t i o n egg p r o d u c t i o n d e c r e a s e s . The i m p l i c a t i o n i s that an F:M mat ing r a t i o >10:1 i n c l u d e s s u r p l u s mat ing p o t e n t i a l which can b u f f e r mat ing p o t e n t i a l l o s t due to f i s h i n g . The e g g s - p e r - r e c r u i t a n a l y s i s i n t h i s s t u d y , which modeled the male and female r e p r o d u c t i v e p r o c e s s e s , suggests tha t h i g h e x p l o i t a t i o n of males above the c u r r e n t minimum l e g a l s i z e l i m i t might reduce e g g s - p e r - r e c r u i t by up to 50% r e l a t i v e to an u n f i s h e d p o p u l a t i o n . In c o n s i d e r a t i o n of t h i s c o n c l u s i o n , the p o s s i b i l i t y of r e c r u i t m e n t - o v e r f i s h i n g i n h e a v i l y e x p l o i t e d f i s h e r i e s s h o u l d be r e i n s t a t e d as a concern f o r f i s h e r i e s manager s . F u l l c o n f i d e n c e i n the e g g s - p e r - r e c r u i t model r e q u i r e s a more complete u n d e r s t a n d i n g of r e p r o d u c t i v e b e h a v i o r . The model p r e s e n t e d i n t h i s s tudy i s based on bes t e s t i m a t e s , and u n c e r t a i n t y i n these e s t i m a t e s , of important p o p u l a t i o n v a r i a b l e s . L i k e most a t tempts to s imula te n a t u r a l proces se s there are u n c e r t a i n t i e s i n (1) the n u m e r i c a l r e p r e s e n t a t i o n of p r o c e s s e s which are g e n e r a l l y u n d e r s t o o d , but are d i f f i c u l t to q u a n t i f y , and (2) i n the conceptua l u n d e r s t a n d i n g of n a t u r a l p r o c e s s e s . In t h i s a n a l y s i s the important n u m e r i c a l u n c e r t a i n t y i s the F:M mat ing r a t i o , and in p a r t i c u l a r the f u n c t i o n a l S e c t i o n 6.4 Page 141 response of the F:M mating r a t i o to female density. The important conceptual uncertainty concerns female moulting frequency and i t s r e l a t i o n s h i p to the a v a i l a b i l i t y of males for mat i ng. Reproductive biology (e.g. age-at-maturity, fecundity, seasonality of egg hatching) has been described for many crab species but information on reproductive behavior in nature (e.g. F:M mating r a t i o s , duration of mating a c t i v i t y , female moulting pattern) is more elusive and remains poorly understood for crustaceans in general. Increased knowledge of reproductive behavior is not only important for understanding the population dynamics of C. magi ster, but may contribute to explanations of the recent sharp declines in landings of the red king crab (Blau 1986) and the A t l a n t i c snow crab (Elner and Bailey 1986). With regard to the present study, there is i n s u f f i c i e n t information to adequately debate whether a female with a pair of sperm packs does, or does not, moult annually. Using r e l a t i v e egg production as a measure of f i t n e s s (Stearns 1976, 1977), the better reproductive strategy is the one that produces the most viable eggs in the future. If mating, moulting and producing a larger clutch of eggs is a higher r i s k for a female, in terms of future population egg production, than not moulting and producing fewer eggs, then the suggestion of Brown and Bennett (1980) that females do not moult i f they have a pair of sperm packs is the more favourable evolutionary argument. If mating and moulting has the lower r i s k , then the more favourable argument is that Section 6.4 Page 142 females s h o u l d not moult wi thout m a t i n g . U n c e r t a i n t y about which l i f e h i s t o r y i s the c o r r e c t e x p l a n a t i o n for C . magi s t e r i n f l u e n c e s how b i o l o g i c a l i n f o r m a t i o n ( e . g . female c a t c h c u r v e s , F i g . 4 . 1 4 . 1 , page 110) i s i n t e r p r e t e d . T h i s can have important i m p l i c a t i o n s for management of the s p e c i e s . Wi th our c u r r e n t u n d e r s t a n d i n g of male and female growth and m o r t a l i t y , there seems to be no n a t u r a l c i rcumstance when females are d e p r i v e d of males s u i t a b l e for m a t i n g . So, i n an u n f i s h e d p o p u l a t i o n a female can expect to be mated, and t h e r e f o r e s h o u l d not moult w i thout mating s i n c e , c o n s i d e r i n g the h i g h n a t u r a l m o r t a l i t y , she has l i t t l e chance of s u r v i v i n g to mate and moult the f o l l o w i n g y e a r . In t h i s c i r c u m s t a n c e , the more f i t f emale , i n terms of f u t u r e egg p r o d u c t i o n , i s the one t h a t d e l a y s m o u l t i n g u n t i l a s u i t a b l e mate i s f o u n d . The consequence of t h i s s t r a t e g y i n a h e a v i l y f i s h e d p o p u l a t i o n would be a s h i f t i n the female s i z e f requency d i s t r i b u t i o n to s m a l l e r s i z e s . U n d e r s t a n d i n g n a t u r a l r e p r o d u c t i v e behav ior r e q u i r e s a knowledge of the p h y s i o l o g i c a l i n t e r a c t i o n s between mat ing males and f emales , and the f a c t o r s that c o n t r o l m a t i n g . The p h y s i o l o g i c a l argument for b r a c h y u r a n crabs i n g e n e r a l i s tha t a female s e c r e t e s a pheromone to a t t r a c t males when she i s p r e p a r i n g to moult ( H a r t n o l l 1969, C h r i s t y 1987) . Once a s u i t a b l e mate i s found, the mat ing r i t u a l and subsequent mat ing o c c u r . For 'female c e n t e r e d c o m p e t i t i o n ' , which i s the l a b e l C h r i s t y (1987) a p p l i e s to the mat ing behav ior of Cancer s p p . , t h i s means that males c o m p e t i t i v e l y search and a g g r e s s i v e l y S e c t i o n 6.4 Page 143 defend t h e i r female p a r t n e r s for a few days b e f o r e , and perhaps a f t e r , the a c t u a l m a t i n g . There i s s t r o n g ev idence of the r e l e a s e of a pheromone to a t t r a c t males for a few p o r t u n i d crabs ( C h r i s t y 1987), and Edwards (1966) suggested t h i s may a l s o occur for C . pagurus . There i s some i n d i r e c t ev idence t h a t c a n c r i d females r e l e a s e a w a t e r - b o r n e pheromone i n t h e i r u r i n e i n the days p r i o r to m o u l t i n g ( C h r i s t y 1987) , but there i s no p r o o f that a mat ing pheromone e x i s t s for any b r a c h y u r a n crab s p e c i e s . It i s c r i t i c a l t h a t we unders tand the r e p r o d u c t i v e p h y s i o l o g y of C . magi s t e r . and determine i f the e n d o c r i n o l o g y of m o u l t i n g and r e p r o d u c t i o n i s d i f f e r e n t for females w i t h and w i t h o u t sperm p a c k s . It needs to be e x p l a i n e d why p o p u l a t i o n i n f o r m a t i o n suggests females do not moult i f s u i t a b l e males are not a v a i l a b l e , yet mature females w i t h sperm packs have been observed to moult i n the absence of males i n l a b o r a t o r y t a n k s . A l s o , the s u g g e s t i o n of Brown and Bennett (1980) t h a t female C . pagurus w i t h sperm packs do not moult does not e x p l a i n how females w i t h sperm packs a t t a i n the l a r g e r i n s t a r s . In t h i s s t u d y , a l l mature C . magi s t e r f emale s , of a l l s i z e s , had sperm packs . An ' exper imenta l management' approach (Wal ters and H i l b o r n 1978, H i l b o r n and W a l t e r s 1981) , where the F:M mat ing r a t i o i s d e l i b e r a t e l y a l t e r e d by v a r y i n g the minimum l e g a l s i z e l i m i t for ma le s , and p r o h i b i t i n g , the l a n d i n g of females , would a l s o h e l p improve our u n d e r s t a n d i n g of C . magi s t e r r e p r o d u c t i o n dynamics . Some q u e s t i o n s r e g a r d i n g r e p r o d u c t i v e behav ior can be a d d r e s s e d S e c t i o n 6.4 Page 144 o n l y by e x p e r i m e n t a t i o n at t h i s s c a l e (Wal ters 1986) . For example, exper iments to t e s t f o r p o s s i b l e changes i n female p o p u l a t i o n s t r u c t u r e r e s u l t i n g from h a r v e s t i n g males above a r e l a t i v e l y low minimum l e g a l s i z e l i m i t , t h e r e b y e l i m i n a t i n g mat ing o p p o r t u n i t i e s , cannot be performed i n a l a b o r a t o r y . Without l arge s c a l e e x p e r i m e n t a t i o n one cannot be c e r t a i n that the r e l a t i o n s h i p observed between the degree of e x p l o i t a t i o n of males and the absence of l a r g e r females ( S e c t i o n 4 .14) i s 'cause and e f f e c t . An i d e a l l o c a t i o n would be a s m a l l , i n t e n s e l y e x p l o i t e d f i s h e r y w i t h an exogenous l a r v a l s u p p l y . Such a l o c a t i o n would ensure that l a r v a l r e c r u i t m e n t to the p o p u l a t i o n would not be a f f e c t e d by e x p e r i m e n t a l t r e a t m e n t s . The s i t e of the p r e s e n t s tudy near T o f i n o (SA 24) a p p a r e n t l y meets these c r i t e r i a s i n c e Jamieson and P h i l l i p s ( i n p r e s s ) suggest that l a r v a e s e t t l i n g near T o f i n o are u n l i k e l y to have h a t c h e d from l o c a l f emales . They are more l i k e l y to have been h a t c h e d from females from a l o n g the coast of Washington , Oregon, C a l i f o r n i a or n o r t h e r n B r i t i s h Columbi a . The b a s i s of such an experiment would i n v o l v e removing males above a minimum l e g a l s i z e l i m i t c o n s i d e r a b l y lower than the c u r r e n t minimum l e g a l s i z e l i m i t of 165 mm CW ( s p i n e - t o - sp ine ) from a C . magi s t e r p o p u l a t i o n . F i g u r e 5 .2 .3 (page 122) suggests a minimum l e g a l s i z e l i m i t of 140 mm CW ( s p i n e - t o - s p i n e ) might i n c r e a s e y i e l d - p e r - r e c r u i t by a f a c t o r of three (at M=4.0) . I f such an experiment were implemented i n SA 24, i n c r e a s e d S e c t i o n 6.4 Page 145 y i e I d - p e r - r e c r u i t might be ev ident i n f u t u r e l a n d i n g s t a t i s t i c s . The h i g h annual e x p l o i t a t i o n r a t e near T o f i n o , of e s s e n t i a l l y a s i n g l e y e a r - c l a s s , suggests l a n d i n g s t a t i s t i c s may r e f l e c t p o p u l a t i o n abundance . I f e x p l o i t i n g males above a minimum l e g a l s i z e l i m i t of 140 mm CW ( s p i n e - t o - s p i n e ) den ies females an o p p o r t u n i t y to mate and m o u l t , then w i t h a h i g h e x p l o i t a t i o n r a t e t h i s s h o u l d a l s o r e s u l t i n v e r y few females >120 mm CW b e i n g mated (See F i g . 4 . 4 . 1 , page 3 1 ) . C o n s e q u e n t l y , a s h i f t i n female s i z e frequency d i s t r i b u t i o n s to s m a l l e r s i z e s s h o u l d occur w i t h few females a t t a i n i n g s i z e s much l a r g e r than one moult increment g r e a t e r than =120 mm CW. There i s a h i g h q u a l i t y data base for a s s e s s i n g t r e n d s i n female s i z e f requency d i s t r i b u t i o n s over t i m e , s ince the Dungeness c r a b f i s h e r y near T o f i n o has been sampled e x t e n s i v e l y s i n c e 1985. An i n c r e a s e i n y i e l d r e s u l t i n g from l o w e r i n g the minimum l e g a l s i z e l i m i t to 140 mm CW near T o f i n o might be d e t e c t e d u s i n g a t ime s e r i e s s tep i n t e r v e n t i o n a n a l y s i s (Noakes 1986) on the l a n d i n g s t a t i s t i c s from SA 24. For example, a t h r e e f o l d i n c r e a s e i n SA 24 l a n d i n g s t a t i s t i c s post -1986 over the mean tonnes landed from 1954-1986, w h i l e m a i n t a i n i n g the v a r i a n c e p r o p o r t i o n a l to the p r e - and post - i n t e r v e n t i o n means, sh ou ld be s t a t i s t i c a l l y d e t e c t e d i n o n l y a few y e a r s . I n t e r v e n t i o n a n a l y s i s on 50 se t s of s i m u l a t e d da ta for y e a r s post -1986 r e c o g n i z e d a s i g n i f i c a n t (oc=.05) i n c r e a s e i n tonnes landed a f t e r one year i n 39 c a s e s . For the r e m a i n i n g 11 cases a s i g n i f i c a n t S e c t i o n 6.4 Page 146 i n c r e a s e was d e t e c t e d i n f i v e years or l e s s . O b v i o u s l y , l e s s d r a m a t i c i n c r e a s e s would take longer to d e t e c t . Land ings would have had to exceeded 433 t i n 1987 for a s i g n i f i c a n t i n c r e a s e over l a n d i n g s p r i o r to 1987 to be d e t e c t e d in 1987. The reader i s r e f e r r e d to Le t t enmaier et a l . (1978) who t e s t e d the power of t ime s e r i e s i n t e r v e n t i o n a n a l y s e s for d e t e c t i n g p e r t u r b a t i o n s to sys tems , and who p r o v i d e g u i d e l i n e s r e g a r d i n g d a t a r e q u i r e m e n t s . There are obvious m a n a g e r i a l and p o l i t i c a l d i f f i c u l t i e s i n implement ing an experiment where the minimum l e g a l s i z e l i m i t i s l o w e r e d . Wi th a l l r e g i o n a l f i s h e r i e s i n B r i t i s h Co lumbia be ing open year round ( w i t h e x c e p t i o n a l c l o s u r e s to p r o t e c t s o f t - s h e l l e d m a l e s ) , enforcement of l a r g e r s i z e l i m i t s i n contemporaneous f i s h e r i e s i n r e g i o n s other than SA 24 c o u l d be d i f f i c u l t . I n i t i a l l y i t would be very d i f f i c u l t t o conv ince f i shermen tha t the T o f i n o a r e a i s perhaps the o n l y r e g i o n b i o l o g i c a l l y s u i t e d to t h i s type of management e x p e r i m e n t . Then l a t e r , i f the experiment i s s u c c e s s f u l , i t w i l l be perhaps more d i f f i c u l t t o t e l l them t h a t they cannot b e n e f i t from t h i s new knowledge because of concerns about the r e l a t i o n s h i p between s tock and r e c r u i t m e n t . M a r k e t i n g s m a l l e r crabs i s not a n t i c i p a t e d to be a problem s i n c e buyers seem to be more i n t e r e s t e d i n l a n d e d volume than c r a b s i z e . T h i s i s p a r t i c u l a r l y t r u e for buyers of crabs to be shucked for t h e i r meat. However, a l l o w i n g males as smal l as 140 mm CW ( s p i n e - t o - s p i n e ) to be landed cou ld r e s u l t i n f i shermen r e q u e s t i n g changes i n r e g u l a t i o n s g o v e r n i n g the s i z e of escape S e c t i o n 6.4 Page 147 por t s . Current ly each trap must have at least one c i r c u l a r escape port with an inside diameter of not less than 100 mm. From Table 4.7.2.2 (page 47) i t can be seen that Traps B and D, which are f ished commercially near Tof ino , have poor retent ion c a p a b i l i t i e s for crabs <145 mm CW. Issues such as th i s which require interventions by f i shery managers tend to lessen the l i k e l i h o o d of experiments of t h i s scale being implemented. 6.5 SUMMARY In conclus ion, the main findings of th i s study of C. magi ster populat ion dynamics near Tof ino, B . C . are: 1 . Males in the 102.9+9.8 mm i n s t a r , which dominated in the summer two years after settlement, moulted twice during the following 1.5 years to a t t a i n the 155.0+11.2 mm i n s t a r , the f i r s t instar with l e g a l - s i z e d males. A mark-recovery program, and size frequency analys i s on commercial trap samples standardized to correct for di f ferences in soak time, showed that the 155.0 mm instar began to form during the spring, three years after settlement, and continued to form throughout the remainder of the year. The size frequency d i s t r i b u t i o n of males with mating marks (Butler 1960) suggested that most males are not sexual ly act ive before a t t a i n i n g the 155.0 mm i n s t a r . 2. Females reach sexual maturity in the 100.7+12.8 mm instar during the summer two years af ter settlement. They f i r s t mate near this size and produce eggs the following winter while in the Section 6.4 Page 148 119.4+11.0 mm i n s t a r . They appear t o moult a n n u a l l y a f t e r t h i s i n s t a r , the b u l k of the m o u l t i n g o c c u r r i n g d u r i n g the summer months when mating a c t i v i t y i s h i g h . 3. There appear t o be o n l y s m a l l d i f f e r e n c e s i n the moult i n c r e m e n t s - a t - s i z e f o r male and female C. magi s t e r from C a l i f o r n i a t o the Queen C h a r l o t t e I s l a n d s . I t c o u l d not be a s c e r t a i n e d i f these d i f f e r e n c e s are b i o l o g i c a l or due t o d i f f e r e n c e s i n measurement. 4. N a t u r a l m o r t a l i t y of males was e s t i m a t e d t o be h i g h . (Female n a t u r a l m o r t a l i t y was not e s t i m a t e d ) . The annual i n s t a n t a n e o u s r a t e of n a t u r a l m o r t a l i t y (M) was e s t i m a t e d at 2.87-4.48 f o r males m a i n l y i n the 155.0 mm i n s t a r . The d a t a suggest t h a t the m o r t a l i t y r a t e may i n c r e a s e as the time a male spends w i t h i n an i n s t a r i n c r e a s e s , and t h a t the m o r t a l i t y r a t e d u r i n g or s h o r t l y a f t e r a moult i s h i g h e r than the i n t e r m o u l t m o r t a l i t y . 5. Movement, as d e t e r m i n e d by mark - r e c o v e r y methodology, was judged not t o be e x t e n s i v e . Most males and females moved, on average, <30 m per day. There was e v i d e n c e t h a t males r e t r e a t t o deeper water d u r i n g the w i n t e r , perhaps t o a v o i d rough w a t e r , and then r e t u r n t o s h a l l o w e r water the f o l l o w i n g s p r i n g . M a t u r i n g females were observed t o move from the c o a s t a l i n l e t s t o the more exposed c o a s t , perhaps t o i n c u b a t e and r e l e a s e t h e i r eggs i n a p r e f e r r e d environment. Sect i on 6.5 Page 149 6. The f i s h e r y near T o f i n o i s composed m a i n l y of males g r e a t e r than the minimum l e g a l s i z e l i m i t of 154 mm CW i n the 155.0+11.2 ram i n s t a r . About 50% of the males i n t h i s i n s t a r enter the f i s h e r y d u r i n g t h e i r f o u r t h year a f t e r s e t t l e m e n t . There remains some u n c e r t a i n t y about the p r o p o r t i o n of t h i s a g e - c l a s s which r e c r u i t s d u r i n g i t s f o u r t h y e a r . Due to h i g h n a t u r a l m o r t a l i t y , t h i s s tudy de termined that l e s s than 10% of s u b l e g a l - s i z e d males tha t a t t a i n e d the 155.0 mm i n s t a r d u r i n g 1985 s u r v i v e d to enter the f i s h e r y the f o l l o w i n g y e a r . However, a s tudy i n C a l i f o r n i a (Warner 1985, 1987) suggests a g r e a t e r percentage of l e g a l - s i z e d males may be caught when o l d e r than four years . 7. The annual i n s t a n t a n e o u s r a t e of f i s h i n g m o r t a l i t y ( F ) of l e g a l - s i z e d males , as de termined from a m a r k - r e c o v e r y program, was e s t i m a t e d at 5 . 1 1 - 6 . 9 0 . T h i s i n d i c a t e s an annua l s u r v i v a l from f i s h i n g of <1%. S i z e f requency a n a l y s i s on commercia l t r a p samples s t a n d a r d i z e d to c o r r e c t for d i f f e r e n c e s i n soak t imes c o n f i r m e d a v e r y h i g h degree of e x p l o i t a t i o n (=60-100%) of l e g a l - s i z e d males . In c o n s i d e r a t i o n of the h i g h n a t u r a l m o r t a l i t y of s u b l e g a l - s i z e d males i n the 155.0 mm i n s t a r , l a n d i n g s t a t i s t i c s from SA 24 may r e f l e c t p o p u l a t i o n abundance and y e a r - c l a s s s t r e n g t h . 8. S i z e f requency and abundance i n f o r m a t i o n from commercial t r a p samples changes w i t h i n c r e a s i n g soak t i m e . D i f f e r e n c e s i n soak t imes for o therwise r e p l i c a t e t r a p samples produce b i a s e s caused by (1) the dynamics of e n t r y and e x i t over t i m e , (2) S e c t i o n 6.5 Page 150 changes i n b a i t e f f e c t i v e n e s s over t i m e , and (3) a g o n i s t i c i n t e r a c t i o n s between crabs w i t h i n a t r a p and crabs a t t e m p t i n g t o en t e r t h a t t r a p . S e v e r a l e x p e r i m e n t s were performed which measured these p r o c e s s e s . The r e s u l t s of these e x p e r i m e n t s were used t o improve the t r a p s a m p l i n g d a t a by c o r r e c t i n g f o r the e f f e c t s of d i f f e r e n t soak t i m e s . 9. Y i e l d - p e r - r e c r u i t a n a l y s i s i n d i c a t e d t h a t the c u r r e n t minimum l e g a l s i z e l i m i t of 165 mm CW ( s p i n e - t o - s p i n e ) i s w e l l above the s i z e l i m i t o p t i m i z i n g y i e l d . For example, l o w e r i n g the minimum l e g a l s i z e l i m i t t o 140 mm CW ( s p i n e - t o - s p i n e ) may r e s u l t i n about a t h r e e f o l d i n c r e a s e i n y i e l d - p e r - r e c r u i t . I f t h i s lower s i z e l i m i t i s t e s t e d e x p e r i m e n t a l l y i n the r e g i o n a l f i s h e r y near T o f i n o , the h y p o t h e s i z e d improvement i s l a r g e enough t h a t i n c r e a s e d l a n d i n g s may be s t a t i s t i c a l l y d e t e c t e d by time s e r i e s a n a l y s i s of annual l a n d i n g s i n l e s s t h a n f i v e y e a r s . The f i s h e r y near T o f i n o i s argues t o be an e x c e l l e n t l o c a t i o n t o p e r f o r m such an e x p e r i m e n t . 10. Data on the carapace w i d t h s of males and females f o r m i n g mating p a i r s p e r m i t t e d a q u a n t i t a t i v e e s t i m a t e of the s i z e of male r e q u i r e d by a female i n a m a t i n g embrace. The r e s u l t s s u g g e s ted females l a r g e r than =140 CW would have d i f f i c u l t y f i n d i n g a male p a r t n e r i n h e a v i l y e x p l o i t e d f i s h e r i e s s i n c e males g r e a t e r than the minimum l e g a l s i z e l i m i t of 154 mm CW would be r a r e . S i n c e females moult when m a t i n g , t h i s might r e s u l t i n growth s t a g n a t i o n at i n s t a r s s m a l l e r than would o t h e r w i s e be a t t a i ned. S e c t i o n 6.5 Page 151 11. A l l f e m a l e s g r e a t e r t h a n =115 mm CW t h a t w e r e d i s s e c t e d i n t h i s s t u d y c o n t a i n e d a p a i r o f s p e r m p a c k s p l a c e d i n t h e i r s p e r m a t h e c a e b y a m a l e d u r i n g m a t i n g . I n c o n s i d e r a t i o n o f t h e r e l a t i v e s i z e s o f m a t i n g p a i r s , s u c h r e s u l t s s t r o n g l y s u g g e s t t h a t no f e m a l e s a t t a i n l a r g e r i n s t a r s w i t h o u t h a v i n g m a t e d w i t h a l a r g e r m a l e . L a r g e m a l e s may n o t be a v a i l a b l e i n a n i n t e n s e l y f i s h e d p o p u l a t i o n . C o m m e r c i a l t r a p s a m p l e s f r o m f o u r r e g i o n a l f i s h e r i e s w h i c h e x p e r i e n c e d l i g h t t o h e a v y f i s h i n g s u p p o r t e d t h i s i n t e r p r e t a t i o n . L a r g e f e m a l e s w e r e most a b u n d a n t i n t h e l i g h t l y f i s h e d r e g i o n a n d l e a s t a b u n d a n t i n t h e mos t h e a v i l y f i s h e d r e g i o n . 12. E g g s - p e r - r e c r u i t a n a l y s i s i n d i c a t e d t h a t i n a n i n t e n s e f i s h e r y p o p u l a t i o n e g g p r o d u c t i o n may be r e d u c e d b y up t o 50% r e l a t i v e t o a n u n f i s h e d p o p u l a t i o n . T h i s r e s u l t s f r o m ( 1 ) a s h i f t i n f e m a l e s i z e f r e q u e n c y d i s t r i b u t i o n s t o s m a l l e r s i z e s due t o g r o w t h s t a g n a t i o n f r o m a l a c k o f m a l e s o f a s i z e s u i t a b l e f o r m a t i n g , ( 2 ) s m a l l e r f e m a l e s p r o d u c i n g f e w e r e g g s , a n d ( 3 ) r e d u c e d f e c u n d i t y e a c h y e a r a f e m a l e f a i l s t o ma te a n d m o u l t . 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