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Growth and survival responses to experimental fishing : models, experiments and lessons from the Northern.. 2006

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Growth and Survival Responses to Experimental Fishing: models, experiments and lessons from the Northern pikeminnow of South Central British Columbia by N a t h a n G a b r i e l T a y l o r B . S c . ( H o n s . ) , T h e 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 , 2001 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y T h e F a c u l t y of G r a d u a t e S t u d i e s ( Z o o l o g y ) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A A u g u s t 2006 © N a t h a n G a b r i e l T a y l o r , 2006 Abstract n Abstract T h e o b j e c t i v e of th i s was s t u d y was to de t e rmine i f species speci f ic f i sh ing c o u l d p r o d u c e " c u l t i v a t i o n - d e p e n s a t i o n effects" i n an a q u a t i c e c o s y s t e m w i t h two p reda to ry , c o m p e t i n g f ish species . I i den t i f i ed a u n i q u e s t o c k of n o r t h e r n p i k e m i n n o w l i v i n g i n series of c o n n e c t e d lakes t ha t has o b l i g a t o r y r e a r i n g i n speci f ic nu r se ry lakes; d e v e l o p e d two nove l l i k e l i h o o d s to measu re the g r o w t h , m o v e m e n t a n d m o r t a l i t y responses; d e v e l o p e d a n e c o s y s t e m m o d e l to p r e d i c t h o w the s y s t e m w o u l d r e s p o n d to fishing, a n d finally, c o m p a r e d the ecosys t em m o d e l i n g p r e d i c t i o n s t o obse rved responses. M y research showed n o r t h e r n p i k e m i n n o w i n S o u t h C e n t r a l B . C . have o b l i g a t o r y r e a r i n g i n specif ic nu r se ry lakes t hen d isperse to o the r lakes as a d u l t s . I a rgue t h a t th i s la rge scale s p a t i a l on togeny c a n be so le ly e x p l a i n e d b y t e m p e r a t u r e cues to s p a w n a n d t h a t the d i s t r i b u t i o n of a d u l t s is deter- m i n e d by dens i t y -dependen t d i s p e r s a l t h a t equa l ize v e r y la rge p r o d u c t i v i t y a n d effective dens i t y differences be tween lakes. I showed tha t i n sp i t e o f b e i n g i n c l u d e d i n m a n y s tock assessments , a n d b e i n g used as p rox ies for n a t u r a l m o r t a l i t y es t imates a n d for e x p l o i t a t i o n ra te ta rgets , v o n B e r t a l a n f f y g r o w t h pa rame te r s are no t gene ra l l y e s t i m a t e d co r rec t ly . T h e d a t a used to d o so are v i r t u a l l y a lways b i a s e d due to : s ize- se lec t ive gears, p o p u l a t i o n s s u b j e c t e d t o f i sh ing a n d n a t u r a l m o r t a l i t y a n d i n some cases, s ize -dependent m o v e m e n t . I deve loped t w o new l i k e l i h o o d s t o s i - m u l t a n e o u s l y e s t ima te g r o w t h a n d m o r t a l i t y pa ramete r s : one for l eng th-age d a t a , a n d ano the r for m a r k - r e c a p t u r e d a t a . T h e first p e r f o r m s w e l l across a range of r e c r u i t m e n t a n o m a l i e s a n d s t eady s ta te fishing m o r t a l i t i e s b u t fai ls w h e n fishing rates have been v a r i a b l e (espec ia l ly inc reas ing) a n d w h e n gear s e l e c t i v i t y is d o m e - s h a p e d . T h e second l i k e l i h o o d w o r k s w e l l w i t h s i m u l a t e d d a t a b u t is no t r obus t t o a s s u m p t i o n s of cons tan t r e c r u i t m e n t a n d measure - m e n t er ror b e i n g v i o l a t e d . I c o m b i n e d length-age a n d m a r k - r e c a p t u r e d a t a to s h o w u s i n g s i m u l a t e d s a m p l i n g t h a t i t is poss ib le to s i m u l t a n e o u s l y es t i - m a t e g r o w t h , m o r t a l i t y , a n d m o v e m e n t pa rame te r s where suff icient n u m b e r s of fish are obse rved m o v i n g . T h e a s s u m p t i o n s r e q u i r e d for these m o d e l s t o Abstract 111 p e r f o r m w e l l are v e r y r e s t r i c t i ve . I used a s i m p l e ecosys t em m o d e l a n d c o m p a r e d the p r e d i c t i o n s to ob- served responses f o l l o w i n g d e p l e t i o n f i sh ing i n two- f i sh lake sys tems w i t h r a i n b o w t r o u t a n d n o r t h e r n p i k e m i n n o w . C o n s i s t e n t w i t h m o d e l p r e d i c t i o n s , g r o w t h was s lower a n d m o r t a l i t y of j u v e n i l e r a i n b o w t r o u t h ighe r r e l a t i ve to the c o n t r o l i n lakes where n o r t h e r n p i k e m i n n o w were r e m o v e d , w h i l e a d u l t r a i n b o w t rou t s u r v i v a l r e m a i n e d u n c h a n g e d . V i s u a l s u r v e y ind ices of n o r t h - e rn p i k e m i n n o w fry i n d i c a t e d s u r v i v a l of 1 + fish w o r s e n e d a n d 2 + i m p r o v e d f o l l o w i n g fishing. C o n s i s t e n t w i t h m o d e l p r e d i c t i o n s , no o b v i o u s m o r t a l - i t y or g r o w t h responses were obse rved i n a d u l t fish i n e i the r r a i n b o w t r o u t or n o r t h e r n p i k e m i n n o w remova l s . W h i l e the agreement be tween the m o d e l a n d obse rva t ions was e n c o u r a g i n g , field t e s t i ng such c o m p l e x p r e d i c t i o n s was f raught w i t h d i f f icu l ty . T h e p r o b a b i l i t y d i s t r i b u t i o n s of the p a r a m e t e r s of i n - terest were v e r y b r o a d . A l s o , the m o d e l p r ed i c t s t h a t s u r v i v a l a n d b e h a v i o r a l d y n a m i c s p r o d u c i n g the greatest differences i n d i r e c t i o n a n d m a g n i t u d e of ecosys t em response o c c u r i n s ize classes of fish a n d g r o u p s of z o o p l a n k t o n tha t are d i f f icu l t to observe . It was no t poss ib le to c o n c l u d e w h e t h e r an a l t e rna te s ta te was p r o d u c e d t h r o u g h c u l t i v a t i o n - d e p e n s a t i o n effects. T o d o so w o u l d requ i re longer t e r m d a t a o n r e c r u i t m e n t responses , v u l n e r a b i l i t y exchange processes a n d s u r v i v a l d a t a of y o u n g age classes of fish. T h i s s t u d y ident i f ies severa l s h o r t c o m i n g s i n ou r a b i l i t y to p r e d i c t a n d detect h o w ecosys tems w i l l r e s p o n d to fishing. F i r s t , ou r a b i l i t y to measure even s i m p l e response va r i ab l e s s u c h as g r o w t h a n d m o r t a l i t y is no t g o o d . Sec- ond ly , even i f we c o u l d , the d i r e c t i o n a n d m a g n i t u d e of these responses c a n be h i g h l y c o u n t e r - i n t u i t i v e . F i n a l l y , those processes w i t h the m o s t v i o l e n t effects o n our p r e d i c t i o n s are those for w h i c h we have v e r y l i t t l e i n f o r m a - t i o n , n a m e l y d y n a m i c s d e t e r m i n i n g the s p a t i a l d i s t r i b u t i o n of the s tock , the d y n a m i c s of y o u n g fish a n d b e h a v i o r a l l y m e d i a t e d p r e d a t i o n rates. Contents iv Contents Abstract i i Contents i v List of Tables v i i List of Figures i x Acknowledgements x v i 1 Introduction 1 1.1 R e v i e w 2 1.1.1 C o m p e n s a t i o n i n fish s tocks 2 1.1.2 S t o c k - R e c r u i t C u r v e A n a l y s i s : C o m p e n s a t i o n Ver sus D e p e n s a t i o n 4 1.2 R e s e a r c h H y p o t h e s i s a n d E x p e r i m e n t 5 1.2.1 T h e C u l t i v a t i o n D e p e n s a t i o n H y p o t h e s i s 5 1.2.2 E x p e r i m e n t a l dep le t ions 8 2 Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 12 2.1 I n t r o d u c t i o n 13 2.2 M e t h o d s 15 2.2.1 S t u d y si te 15 2.2:2 S p a w n i n g a n d V i s u a l S u r v e y s ' • • • 16 2.2.3 A p p a r e n t m o r t a l i t y 18 2.2.4 H y d r o g r a p h y a n d P r o d u c t i v i t y 20 2.2.5 B i o e n e r g e t i c s m o d e l i n g . 20 2.2.6 L a k e feeding l o a d 25 2.3 R e s u l t s 26 2.3.1 S p a w n i n g a n d V i s u a l S u r v e y s 26 Contents v 2.3.2 A p p a r e n t m o r t a l i t y 27 2.3.3 H y d r o g r a p h y a n d P r o d u c t i v i t y 27 2.3.4 B i o e n e r g e t i c s p r e d i c t i o n s 30 2.4 D i s c u s s i o n 36 2.5 A p p e n d i x 41 3 Estimating Growth from Length At Age Data 50 3.1 I n t r o d u c t i o n 51 3.2 M e t h o d s 54 3.2.1 L i k e l i h o o d d e r i v a t i o n 54 3.2.2 M o d e l 1 g r o w t h w i t h no h i s t o r y of f i sh ing 54 3.2.3 M o d e l 2 r e d u c e d l i k e l i h o o d 57 3.2.4 M o d e l 3 g r o w t h u n d e r h a r v e s t i n g 59 3.2.5 M o d e l 4 R e d u c e d l i k e l i h o o d w i t h f i sh ing 62 3.2.6 S i m u l a t i o n s 62 3.2.7 G r o w t h pa r ame te r e s t i m a t i o n for n o r t h e r n p i k e m i n n o w 64 3.3 R e s u l t s 65 3.3.1 N o r t h e r n p i k e m i n n o w g r o w t h p a r a m e t e r e s t ima tes . . . 73 3.4 D i s c u s s i o n 75 3.5 A c k n o w l e d g e m e n t s 79 4 Estimating movement and growth parameters given size-dependent spatial ontogeny 81 4.1 I n t r o d u c t i o n 81 4.2 M e t h o d s 84 4.2.1 L e n g t h - a g e l i k e l i h o o d 84 4.2.2 M a r k - R e c a p t u r e D a t a 87 4.2.3 M a r k - R e c a p t u r e L i k e l i h o o d for G r o w t h 89 4.2.4 M a r k - R e c a p t u r e L i k e l i h o o d for S u r v i v a l w i t h no M o v e - m e n t 91 4.2.5 M a r k - R e c a p t u r e L i k e l i h o o d for e s t i m a t i n g s u r v i v a l p a - r amete r s a n d m o v e m e n t 94 4.2.6 M o v e m e n t M o d e l 97 4.2.7 C o m b i n e d L i k e l i h o o d s 100 4.2.8 S i m u l a t i o n S t o c k - A s s e s s m e n t U s i n g C o m b i n e d L i k e l i - h o o d s w i t h N o M o v e m e n t 101 4.2.9 S i m u l a t i o n of g r o w t h p a r a m e t e r e s t ima tes w i t h l e n g t h - dependen t m o v e m e n t 105 Contents vi 4.2.10 Effects of G e a r S e l e c t i v i t y a n d C a p t u r e P r o b a b i l i t y o n M o r t a l i t y a n d M o v e m e n t P a r a m e t e r s 106 4.3 R e s u l t s 107 4.3.1 E s t i m a t i o n T r i a l s w i t h N o M o v e m e n t 107 4.3.2 S i m u l a t i o n of g r o w t h p a r a m e t e r e s t i m a t i o n w i t h l e n g t h - dependen t m o v e m e n t 112 4.3.3 Effects of G e a r S e l e c t i v i t y a n d C a p t u r e P r o b a b i l i t y o n M o r t a l i t y a n d M o v e m e n t P a r a m e t e r s 114 4.4 D i s c u s s i o n 118 5 Predicted and Observed Ecosystem Responses to Fishing . 124 5.1 I n t r o d u c t i o n 125 5.2 M e t h o d s 128 5.2.1 E c o s i m M o d e l of P r e d i c t e d O b s e r v a t i o n s 128 5.2.2 E x p e r i m e n t a l f i sh ing 135 5.2.3 F i s h age ing 138 5.2.4 D e p l e t i o n E x p e r i m e n t s 140 5.2.5 V i s u a l S u r v e y s 141 5.2.6 E s t i m a t i o n of S u r v i v a l a n d G r o w t h P a r a m e t e r s . . . . 142 5.2.7 P r i o r D i s t r i b u t i o n s 146 5.2.8 M a r k o v C h a i n M o n t e C a r l o S a m p l i n g for p a r a m e t e r u n c e r t a i n t y 147 5.3 R e s u l t s 148 5.3.1 P r e d i c t e d responses to e x p e r i m e n t a l f i sh ing of u s i n g E c o s i m 148 5.3.2 E s t i m a t e d D e p l e t i o n 150 5.3.3 V i s u a l S u r v e y s 163 5.3.4 N o r t h e r n p i k e m i n n o w g r o w t h , m o r t a l i t y a n d m o v e m e n t pa r ame te r es t imates '. 163 5.3.5 R a i n b o w t r o u t g r o w t h a n d m o r t a l i t y es t imates 166 5.4 D i s c u s s i o n 173 6 General Conclusions 181 6.1 T h e d i f f i cu l ty of p r o p e r l y e s t i m a t i n g g r o w t h a n d m o r t a l i t y p a - r ame te r s 181 6.2 E v a l u a t i n g E c o s y s t e m I m p a c t s of F i s h i n g 183 Bibliography 186 List of Tables v i i List of Tables 2.1 Table of lake areas, maximum depths and perimeters 16 2.2 Parameter values used in northern pikeminnow bioenergetics model from Petersen and Ward (1999) 22 2.3 Table of fish marked, marked fish killed during handling, re- captured, and unmarked by date and length-converted age in Dad's lake 42 2.4 Table of fish marked, marked fish killed during handling, re- captured, and unmarked by date and length-converted age for July, August and September 2002 in Mom's lake 43 2.5 Table of fish marked, marked fish killed during handling, re- captured, and unmarked from June to August 2002 by length- converted age in Nestor lake 44 2.6 Table of fish marked, marked fish killed during handling, re- captured, and unmarked from August to September 2002 by length-converted age in Nestor lake 45 2.7 Table of fish marked, marked fish killed during handling, re- captured, and unmarked by length converted age from June to August 22 2002 in Moose Pasture Lake 46 2.8 Table of fish marked, marked fish killed or removed during handling, recaptured, and unmarked by length converted age for August 23 to September 2002 in Moose Pasture Lake. ... 47 2.9 Table of fish marked, marked fish killed or removed during handling, recaptured, and unmarked by length converted age from June to September in Cheryl Lake 48 2.10 Table of fish marked, marked fish killed or removed during handling, recaptured, and unmarked by length converted age from June to September in Wilderness Lake 49 3.1 Parameters used to generate fake data 64 3.2 Estimated parameter values for each model 75 List of Tables v i i i 4.1 F o r m a t of m a r k - r e c a p t u r e d a t a by cohor t R re leased a n d re- c a p t u r e d at t imes t a n d e s t i m a t e d p a r a m e t e r s for s u r v i v a l <j)t a n d c a p t u r e p r o b a b i l i t y pt ' 88 4.2 P a r a m e t e r s u sed to genera te fake d a t a for c o m b i n e d l i k e l i h o o d s 102 5.1 P a r a m e t e r s for m u l t i - s t a n z a r ep resen ta t ion of n o r t h e r n p i k e m i n n o w a n d r a i n b o w t r o u t p o p u l a t i o n s 132 5.2 D i e t c o m p o s i t i o n m a t r i x for E c o p a t h m o d e l . E a c h c o l u m n is the d ie t c o m p o s i t i o n o f a p a r t i c u l a r p r eda to r , as a p r o p o r t i o n of t o t a l a n n u a l b i o m a s s f o o d in t ake 133 5.3 B a s i c p a r a m e t e r i n p u t s for E c o p a t h M o d e l 134 5.4 T o t a l l e n g t h a n d p r o p o r t i o n s by bar l e n g t h (cm) C h e r y l L a k e 136 5.5 T o t a l l e n g t h a n d p r o p o r t i o n s by bar l e n g t h ( cm) M o m ' s L a k e . 136 5.6 T o t a l n u m b e r of m a r k e d a n d r e c a p t u r e d n o r t h e r n p i k e m i n n o w b y d ra inage , l ake a n d t r ea tmen t . N P M = n o r t h e r n p i k e m i n n o w , R B T = r a i n b o w t r o u t a n d d e p = d e p l e t i o n 143 5.7 T o t a l n u m b e r o f m a r k e d a n d r e c a p t u r e d r a i n b o w t r o u t b y size g r o u p a n d lake 144 List of Figures i x List of Figures 1.1 T r o p h i c t r i a n g l e d e s c r i b i n g where the s u r v i v a l o f the j u v e n i l e of the d o m i n a n t is n e g a t i v e l y affected b y the p r e y of the d o m - i n a n t species . 9 2.1 M a p of s t u d y lakes . A r r o w s i n d i c a t e the d i r e c t i o n o f s t r e a m flow a n d l i g h t g rey c o l o r e d lakes represent nu r se ry lakes. . . . 17 2.2 M e a n t e m p e r a t u r e i n t e g r a t e d f rom lake surface to 1 m i n d e p t h for D a d ' s L a k e (squares) a n d M o m ' s L a k e ( d i a m o n d s ) . L i n e s represent l i nea r i n t e r p o l a t i o n s be tween obse rved t e m p e r a t u r e s 24 2.3 M a x i m u m l i k e l i h o o d es t ima tes of n u m b e r s at each l e n g t h con - ve r t ed age. T h e p a s t e d t ex t is the s lope o f the fit l i ne t h r o u g h the l o g n u m b e r s at a,ge ( log N a ) r ep re sen t i ng the appa ren t m o r t a l i t y o f fu l ly r e c r u i t e d ages (5+) 28 2.4 C h l o r o p h y l l A ( / / g C / i M L _ 1 ) m e a s u r e m e n t s over t i m e . T o p p a n e l is W e s t e r n d ra inage : D a d ' s L a k e (squares) , M o m ' s L a k e ( d i a m o n d s ) a n d N e s t o r L a k e ( t r i ang les ) . B o t t o m p a n e l is E a s t e r n d ra inage : M o o s e P a s t u r e (squares) , C h e r y l L a k e ( d i - a m o n d s ) a n d W i l d e r n e s s L a k e ( t r iangles) 29 2.5 Ef fec t ive d e n s i t y per hec ta re as represen ted b y the s u m of s q u a r e d f ish l eng ths l 2ha~ l ( top) Ef fec t ive d e n s i t y pe r hec ta re per figChlAL^ 1 as represen ted b y the s u m of s q u a r e d fish l engths pe r hec ta re l 2ha~ x d i v i d e d b y m e a n ChlA (figL -1 for D a d ' s (d) , M o o s e P a s t u r e (p) , M o m ' s ( m ) , C h e r y l (c) , N e s t o r (n) a n d W i l d e r n e s s (w) lakes 31 2.6 P r o p o r t i o n o f the t o t a l lake a rea b y d e p t h c o n t o u r , D a d ' s o p e n c i rc les , M o m ' s o p e n squares, N e s t o r , o p e n d i a m o n d s , M o o s e P a s t u r e c losed c i rc les , C h e r y l c losed squares , W i l d e r - ness c losed d i a m o n d s 32 List of Figures x 2.7 P r e d i c t e d we igh t s ( i n g rams) of fit b ioenerge t i c s m o d e l to ob- served we igh t at age i n the nu r se ry a r ea (open c i rc les , P = 0.14) a n d the p r e d i c t e d we igh t at age of a fish h a t c h e d 15 days la te r i n the head lake ( so l id l ine , P = 0.18) 33 2.8 F i t w e i g h t - l e n g t h r e l a t i o n s h i p of n o r t h e r n p i k e m i n n o w weigh t as a f u n c t i o n of l e n g t h 34 2.9 P r e d i c t e d p r o p o r t i o n of m a x i m u m c o n s u m p t i o n ra te Piiead ( top) r e q u i r e d to r each obse rved s ize at age 1 a n d Phead/Pnursery ( b o t t o m ) vs . de lays i n headwa te r l ake h a t c h da te 35 3.1 P r o p o r t i o n a l e r ror i n p a r a m e t e r e s t ima tes for each l i k e l i h o o d f o r m u l a t i o n w i t h F = 0. (a) Fabens , (b) m o d e l 1, (c) m o d e l 2, (d) m o d e l 3, a n d (e) m o d e l 4, (c i rc les represent ou t l i e r s ) . . . 67 3.2 P r o p o r t i o n a l e r ror i n p a r a m e t e r e s t ima tes for each l i k e l i h o o d f o r m u l a t i o n w i t h F = K. (a) F a b e n s , (b) m o d e l 1, (c) m o d e l 2, (d) m o d e l 3, a n d (e) m o d e l 4, (c i rc les represent ou t l i e r s ) . . . 68 3.3 P r o p o r t i o n a l e r ror i n pa r ame te r e s t ima tes for each l i k e l i h o o d f o r m u l a t i o n w i t h F — 1. (a) F a b e n s , (b) m o d e l 1, (c) m o d e l 2, (d) m o d e l 3, a n d (e) m o d e l 4, (c i rc les represent ou t l i e r s ) . . . 69 3.4 P r o p o r t i o n a l e r ror o f F a b e n s (a ,b) , m o d e l 3 (c ,d) , m o d e l 4 (e,f), whe re F increases i n i n c r e m e n t s o f 0.1 to F = 0.5 (a,c,e) a n d to F = 1.0 (b ,d , f ) . F over t i m e was e s t i m a t e d b u t the p r o p o r t i o n a l b ias is n o t i n c l u d e d here s ince the t rue F used to s i m u l a t e the d a t a c h a n g e d a n n u a l l y 71 3.5 G r o w t h curves fit to n o r t h e r n p i k e m i n n o w d a t a u s i n g a l l 5 m o d e l s : so l i d= fabens , d a s h e d = f u l l l i k e l i h o o d , d o t t e d = r e d u c e d l i k e l i h o o d , d o t d a s h = f u l l l i k e l i h o o d w i t h f i sh ing , l o n g d a s h = r e d u c e d l i k e l i h o o d w i t h f i sh ing 74 3.6 P l o t o f v u l n e r a b i l i t y c u r v e ( so l id l ine) for n o r t h e r n p i k e m i n n o w e s t i m a t e d u s i n g l i k e l i h o o d 3 a n d d i r ec t e s t ima tes of v u l n e r a - b i l i t y u s i n g m a r k - r e c a p t u r e 76 4.1 M o v e m e n t m o d e l used to s i m u l a t e d a t a . F i s h enter the move- m e n t p o o l at the l eng th -dependen t m o v e m e n t ra te a-i f r om the nu r se ry a rea t h e n d i v i d e i n t o areas 2 a n d 3 w i t h the p r o p o r - t i o n /i2 g o i n g to a rea 2, 1 — fi2 g o i n g to a r ea 3, a n d 1 — <L\ s t a y i n g i n the nu r se ry a rea 96 L i s t of Figures x i 4.2 P r o p o r t i o n of the p o p u l a t i o n i n each a r ea as a f u n c t i o n of l e n g t h ipi, i n a rea 2 ( red, ip2) a n d 3 (green ip3). 99 4.3 P l o t o f a used to s i m u l a t e age ing e r ror 104 4.4 B o x p l o t s of p r o p o r t i o n a l b ias ((true — estimate)/true) of 100 g r o w t h a n d m o r t a l i t y p a r a m e t e r e s t ima tes for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss u s i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b) d a t a genera ted w i t h t ag loss a n d fit a s s u m i n g no t ag loss us- i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4.17) , c) d a t a gene ra t ed w i t h t a g loss a n d es- t i m a t i n g th i s t ag loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4 .17) , a n d d) d a t a gener- a t ed w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s i n g length-age (L\), g r o w t h i n c r e m e n t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s ( L 3 ) ( E q s . 4 .8, 4.17 a n d 4.1) w i t h CVR = 0, no measu remen t or age ing er ror 108 4.5 B o x p l o t s of p r o p o r t i o n a l b ias ((true — estimate)/true) of 100 g r o w t h a n d m o r t a l i t y p a r a m e t e r e s t ima tes for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss u s i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b) d a t a genera ted w i t h tag loss a n d fit a s s u m i n g no t a g loss us- i n g the g r o w t h i nc remen t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4.17) , c) d a t a gene ra t ed w i t h t a g loss a n d es- t i m a t i n g th i s t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L3 ( E q s . 4.8 a n d 4 .17) , a n d d) d a t a gener- a t e d w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s i n g length-age (Li), g r o w t h i nc remen t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s ( L 3 ) ( E q s . 4.8, 4.17 a n d 4.1) w i t h CVR = 0.2, no age ing er ror , m e a s u r e m e n t e r r o r = 5 m m 110 List of Figures 4.6 B o x p l o t s of p r o p o r t i o n a l b ias ((true — estimate)/true) o f 100 g r o w t h a n d m o r t a l i t y p a r a m e t e r e s t ima tes for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss us- i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b) d a t a genera ted w i t h t a g loss a n d fit a s s u m i n g no t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4.17) , c) d a t a gene ra t ed w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i ke - l i h o o d s L 3 (Eqs . 4.8 a n d 4 .17) , a n d d) d a t a genera ted w i t h t a g loss a n d e s t i m a t i n g t h i s t a g loss u s i n g length-age (L\), g r o w t h i n c r e m e n t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s (L 3 ) ( E q s . 4.8, 4 .17 a n d 4.1) w i t h CVR = 0.2, age ing error , m e a s u r e m e n t e r ror = 5 m m " I l l 4.7 B o x p l o t s of p r o p o r t i o n a l b ias ((true — estimate)/true) o f 100 g r o w t h a n d m o r t a l i t y p a r a m e t e r es t imates for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss us- i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b) d a t a genera ted w i t h t a g loss a n d fit a s s u m i n g no t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4 .17) , c) d a t a gene ra t ed w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i - h o o d s L 3 ( E q s . 4.8 a n d 4 .17) , a n d d) d a t a genera ted w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s i n g length-age (Li), g r o w t h i n c r e m e n t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s (L 3 ) ( E q s . 4 .8 , 4.17 a n d 4.1) w i t h va r i ance i n l e n g t h at age p a r a m e t e r s (A] a n d A2 f ixed at the i r t rue values) 113 4.8 B o x p l o t s of p r o p o r t i o n a l b ias ((true — estimate)/true) o f 100 g r o w t h (Loo, K, A i , A 2 ) , m o r t a l i t y (M), l e n g t h at h a l f g e a r s e l e c t i v i t y (//,), a n d gear s e l e c t i v i t y f u n c t i o n s lope ( 7 ) p a r a m - eters w h e n each a r ea is a s s u m e d to be separa te s tock , w h i l e s i m u l a t e d d a t a come f rom a s tock w i t h on togene t i c m o v e m e n t f r o m a rea 1 to areas 2 a n d 3 115 4.9 B o x p l o t s o f p r o p o r t i o n a l b ias ((true — estimate)/true) i n 100 es t imates of M a n d m o v e m e n t pa rame te r s w i t h c a p t u r e p r o b - a b i l i t y ( rows) set to 0.05, 0.35, 0,55 a n d w i t h r a t i o o f l e n g t h at h a l f gear s e l ec t i v i t y to the m e a n l e n g t h at m o v e m e n t set to 0.16, 1.16 a n d 1.83 117 L i s t of Figures x i i i 5.1 P r o p o r t i o n of g i l l n e t meshes used on a l l dep l e t i ons 137 5.2 M a p of e x p e r i m e n t a l lakes s h o w i n g the l o c a t i o n of r a i n b o w t r o u t dens i t y r e d u c t i o n s ( R B T d e p l e t i o n ) , a n d n o r t h e r n p i k e m i n n o w dens i t y r e d u c t i o n s ( N P M dep le t ion ) 139 5.3 P r e d i c t e d r e l a t i ve b i o m a s s (B) changes after d e p l e t i o n f i sh ing of 4 + n o r t h e r n p i k e m i n n o w . T h e b iomass of 2 + R B T a n d 4 + N P M have been a r b i t a r i l y set to 1 a n d the o the r g roups sca l ed a c c o r d i n g l y 151 5.4 P r e d i c t e d changes i n M after s i m u l a t e d d e p l e t i o n fishing of 4 + n o r t h e r n p i k e m i n n o w 152 5.5 P r e d i c t e d b o d y we igh t changes (kg) after 4 + n o r t h e r n p i k e m i n n o w d e p l e t i o n fishing 153 5.6 P r e d i c t e d changes i n r e l a t i ve feeding t i m e after 4 + n o r t h e r n m i k e m i n n o w d e p l e t i o n fishing • • • • 154 5.7 P r e d i c t e d r e l a t ive changes i n b iomass B f o l l o w i n g 2 + r a i n - b o w t rou t d e p l e t i o n fishing. T h e b iomass of 2 + R B T a n d 4 + N P M have been a r b i t a r i l y set to 1 a n d the o ther g r o u p s sca led a c c o r d i n g l y 155 5.8 P r e d i c t e d changes i n M f o l l o w i n g 2 + r a i n b o w t r o u t d e p l e t i o n fishing 156 5.9 P r e d i c t e d changes i n we igh t ( i n kg) after r a i n b o w t r o u t dep le - t i o n fishing 157 5.10 P r e d i c t e d r e l a t ive changes i n feeding t i m e after r a i n b o w t r o u t d e p l e t i o n fishing.' ' . . . . 158 5.11 D e p l e t i o n ca tches of n o r t h e r n p i k e m i n n o w ( in n u m b e r s ) b y da te for C h e r y l lake i n 2001 ( top) , M o m ' s lake i n 2001 ( m i d d l e ) a n d M o o s e P a s t u r e l ake i n 2002 ( b o t t o m ) . . 159 5.12 E s t i m a t e d n o r t h e r n p i k e m i n n o w v u l n e r a b l e n u m b e r s (N) a n d percen t d e p l e t i o n es t ima tes b y l e n g t h for C h e r y l a n d M o m ' s lake 160 5.13 N o r t h e r n p i k e m i n n o w p o p u l a t i o n a n d percen t d e p l e t i o n es t i - ma te s b y l e n g t h , V represent 95 percent C I 161 5.14 F i t of p r o p o r t i o n n o r t h e r n p i k e m i n n o w l e a v i n g the nu r se ry a rea f u n c t i o n b y l e n g t h for each d ra inage 162 5.15 P e r c e n t change i n v i s u a l su rvey i n d e x i n D a d ' s (b lue) a n d M o o s e P a s t u r e (red) 164 List of Figures x i v 5.16 F i t o f v o n B e r t a l a n f f y g r o w t h cu rve t h r o u g h length-age d a t a i n wes te rn ( top) a n d eas te rn ( b o t t o m ) d a t a . J i t t e r a d d e d to be t t e r see over l ay 165 5.17 P o s t e r i o r s ample s of g r o w t h pa rame te r s ( / o g ( L 0 0 ) , . K), h i s t o r - i c a l n a t u r a l m o t a l i t y M , a n d t a g loss tl for unfishecl wes te rn (left c o l u m n ) a n d f ished eas te rn d ra inage ( r igh t c o l u m n ) . . . . 167 5.18 P o s t e r i o r s ample s o f m o v e m e n t pa r ame te r s ( m a x i m u m pro - p o r t i o n l e a v i n g the nu r se ry a rea fin, p r o p o r t i o n of the m o v i n g p o o l g o i n g to l ake 2 ^2 ( C h e r y l a n d M o m ' s ) , a n d the b e t a d is - t r i b u t i o n p a r a m e t e r (3 for the unf i shed wes t e rn (left c o l u m n ) a n d f ished eas te rn d ra inage 168 5.19 P o s t e r i o r s ample s of n o r t h e r n squawf i sh t agged c o h o r t m o r - t a l i t y Mt b y l ake '. 169 5.20 P o s t e r i o r s ample s of Mt for r a i n b o w t r o u t greater t h a n 200 mm b y l ake 170 5.21 P o s t e r i o r s ample s of the log a s y m p t o t i c l e n g t h log^^ for r a i n - b o w t r o u t s m a l l e r t h a n 200 mm by lake 171 5.22 P o s t e r i o r s ample s of the v o n Be r t a l a n f fy K for r a i n b o w t r o u t sma l l e r t h a n 200 mm b y lake 172 5.23 P o s t e r i o r s a m p l e s of the i n s t an t aneous a n n u a l m o r t a l i t y of t agged f ish b y l ake for r a i n b o w t r o u t s m a l l e r t h a n 200 mm. . . 174 List of Figures x v Prior Publications T a y l o r , N . , W a l t e r s , C , a n d M a r t e l l , S. A new l i k e l i h o o d for s i m u l t a n e - ous ly e s t i m a t i n g the v o n B e r t a l a n f f y g r o w t h pa r ame te r s , v u l n e r a b i l i t y , na t - u r a l m o r t a l i t y a n d f i sh ing m o r t a l i t y . Canadian Journal of Fisheries and Aquatic Sciences. 62:215-223 A ckn owledgem en ts x v i Acknowledgements F i n a n c i a l s u p p o r t for th i s p ro jec t was p r o v i d e d b y N S E R C a n d P e w F e l - l o w s h i p s to m y supe rv i so r , C a r l W a l t e r s a n d b y H a b i t a t C o n s e r v a t i o n T r u s t F u n d G r a n t s to E r i c P a r k i n s o n . I owe a c o n s i d e r a b l e debt to the peop le w o r k i n g i n the M i n i s t r y of W a t e r , L a n d a n d A i r p r o t e c t i o n i n K a m l o o p s w h o p r o v i d e d m u c h i n t e rms of e q u i p m e n t a n d a d v i c e to th i s p ro jec t . In a d d i t i o n to f i n a n c i a l s u p p o r t , the p ro jec t w o u l d n o t have been poss ib le at a l l w i t h o u t the p r a c t i c a l a n d i n t e l l e c t u a l c o n t r i b u t i o n s of E r i c P a r k i n s o n . I a m g ra t e fu l to m y fel low g radua t e s tuden t s d u r i n g the research a n d w r i t i n g of th i s P h D . In p a r t i c u l a r , a l l the f ie ld w o r k for th i s p ro jec t was done w i t h m y fe l low P h D c a n d i d a t e D a v i d O ' B r i e n w h o s e exper ience a n d g o o d h u - m o u r m a d e f ie ld w o r k poss ib le a n d u n d e r m a n y d i f f icu l t c i r cums tances , fun . O u t s t a n d i n g f ie ld he lp was p r o v i d e d b y S h e l d o n R e d d e c o p p , S h a u n M a c - G l o u g h l a n , C l a r k B a r t l e t t , H a n n a h M u r p h y , A n n i e B r o w n , G a r e t t C o o p e r a n d C h r i s t i e S t e w a r t . I owe R o b A h r e n s a n d B o b L e s s a r d a lo t for the i r t i m e a n d tu te lage l e a r n i n g n e w software, a n a l y t i c a l t echn iques , beers to m a k e the w h o l e process to l e rab le . I n a d d i t i o n to his c o n t r i b u t i o n to the l a t t e r , I owe m u c h to S teve M a r t e l l , s ince m y p a r t i c i p a t i o n i n h is mas t e r ' s thes is r e su l t ed i n the cascade of acc iden t s t h a t b r o u g h t m e to s t u d y f ish at U B C i n the first p lace . W h i l e m y s u p e r v i s o r f requent ly i n t r o d u c e s me as a first e x p e r i m e n t at- t e m p t i n g to supe rv i s e a P h D s tuden t w i t h o n l y "don ' t sc rew up" as adv i ce , n o t h i n g c o u l d be fur ther f r o m the t r u t h . M u c h of the i n t e l l e c t u a l con ten t of t h i s thesis s t ems f r o m conversa t ions w i t h C a r l w h i l e c a r r y i n g e q u i p m e n t , s m o k i n g ou t s ide the hu t s a n d s i t t i n g i n o n courses . F i n a l l y none of th i s w o u l d have been poss ib l e w i t h o u t cons ide rab le f i nan - c i a l a n d e m o t i o n a l s u p p o r t of m y pa ren t s a n d l o v e d ones. 1 Chapter 1 Introduction F i s h e r i e s sc ience t y p i c a l l y assumes the r e l a t i o n s h i p be tween the n u m b e r o f new j u v e n i l e f ish p r o d u c e d a n d a d u l t b i o m a s s to be dens i t y -dependen t so t h a t the n u m b e r of juven i l e s p r o d u c e d per a d u l t increases as a d u l t p o p u - l a t i o n s ize decreases (ca l l ed c o m p e n s a t i o n ) . It is a lso ea rnes t ly h o p e d t h a t th i s r e l a t i o n s h i p is s t a t iona ry , m e a n i n g p a r a m e t e r s d e s c r i b i n g i t do n o t v a r y w i t h t i m e . E x p l a i n i n g the fa i lure o f some f ish s tocks to recover f o l l o w i n g s u s t a i n e d f i sh ing , n o t a b l y N e w f o u n d l a n d c o d (Gadus morhua) ( S h e l t o n a n d H a r l e y , 1999; R o s e et a l . , 2001) , has l e d to the d e v e l o p m e n t o f a n e w hy- po thes i s c a l l e d C u l t i v a t i o n - D e p e n s a t i o n ( W a l t e r s a n d K i t c h e l l , 2001) t h a t p r e d i c t s h o w t r o p h i c i n t e r ac t ions c a n cause j u v e n i l e fish s u r v i v a l to dec l ine at l o w s t o c k size ( ca l l ed depensa t ion ) i n a p a t t e r n t h a t m a y no t be s t a t i ona ry . H e r e I r e v i e w the t r a d i t i o n a l t h e o r y u s e d to desc r ibe fish p o p u l a t i o n d y n a m - ics, i n t r o d u c e the C u l t i v a t i o n - D e p e n s a t i o n h y p o t h e s i s a n d desc r ibe m o d e l i n g a n d e x p e r i m e n t a l research t e s t ing th i s h y p o t h e s i s u s i n g lake ecosys tems w i t h o n l y t w o fish species, r a i n b o w t r o u t a n d s t u n t e d n o r t h e r n p i k e m i n n o w Pty- chocheilus .oregonensis. Chapter 1. Introduction 2 1.1 Review 1.1.1 Compensation in fish stocks T h e r e has been cons ide rab le deba te a b o u t dens i t y -dependen t increases i n s tock p r o d u c t i v i t y at l o w s tock s ize, or c o m p e n s a t i o n , b u t there is l i t t l e deba te t h a t some resource w i l l e v e n t u a l l y l i m i t the size of a f ish p o p u l a t i o n ( R o s e et a l . , 2001) . T h e m a j o r i t y of the r e m a i n i n g deba te is a b o u t the m a g n i t u d e of c o m p e n s a t i o n a n d processes t ha t cause i t (Rose et a l . , 2001) . T h e processes t ha t c a n p r o d u c e c o m p e n s a t i o n c a n be e x a m i n e d b y l o o k i n g at the f o l l o w i n g p o p u l a t i o n d y n a m i c s t a u t o l o g y ( W a l t e r s a n d M a r t e l l , 2004): w h e r e Nt represents a b u n d a n c e at t i m e t, Sa a d u l t s u r v i v a l , F t he m e a n f e c u n d i t y of i n d i v i d u a l s , a n d Sj j u v e n i l e s u r v i v a l . If a p o p u l a t i o n is at equ i - l i b r i u m , so t h a t Nt — Nt-i t h e n E q . 1.1 reduces to the f o l l o w i n g : I n o rder t h a t th i s r e l a t i o n s h i p be sa t i s f ied where h a r v e s t i n g has r e d u c e d Sa a n d / o r Sj, at least one of the three ra tes m u s t show c o m p e n s a t o r y change . T h o u g h dens i ty -dependen t changes i n f e c u n d i t y have been r e p o r t e d ( R o t h c h i l d et a l . , 1989) some au tho r s d o u b t the w h e t h e r changes i n f e c u n d i t y are suffi- c ien t to s t a b i l i z e p o p u l a t i o n s ( C r a i g a n d K i p l i n g , 1983; K o s l o w , 1992; K o s l o w Nt = Nt_iSa + FNt^Sj (1.1) 1 = Sa + FSj. (1.2) Chapter 1. Introduction 3 et a l . , 1995) a n d i n any case, h a r v e s t i n g fish t y p i c a l l y reduces m e a n s ize hence F because i n semelpa rous species increases i n size of ten resu l t i n h ighe r fecun- d i t i e s . H o w e v e r , the t o t a l f e c u n d i t y of a p o p u l a t i o n has been d o c u m e n t e d to change i n response to changes i n dens i ty , w i t h younge r i n d i v i d u a l s s p a w n i n g ear l ie r ( F u n a k o s h i , 1994) or w i t h a greater p r o p o r t i o n o f females s p a w n i n g ( K o s l o w et a l . , 1995). D o c u m e n t e d changes i n a d u l t s u r v i v a l as a f u n c t i o n of d e n s i t y are r e l a t i v e l y rare . T h e m o s t c o m p e l l i n g a r g u m e n t s a b o u t w h i c h ra te is c o m p e n s a t o r y are those i n v o l v i n g dens i t y dependen t responses o c c u r r i n g i n the ea r ly stages o f life i .e. those processes t h a t affect Sj. G i v e n the appa ren t s t a b i l i t y a n d / o r a m b i g u i t i e s i n the r e l a t i o n s h i p be- tween fecundi ty , a d u l t s u r v i v a l a n d a d u l t densi ty , i t is r easonab le to assume t h a t mos t of the a c t u a l c o m p e n s a t o r y responses i n f ish s t o c k s are o c c u r r i n g w i t h the younge r i n d i v i d u a l s . T h e r e are some excel lent f ie ld e x a m p l e s o f den- s i ty dependen t s u r v i v a l at va r i ous ea r ly life stages. B e v e r t o n a n d l i e s (1992) d o c u m e n t h o w the d e n s i t y dependen t c o m p o n e n t o f m o r t a l i t y changes over th ree t i m e pe r iods be tween se t t l ement a n d the second year . T h e y were able t o s h o w t h a t the d r a m a t i c d a m p e n i n g effect of dens i t y d e p e n d e n t m o r t a l i t y of j u v e n i l e s was sufficient to reduce the 200 fo ld v a r i a t i o n i n a d u l t a b u n d a n c e to l a r v a l se t t l ement to o n l y a 4 fo ld v a r i a t i o n i n the second year . U s i n g 14 p o p - u l a t i o n s o f A t l a n t i c c o d (Gadus morhua), h a d d o c k (Melanogrammus aieglefi- nus), w h i t i n g (Merlangius merlangus), p lace (Pleuronectes platessa) a n d sole (Solea vulgaris) M y e r s a n d C a d i g a n (1993) showed b o t h s t r o n g ev idence o f d e n s i t y - d e p e n d e d m o r t a l i t y w i t h i n cohor t s a n d r e l a t i v e l y l i t t l e i n t e r a n n u a l Chapter 1. Introduction 4 v a r i a b i l i t y i n the d e n s i t y - i n d e p e n d e n t c o m p o n e n t o f j u v e n i l e m o r t a l i t y . J u v e n i l e s u r v i v a l is of ten r e l a t ed to the ra te a t w h i c h j u v e n i l e fish c a n reach sizes t h a t m a k e t h e m i n v u l n e r a b l e to p r e d a t i o n . P o s t et a l . (1999) showed u s i n g a series of e x p e r i m e n t a l lakes s t o c k e d at different dens i t ies t ha t at l ow dens i ty , age-1 g r o w t h inc reased a n d there was a c o r r e s p o n d i n g increase i n j u v e n i l e s u r v i v a l . H e a l e y (1980) showed tha t e x p l o i t e d lakes o f w h i t e f i s h h a d a h ighe r f requency of inc reased g r o w t h a n d r e c r u i t m e n t t h a n u n e x p l o i t e d lakes. H e also d o c u m e n t e d s o m e w h a t a m b i g u o u s changes i n f e c u n d i t y a n d p r o p o s e d t h a t a d u l t s u p p r e s s i o n of y o u n g c o u l d be the resu l t o f a d u l t s c o n - f in ing j u v e n i l e s to m a r g i n a l h a b i t a t s . M a r s h a l l a n d F r a n k (1999) a lso s h o w e m p i r i c a l ev idence t h a t m e a n l e n g t h of age-1 h a d d o c k were n e g a t i v e l y r e l a t ed to the d e n s i t y of age-4 a n d o lder f i sh , tha t differences i n age-1 l e n g t h were pers i s ten t t h r o u g h l i fe , a n d t h a t r e c r u i t m e n t was p o s i t i v e l y r e l a t e d to l e n g t h at age-4. 1.1.2 Stock-Recruit Curve Analysis: Compensation Versus Depensation Regard le s s of the m e c h a n i s m s b y w h i c h c o m p e n s a t i o n is t a k i n g p lace , there is n o w a cons ide rab l e a m o u n t o f d a t a f rom s tock r e c r u i t m e n t r e l a t i o n s h i p s to s u p p o r t s u c h an asse r t ion . T h e m o s t i m p o r t a n t c o n t r i b u t i o n comes f r o m the w o r k of M y e r s et a l . (1995b) w h o a n a l y z e d over 700 s p a w n e r - r e c r u i t m e n t series l o o k i n g for p a r a m e t e r s t h a t were cons tan t at the species l eve l . T h e i r Chapter 1. Introduction 5 w o r k shows a r e m a r k a b l e resu l t , t ha t the s t a n d a r d i z e d s lope at the o r i g i n o f a s tock r e c r u i t m e n t c u r v e (or the m a x i m u m r e p r o d u c t i v e rate) is cons i s t en t ly be tween 1 a n d 5, i .e. j u v e n i l e s u r v i v a l r a t e s ' a t l o w d e n s i t y are 1 to 5 t imes h igher t h a n at n a t u r a l "unf i shed" dens i t ies . E q u a l l y i m p o r t a n t l y , M y e r s et a l . (1995a) s h o w m o s t (125 /128) fish s tocks d o no t s h o w any ev idence of d e p e n s a t i o n (or dec reas ing j u v e n i l e s u r v i v a l a t l o w s t o c k s ize) . C o n s i d e r a b l e w o r k fo l l owed M y e r s et a l . (1995a) 's ana ly s i s o f s t ock - r ec ru i t d a t a w i t h p a r t i c u l a r a t t e n t i o n d e v o t e d to d e t e r m i n i n g w h e t h e r or no t m o d - els p a r a m e t e r i z e d w i t h d e p e n s a t i o n fit the d a t a be t t e r t h a n those w i t h o u t i t ( L i e r m a n n a n d H i l b o r n , 1997; S h e l t o n a n d H a r l e y , 1999; L i e r m a n n a n d H i l b o r n , 2001; F r a n k a n d B r i c k m a n , 2000) . H o w e v e r , m o s t s tudies c o n c e r n e d themselves w i t h d e t e c t i n g a s t a t i o n a r y d e p e n s a t o r y r e l a t i o n s h i p ; t ha t is , one w i t h a d o m a i n o n the s t o c k r e c r u i t m e n t c u r v e where j u v e n i l e s u r v i v a l c o n - s i s ten t ly a n d i m m e d i a t e l y decreases as a d u l t d e n s i t y decreases r e s u l t i n g i n a second low d e n s i t y e q u i l i b r i u m for the f ished species . 1.2 Research Hypothesis and Experiment 1.2.1 The Cu l t i va t ion Depensation Hypothesis T h e m a i n difference be tween the c u l t i v a t i o n - d e p e n s a t i o n h y p o t h e s i s a n d c las- s i c a l d e p e n s a t i o n is r o o t e d i n fo rag ing a r e n a t h e o r y ( W a l t e r s a n d Juanes , 1993). I n c l a s s i c a l m o d e l s o f d e p e n s a t i o n s u c h as t h a t o f H o l l i n g (1959), the p r o p o r t i o n of p r e y c o n s u m e d by a p r e d a t o r is l i m i t e d b y h a n d l i n g t i m e or b y Chapter 1. Introduction 6 s a t i a t i o n . C l a s s i c a l d e p e n s a t i o n ( H o l l i n g , 1959) arises by a s s u m i n g t h a t the p r o b a b i l i t y o f p r e y e n c o u n t e r i n g p r e d a t o r is a l i nea r f u n c t i o n of the dens i t i es of p r eda to r s a n d p rey ( a k i n to first o rder c h e m i c a l k ine t i c s ) b u t w i t h p r eda - tor s ea r ch ing t imes r educed at h ighe r p rey dens i t i es clue to h a n d l i n g t i m e effects, so t h a t as p r e y d e n s i t y is r e d u c e d , the p r o p o r t i o n of p rey r e m o v e d by p reda to r s increases . F o r a g i n g a r ena t h e o r y ( W a l t e r s a n d Juanes , 1993) o n the o the r h a n d p red i c t s t h a t r i sk - sens i t i ve fo rag ing o n the p a r t of the p rey ( juveni le f ish i n th i s case) m i t i g a t e s t he i r i n t e r a c t i o n w i t h p reda to r s t h r o u g h exchange ra tes be tween the v u l n e r a b l e p rey p o o l ( ava i l ab le to p reda to r s ) a n d the n o n - v u l n e r a b l e p o o l . It assumes t h a t j u v e n i l e s are conf ined to refuges away f r o m p reda to r s ( inshore s h a l l o w h a b i t a t s , h i d i n g places etc.) a n d t h a t p r e d a t i o n o c c u r s m a i n l y w h e n juven i l e s are forced to enter r i s k y s tates ( the fo rag ing a rena , W a l t e r s a n d Juanes 1993; W a l t e r s a n d K i t c h e l l 2001) . I n a q u a t i c sys t ems there is a g r o w i n g b o d y of ev idence to s u p p o r t such a r i sk sens i t ive fo rag ing s t r u c t u r e ( T o n n a n d P a s z k o w s k i , 1992; T o n n et a l . , 1994; P o s t et a l , 1999) . F o r a g i n g a r ena t heo ry p r ed i c t s t h a t a key fac tor d e t e r m i n i n g the p r o b - a b i l i t y of a n encoun te r of p r eda to r w i t h p r e y is p r e y behav io r , no t o v e r a l l p r ey dens i ty . A t h i g h dens i t ies , p r e y are forced to m a k e m o r e r i s k y forag- i n g t r i p s i n o rder to meet the i r energy d e m a n d s because food d e n s i t y i n the refuges is depressed . F o r a g i n g a r e n a t h e o r y p r e d i c t s t h a t i n the absence of o the r t r o p h i c effects, w h e n a d u l t d e n s i t y is r e d u c e d there is a c o r r e s p o n d i n g decrease i n the d e n s i t y of j u v e n i l e s i n the refuge areas m e a n i n g h igher l o - Chapter 1. Introduction 7 c a i f o o d dens i t ies a n d hence fewer r i s k y t r i p s i n the fo rag ing a r e n a to feed. O n e o f the emergent p rope r t i e s o f fo rag ing a r e n a t heo ry is t h a t i t g ives rise to the c lass ic c o m p e n s a t o r y B e v e r t o n - H o l t spawner - r ec ru i t m o d e l ( B e v e r t o n a n d H o l t , 1958; W a l t e r s a n d K o r m a n 1999) a n d severa l t es tab le hypo theses a b o u t h o w changes i n behav io r , p r o d u c t i v i t y , a n d p r e d a t i o n r i sk c a n a l te r the r e l a t i o n s h i p be tween the n u m b e r of r ec ru i t s p r o d u c e d per spawner . T h e r e are m a n y hypotheses t h a t e x p l a i n the exis tence o f a l t e rna t e s t ab le s ta tes i n ecosys tems ( rev iewed i n Scheffer et a l . 2001a) . T h e C u l t i v a t i o n D e p e n s a t i o n hypo thes i s ( W a l t e r s a n d K i t c h e l l , 2001) argues t h a t f i sh ing a n d j u v e n i l e d y n a m i c s c a n be the c r u c i a l e lements i n p r o d u c i n g a ' f l i p ' i n the e c o s y s t e m s ta te . C u l t i v a t i o n - d e p e n s a t i o n effects ar ise i n E c o s i m II ( W a l t e r s et a l . , 2000) m o d e l s t h o u g h the f o l l o w i n g sequence of events ( W a l t e r s a n d K i t c h e l l 2001, represented i n F i g . 1.1). F i s h i n g reduces the a d u l t p o p u l a t i o n s ize of a " d o m i n a n t " fish species a n d hence, the t o t a l n u m b e r o f j u v e n i l e s i n p r e d a t i o n refuges. J u v e n i l e s r educe feeding t i m e or t i m e spen t at b o d y sizes s m a l l enough to be v u l n e r a b l e to p r e d a t i o n r i sk . J u v e n i l e m o r t a l i t y t h e n decreases so t h a t the net n u m b e r o f r ec ru i t s s t ays n e a r l y cons t an t even t h o u g h fewer j u v e n i l e s are b e i n g p r o d u c e d . H o w e v e r , i f there is h i g h p r e d a t i o n b y the a d u l t fish o n some sma l l e r p r e d a t o r or c o m p e t i t o r o f the j u v e n i l e s (a ' forage ' fish) t h e n as a d u l t dens i t y is r e d u c e d , the forage fish is re leased to increase i n a b u n d a n c e . T h e n one or two nega t ive effects c a n occu r . If the forage fish p r e y d i r e c t l y o n juven i l e s , t h e n p r e d a t i o n m o r t a l i t y is d i r e c t l y inc reased . I f the forage fish a n d juven i l e s are c o m p e t i t o r s , i nc reased forage fish a b u n d a n c e Chapter 1. Introduction 8 leads to r e d u c e d f o o d dens i t y a n d hence, i nc reased j u v e n i l e f o r a g i n g t i m e a n d gene ra l p r e d a t i o n r i sk . D i r e c t p r e d a t i o n of forage fish o n the j uven i l e s o f the d o m i n a n t fish species is no t necessary for c u l t i v a t i o n - d e p e n s a t i o n . If the forage f ish species is "re- leased" to increase i n a b u n d a n c e , the forage f ish m a y d i r e c t l y p r e y o n j u v e - ni les of the d o m i n a n t species b u t i f some foods are sha red , t h e n inc reased forage f ish dens i t y m e a n s r e d u c e d food dens i t y a n d hence inc reased j u v e n i l e fo rag ing t i m e ( W a l t e r s a n d K i t c h e l l , 2001). F r o m a m a n a g e m e n t p e r s p e c t i v e c u l t i v a t i o n - d e p e n s a t i o n effects c a n have p r o f o u n d i m p a c t s . F i r s t l y , t h e y m e a n t h a t excessive f i sh ing c a n p r o d u c e a p e r m a n e n t l o w dens i ty s ta te of the ta rge t (or d o m i n a n t p r e d a t o r ) species. T h e y also m e a n tha t e cosys t em "f l ips" c a n h a p p e n i n the o p p o s i t e d i rec - t i o n ; ecosys tems d o m i n a t e d b y the forage species c a n be f l i p p e d b a c k to the d o m i n a n t p r eda to r s ta te . S u c h t r a n s i t i o n s need n o t be so le ly the p r o d u c t of f i sh ing e i ther , s ince i t is the r a t i o o f r i sk to p r o d u c t i v i t y t h a t de t e rmines the n u m b e r of r ec ru i t s per spawner ( W a l t e r s a n d Juanes , 1993) . W h e t h e r c o n c u r r e n t w i t h changes i n p r o d u c t i v i t y or no t , cessa t ion of f i sh ing i n a s t o c k p u s h e d i n t o the forage f ish d o m i n a t e d s ta te w i l l n o t recover w i t h o u t some a d d i t i o n a l m a n a g e m e n t i n t e r v e n t i o n (such as f i sh ing the forage species) . 1.2.2 Experimental depletions T h e c u l t i v a t i o n - d e p e n s a t i o n h y p o t h e s i s is w e l l s u i t e d t o t e s t i n g u s i n g ex- p e r i m e n t a l dep le t ions s ince i t makes specif ic p r e d i c t i o n s a b o u t h o w s u r v i v a l , Chapter 1-. Introduction 9 Figure 1.1: Trophic triangle describing where the survival of the juvenile of the dominant is negatively affected by the prey of the dominant species. Chapter 1. Introduction 10 g r o w t h a n d fo rag ing t i m e s h o u l d change i n response to dens i t y m a n i p u l a t i o n s . In th i s s tudy , I t e s ted i f c u l t i v a t i o n - d e p e n s a t i o n effects d e s c r i b e d above c o u l d be p r o d u c e d i n the field u s i n g d e p l e t i o n fishing. Spec i f i c p r e d i c t i o n s i n c l u d e ( W a l t e r s a n d K i t c h e l l , 2001): • Increase i n a b u n d a n c e of s m a l l forage fishes or i nve r t eb ra t e s i f p r eda - t o r y s tock s ize decreases • i n c r e a s i n g r a the r t h a n decreas ing j u v e n i l e fo rag ing t i m e w h e n a d u l t a b u n d a n c e is l o w due to c o m p e t i t i o n w i t h forage fishes • decreased j u v e n i l e s u r v i v a l ra te at l ow a d u l t p o p u l a t i o n s ize due to inc reased f o r a g i n g t i m e a n d (or) d i r ec t p r e d a t i o n b y forage species. • d i e t a n d h a b i t a t ove r l ap be tween j u v e n i l e fish a n d the forage f ish a n d / o r d i r ec t ev idence of p r e d a t i o n b y the forage fish o n j u v e n i l e s s h o u l d be obse rved i n s t o m a c h contents . I c o n d u c t e d d e p l e t i o n fishing of n o r t h e r n p i k m m i n o w Ptychocheilus orego- nensis i n a series of lakes o n B o n a p a r t e P l a t e a u i n S o u t h C e n t r a l B . C . h a v i n g two p redac ious species: r a i n b o w t r o u t Onchorhynchus mykiss a n d s t u n t e d n o r t h e r n p i k e m i n n o w . T h e ob jec t ives of m y s t u d y were a) to m o d e l the s y s t e m to see unde r w h a t pa r ame te r c o m b i n a t i o n s c u l t i v a t i o n - d e p e n s a t i o n effects c o u l d be obse rved , b) fish the s y s t e m a n d c) measu re h o w g r o w t h a n d s u r v i v a l va r i ab le s of b o t h species r e sponded to d e p l e t i o n fishing. I first i d e n - t i f ied a u n i q u e s y s t e m o f lakes where n o r t h e r n p i k e m i n n o w have o b l i g a t o r y Chapter 1. Introduction 11 r ea r i ng i n nu r se ry lakes; I c o n d u c t e d d e p l e t i o n f i sh ing; I deve loped new s ta t i s - t i c a l m e t h o d o l o g i e s to measure g r o w t h a n d s u r v i v a l responses to such f i sh ing; I d e v e l o p e d a n e c o s y s t e m m o d e l of the s t u d y s y s t e m to see w h a t p a r a m e t e r c o m b i n a t i o n s w o u l d p r o d u c e c u l t i v a t i o n - d e p e n s a t i o n ( W a l t e r s a n d K i t c h e l l , 2001) effects; a n d f ina l l y c o m p a r e d the p r e d i c t e d a n d obse rved responses to the e x p e r i m e n t a l m a n i p u l a t i o n s ; Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 12 Chapter 2 Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow Abstract T h i s is the first r epo r t of a f reshwater f ish p o p u l a t i o n t h a t has o b l i g a t o r y r e a r i n g i n specif ic ' nu r se ry ' lakes. I n t w o S o u t h C e n t r a l B r i t i s h C o l u m b i a d ra inages , I iden t i f i ed two n o r t h e r n p i k e m i n n o w p o p u l a t i o n s h a v i n g e i ther a s ingle or m u l t i p l e lake l i f e -h i s to ry t ype . I a rgue t h a t such la rge scale s p a t i a l o r g a n i z a t i o n is c o n t r o l l e d b y t e m p e r a t u r e d r i v e n s p a w n i n g cues a n d d e n s i t y - d e p e n d e n t m i g r a t i o n f rom the nur se ry areas to o u t l y i n g lakes. I used v i s u a l su rveys a n d m a r k - r e c a p t u r e e x p e r i m e n t s t o show the p o s i t i o n of fry a n d a p p a r e n t m o r t a l i t y rates i n each d ra inage . I u sed b ioenerge t ics m o d e l i n g a n d showed i t is p h y s i o l o g i c a l l y poss ib le to s p a w n a n d h a t c h i n the h e a d w a t e r lakes, b u t cons ide rab l e a d d i t i o n a l c o n s u m p t i o n w o u l d be requ i red , for fish r e a r i n g i n non-nu r se ry lakes to reach the same mass obse rved i n nu r se ry areas b y the f o l l o w i n g year to c o m p e n s a t e for de lays i n s p a w n i n g . U s i n g C h l o r o p h y l l A, I showed the nur se ry lakes to be more p r o d u c t i v e b u t t h a t th i s advan tage d i sappea r s once sca l ed t o the effective dens i t y o f n o r t h e r n p i k e m i n n o w be tween nur se ry a n d n o n - n u r s e r y areas. keywords: u n i t s tock , n o r t h e r n p i k e m i n n o w , on togene t ic shif t Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 2.1 Introduction F i s h e r i e s b io log i s t s t y p i c a l l y t rea t lakes as u n i t s tocks where l i t t l e m o v e m e n t be tween lakes is a s sumed even w h e r e m o v e m e n t is poss ib le a n d there are g rad i en t s i n p r o d u c t i v i t y a n d d e n s i t y be tween lakes . W h i l e i t is u n d e r s t o o d t h a t fish move be tween lakes over l o n g t i m e scales, the p o p u l a t i o n d y n a m i c s of a t y p i c a l l ake p o p u l a t i o n are a s s u m e d to be d o m i n a t e d b y l o c a l b i r t h a n d d e a t h processes. F o l l o w i n g the research of G e r k i n g (1959), m a n y s t r e a m p o p - u l a t i o n s are also a s sumed . to o c c u p y o n l y a s m a l l range of the s t r e a m i n sp i t e of the fact t ha t m a n y of the m e t h o d s used to e s t ima t e the t o t a l d i s p l a c e m e n t of f ish p o p u l a t i o n are b iased aga ins t d e t e c t i n g larger scale d i s p e r s a l i n the first p l ace ( G o w e n et a l . , 1994). H o w e v e r , at d r a inage scale, lakes are b o t h c o n n e c t e d to each o the r a n d have g rad ien t s o f t e m p e r a t u r e , s ed imen t s , wa te r , nu t r i en t s , a n d o rgan ic m a t t e r ( G o m i et a l . , 2002) t ha t a n i m a l s c o u l d u t i l i z e over the course of the i r on togeny p r o v i d e d t h a t s t r eams be tween lakes p e r m i t m o v e m e n t be tween t h e m . U s e of m o r e t h a n one lake has been obse rved i n A r c t i c cha r r i n response to p r o d u c t i v i t y a n d t e m p e r a t u r e difference be tween lakes ( N a s l u n d , 1990). O n t o g e n e t i c m o v e m e n t c a n h a p p e n over v e r y la rge scales i n m a r i n e sys tems ( R o o k e r et a l , 2003) . E c o l o g i c a l t heo ry has l o n g p r e d i c t e d on togene t i c n iche shif ts i n response to on togene t i c changes i n resource a n d p r e d a t i o n g rad ien t s ( r ev i ewed i n W e r n e r a n d G i l l i a m , 1984) a n d m o r e r ecen t ly i n response to p r e d a t i o n r i sk f r o m la rger s i zed fish of the s ame or different species (Pe r s son a n d E k l o v , Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 14 1995). I n fresh-water sys t ems , h a b i t a t shifts i n response to s u c h g rad ien t s are obse rved , b u t the scale o f these shifts a n d the e x p e r i m e n t a l des igns to de tec t t h e m t e n d to be at s m a l l scale, for e x a m p l e , h a b i t a t refuges i n s m a l l p o n d s or enclosures (Pe r s son a n d E k l o v . 1995; O l s o n , 1996; O s e n b e r g et a l . , 1994) . F i s h i n seasonal e n v i r o n m e n t s such as t e m p e r a t e lakes have o n l y a shor t g r o w i n g season to acqu i r e sufficient energy to s u r v i v e w i n t e r . Y o u n g f ish face a ve ry s t r o n g t radeof f be tween g r o w i n g large e n o u g h to s u r v i v e w i n - ter versus the p r e d a t i o n r i sk a s soc ia t ed w i t h the a d d i t i o n a l feed ing needed to d o th i s (Pos t a n d P a r k i n s o n , 2001; B i r o et a l . , 2005) . A l s o , b ioenerget - ics ( K e r r , 1971; K i t c h e l l et a l . , 1977) s h o w s t r o n g dependence of s w i m m i n g , c o n s u m p t i o n a n d d i g e s t i o n o n t e m p e r a t u r e . T h e e n d of season l e n g t h for age 0 + p e r c h e x h i b i t a n e a r l y l i nea r r e l a t i o n s h i p be tween l e n g t h a n d c u m u l a t i v e degree days (Power a n d v a n den H e u v e l , 1999). F i n a l l y , the n u m b e r o f degree days for r e c r u i t m e n t a lso seems to l i m i t the n o r t h e r n edge of range for m a n y species (Schu te r a n d P o s t , 1990) w h e n the g r o w i n g season (as d i c t a t e d b y each species b ioenerge t ics ) is no t l o n g e n o u g h for species to r each sizes large e n o u g h to a v o i d b e i n g ea ten , have suf f ic ient ly large l i p i d reserves to s u r v i v e w i n t e r . N o r t h e r n p i k e m i n n o w Ptychocheilus oregonensis ( C y p r i n d a e ) are d i s t r i b u t e d f r o m O r e g o n to S o u t h C e n t r a l B r i t i s h C o l u m b i a . T h e y have been s t u d i e d ex t ens ive ly as the ta rge t o f p r e d a t o r r e m o v a l p r o g r a m s i n I d a h o ( J e p p s o n , 1959), B r i t i s h C o l u m b i a ( R i c k e r , 1941) a n d m o s t r ecen t ly i n the C o l u m b i a R i v e r ( R i e m a n a n d Beamesder fe r , 1990; Beamesder fe r , 1992b; F r i e s e n a n d Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 15 W a r d , 1999). I n m o r e t e m p e r a t e c l i m e s n o r t h e r n p i k e m i n n o w g r o w to a s y m p - t o t i c lengths of 350 — 4 5 0 m m F . L . at w h i c h sizes t h e y are p ro l i f i c p reda to r s (Pe te r sen a n d D e A n g e l i s , 1992) . A t the n o r t h e r n l i m i t o f the i r d i s t r i b u t i o n , t hey appea r to be s t u n t e d g r o w i n g o n l y to a p p r o x i m a t e l y a s y m p t o t i c lengths 2 0 0 m m . H e r e I d o c u m e n t the first p o p u l a t i o n of s t u n t e d n o r t h e r n p i k e m i n n o w tha t takes advan tage of t e m p e r a t u r e , p r o d u c t i v i t y a n d d e n s i t y g rad ien t s be- tween lakes. I use b ioenerge t i cs m o d e l i n g to s h o w t h a t la rge differences i n c o n s u m p t i o n ra tes w o u l d be needed i n o rder to c o m p e n s a t e for de layed s p a w n i n g caused b y coo le r t empera tu re s , a n d argue t h a t the d i s t r i b u t i o n o f a d u l t s is d e t e r m i n e d b y the r a t i o of effective d e n s i t y t o p r o d u c t i v i t y . 2.2 Methods 2.2.1 Study site T h e s t u d y s i te was a p p r o x i m a t e l y 100 km N o r t h o f K a m l o o p s i n S o u t h C e n - t r a l B r i t i s h C o l u m b i a , C a n a d a . I s t u d i e d n o r t h e r n p i k e m i n n o w i n two sep- ara te sub-d ra inages o f the T h o m p s o n R i v e r s y s t e m . T h e wes t e rn d r a i n a g e ( F i g . 2.1) i nc ludes D a d ' s L a k e , w i t h two ' head -end ' lakes above i t : M o m ' s a n d N e s t o r . I n the eas te rn d ra inage I i n t e n s i v e l y s t u d i e d M o o s e P a s t u r e L a k e , w h i c h a lso h a d t w o lakes above i t c a l l e d C h e r y l a n d W i l d e r n e s s ( F i g . 2.1). T h e eas te rn lakes d r a i n i n t o the D e a d m a n R i v e r a n d the wes te rn ones d i r e c t l y i n t o the T h o m p s o n R i v e r . T h e o ther lakes i n F i g . 2.1 were g i v e n cur - Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 16 T a b l e 2 .1: T a b l e of l ake areas, m a x i m u m dep th s a n d pe r ime te r s L a k e T o t a l A r e a (ha) M a x D e p t h (m) P e r i m e t e r ( m ) C h e r y l 13.5 15 1563 W i l d e r n e s s 11.9 11 1628 M o o s e . P a s t u r e 7.3 10 1411 D a d s * ' 9.8 9 2044 Nes tor . . . 7.3 ' 12 1531 M o m s 7.1 15 1213 s o r i a l v i s u a l su rveys to check for the presence or absence of j u v e n i l e n o r t h e r n p i k e m i n n o w . L a r g e r p i k e m i n n o w were a b u n d a n t i n a l l lakes . S ince M o o s e P a s t u r e a n d D a d ' s lakes were the o n l y lakes where j u v e n i l e s were f o u n d , f refer to t h e m as ' nu r se ry lakes ' a n d the lakes above t h e m as ' head -end ' lakes. E v i d e n c e o f the s p a t i a l o r g a n i z a t i o n of these t w o s tocks c a m e f rom two sources: v i s u a l su rveys of fry (0+) a n d ea r ly j u v e n i l e s (1 — 3 + ) i n each lake , a n d the age s t r u c t u r e o f each lake e s t i m a t e d f r o m p o p u l a t i o n sizes at age. T h e area , d e p t h a n d pe r ime te r s of the s t u d y lakes are l i s t e d i n t ab l e 2 .2 .1 . 2.2.2 Spawning and Visual Surveys F r o m m i d - J u n e to m i d - J u l y 2002, I obse rved the l o c a t i o n of s p a w n i n g i n the in f low a n d ou t f l ow creeks of W i l d e r n e s s , M o o s e P a s t u r e , C h e r y l , D a d ' s , N e s t o r a n d M o m ' s lakes . D u r i n g th i s p e r i o d I a l so po le se igned a n d elec- t rof i shed i n these same creeks every 2-3 days . I n A u g u s t o f 2002 a n d 2003 I s u r v e y e d a l l the lakes i n c l u d e d i n figure 2.1 for the presence of absence of e m e r g i n g fry. f n A u g u s t of t ha t same year i n D a d ' s a n d M o o s e P a s t u r e lakes,  Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 18 I e n u m e r a t e d the n u m b e r of 0 + , 1 + a n d 2 + a n d greater t h a n 2 + fish v i s i b l e a r o u n d the p e r i m e t e r of the lake . I n every case I c o u n t e d u s i n g p o l a r i z e d sunglasses a n d e i ther w a l k i n g the shore l ine , or b y boa t be tween the hour s of 10:00 a n d 14:00. T h e g l o b a l p o s i t i o n i n g sa te l l i t e ( G P S ) p o s i t i o n of each agg rega t ion of j uven i l e s was r eco rded ( v i r t u a l l y a l l j uven i l e s obse rved were i n schools of 5-200 i n d i v i d u a l s each) . 2.2.3 A p p a r e n t m o r t a l i t y I e s t i m a t e d the apparen t m o r t a l i t y u s i n g l e n g t h c o n v e r t e d c a t c h curves ( P a u l y , 1990) . T h i s was done because any m i g r a t i o n f rom nur se ry lakes to head -end lakes w o u l d appea r as h igher appa ren t m o r t a l i t y (as fish leave) . F r o m J u n e to S e p t e m b e r 2002, f ish were c o n t i n u o u s l y tagged u s i n g 5 or 15 mm F l o y n u m b e r e d tags d u r i n g b o u t s o f m a r k - r e c a p t u r e i n each lake c o n d u c t e d at 1-2 week in t e rva l s . F i s h as s m a l l as 55 mm were m a r k e d a n d o n l y those fish re leased i n perfect c o n d i t i o n were i n c l u d e d i n th i s ana lys i s . S u m m a r i e s of m a r k e d , r e c a p t u r e d , u n m a r k e d a n d k i l l e d f ish b y da te , l eng th-conver ted-age , a n d l ake are i n sec t ion 2.5. I c o n v e r t e d obse rved l eng ths i n t o ages u s i n g the v o n B e r t a l a n f f y g r o w t h p a r a m e t e r e s t ima tes fit to length-age d a t a u s i n g the r e d u c e d l i k e l i h o o d w i t h f i sh ing m o d e l 4 (chapte r 3, t ab l e 3.2) f o l l o w i n g P a u l y (1990) b u t a s s u m i n g no seasona l g r o w t h . W h i l e P a u l y (1990) show t h a t cons ide rab l e b ias c a n be p r o d u c e d i n g r o w t h pa rame te r s b y n o t i n c l u d i n g seasonal i ty , I d i d no t a t t e m p t to e s t ima te the pa rame te r s to d o so. F i r s t l y , there were n o l e n g t h - Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 19 age d a t a co l l ec t ed d u r i n g the co lde r m o n t h s to p r o v i d e any con t r a s t be tween s low a n d fast g r o w i n g p e r i o d s . I n w i n t e r m o n t h s lakes are f rozen a n d access is i m p o s s i b l e . T h e b ioenerge t ics d a t a for the C o l u m b i a R i v e r i n d i c a t e d tha t g r o w t h i n l e n g t h b e l o w 4 C was effect ively zero, I a s s u m e d t h a t g r o w t h i n l e n g t h is a s sumed to be zero f rom N o v e m b e r to e n d of A p r i l . Second ly , I was o n l y in te res ted i n the r e l a t i ve c o m p a r i s o n s of apparen t m o r t a l i t y , so as l o n g as g r o w t h pa r ame te r biases ( a n d c o r r e s p o n d i n g appa ren t m o r t a l i t y ) c a n be a s s u m e d cons tan t across lakes, t h e n the abso lu te b ias the a p p a r e n t m o r t a l i t y es t ima tes is i r re levan t . N o r t h e r n p i k e m i n n o w dep l e t i ons were c o n d u c t e d i n 2001 i n C h e r y l a n d M o m ' s lakes (desc r ibed i n s e c t i o n 5.2.2). There fo re , ca t ches -a t - l eng th f rom the d e p l e t i o n were also c o n v e r t e d to ages, s u r v i v e d f o r w a r d b y one year at a ra te o f 0.7 ( R i e m a n a n d Beamesde r fe r , 1990), a n d a d d e d to the e s t i m a t e d n u m b e r s at age i n 2002 f r o m the m a r k - r e c a p t u r e . T h e appa ren t m o r t a l i t y Z was c a l c u l a t e d as the s lope o f the l o g n u m b e r s - at-age of fu l ly r e c r u i t e d (5+) f ish , f used a P e t e r s o n e s t i m a t o r to e s t ima te n u m b e r s at age Na whe re the nega t ive log l i k e l i h o o d o f b o t h the m a r k e d a n d u n m a r k e d fish ( E q . 2.1) was: J2Ralog(Pa) + Ua\og(l-Pa) (2.1) I where Ra is the n u m b e r o f r e c a p t u r e d f ish at age a a n d pa is the p r o p o r t i o n of m a r k e d fish Ma to the e s t i m a t e d n u m b e r at age Na i n t h a t lake . W h i l e Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow tag-loss a n d m o r t a l i t y were su re ly present , the p u r p o s e o f th i s ana lys i s was to c o m p a r e across lakes so I i m p l i c i t l y a s sumed these to be cons t an t across a l l lakes . 2.2.4 H y d r o g r a p h y a n d P r o d u c t i v i t y I m a d e c o n t o u r m a p s o f lake d e p t h b y m e a s u r i n g d e p t h at 10 t ransec t s per l ake at a p p r o x i m a t e l y 10 m i n t e rva l s . T h e G P S p o s i t i o n of each d e p t h m e a - su remen t was r e c o r d e d a n d 1 m d e p t h c o n t o u r p lo t s m a d e . T h e p r o p o r t i o n of the t o t a l lake a rea o c c u p i e d b y each d e p t h c o n t o u r was c a l c u l a t e d u s i n g A r c V i e w 3.0. A s a measure of lake sha l lowness , I p l o t t e d the t o t a l p r o p o r t i o n of l ake a rea versus d e p t h i n meters (m). A t a p p r o x i m a t e l y t w o week in te rva l s , I m e a s u r e d C h l o r o p h y l l A at f ixed s t a t i ons i n the m i d d l e of each l ake b y f i l t e r i ng 50 m l of l ake w a t e r t h r o u g h 2 400 um f i l ter . F i l t e r s were t h e n d i s so lved i n acetone o v e r n i g h t a n d C h l o r o - p h y l l A was m e a s u r e d u s i n g mass spec t roscopy. 2.2.5 B i o e n e r g e t i c s m o d e l i n g T h e g o a l o f the b ioenerge t i c s m o d e l i n g was to c o m p a r e , a l l o the r t h i n g s b e i n g equa l , w h a t p r o p o r t i o n P of the m a x i m u m p h y s i o l o g i c a l c o n s u m p t i o n ra te a n age 0 + fish w o u l d have to use i n o rder to c o m p e n s a t e for de lays i n h a t c h i n g . I n p a r t i c u l a r , g i v e n e x p e c t e d de lays i n s p a w n i n g a n d h a t c h i n g due to coo le r wa te r i n inf lows creeks (Beamesder fer , 1992a) , I was in te res t ed i n Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow d e t e r m i n i n g w h e t h e r or n o t n o r t h e r n p i k e m i n n o w c o u l d h a t c h a n d rear to age 1 i n head -end s t r e a m s / l a k e s a n d i f so, h o w m u c h a d d i t i o n a l c o n s u m p t i o n w o u l d be needed i n o rder to m a k e u p for any de lays i n s p a w n i n g p r o d u c e d by co lder in f low creeks . I l a c k e d specif ic d a t a o n h a t c h t i m e , weight at h a t c h i n g a n d age 1 for n o r t h e r n p i k e m i n n o w , so a n u m b e r of a s s u m p t i o n s were needed.. I set the h a t c h da te (t = 0) i n the ou t f low creeks to J u l y 15. I u sed the v o n B e r t a l a n f f y g r o w t h m o d e l to p r e d i c t weight -a t -age 0 a n d 1, f r o m l eng ths ( m o d e l 4, chap- ter 3, t ab l e 3.2). I fit obse rved we igh t at l e n g t h b y fitting w = al13 to 1001 obse rva t ions of l e n g t h a n d weigh t i n the W e s t e r n d r a i n a g e . I t h e n conve r t ed p r e d i c t e d l eng ths t o we igh t s u s i n g the fit a a n d (5 va lues . I e s t i m a t e d P b y f i t t i n g the b ioenerge t i c s m o d e l to these ' obse rved we igh t s ' at age 0 a n d 1. I used the b ioene rge t i c p a r a m e t e r set for n o r t h e r n p i k e m i n n o w d e v e l o p e d by Pe te r sen a n d W a r d (1999) . I a s sumed the d ie t c o m p o s i t i o n of 0 + n o r t h e r n p i k e m i n n o w to be 100 % z o o p l a n k t o n . T h e s e p a r a m e t e r va lues are l i s t e d i n t ab le 2.2.5. T o s i m u l a t e the effects of de layed h a t c h i n g w i t h i n f l ow creek s p a w n i n g i n M o m ' s lake , I s i m p l y de l ayed s p a w n i n g by i n c r e m e n t s of one day a n d c o m p a r e d the P v a l u e i n M o m ' s lake tha t w o u l d have b e e n needed to see the ' obse rved ' size at of age 1 fish i n D a d ' s lake . I c o m p a r e d the Phead f r om the s i m u l a t i o n s to the obse rved P o f fish reared i n the n u r s e r y a r ea PnUrs- I d rove the b ioenerge t i c s m o d e l w i t h obse rved t e m p e r a t u r e s i n t e g r a t e d over the first me te r o f the wate r c o l u m n i n D a d ' s a n d M o m ' s lakes. T e m p e r - Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 22 P a r a m e t e r d e s c r i p t i o n S y m b o l V a l u e Consumption parameters A l l o m e t r i c s c a l i n g p a r a m e t e r Ac 0.278 s lope of a l l o m e t r i c mass func t i on Be -0 .197 Temperature dependent growth function t h r e s h o l d T 1 ( C ) tel 0 t h r e s h o l d T 2 ( C ) te2 20.1 t h r e s h o l d T 3 ( C ) teS 22.7 t h r e s h o l d T 4 ( C ) te4 27 p r o p o r t i o n c o n s u m e d at t h r e s h o l d t e m p 1 xkl 0.001 p r o p o r t i o n c o n s u m e d at t h r e s h o l d t e m p 2 xk2 0.98 p r o p o r t i o n c o n s u m e d at t h r e s h o l d t e m p 3 xkS 0.98 p r o p o r t i o n c o n s u m e d at t h r e s h o l d t e m p 4 xk4 0.01 Respiration Parameters In te rcep t o f a l l o m e t r i c mass func t i on for r e s p i r a t i o n Ar 0.00165 s lope o f a l l o m e t r i c mass f u n c t i o n for r e s p i r a t i o n Br -0 .085 Q l O a p p r o x i m a t i o n Cr 0.18 Coeff icent of s w i m speed to m e t a b o l i s m Dr 0.003 s lope fo the f u n c t i o n for t e m p e r a t u r e effect o n r e s p i r a t i o n ra te tau 0.105 Activity Parameters In te rcep t o f a l l o m e t r i c mass f u n c t i o n Aa 0.1 s lope o f a l l o m e t r i c mass f u n c t i o n Ba 0.149 Q l O a p p r o x i m a t i o n Ca 0.149 Diet Energy Density Z o o p l a n k t o n E n e r g y D e n s i t y E d ( J / g 0 2 ) .. Ed 2500 Egestion and Excretion P r o p o r t i o n o f c o n s u m p t i o n egested Af 0.2 P r o p o r t i o n o f ( consumpt ion-eges t ed ) Ae 0.07 Spec i f ic D y n a m i c A c t i o n SDA 0.163 T a b l e 2.2: P a r a m e t e r values used i n n o r t h e r n p i k e m i n n o w b ioenerge t i cs m o d e l f r o m Pe t e r sen a n d W a r d (1999) Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 23 a ture prof i les were t aken at m i d - d a y f r o m f i x e d s t a t i ons at two-week i n t e rva l s over the s u m m e r a n d the i n p u t t e m p e r a t u r e s for the s i m u l a t i o n s were in te - g r a t e d over the first me te r o f the wa te r c o l u m n . T h e choice of d e p t h to measure t e m p e r a t u r e was cons is ten t w i t h obse rva t ions of fry p o s i t i o n a n d those of B a r f o o t et a l . (1999) a n d G a d o m s k i et a l . (2001) s h o w i n g fry prefer- ence for s h a l l o w w a r m wate r . T e m p e r a t u r e s be tween obse rva t ions were l i nea r i n t e r p o l a t i o n s of t h e obse rved t e m p e r a t u r e . A n u m b e r of a d d i t i o n a l p a r a m e t e r a s s u m p t i o n s were needed i n o rder to c o m p l e t e l y p a r a m e t e r i z e the m o d e l . L a c k i n g d a t a o n s w i m m i n g speed of fry or any p u b l i s h e d f u n c t i o n a l r e l a t i o n s h i p , I set s w i m m i n g speeds of l a r - vae i n t e r m s of b o d y l e n g t h per second to those of the n o r t h e r n squawf i sh ' s congener the C o l o r a d o p i k e m i n n o w Ptychocheilus lucius. B a i n b r i d g e (1958) m e a s u r e d the s u s t a i n e d s w i m m i n g speed of 30, 43 a n d 52 mm T L for C o l - o r a d o p i k e m i n n o w as 4.00 b o d y leng ths p e r second . S i m i l a r speeds for l a r v a l C o l o r a d o p i k e m i n n o w were m e a s u r e d m o r e r ecen t ly b y C h i l d s a n d C l a r k s o n (1996) across a range of t empe ra tu r e s . I a s s u m e d the s w i m m i n g speed of n o r t h e r n p i k e m i n n o w 0 + fish to be the s ame as C o l o r a d o p i k e m i n n o w i n t e rms of b o d y l eng ths per second a n d used the v o n B e r t a l a n f f y p r e d i c t i o n s of l ength-a t -age (chap te r 3, t ab l e 3.2) c a l c u l a t e d over d a i l y r a the r t h a n a n n u a l t i m e steps. Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow F i g u r e 2.2: M e a n t e m p e r a t u r e i n t e g r a t e d f r o m lake surface to 1 m i n d e p t h for D a d ' s L a k e (squares) a n d M o m ' s L a k e ( d i a m o n d s ) . L i n e s represent l i nea r i n t e r p o l a t i o n s be tween obse rved t e m p e r a t u r e s Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 25 2.2.6 Lake feeding load F o l l o w i n g W a l t e r s a n d P o s t (1993) , I m e a s u r e d the effective dens i t y De of n o r t h e r n p i k e m i n n o w per hec ta re i n each lake s u m m e d across ages a as T h i s m e t r i c assumes the 'effective d e n s i t y ' (Pos t et a l . , 1999; W a l t e r s a n d P o s t , 1993) of any age class i n a s ize ' s t r u c t u r e d p r e d a t o r (or c o m p e t i t o r ) o n the p r e y p o p u l a t i o n is the p r o d u c t of two l eng th -dependen t factors : the p r e d a t o r gape size a n d s w i m m i n g speed . S u c h a m e t r i c was necessary to c o m p a r e the effective d e n s i t y of those lakes w i t h m a n y s m a l l f ish versus those w i t h fewer larger ones. S i n c e lakes differed i n p r o d u c t i v i t y , I s ca l ed E q . 2.2 to r e l a t i ve p r o d u c t i v e i n p u t s as a p p r o x i m a t e d b y m e a s u r e d m e a n seasonal c h l o r o p h y l l A i n p,gL~l, p,gChlAL~x so t h a t the s t a n d a r d i z e d effective dens i ty Ds was c a l c u l a t e d as n De oc ^ l2ha - l (2.2) n DsocJ2 l2harl[igChlA-xL. (2.3) a-l Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 26 2.3 Results 2.3.1 Spawning and Visual Surveys I obse rved large s p a w n i n g aggrega t ions i n the ou t f low creeks of C h e r y l , M o o s e P a s t u r e , T a s h a , N e s t o r a n d M o m ' s lakes over la rge cobb l e . E v e n t h o u g h s u i t a b l e cobb le a n d flow rates were ava i l ab l e i n the in f lows of C h e r y l , M o m ' s , N e s t o r a n d W i l d e r n e s s lakes , no f ish were ever obse rved or c a p t u r e d i n f i sh ing gear i n these in f low creeks . I obse rved no fish s p a w n i n g i n the ou t f l ow creek of D a d ' s L a k e a l t h o u g h the ou t f low creek of th i s lake is d a m m e d so i t w o u l d no t have been poss ib le for la rge n u m b e r s of n o r t h e r n p i k e m i n n o w f r o m D a d ' s l ake to a c t u a l l y f o r m s p a w n i n g aggrega t ions there . H a t c h i n g n o r t h e r n p i k e m i n n o w are p o o r s w i m m e r s ? ? a n d a p p a r e n t l y u n a b l e to s w i m u p s t r e a m i n t o head -end lakes f rom o u t f l o w creek s p a w n i n g areas. H e n c e the fry dr i f t d o w n s t r e a m to deve lop i n the nu r se ry lakes ( D a d ' s , M o o s e P a s t u r e ) . T h e r e were fry a n d j u v e n i l e n o r t h e r n p i k e m i n n o w o n l y i n D a d ' s , M o o s e P a s t u r e , N o r t h I s l and , T a s h a a n d E s t e l l e lakes ( F i g . 2.1) . F r y a p p e a r e d i n schools v a r y i n g be tween 5-1000 i n d i v i d u a l s a l o n g the l i t t o r a l a r ea b y ea r ly A u g u s t . T h e y prefer red the v e r y s h a l l o w m a r g i n s o f the lakes i n w a t e r gen- e r a l l y no deeper t h a n 10 cm, w i t h some p l a n t cover . S u c h schools were o n l y v i s i b l e at m i d - d a y a n d at w a r m t empera tu re s . F r y were o n l y present i n those lakes where the re was a lake u p s t r e a m w i t h n o r t h e r n p i k e m i n n o w . B o t h M o m ' s a n d C h e r y l lakes have lakes u p s t r e a m of t h e m , b u t these u p - Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 27 s t r e a m lakes have no n o r t h e r n p i k e m i n n o w . N o r t h e r n p i k e m i n n o w i n b o t h cases have no access to the u p s t r e a m lakes due to s m a l l wate r fa l l s . 2.3.2 A p p a r e n t m o r t a l i t y T h e apparen t M was s i m i l a r i n a l l lakes excep t for W i l d e r n e s s . S ince move - men t s h o u l d a p p e a r as h ighe r apparen t m o r t a l i t y , represen ted b y the s lope of the l e n g t h - c o n v e r t e d - c a t c h cu rve , p o p u l a t i o n e s t ima tes i n F i g . 2.3 showed tha t m o s t f ish m u s t m o v e before the age of 5 + . T h e r e were v e r y h i g h n u m - bers of 1-3+ age classes i n the two nur se ry lakes, a n d c o r r e s p o n d i n g l y few or none e s t i m a t e d i n the head -end lakes. If m o v e m e n t were o c c u r r i n g i n fu l ly r e c r u i t e d age classes, the appa ren t m o r t a l i t y w o u l d be s i g n i f i c a n t l y h igher i n the M o o s e P a s t u r e a n d D a d ' s lakes. 2.3.3 H y d r o g r a p h y a n d P r o d u c t i v i t y T h e t w o nur se ry lakes were b o t h more p r o d u c t i v e w i t h respect to t he i r m e a n \igChlAL~1 va lues t h a n the head-end lakes i n t he i r r e spec t ive d ra inages ( F i g . 2.4) . T h e difference is p a r t i c u l a r l y s t r i k i n g i n the case of D a d ' s lake . H e r e the m e a n c h l o r o p h y l l A was 23.59 u,gL~l c o m p a r e d to va lues of 3.29 a n d 3.41 fj,gL~l i n M o m ' s a n d N e s t o r lakes. I n the case of the eas te rn d ra inage th i s difference was m u c h s m a l l e r w i t h the nurse ry l ake ( M o o s e P a s t u r e ) h a v i n g a m e a n Chi A of 2.92 ngL~l c o m p a r e d to 2.29 a n d 2.12 i n W i l d e r n e s s a n d C h e r y l lakes respec t ive ly . T h e effective dens i t y of f ish i n the nu r se ry lakes Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 28 F i g u r e 2.3: M a x i m u m l i k e l i h o o d es t ima tes o f n u m b e r s at each l e n g t h c o n - v e r t e d age. T h e pas t ed t e x t is the s lope o f the fit l i ne t h r o u g h the l o g n u m b e r s at age ( log N a ) r ep re sen t ing the appa ren t m o r - t a l i t y o f fu l ly r e c r u i t e d ages (5+) Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 29 < JZ O o o oo o c\i "i 1 r Jul Aug Sep Oct Date F i g u r e 2.4: C h l o r o p h y l l A ( / / g C / i M L - 1 ) m e a s u r e m e n t s over t i m e . T o p p a n e l is W e s t e r n d ra inage : D a d ' s L a k e (squares) , M o m ' s L a k e (d i a - m o n d s ) a n d N e s t o r L a k e ( t r i ang les ) . B o t t o m p a n e l is E a s t e r n d ra inage : M o o s e P a s t u r e (squares) , C h e r y l L a k e ( d i a m o n d s ) a n d W i l d e r n e s s L a k e ( t r i ang les ) . Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow is c o r r e s p o n d i n g l y ve ry h i g h ( F i g . 2.5 t o p pane l ) . So w h i l e the p r o d u c t i v i t y of the nurse ry lakes is h ighe r t h a n the head -end lakes ( F i g . 2.4), once i t is p a r t i t i o n e d a m o n g the greater n u m b e r of m o u t h s i n D a d ' s a n d M o o s e P a s t u r e , these lakes are o n p a r o r ( i n the case of D a d ' s ) , have even h igher Dc t h a t the headwate r lakes ( F i g . 2.5 b o t t o m ) . T h e nurse ry lakes also have a greater p r o p o r t i o n of s h a l l o w l i t t o r a f area , the prefer red h a b i t a t of the n o r t h e r n p i k e m i n n o w juven i l e s . G r e a t e r t h a n 60 % of the c u m u l a t i v e a rea of D a d ' s a n d M o o s e P a s t u r e lakes is i n w a t e r be tween 0 a n d 3 m (figure 2.6) . 2.3.4 Bioenergetics predictions T h e m o d e l showed t h a t i t was p h y s i o l o g i c a l l y poss ib le for f i sh to h a t c h as m a n y as 50 days after the nu r se ry h a t c h da te a n d s t i l l be the s ame size the one year la ter . I n order to d o so however , very large increases i n Phead were needed ( F i g . 2.9 top ) . I n t e rp re t ed i n a b e h a v i o r a l sense, those f ish h a t c h e d i n in f low creeks w o u l d have to s p e n d m o r e t i m e feeding r e l a t i ve t o those h a t c h e d ear l ie r i n ou t f lows ( F i g . 2.9 b o t t o m ) i n o rder to be the s ame size one year l a t e r a n d m o s t of t ha t feeding w o u l d have to t ake p lace before w i n t e r ( F i g . 2.7). Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 31 F i g u r e 2.5: Ef fec t ive dens i t y per hec tare as represen ted b y the s u m of squa red fish l eng ths l 2ha~ l ( top) Effec t ive d e n s i t y pe r hec tare per figChlAL -1 as represented b y the s u m of s q u a r e d f ish lengths per hec ta re Z 2 / i a _ 1 d i v i d e d by m e a n ChlA (figL~ l for D a d ' s (d) , M o o s e P a s t u r e (p) , M o m ' s ( m ) , C h e r y l (c) , N e s t o r (n) a n d W i l d e r n e s s (w) lakes Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow Depth contour F i g u r e 2.6: P r o p o r t i o n of the t o t a l lake a rea b y d e p t h c o n t o u r , D a d ' s o p e n c i rc les , M o m ' s o p e n squares, N e s t o r , o p e n d i a m o n d s , M o o s e P a s - tu re c losed c i rc les , C h e r y l c losed squares , W i l d e r n e s s c losed d i a - m o n d s Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 33 0 1 0 0 2 0 0 3 0 0 D a y o f H a t c h i n g F i g u r e 2.7: P r e d i c t e d weights ( in g rams) of fit b ioenerge t i c s m o d e l to ob- served we igh t at age i n the nu r se ry a rea (open c i rc les , P = 0.14) a n d the p r e d i c t e d we igh t at age of a f i sh h a t c h e d 15 days la te r i n the h e a d l ake (so l id l ine , P — 0.18) Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 34 50 100 150 2 0 0 250 Fork Length (mm) F i g u r e 2,8: F i t w e i g h t - l e n g t h r e l a t i o n s h i p of n o r t h e r n p i k e m i n n o w we igh t as a f u n c t i o n of l e n g t h . Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 35 F i g u r e 2.9: P r e d i c t e d p r o p o r t i o n of m a x i m u m c o n s u m p t i o n ra te Phead ( top) r e q u i r e d to reach obse rved size at age 1 a n d Phead/Pnursery (bo t - t o m ) vs . de lays i n h e a d w a t e r l ake h a t c h date . Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 36 2.4 Discussion I s h o w tha t fish unde rgo large-scale on togene t i c shif ts be tween lakes . N o fry were ever obse rved i n n o n - n u r s e r y lakes. I n a d d i t i o n , the differences i n the age s t ruc tu res of the nu r se ry lakes a n d h e a d e n d lakes i n d i c a t e m i g r a t i o n occu r s be tween the ages o f 1 a n d 5 + . T h e o n l y d i s t i n c t i v e feature of the nur se ry lakes is the presence of a l ake c o n t a i n i n g n o r t h e r n p i k e m i n n o w above i t . N o t e t ha t b o t h C h e r y l a n d M o m ' s lake have lakes i n the d r a i n a g e above t h e m ( F i g . 2.1), b u t ne i the r of these has n o r t h e r n p i k e m i n n o w . T h i s p a t t e r n h o l d s at a r easonab ly la rge scale a n d i n two r ive r d ra inages . T h e r a t i o of effective d e n s i t y to ChlAL~x as a n i n d e x of the r e l a t i ve p r o - d u c t i v i t y o f the lakes is ve ry i m p o r t a n t for d e t e r m i n i n g the d i s t r i b u t i o n of the adu l t s . A n y advan tage of the a d d i t i o n a l p r o d u c t i v i t y of D a d ' s L a k e or M o o s e P a s t u r e is e l i m i n a t e d b y the v e r y h i g h d e n s i t y of n o r t h e r n p i k e m i n n o w there . D a d ' s L a k e is a p p a r e n t l y m u c h m o r e p r o d u c t i v e t h a n any of the o ther lakes b u t the benefits of such h i g h p r o d u c t i v i t y are c o m p l e t e l y n e u t r a l i z e d by the h igher dens i t y of fish there . W h i l e M o o s e P a s t u r e L a k e was no t s i g n i f i c a n t l y m o r e p r o d u c t i v e t h a n any of the headwa te r lakes , t he r a t i o o f l2ha"1pJgChlA~1L makes t h a t l ake a m u c h worse lake to rear i n t h a n those head -end lakes near i t . C o n t r a r y t o the s i t u a t i o n w i t h D a d ' s , t he lakes above M o o s e P a s t u r e are a c t u a l l y larger a n d s u p p o r t m o r e a d u l t fish, so t h a t re la - t ive t o i t s size a n d p r o d u c t i v i t y , M o o s e P a s t u r e receives m a n y m o r e fry t h a n D a d ' s does. Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 37 T h e b ioenerge t ics m o d e l i n g shows the m o s t l i k e l y reason for the s p a t i a l d i s t r i b u t i o n of fry is t e m p e r a t u r e dependen t s p a w n i n g b e h a v i o r , r a the r t h a n p r o d u c t i v i t y a n d h y d r o g r a p h i c differences be tween the lakes . W h i l e I d i d not have s t r e a m t e m p e r a t u r e d a t a to s u p p o r t th i s a r g u m e n t d i r e c t l y , i t is reason- able to assume tha t the in f low creeks t e m p e r a t u r e to be a p p r o x i m a t e l y the same as the m e a n a n n u a l a i r t e m p e r a t u r e (2-5 C ) for th i s M o n t a n e S p r u c e b i o g e o c l i m a t i c Z o n e (?) a n d the ou t f low creek t e m p e r a t u r e to be the same as the lake t e m p e r a t u r e . If the p r o p o r t i o n of the m a x i m u m c o n s u m p t i o n ra te is i n t e rp re t ed i n a b e h a v i o r a l sense (a h igher p r o p o r t i o n o f the m a x i - m u m c o n s u m p t i o n ra te is equ iva l en t to greater t i m e spen t i n r i s k y fo rag ing b e h a v i o r i n s t ead of h i d i n g a n d g r o w i n g ) t h e n de lays i n s p a w n i n g are p a i d for by i nc rea s ing p r e d a t i o n r i sk . A de lay of 25 days co r r e sponds to d o u b l i n g th i s r i sk . N a t u r a l se l ec t ion p r e d i c t s s t r o n g se lec t ion aga ins t such inc reased r i sk t a k i n g . F u r t h e r m o r e , the resul t s are o p t i m i s t i c p r e d i c t i o n s of g r o w t h a n d s p a w n i n g p o t e n t i a l i n the head -end sys tems . Inf low creeks go d r y i n l o w r a i n / s n o w years by the e n d of J u l y . So w h i l e i t m i g h t be pos s ib l e to rear i n a head -end lake a n d s t i l l r each the same size as i n a nu r se ry l ake as l a te as fifty days after s p a w n i n g i n a n ou t f l ow creek, there m a y be no in f low creek left to h a t c h / e m e r g e f r o m . T h e b ioenerge t ics p r e d i c t i o n s s h o u l d be v i e w e d w i t h cons ide rab l e c a u t i o n . T h e s e p r e d i c t i o n s d e p e n d o n t w o a s s u m p t i o n s not t es ted a n d l i k e l y i nco r r ec t . T h e Pe t e r sen a n d W a r d (1999) p a r a m e t e r values c o m e f r o m a d u l t f ish i n the C o l u m b i a r ive r s y s t e m . F i s h i n the s t u d y s y s t e m are v e r y different to those Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 38 i n the C o l u m b i a . T h e fish i n th i s s t u d y s y s t e m are m u c h sma l l e r t h a n i n the C o l u m b i a , r e a c h i n g a s y m p t o t i c l eng ths of 200 m m , c o m p a r e d to the m a x i m u m size of 350 m m + observed i n the C o l u m b i a . W h e t h e r or no t these differences are the resu l t of p h e n o t y p i c p l a s t i c i t y or gene t ic differences is no t k n o w n . L o c a l p h y s i o l o g i c a l a d a p t a t i o n s have been s h o w n to m a k e la rge difference i n the b ioenerge t i cs pa rame te r s ( M u n c h a n d C o n o v e r , 2002) . Second ly , the p r e d i c t i o n s r e ly o n the a s s u m p t i o n t h a t the pa rame te r s are s i m i l a r be tween a d u l t s a n d juven i l e s w h i c h is a lso i nco r r ec t (Pos t , 1990). T h a t s a id , the p u r p o s e of the m o d e l i n g exercise was to d e t e r m i n e h o w m u c h a d d i t i o n c o n s u m p t i o n w o u l d be r equ i r ed i n o rder to c o m p e n s a t e for la te r s p a w n i n g . T h e t e m p e r a t u r e profi les i n each lake were a l m o s t i d e n t i c a l so any biases i n P p r o d u c e d by incor rec t p a r a m e t r i z a t i o n w o u l d be cons is ten t be tween nur se ry a n d h e a d areas so the c o m p a r i s o n b e t w e e n the t w o is s t i l l l e g i t i m a t e . T h e n u m b e r of g r o w i n g degree days seems to l i m i t the n o r t h e r n d i s t r i b u - t i o n of p e r c h a n d bass species (Schuter a n d P o s t , 1990) . N o r t h e r p i k e m i n n o w fry i n the s t u d y a rea l i k e l y face a s i m i l a r g r o w t h s u r v i v a l t rade-off to t h a t obse rved i n r a i n b o w t r o u t s tud ies 200 k m S o u t h of the s t u d y area. P o s t a n d P a r k i n s o n (2001) s h o w r a i n b o w t rou t i n s m a l l B . C . lakes face a t radeoff be tween a l l o c a t i n g energy to s o m a t i c g r o w t h or to l i p i d s . E n e r g y a l l o c a t e d to s o m a t i c g r o w t h i m p r o v e s fitness of la rger i n d i v i d u a l s b y r e d u c i n g size- dependen t p r e d a t i o n r i s k b u t at the expense of lower w i n t e r s u r v i v a l . P o s t a n d P a r k i n s o n (2001) s h o w e d t h a t once f ish r each a s ize la rge e n o u g h to Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 39 reduce the i r p r e d a t i o n r i sk , t hey a l loca te resources t o l i p i d stores for w i n - ter s u r v i v a l r a t he r t h a n to s o m a t i c g r o w t h . F o r b o t h r e d u c i n g p r e d a t i o n a n d for s t o r i n g l i p i d s to s u r v i v e w i n t e r ea r ly h a t c h i n g is c r i t i c a l for n o r t h e r n p i k e m i n n o w . T h e s p a t i a l o r g a n i z a t i o n of these s tocks of n o r t h e r n p i k e m i n n o w is s i m i l a r to t h a t obse rved i n r i ve r sys tems w i t h respect to the h a b i t a t preference for r e a r i ng areas. G a d o m s k i et a l . (2001) d e s c r i b e d a m o d e l o f ea r ly life h i s t o r y i n the C o l u m b i a R i v e r . I n i t , adu l t s s p a w n i n t r i b u t a r i e s at 18-20 C , p l a n k t o n i c la rvae dr i f t i n t o the m a i n s t e m a n d t h e n rear i n b a c k w a t e r s w i t h fine s ed imen t or s a n d subs t ra tes . O u r obse rva t ions are i d e n t i c a l , excep t t h a t the prefer red areas for r e a r i n g are en t i re lakes, no t r ive r b a c k w a t e r s . H o w u n i t s t ocks are def ined s p a t i a l l y needs c loser e x a m i n a t i o n i n l acus- t r ine sys tems , e s p e c i a l l y where lakes are no t i s o l a t e d f r o m each o ther . T h e o r y p red ic t s on togene t i c m o v e m e n t s h o u l d be w i d e s p r e a d i n s i z e - s t r u c t u r e d p o p - u la t i ons . I n a d d i t i o n , there are b o t h exce l len t t h e o r e t i c a l a n d f ie ld e x a m p l e s of i t i n f ish p o p u l a t i o n s . I n response to different resources g rad ien t s , shif ts o c c u r p a r t i c u l a r l y i n s i t u a t i o n s where adu l t s present a p r e d a t i o n r i sk to j u v e - ni les (Pe r s son a n d G r e e n b e r g , 1990; G o w e n et a l . , 1994; de R o o s et a l . , 2002) . H o w e v e r the scale of s u c h m o d e l i n g a n d f ie ld s tud ies t ends to be s m a l l , t h a t is, w i t h i n lakes . I n the s t u d y sys tems there are p r o d u c t i v i t y (ChlA) a n d t e m p e r a t u r e g r ad i en t s be tween uppe r e n d a n d n u r s e r y lakes. W a t e r s h e d sys- tems i n genera l have s u c h g rad ien t s on larger ( m u l t i - l a k e ) scales ( G o m i et a l . , 2002) , a n d i n m y wa te r sheds fish s h o u l d have no d i f f i cu l ty d i s t r i b u t i n g t h e m - Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 40 selves a t s u c h scales, p r o v i d e d s t r eams are seasona l ly adequa te to p e r m i t m o v e m e n t . E x a m p l e s of fish m o v e m e n t at l a rger scale are a p p e a r i n g i n the l i t e r a t u r e . N a s l u n d (1990) showed s p e c t a c u l a r dens i t y -dependen t m i g r a t i o n s be tween lakes of a r c t i c char . M o v e m e n t f r o m s t r eams to lakes has a lso been obse rved ( O l s s o n a n d G r e e n b e r g , 2004) . C o n t r a r y to the " re s t r i c t ed move - m e n t p a r a d i g m " ( G e r k i n g 1959), there is an i n c r e a s i n g n u m b e r of e x a m p l e s where m o v e m e n t i n s t r eams is s ign i f ican t ( G o w e n et a l . , 1994) a n d references the re in ) a n d m a n y example s s u p p o s e d l y c o n f i r m i n g the r e s t r i c t e d m o v e m e n t p a r a d i g m use m e t h o d s b i a sed aga ins t d e t e c t i n g any such m o v e m e n t ( G o w e n et a l . , 1994) . J u v e n i l e f ish l i v i n g i n seasonal e n v i r o n m e n t s have to choose l i f e -h i s to ry s t ra tegies t h a t a l l o w t h e m m a x i m i z e t he i r g r o w t h advan tage w h i l e n o t ex- p o s i n g themse lves to s ign i f ican t p r e d a t i o n i n o rder to do so. I s h o w here tha t i n a d d i t i o n to s o l v i n g the s m a l l s p a c e / t i m e scale p r o b l e m o f b a l a n c i n g g r o w t h w i t h p r e d a t i o n r i sk , n o r t h e r n p i k e m i n n o w m u s t a lso solve a la rger s p a c e / t i m e scale p r o b l e m of c h o o s i n g l i f e -h i s to ry s t ra tegies t h a t are p h y s - i o l o g i c a l l y favorab le , i n t e rms of a l l o w i n g for the greatest a m o u n t of t i m e to g row. S i n c e there are large scale g rad ien t s i n p r o d u c t i v i t y a n d t e m p e r a - tu re b e t w e e n lakes , a n d i n m a n y cases r e l a t i v e l y s i m p l e connec t i ons be tween t h e m , the a p p l i e d i m p l i c a t i o n is t ha t the i n i t i a l su rvey effort i n l a c r u s t i n e sys t ems s h o u l d be d i s t r i b u t e d w i d e l y before a s s u m i n g tha t lakes cons i s t o f i n d i v i d u a l s tocks . W e t y p i c a l l y assume t h a t on togene t ic l i f e -h i s to ry m o v e m e n t s are s h a p e d Chapter 2. Ontogenetic Habitat Shifts Between Lakes by the Pygmy Pikeminnow 41 b y se lec t ions o n a va r i e ty of p h e n o l o g i c a l ( t i m i n g ) , b ioenerge t i c , a n d be- h a v i o r a l t r a i t s so as to m a x i m i z e fi tness g i v e n l o c a l e n v i r o n m e n t a l c o n d i - t ions . B u t i n the s t u n t e d p i k e m i n n o w case, we m a y s i m p l y be seeing t w o key p r e a d a p t a t i o n s , a m i n i m u m t e m p e r a t u r e for s p a w n i n g , a n d a t e n d e n c y to d i sperse u p s t r e a m f rom c r o w d e d areas. J u s t the m i n i m u m t e m p e r a t u r e t r a i t w o u l d l ead to avo idance of in f low s p a w n i n g i n headwa te r lakes a n d hence t o d o w n s t r e a m fry d i spe r sa l . A l l t ha t w o u l d be needed for the obse rved d r a i n a g e w i d e o r g a n i z a t i o n is u p s t r e a m r e t u r n la ter ' i n l ife. 2.5 Appendix age 0 4 - J u l 3 1 - J u l 0 1 - A u g 1 0 - A u g 1 3 - A u g 2 1 - A u g 2 2 - A u g 2 8 - A u g 06-Sep 10-Sep 17-Sep 25-Sep 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 27 25 0 0 0 39 0 0 0 0 3 0 0 64 85 0 0 0 191 0 0 0 0 4 0 0 8 49 0 0 0 8 0 0 0 0 5 70 0 25 69 0 0 0 9 0 0 0 0 6 90  22 41 0 0 0 3 0 0 0 0 7 51 0 11 26 0 0 0 2 0 0 0 0 8 29 0 5 11 0 0 0 0 0 0 0 0 9 25 0 0 13 n 0 0 2 0 0 0 0 10 23 0 1 6 0 0 0 2 0 0 0 0 11 14 0 0 7 0 0 0 0 0 0 0 0 12 10 0 0 5 0 0 0 1 0 0 0 0 13 5 0 0 5 0 0 0 0 0 0 0 0 14 3 0 0 2 0 0 0 0 0 0 0 0 15 7 0 0 6 0 0 0 0 0 0 0 0 16 + 24 0 1 15 0 0 0 1 1 0 0 K i l l e d 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 U 0 0 0 0 0 0 0 0 a 0 0 0 0 0 0 0 0 2 0 0 0 4 0 0 0 0 0 0 0 0 3 0 0 0 5 0 2 0 0 0 0 0 0 . 1 0 0 0 G 0 2 0 0 0 0 u 0 4 0 0 0 7 0 2 0 0 0 u 0 0 2 0 0 0 8 1 3 0 0 0 0 0 0 0 0 0 0 U 1 1 u 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 1 0 0 0 1 0 2  0 0 0 0 0 0 0 0 0 12 0 1 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 0 0 14 0 1 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 10+ 0 0 0 0 0 0 0 0 0 0 0 0 R e c a p t u r e d 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 3 0    0 0 0 4 4 0 0 0 4 0 0 0 0 0 0 0 0 5 0 1 0 5 0 1 0 5 0 0 0 2 13 1 • 0 1 6 0  0 4 0 0 0 0 15 0 0 2 7 0 1 0 4 0 0 0 0 7 0 0 0 8 0 1 1 2 1 0 0 0 11 0 0 1 9 0 1 0 0 0 0 0 1 5 0 0 0 10 0 0 0 5 0 0 0 0 3 0 0 0 11 0 1 0 0 n 0 1 0 4 0 0 0 12 0 1 0 0 0 0 0 0 3 0 0 0 13 0 0 0 0 0 1 0 0 1 0 0 0 14 0 1 0 2 0 0 0 0 1 0 0 0 15 0 0 0 1 0 0 0 0 2 0 0 0 10 + 0 0 0 1 0 2 0 0 17 0 0 0 U n m a r k e d 1 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 27 25 0 0 0 53 27 0 0 1 3 0 0 05 103 0 0 0 218 374 0 0 22 4 2 0 8 93 0 0 0 9 150 0 0 4 5 74 50 25 163 0 16 0 9 235 u 10 18 0 98 10G 22 109 0 12 0 3 176 0 23 13 7 51 55 11 56 0 2 0 2 59 0 2 11 8 31 31 5 28 0 1 0 0 26 0 0 8 9 27 29 0 29 0 0 0 2 10 0 2 5 10 24 13 1 15 0 1 0 2 12 0 0 6 1 10 9 0 13 0 0 0 0 7 0 0 0 12 10 9 0 10 0 0 0 1 5 0 0 5 13 5 2 0 9 0 0 0 0 3 0 0 2 14 5 0 0 4 0 0 0 0 2 0 0 0 15 8 4 0 7 0 0 0 0 3 0 1 2 10+ 33 27 1 26 0 0 0 1 14 0 2 13 Q I 4^ t o T a b l e 2.3: T a b l e of fish m a r k e d , m a r k e d fish k i l l e d d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d b y da te a n d l eng th -conve r t ed age i n D a d ' s lake . age 2 0 - J u n 2 6 - J u n 3 0 - J u l 3 1 - J u l 1 2 - A u g 2 2 - A u g 2 7 - A u g 08-Sep 23-Sep 2 1 0 0 0 0 0 4 0 0 3 7 0 0 0 10 0 18 0 0 4 15 12 0 0 3 0 0 0 0 5 8 30 0 0 1 0 1 0 0 0 5 12 0 0 0 0 0 0 0 7 3 8 0 0 1 0 0 0 0 S 8 0 0 0 0 0 1 u 0 i) 5 0 0 0 0 0 0 0 0 10 1 2 0 0 0 0 0 0 0 11 1 4 0 0 0 0 0 0 0 12 1 1 0 0 0 0 0 0 0 13 1 3 I) 0 0 0 0 0 0 14 0 1 0 0 0 u 1 0 0 15 0 1 I) 0 0 0 0 0 0 10 + 4 a •"' 0 0 0 u 0 0 l e c a p t u r e d 2 U 0 0 0 0 0 0 0 0 3 0 2 0 0 0 0 1 10 0 4 0 0 1 u 0 0 0 0 0 5 0 7 2 0 0 0 0 4 0 0 0 3 3 0 1 1 0 12 0 7 0 4 0 0 1 1 u 15 0 8 0 8 0 0 0 0 u 8 0 9 0 5 0 0 0 4 0 1 0 10 0 2 0 0 0 1 0 2 0 11 0 3 0 1 0 1 0 1 0 12 0 0 0 0 1 0 0 1 0 13 0 4 2 7 2 6 0 2 0 14 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 10 + 0 1 0 0 0 0 0 0 0 U n m a r k e d 2 1 0 0 0 0 0- 4 0 0 3 7 1 0 0 10 0 18 3 0 4 17 13 0 0 3 0 0 0 0 5 9 39 5 0 1 0 1 1 1 G 5 13 G 0 0 0 0 1 8 7 3 10 U 0 1 1 0 1 1 8 8 0 0 0 0 2 1 0 2 D 5 G 0 1 0 0 0 0 2 10 1 3 1 0 0 0 0 0 0 11 1 4 1) 0 0 0 0 0 0 12 1 1 0 1 0 0 0 0 0 13 1 3 0 0 0 0 0 0 0 14 0 1 0 0 0 0 1 0 0 lo 0 1 0 0 0 0 0 0 0 10 + 4 13 1 2 u 1 0 30 1 Q T a b l e 2.4: T a b l e of fish m a r k e d , m a r k e d fish k i l l e d d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d b y da te a n d l eng th - conve r t ed age for J u l y , A u g u s t a n d Sep tember 2002 i n M o m ' s lake. o 4^ CO M a r k i n g age 2 6 - J u n 0 6 - J u l 1 4 - J u l 1 5 - J u l 2 3 - J u l 2 4 - J u l 2 5 - J u l 2 6 - J u l 2 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 4 14 8 0 0 0 0 0 0 5 44 50 1 11 0 0 0 0 (i 36 52 0 13 1 0 0 0 7 25 44 1 3 0 0 0 1 8 1 9 35 2 I 0 u 0 1 9 10 27 0 0 0 0 0 0 10 9 13 0 0 0 0 0 0 11 8 12 0 0 0 0 0 0 12 2 9 0 0 0 0 0 1 13 2 5 0 0 0 0 0 0 14 3 6 0 0 0 0 0 0 15 0 2 0 0 0 0 0 0 16 + 5 10 0 1 0 0 0 1 K i l l e d 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 0 0 1 0 0 0 0 5 0 0 0 1 3 0 0 0 6 0 0 0 0 2 2 0 1 7 0 0 0 2 10 6 3 2 8 0 0 0 0 15 6 3 1 9 0 0 0 0 14 0 0 1 10 0 0 0 0 13 6 2 1 11 0 0 0 0 12 8 0 1 12 0 0 0 0 3 2 0 1 13 0 0 0 0 5 2 0 0 14 0 0 0 0 2 0 2 1 15 0 0 0 0 2 0 0 1 10+ 0 0 0 0 4 0 0 0 R e c a p t u r e d 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 0 0 1 0 0 0 0 5 4 8 0 1 2 0 0 0 0 6 6 0 3 4 0 0 0 7 1 4 2 2 2 4 2 1 S 0 4 0 2 10 4 2 2 9 0 3 1 1 14 4 2 0 10 2 7 0 0 16 2 0 1 11 0 4 1 0 12 2 2 2 12 0 2 0 0 4 0 0 0 13 0 1 0 0 16 8 0 0 14 0 2 0 0 2 4 0 0 15 0 0 0 0 4 2 2 1 16 + 0 1 0 0 16 10 2 5 U n m a r k e d 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 4 14 8 0 3 0 0 0 0 5 44 52 3 26 2 0 4 0 6 36 52 7 33 18 4 6 1 7 25 44 1 6 50 12 3 3 8 19 35 3 3 58 2 9 5 9 10 27 0 1 14 4 0 0 10 9 13 0 0 16 12 0 1 11 8 12 3 0 14 0 2 2 12 2 9 0 0 6 4 2 3 13 2 5 0 0 4 0 0 0 14 3 0 0 0 6 0 0 0 15 0 2 0 0 0 0 1 1 10 + 5 11 0 1 10 10 2 4 T a b l e 2.5: T a b l e of f ish m a r k e d , m a r k e d fish k i l l e d d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d f rom J u n e to A u g u s t 2002 b y l eng th -conve r t ed age i n N e s t o r lake . M a r k i n g age O l - A u g 1 2 - A u g 1 3 - A u g 2 0 - A u g 2 1 - A u g 2 2 - A u g 2 3 - A u g 2 7 - A u g 07-Sep 18-Sep 24-Sep 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 3 0 0 0 0 0 0 ' 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 K i l l e d 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 O D O O 1 0 0 0 0 5 0 1 0 0 0 0 2 3 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 7 1 1 0 0 0 0 1 0 0 0 0 14 2 0 0 0 0 0 0 0 0 0 0 5 1 0 o - o 0 0 0 0 0 0 0 G O 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1G+ 0 0 0 1 0 0 0 0 0 0 0 R e c a p t u r e d 2 0 0 0 0 0 0 , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 0 0 0 0 1 1 2 1 3 0 0 ()' 0 0 2 1 3 0 7 0 1 0 0 . 0 . 0 0 G 0 1 0 4 0 5 2 2 1 0 0 4 0 3 1 1 1 1 1 2 0 0 0 3 0 0 0 2 0 1 3 1 1 0 0 1 0 2 0 0 0 2 11 0 1 0 0 0 1 0 0 0 0 2 8 2 0 0 0 0 0 0 0 0 0 0 G 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 5 0 0 0 0 0 0 0 0 0 0 0 1 0 . 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 U n m a r k e d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 3 0 1 0 13 0 9 0 1 0 0 0 9 0 4 0 15 0 18 4 3 1 - 2 1 10 1 15 0 12 0 15 7 9 3 5 0 13 3 28 0 3 0 7 14 14 0 9 1 9 1 6 0 1 0 4 12 4 0 8 0 5 1 1 0 0 0 1 20 3 0 4 0 1 0 2 0 1 0 0 14 0 0 4 0 0 0 0 0 0 0 2 5 1 1 1 0 0 0 0 0 0 0 0 5 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 Q I 0 0 1 0 0 0 0 0 0 0 jljj T a b l e 2.6: T a b l e of fish m a r k e d , m a r k e d fish k i l l e d d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d f rom to S e p t e m b e r 2002 b y l eng th -conver t ed age i n N e s t o r lake. A u g u s t M a r k i n g 0 4 - J u n 1 8 - J u n 2 7 - J u n 0 8 - J u l 1 0 - J u l 0 2 - A u g 0 7 - A u g 0 8 - A u g 1 6 - A u g 1 8 - A u g 1 9 - A u g 2 2 - A u g 1 0 0 0 0 6 1 0 4 0 0 0 1 2 3 0 0 4 3 2 8 145 0 19 142 47 3 3 3 4 0 1 0 85 28 0 9 31 10 4 0 32 2 1 0 0 71 12 0 1 26 23 5 0 14 2 0 0 0 13 4 0 0 19 0 6 0 16 3 0 0 0 8 2 0 0 8 n 7 0 17 1 0 1 0 4 2 0 0 6 0 8 0 21 0 0 0 1 10 0 0 0 9 0 9 0 13 1 0 0 0 2 0 0 0 4 4 10 0 7 2 0 0 n 4 0 0 0 1 5 11 0 5 0 0 0 0 1 0 0 0 0 0 12 0 1 0 0 0 0 2 0 0 0 0 0 13 0 4 0 0 0 0 2 0 0 0 0 0 14 0 2 0 0 0 0 1 0 0 0 1 0 15 0 1 0 0 0 0. 1 0 0 0 0 0 16 + 0 12 1 0 0 0 10 0 0 1 1 1 K i l l e d or R e m o v e d 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 • 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 ' 0 0 0 0 0 0 0 0 0 0 0 0 n 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 - 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 u 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 u 0 15 0 0 0 0 0 0 0 0 0 0 0 0 16 + 0 0 0 0 0 0 0 0 0 0 0 0 ures 1 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 2 ' 0 0 1 0 0 1 8 3 0 0 0 0 0 0 2 1 0 0 9 8 4 0 0 0 0 0 0 3 1 0 0 10 17 5 0 0 0 0 0 0' 1 0 0 0 4 6 6 0 0 0 0 0 0 3 0 0 0 3 5 7 0 0 0 0 0 0 3 0 0 0 2 0 8 0 0 0 0 0 0 3 0 0 0 f> 11 9 0 0 0 0 0 0 3 1 0 0 3 13 10 0 0 0 0 0 0 2 1 0 0 2 5 11 0 0 0 0 0 0 4 0 0 0 1 4 12 0 0 0 0 0 0 3 0 0 0 1 5 13 0 0 0 0 0 0 0 0 0 0 0 1 14 0 0 0 0 0 0 3 0 0 0 0 4 15 0 0 0 0 0 0 1 0 0 0 0 4 10+ 0 0 0 0 0 0 5 0 0 0 3 10 rked 1 19 0 0 1 7 3' 0 4 7 0 0 10 2 7 0 0 4 3 2 14 148 0 24 147 509 3 3 0 4 0 1 0 190 28 0 2 51 50 4 0 33 2 1 0 0,., • 200 12 0 1 52 50 5 0 16 2 0 0 0 42 4 0 0 28 12 C 0 16 3 0 0 0 28 2 0 0 11 0 7 0 17 1 0 1 0 19 2 0 0 6 5 8 0 21 1 0 0 • 1 20 0 ' 0 0 9 10 9 0 13 1 0 0 0 10 0 0 0 5 4 10 0 8 2 0 0 0 10 0 0 0 1 8 11 u 5 0 0 0 0 7 0 0 0 2 4 12 0 1 0 0 0 0 3 0 0 0 0 2 13 0 4 0 0 0 0 6 0 0 0 0 3 14 0 2 0 0 0 0 3 0 0 0 1 3 15 0 1 0 0 0 0 2 0 0 0 0 0 16+ 0 12 1 0 0 0 19 1 0 1 4 17 T a b l e 2.7: T a b l e of f ish m a r k e d , m a r k e d fish k i l l e d d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d b y l e n g t h c o n v e r t e d age f rom J u n e to A u g u s t 22 2002 i n M o o s e P a s t u r e L a k e . M a r k i n g 2 3 - A u g 2 5 - A u g 09-Sep 10-Sep 11-Sep 13-Sep 14-Sep 15-Sep 16-Sep 27-Sep 1 1 0 0 0 0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 20 3 0 0 0 0 1 0 0 0 0 0 4 0 0 0 0 ' 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 9 0 0 1 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 16 + 0 . 0 0 0 0 0 0 0 0 0 or R e m o v e d 1 0 0 0 0 0 0 0 0 0 0 2 0 0 7 6 3 18 1 1 0 1 3 0 0 113 17 10 31 0 1 0 0 4 0 0 134 13 5 15 0 0 0 0 5 0 2 25 9 4 6 0 0 0 0 6 0 0 23 4 3 3 0 0 0 0 7 0 0 9 4 3 4 0 0 0 0 8 0 0 19 6 11 8 0 0 0 1 9 0 0 12 6 7 1 1 0 0 0 10 0 1 3 5 2 5 0 0 0 0 11 0 0 2 3 3 0 0 0 0 0 12 0 0 1 1 1 1 0 0 0 0 13 0 0 0 1 2 0 0 0 0 0 14 0 0 0 2 2 0. 0 0 0 0 15 0 0 1 1 0 0 0 0 0 0 16 + 0 0 0 5 4 0 0 0 0 0 R e c a p t u r e s 1 0 0 0 0 0 0 0 0 0 0 2 3 0 0 6 3 23 7 6 0 5 3 0 0 56 17 15 28 2 3 0 1 4 0 0 71 13 5 16 1 1 0 0 5 0 2 13 9 3 7 0 0 0 0 6 0 0 12 4 1 3 0 0 0 0 7 0 0 4 ' 4 • 3 5 0 0 0 1 8 0 0 7 6 6 5 0 0 0 0 9 0 0 9 6 4 2 0 0 0 1 10 0 1 2 5 1 5 1 0 0 0 11 0 0 1 3 2 1 0 0 0 0 12 0 0 1 1 1 0 0 0 0 0 13 0 0 0 1 1 1 0 0 0 0 14 0 0 0 2 0 0 0 0 0 0 15 0 0 0 1 0 0 0 0 0 0 16 + 0 0 5 5 4 6 0 0 0 1 U n m a r k e d 1 3 0 0 6 11 38 11 3 26 11 2 20 0 26 42 178 725 425 67 54 40 3 1 0 258 43 81 131 34 7 5 0 4 1 0 143 25 20 46 6 2 0 0 5 2 1 27 6 8 10 1 0 0 0 6 0 0 15 6 4 4 0 0 0 0 7 0 0 8 5 •i 4 1 0 0 0 8 0 0 6 3 0 0 0 0 0 0 9 0 0 1 0 0 0 1 0 0 0 10 0 0 0 0 1 1 1 0 0 0 11 0 0 0 0 0 1 0 0 0 0 12 0 0 0 4 0 1 0 0 0 0 13 0 0 1 0 2 0 0 0 0 0 14 0 0 0 2 1 0 0 0 0 0 15 0 0 1 1 1 2 0 0 0 0 16 + 0 1 12 4 4 5 0 2 0 0 o T a b l e 2.8: T a b l e of fish m a r k e d , m a r k e d fish k i l l e d or r emoved d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d b y l e n g t h conve r t ed age for A u g u s t 23 to Sep tember 2002 i n M o o s e P a s t u r e L a k e . M a r k i n g age 1 9 - J u n 2 5 - J u n 2 6 - J u n or- jui 0 9 - A u g 2 3 - A u g 2 5 - A u g OS-Sep 16-Sep 26-Sep 1 3 0 0 l 0 0 0 0 0 0 2 0 0 0 4 0 0 109 0 0 0 3 0 0 30 1 31 0 74 0 0 0 4 0 1 00 0 57 0 27 0 0 0 5 0 1 13 0 20 9 7 0 0 0 a 0 0 0 0 8 0 2 0 0 0 7 0 0 2 0 1 0 2 0 0 0 8 0 0 4 0 4 0 0 0 0 0 9 0 0 1 0 1 0 0 0 0 0 10 0 0 0 0 1 0 1 0 0 0 11 0 0 1 0 0 0 0 0 0 0 12 + 1 0 2 0 0 0 1 0 0 0 K i l l e d age 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 4 0 0 0 0 0 0 0 1 0 1 5 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 1 0 0 7 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 0 0 0 12 + 0 0 0 0 0 - 0 0 0 0 0 R e c a p t u r e s age 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 5 0 0 0 3 0 0 0 0 0 0 0 0 0 0 4 0 0 5 0 4 0 7 1 0 0 5 0 0 1 0 2 i 1 0 1 4 0 0 0 0 0 0 0 i 1 1 0 7 0 0 1 0 0 0 0 0 0 0 8 0 0 0 0 1 0 2 0 0 0 9 0 0 0 0 0 0 1 0 0 0 10 0 0 0 0 1 0 0 0 0 1 11 0 0 0 0 0 0 0 0 1 0 12 + 0 0 0 0 2 0 1 0 0 0 U n m a r k e d age 1 3 0 0 2 1 0 0 0 0 0 2 0 0 0 4 1 0 120 1 0 1 3 0 2 143 1 31 0 86 6 0 4 4 0 1 118- 1 59 3 38 6 8 12 0 1 21 0 20 13 11 12 12 18 6 0 0 0 0 8 1 3 3 4 5 7 0 0 2 0 1 1 2 0 1 2 8 0 0 4 0 4 1 1 1 0 0 9 0 0 1 0 1 1 0 0 0 1 10 0 0 0 0 1 1 1 0 0 1 11 0 0 1 0 0 0 0 0 0 1 12 + 1 0 6 0 0 0 2 0 1 0 T a b l e 2.9: T a b l e of f ish m a r k e d , m a r k e d f ish k i l l e d or r emoved d u r i n g h a n d l i n g , r ecap tu red , a n d u n m a r k e d b y l e n g t h c o n v e r t e d age f rom J u n e to Sep tember i n C h e r y l L a k e . Q r—) •8 o OO M a r k i n g age 1 6 - J u n 1 8 - J u n 19 -Jun 1 3 - J u l 1 4 - J u l 2 7 - J u l 0 7 - A u g 2 6 - A u g 04-Sep 14-Sep 16-Sep 28-Sep 2 0 3 0 0 0 0 0 0 1 0 0 0 3 0 70 1 0 0 0 23 0 0 0 9 0 4 0 49 0 0 1 0 24 0 0 0 5 0 5 0 24 0 0 0 0 6 0 1 0 1 0 6 0 26 0 0 0 0 2 0 0 0 4 0 7 0 6 0 0 0 0 2 0 0 0 3 0 8 0 12 0 0 0 0 2 0 0 0 1 0 9 0 3 0 0 0 0 2 0 0 0 0 0 10 0 1 0 0 0 0 1 0 0 0 0 0 11 + 0 1 0 0 0 0 0 0 0 0 0 0 R e c a p t u r e s age 2 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 1 0 0 0 1 0 5 0 1 0 0 0 0 1 2 2 0 0 1 6 0 0 0 0 1 0 0 1 1 0 0 0 7 0 2 0 0 0 0 1 0 0 0 0 0 8 0 0 0 0 0 0 1 0 1 0 0 0 9 0 0 0 0 0 0 1 1 0 0 0 0 10 0 0 0 0 1 0 0 0 ' 0 0 0 0 11 + 0 0 0 0 0 0 0 0 1 0 0 1 U n m a r k e d age 2 0 3 1 0 0 0 0 0 5 0 0 24 3 7 82 1 0 c 0 25 0 12 0 9 6 4 5 53 0 0 1 0 24 12 18 1 5 1 5 1 25 0 0 5 0 6 17 10 2 1 1 6 4 28 0 0 0 6 ' 2 10 1 0 4 0 7 3 6 0 0 1 4 2 6 2 0 3 0 8 1 13 0 0 0 0 2 1 0 0 1 0 9 0 3 0 0 0 1 2 1 1 1 0 2 10 0 1 0 0 0 0 1 0 0 0 0 0 11 + 0 0 0 0 0 c 0 0 1 0 0 1 Table 2.10: Table of fish marked, marked fish killed or removed during handling, recaptured, and unmarked by length converted age from June to September in Wilderness Lake. Q to Chapter 3. Estimating Growth from Length At Age Data 50 Chapter 3 Estimating Growth from Length A t Age Data Abstract G e a r s e l ec t i v i t y a n d c u m u l a t i v e effects o f s ize-se lec t ive f i sh ing bias l e n g t h - at-age samples u sed to e s t ima t e the v o n B e r t a l a n f f y g r o w t h pa ramete r s . I n f ished p o p u l a t i o n s , fast g r o w i n g y o u n g fish a n d s low g r o w i n g o l d fish are over represented i n size-age samples . T o accoun t for s u c h effects, I t r ea t ed size- at-age obse rva t ions as m u l t i n o m i a l samples , w i t h e x p e c t e d catches i n each size-age ca tegory dependen t on g r o w t h pa rame te r s , g r o w t h v a r i a t i o n , size se- l e c t i v i t y , a b u n d a n c e at age, a n d the h i s t o r y of e x p l o i t a t i o n . U s i n g s i m u l a t e d d a t a sets, e s t i m a t e d g r o w t h pa rame te r s u s i n g the m u l t i n o m i a l l i k e l i h o o d were u n b i a s e d w h e n ' f i shing m o r t a l i t y was no t t oo h i g h a n d the shape of the v u l - n e r a b i l i t y f u n c t i o n was cor rec t . I n con t ras t , e s t i m a t e d g r o w t h ' pa r ame te r s u s i n g a least squares a p p r o a c h ove r - e s t ima ted the m e t a b o l i c g r o w t h coeffi- c ien t (K) a n d u n d e r - e s t i m a t e d m e a n a s y m p t o t i c l e n g t h (Leo). I e s t i m a t e d g r o w t h pa rame te r s for the n o r t h e r n p i k e m i n n o w Ptychocheilus oregonensis as an e x a m p l e o f the m e t h o d a n d d o c u m e n t e d a s t u n t e d " p i g m y " p o p u l a t i o n w i t h a n L^ of 175 mm f o r k - l e n g t h ( F L ) , a t t r i b u t i n g i t s s m a l l size to effects of h i g h dens i t y a n d / o r a shor t g r o w i n g season. keywords: g r o w t h e s t i m a t i o n , v o n Ber ta l an f fy , s ize-se lec t ive f i sh ing , gear se lec t ion Chapter 3. Estimating Growth from Length At Age Data 51 3.1 Introduction E s t i m a t i n g p a r a m e t e r s for the v o n B e r t a l a n f f y g r o w t h m o d e l assumes a rep- resenta t ive s a m p l e of l eng ths f rom each age class has been co l l ec t ed , t h e n e i ther fitting the g r o w t h f u n c t i o n to length-age d a t a d i r e c t l y or to d a t a o n changes i n l e n g t h be tween the t i m e of m a r k i n g a n d t i m e of r ecap tu re s u c h as F a b e n s (1965) . T h i s a s s u m p t i o n c a n fa i l i f t he s a m p l i n g process is s ize se lec t ive a n d there are c u m u l a t i v e effects o f fishing o n the d i s t r i b u t i o n of s ize-at-age. G r o w t h ra tes v a r y a m o n g i n d i v i d u a l s ( Sa in sb u r y , 1980; B u r r a n d D o k s u m , 1980) a n d in t ens ive size se lec t ive h a r v e s t i n g removes faster g r o w i n g i n d i v i d u a l s . T h e resu l t is t ha t length-age s amples are b i a sed for la rger fast g r o w i n g y o u n g i n d i v i d u a l s , a n d b iased for o lder s l ow g r o w i n g i n d i v i d u a l s t h a t a v o i d e d c a p t u r e (Lee , 1912; f l i c k e r . 1969; S i n c l a i r et a l . , 2002a) . A l m o s t ' a l l l ength-age d a t a sets co l l ec t ed for g r o w t h ana lys i s i n v o l v e s ize-se lect ive cap- tu re m e t h o d s t h a t favor fast g r o w i n g i n d i v i d u a l s . I n a d d i t i o n , m a n y c o m e f r o m p o p u l a t i o n s t h a t have h i s t o r i c a l l y been e x p o s e d to harves t so as to p r o d u c e c u m u l a t i v e effects o n s ize - s t ruc tu re at age ( H a n s o n a n d C h o u i n a r d , 1992; K r i s t i a n s e n a n d S v a s a n d , 1998). I n b o t h cases, the resu l t is a d o w n - w a r d b ias i n e s t i m a t i o n of m e a n a s y m p t o t i c l e n g t h (Loo), u p w a r d bias o f the m e t a b o l i c g r o w t h p a r a m e t e r (K) a n d u p w a r d b ias i n the appa ren t age where l e n g t h is ze ro tQ. B i a s e d e s t ima tes of g r o w t h pa ramete r s w i l l cause b ias i n m o r t a l i t y ra te es t imates (where length-age keys are used to conve r t l e n g t h to age), b io - Chapter 3. Estimating Growth from Length At Age Data 52 l o g i c a l reference p o i n t s for m a n a g e m e n t s u c h as y i e l d per r e c r u i t ( R i c k e r , 1969; P a r m a a n d D e r i s o , 1990), a n d m a n a g e m e n t ac t ions (quotas for ex- a m p l e ) . C h a n g e s i n s i ze - se lec t iv i ty over the course of a f ishery c o m p l i c a t e m a t t e r s fur ther , whe re s ize s e l e c t i v i t y changes m a y be m i s - i n t e r p r e t e d as changes i n g r o w t h rates. S i n c l a i r et a l . (2002b) d o c u m e n t e d changes i n s ize s e l e c t i v i t y for the A t l a n t i c c o d (Gadus morhua) fishery i n the s o u t h e r n G u l f of S t . L a w r e n c e , a n d S i n c l a i r et a l . (2002a) n o t e d tha t h i s t o r i c a l effects o f t e m p e r a t u r e o n m e a s u r e d a n n u a l g r o w t h i n c r e m e n t a n d d e n s i t y - d e p e n d e n t increases i n g r o w t h ra te were r e l a t i v e l y s m a l l i n c o m p a r i s o n to the effect o f size se lec t ive m o r t a l i t y caused b y the fishery. I n some cases, researchers w i s h t o so le ly e s t ima t e g r o w t h p a r a m e t e r s de- s c r i b i n g the age s t r u c t u r e of the cu r r en t p o p u l a t i o n ava i l ab le to harves t w i t h the u n d e r s t a n d i n g t h a t these g r o w t h p a r a m e t e r s represent the r e m a i n i n g fish t ha t are t a rge ted , fn th i s case, the effects o f s ize-se lect ive f i sh ing d o no t need to be a c c o u n t e d for. H o w e v e r g r o w t h p a r a m e t e r s d e s c r i b i n g the h a r v e s t e d t a rge t ed p o p u l a t i o n w i l l change as v u l n e r a b i l i t y changes (as fishers t a rge t s m a l l e r fish for e x a m p l e ) . If a researcher wishes to e s t ima te the p o t e n t i a l g r o w t h u n d e r no h a r v e s t i n g or unde r m a n a g e d s e l e c t i v i t y changes (e.g. s ize l i m i t s ) , t h e n g r o w t h pa rame te r s r ep resen t ing en t i re p o p u l a t i o n are needed . R e c e n t l y , L a s l e t t et a l . (2002) d e r i v e d a l i k e l i h o o d f u n c t i o n for a n a l y s i s o f g r o w t h d a t a f r o m t a g g i n g e x p e r i m e n t s , t h a t accoun t s for i n d i v i d u a l v a r i a t i o n i n g r o w t h t h r o u g h v a r i a t i o n i n i n d i v i d u a l a s y m p t o t i c l eng ths L^, measure - men t e r rors , a n d poss ib le changes i n the v o n B e r t a l a n f f y m e t a b o l i c p a r a m e t e r Chapter 3. Estimating Growth from Length At Age Data ' 53 K w i t h fish age. U n f o r t u n a t e l y , t hey fo l low p r e v i o u s worker s ( J ames , 1991; P a l m e r et a l . , 1991; W a n g et a l . , 1995) i n a s s u m i n g away one of the m o s t c o m - m o n sources of b ias i n g r o w t h d a t a ; t h e y assume independence of s a m p l e d i n d i v i d u a l L x a n d age desp i te m u c h ev idence t h a t h igher L^ (fast g r o w i n g ) i n d i v i d u a l s have a h igher c a p t u r e p r o b a b i l i t y i n f i sh ing a n d s a m p l i n g gear used to co l l ec t the length-age samples . T o d e a l w i t h n o n - i n d e p e n d e n c e of age a n d i n d i v i d u a l L^, l i k e l i h o o d func- t ions for the ana ly s i s of l eng th-age s amples s h o u l d i n c l u d e p a r a m e t e r s repre- sen t ing p r o b a b i l i t i e s of cap ture -a t -age a n d p r o b a b i l i t i e s of c a p t u r e - a t - l e n g t h (i .e. , s ize s e l e c t i v i t y ) . W h e r e a p p l i c a b l e , the c u m u l a t i v e effects of s ize selec- t ive h a r v e s t i n g o n apparen t g r o w t h s h o u l d a lso be cons ide red . In th i s pape r , I de r ive l i k e l i h o o d func t ions t h a t i n c l u d e s ize se lec t iv i ty , m o r t a l i t y , a n d g r o w t h p a r a m e t e r s based o n the a s s u m p t i o n t h a t size-age d a t a are s a m p l e d f r o m a m u l t i n o m i a l d i s t r i b u t i o n . I de r ive four l i k e l i h o o d s : (1) a f u l l l i k e l i h o o d a n d (2) a " reduced" l i k e l i h o o d u s i n g the c o n d i t i o n a l m a x i m u m l i k e l i h o o d es t i - ma te s for n u m b e r s at age i n s t e a d of e s t i m a t i n g t o t a l m o r t a l i t y , (3) a f u l l l i k e l i h o o d t h a t i nc ludes c u m u l a t i v e effects of F, a n d (4) a r e d u c e d l i k e l i h o o d w i t h c u m u l a t i v e effects of F. I test the pe r fo rmance of these f o r m u l a t i o n s w i t h 100 s i m u l a t e d d a t a sets, a n d s h o w t h a t t hey are be t t e r e s t i m a t o r s o f g r o w t h pa rame te r s t h a n p r e v i o u s s t a t i s t i c a l m o d e l s for g r o w t h d a t a . F i - na l l y , I fit a l l four mode l s to r ea l l eng th-a t -age d a t a f rom the p i g m y n o r t h e r n p i k e m i n n o w (Ptychocheilus oregonensis) of s o u t h cen t r a l B r i t i s h C o l u m b i a . Chapter 3. Estimating Growth from Length At Age Data 54 3.2 Methods 3.2.1 L i k e l i h o o d d e r i v a t i o n I a ssume tha t the bas ic d a t a ava i l ab l e for ana lys i s cons is ts o f a m a t r i x n ^ a w i t h e lements n u m b e r s o f f ish s a m p l e d at (discrete) l eng ths / a n d ages a, a n d t h a t th i s is a r a n d o m s a m p l e o f the n u m b e r of v u l n e r a b l e fish of l e n g t h I a n d age a ava i l ab le i n the p o p u l a t i o n to be s a m p l e d . I n th i s case, the genera l f o r m of the l i k e l i h o o d for nita g i v e n the p a r a m e t e r vec tor (O) used to p r e d i c t nita is m u l t i n o m i a l , a n d the l o g l i k e l i h o o d is the p r o d u c t of the d a t a ni, a a n d the l o g of the p r e d i c t e d p r o p o r t i o n s pi<a of l e n g t h I a n d age a: In L1(n\e) = Y,2Z ni,*HPi,a) (3.1) H o w the pi<a t e r m of the l i k e l i h o o d is c o m p u t e d depends o n w h i c h of the four l i k e l i h o o d s presented b e l o w is b e i n g used. 3.2.2 M o d e l 1 g r o w t h w i t h no h i s t o r y o f f i sh ing W h e r e there has been no h i s t o r y o f f i sh ing , I c a l cu l a t e the p r e d i c t e d p r o p o r - t ions i n the m a t r i x piiU as the p r o p o r t i o n of v u l n e r a b l e n u m b e r s o f fish at age a a n d l e n g t h I ( i n mm fork l e n g t h ( F L ) ) i n the t o t a l p o p u l a t i o n VT of v u l n e r a b l e f ish. Pi,a = ViJVT, where VT = ]T ]T Vla. I a (3.2) Chapter 3. Estimating Growth from Length At Age Data 55 I b e g i n b y a s s u m i n g tha t V[A c a n be expressed as the p r o d u c t of three factors: a size dependen t v u l n e r a b i l i t y ui t h a t depends o n size I b u t n o t age, r e la t ive a b u n d a n c e Na of age a f i sh , a n d the c o n d i t i o n a l p r o b a b i l i t y P(l\a) o f b e i n g i n a d i scre te l e n g t h i n t e r v a l I g i v e n age a: Vla = viNaP(l\a). (3.3) I a ssume t h a t vi has a f u n c t i o n a l f o r m w i t h i n c r e a s i n g v u l n e r a b i l i t y at l e n g t h "O = ( 1 + e - V - . > ) < " ) I desc r ibe the l e n g t h at 50 % v u l n e r a b i l i t y (//,) as a f r a c t i o n of L^ a n d a shape pa r ame te r ( 7 ) t ha t descr ibes the s lope of the c u r v e t h r o u g h lh (De r i so et a l . , 1985). If I a ssume a s t ab le r e c r u i t m e n t i n the p o p u l a t i o n , t h e n r e l a t ive numbers -a t -age (Na) c a n be c a l c u l a t e d us ing : Na = Re-M<a-1). (3.5) E q u a t i o n 3.5 c o m p u t e s the e x p o n e n t i a l decay of o lder c o h o r t s r e l a t i ve to a n a r b i t r a r y r e c r u i t m e n t ra te R of age 1 i n d i v i d u a l s . T h e n a t u r a l m o r t a l i t y ra te M is e s t i m a t e d w i t h the g r o w t h a n d v u l n e r a b i l i t y p a r a m e t e r s u s i n g E q . 3 .1. W h e r e the a s s u m p t i o n of a s t ab le r e c r u i t m e n t fai ls , i t c a n be r e l a x e d i n the r e d u c e d l i k e l i h o o d s d e s c r i b e d be low. I f I a ssume v a r i a t i o n i n g r o w t h a m o n g i n d i v i d u a l s o f age a is caused Chapter 3. Estimating Growth from Length At Age Data 56 m a i n l y by v a r i a t i o n i n i n d i v i d u a l a s y m p t o t i c l eng ths L^^ ( W a n g et a l . , 1995), t h e n the v o n B e r t a l a n f f y p r e d i c t i o n of size a t age for a n y i n d i v i d u a l i is L00tif(o) where the bas ic age effect / ( a ) is s h a r e d b y a l l i n d i v i d u a l s i. U s i n g the v o n B e r t a l a n f f y g r o w t h m o d e l th is sha red effect is d e s c r i b e d by: / ( a ) = 1 - e ( - ^ « - * - ) ) ) (3.6) where K is the m e t a b o l i c g r o w t h pa r ame te r a n d t0 is the t h e o r e t i c a l t i m e of zero l e n g t h . A s s u m i n g t h a t i n d i v i d u a l s w i t h L ^ , present at the s t a r t of cohor t l ife are d r a w n f r o m a n o r m a l d i s t r i b u t i o n w i t h m e a n L ^ , a n d v a r i a n c e o^, any sub- c o h o r t w i t h a speci f ic w i l l fo l low a g r o w t h t r a j e c t o r y d e t e r m i n e d b y the Loo,i w i t h w h i c h t h e y were b o r n . T h i s i m p l i e s t h a t the i n t e g r a l de f in ing P(l\a) for each age a s h o u l d be eva lua t ed w i t h m e a n la = Locf(a) a n d v a r i a n c e i n m e a n l e n g t h at age o\. 1 rl+d P(l\a) = j= \ exp CTav27T Jl-d where I is the l e n g t h of the f ish, d is h a l f the l e n g t h i n t e r v a l w i d t h , la is the m e a n length-a t -age , a n d o~\ is the va r i ance i n l eng th-a t -age . In m o s t species of f i sh , the abso lu te va lue of o~\ increases w i t h age (o\ gets la rger as a increases) . I n o rder to a v o i d e s t i m a t i n g o\ for each age, I assume t h a t s t a n d a r d d e v i a t i o n at age oa c a n be expressed as a s i m p l e f u n c t i o n of the m e a n l e n g t h at age la. T h i s f unc t i on c a n be la m u l t i p l i e d b y some coefficient 2ol dl (3.7) Chapter 3. Estimating Growth from Length At Age Data 57 of v a r i a t i o n (cv) w h i c h is a s sume d to be cons t an t across a l l ages, or m o r e c o m p l i c a t e d func t ions c a n be used, f chose to use e q u a t i o n 3.8 d e r i v e d b y F o u r n i e r a n d S i b e r t (1991) . a a = A l 6 A 2 ( - 1 + 2 ^ ) (3.8) I n th i s f o r m u l a t i o n p is the B r o d y g r o w t h coefficient (p = e^~K^), A, the n u m - ber of ages, A i represents the m a g n i t u d e of the s t a n d a r d d e v i a t i o n s at age a a n d A 2 d e t e rmines the l e n g t h dependen t t r e n d i n the s t a n d a r d d e v i a t i o n s (if A 2 = 0 , the s t a n d a r d d e v i a t i o n s are i n d e p e n d e n t o f l eng th ) ( F o u r n i e r a n d S i b e r t , 1991) . T h i s f o r m u l a t i o n has the d i s advan t age of a d d i n g two p a r a m - eters r a t he r t h a n one i f o\ is expressed as cv * la. T h e r a t i o n a l e for u s i n g i t however , is t h a t i t makes a less r e s t r i c t i ve a s s u m p t i o n a b o u t h o w oa changes as f ish g r o w older , ft a lso reduces the c o v a r i a t i o n i n the pa rame te r s b y m a k - i n g the s t a n d a r d d e v i a t i o n of length-a t -age d e p e n d o n one g r o w t h p a r a m e t e r (p = eK) r a t he r t h a n a l l three as i t w o u l d i f i t were expressed as la * cv. 3.2.3 Model 2 reduced likelihood A n o p t i o n for a v o i d i n g the a s s u m p t i o n of s t ab le r e c r u i t m e n t is to c o n s t r u c t the m o d e l u s i n g the c o n d i t i o n a l m a x i m u m l i k e l i h o o d e s t ima tes for n u m b e r s - at-age Na a n d u s i n g these i n the p r e d i c t e d s a m p l e p r o p o r t i o n s at l e n g t h a n d age (pi,a) i n s t e a d of the Na p r e d i c t e d b y e q u a t i o n 3.5. T h i s re laxes the as- s u m p t i o n of s t ab l e age s t r u c t u r e w h i c h w o u l d be v i o l a t e d w i t h h i g h l y v a r i a b l e Chapter 3. Estimating Growth from Length At Age Data 58 r e c r u i t m e n t . D i f f e r e n t i a t i n g the l o g l i k e l i h o o d w i t h respect to N-a, s e t t i n g th i s d e r i v a t i v e to ze ro a n d s o l v i n g for Na g ives the c o n d i t i o n a l m a x i m u m l i k e l i - h o o d e s t ima tes Na: < M > where TIT is the t o t a l of the n u m b e r aged i n the s amp le , na is the t o t a l n u m b e r i n the s a m p l e d aged a years , Vr the t o t a l v u l n e r a b l e n u m b e r s f r o m e q u a t i o n 3.2. T h e . va lue of va m u s t first be c a l c u l a t e d f r o m the p r o d u c t of v u l n e r a b i l i t y - a t - l e n g t h a n d the c o n d i t i o n a l p r o b a b i l i t y of b e i n g i n l e n g t h i n t e r v a l I g i v e n age a: * a = £ ^ ( * | a ) - (3.10) i w h i c h is the s u m of the we igh ted m e a n v u l n e r a b i l i t y for age a, w i t h v u l n e r - a b i l i t i e s a t l e n g t h we igh ted b y P(l\a). I f t he p r e d i c t i o n of Na f r om t o t a l m o r t a l i t y ra te ( equa t i on 3.5) is r e p l a c e d i n the l i k e l i h o o d b y these c o n d i t i o n a l m a x i m u m l i k e l i h o o d Na e s t ima tes (a l - l o w i n g for a n y poss ib le age s t r u c t u r e i n p o p u l a t i o n b e i n g s a m p l e d ) , the m u l - t i p l i c a t i v e t e r m ^ w h i c h does no t v a r y w i t h the pa rame te r s c a n be d r o p p e d ( a long w i t h Vr) a n d p^a expressed as: Pl,a OC (3.11) i n s t e a d of e q u a t i o n 3.2, so the r e d u c e d l i k e l i h o o d ( L 2 ) to be m a x i m i z e d w i t h - Chapter 3. Estimating Growth from Length At Age Data 59 ou t M becomes: l n L 2 oc X ^ z C 7 V l n a ( utP(l\a) a ) (3.12) 3.2.4 Model 3 growth under harvesting T o m o d e l the effects of g r o w t h u n d e r h a r v e s t i n g , I ag a in take the a p p r o a c h t h a t n / i 0 is a r a n d o m s a m p l e f r o m a p o p u l a t i o n where ViA is the t o t a l n u m b e r of v u l n e r a b l e fish of l e n g t h I a n d age a. T h e same genera l f o r m of the l i k e l i h o o d f u n c t i o n ( equa t i on 3.1) app l i e s b u t a h i s t o r i c a l f i sh ing ra te (F) m u s t n o w be i n c o r p o r a t e d i n t o the e s t i m a t e d s a m p l e p r o p o r t i o n s pi>a. T o do t h i s I m u l t i p l y each V / i ( l e lement b y a l e n g t h a n d age specif ic s u r v i v o r s h i p £ita t h a t accoun t s for a g r o w t h p a t t e r n t h a t exposes each i n d i v i d u a l f ish to a p o s s i b l y u n i q u e h i s t o r y of the c u m u l a t i v e i m p a c t o f f i sh ing a n d n a t u r a l m o r t a l i t y . A b s e n t t e m p o r a l i n f o r m a t i o n o n pas t v a r i a t i o n i n r e c r u i t m e n t , n a t u r a l m o r t a l i t y ra te M, a n d o v e r a l l ( fu l ly v u l n e r a b l e ages) f i sh ing m o r t a l i t y ra te F, I t rea t these factors as h a v i n g been s tab le for enough years to resu l t i n a s t ab le age-size d i s t r i b u t i o n . W h e n a p o p u l a t i o n has been s u b j e c t e d to a fishery, the n u m b e r s at each age c a n n o t be de sc r ibed b y e q u a t i o n 3.5 because each i n d i v i d u a l f ish w i l l be sub j ec t to a f i sh ing m o r t a l i t y d e p e n d e n t o n the g r o w t h t r a j ec to ry of t h a t i n d i v i d u a l . I n th i s case, the Na c o m p o n e n t of ViA i n e q u a t i o n 3.3 becomes Ni<a w h i c h m u s t be c o m p u t e d for each I a n d a c o m b i n a t i o n . Ni_a represents the s u r v i v o r s of fish t h a t h a d i n d i v i d u a l Loo,i e q u a l to / / / ( a ) , i.e. f o l l owed a g r o w t h p a t t e r n tha t s u b j e c t e d t h e m to Chapter 3. Estimating Growth from Length At Age Data 60 c u m u l a t i v e i n s t an t aneous m o r t a l i t y (now i n c l u d i n g the fishing m o r t a l i t y F) at l e n g t h a n d age: Zl,a = zZ{M + vl(6)F}, (3.13) d to g ive NUa = Re~z>>\ (3.14) where the s u m (or in tegra l ) over d represents m o r t a l i t y over ages u p to age a a n d where represents t he t i m e sequence of vi v u l n e r a b i l i t i e s seen by fish t h a t fo l lowed the g r o w t h t r a j e c t o r y l& = L0Oiif(d) = [1/f(a)]f(d) over ages a. T h e i n i t i a l r e c r u i t m e n t c a n be set to R = 1 for conven ience , s ince o n l y the ra t ios of the Vit„, to t o t a l Vf appea r i n the l i k e l i h o o d f u n c t i o n ( the c o m p o s i t i o n i n f o r m a t i o n ni>a c a r r y no d i r ec t i n f o r m a t i o n o n t o t a l p o p u l a t i o n s ize) . F o r t y p i c a l v u l n e r a b i l i t y func t ions v(l) d e s c r i b i n g vi, there is no s i m p l e a n a l y t i c a l s o l u t i o n for the s u m or i n t eg ra l of values over ages d, b u t these s u m s c a n be eas i ly e v a l u a t e d n u m e r i c a l l y g i v e n any a s s u m e d f o r m for p(l). T h i s i n t e g r a l needs to be e v a l u a t e d for a l l I, a c o m b i n a t i o n s , s ince each such c o m b i n a t i o n is a s s u m e d to have h a d a different a n d hence a different e x p l o i t a t i o n h i s tory . W i t h a h i s t o r y of e x p l o i t a t i o n , the v u l n e r a b l e n u m b e r s at age a n d l e n g t h V^a are c a l c u l a t e d as: Vla = viRe-Zl-'P{l\a) (3.15) Pita i n e q u a t i o n 3.1 is n o w c a l c u l a t e d w i t h Via c a l c u l a t e d u s i n g e q u a t i o n Chapter 3. Estimating Growth from Length At Age Data 61 3.15: Vla VlRe-z^P{l\a) = VT = Vr ( 3 - 1 6 ) so t h a t the fu l l l i k e l i h o o d ( L 3 ) t h a t i nc ludes size se lec t ive f i sh ing m o r t a l i t y i s : -z, 2 a ' T T h e o n l y n u m e r i c a l l y c o m p l e x pa r t of th i s g r o w t h u n d e r f i sh ing f o r m u l a t i o n is c o m p u t i n g the l eng th-age specif ic s u r v i v o r s h i p ( e z ' - n ) for each /, a e lement . C o n s i d e r for e x a m p l e , the f u n c t i o n i n e q u a t i o n 3.4. R e p r e s e n t i n g 1(d) as 1(d) = L00iif(d), t h e n th i s age f u n c t i o n c a n be s u b s t i t u t e d for l eng ths i n the v u l n e r a b i l i t y f u n c t i o n for a l l l e n g t h in te rva l s /. F o r e x a m p l e , the s u b s t i t u t i o n for the v u l n e r a b i l i t y f u n c t i o n i n e q u a t i o n 3.4 is: uAd) = -. (3.18) w h i c h t hen has to be i n t e g r a t e d over d a n d t h e n m u l t i p l i e d b y F i n order to p r e d i c t c u m u l a t i v e f i sh ing m o r t a l i t y effects o n the " s u b c o h o r t " of fish t h a t s t a r t e d life w i t h a s y m p t o t i c s ize L^^. F o r a l t e rna t i ve v u l n e r a b i l i t y func t ions t h a t are d i f f icu l t to in tegra te (i.e. d o m e - s h a p e d curves ) , I r e c o m m e n d s i m p l y s u m m i n g the f u n c t i o n over ages d f r o m 1 to a, u s i n g a age s teps of 1-year for l o n g - l i v e d fish a n d shor te r s teps (e.g. 0.5 year) for fish t h a t l i ve o n l y a few years . Chapter 3. Estimating Growth from Length At Age Data 62 3.2.5 Model 4 Reduced likelihood with fishing C a l c u l a t i n g the r e d u c e d l i k e l i h o o d i n the f i sh ing case is essen t ia l ly the same as i n the n o n - f i s h i n g case i n the sense tha t the J V a ' s are r ep l aced by the i r c o n d i t i o n a l m a x i m u m l i k e l i h o o d es t imates . H o w e v e r , t he c u m u l a t i v e effect of F o n each I a n d a e lement m u s t be i n c l u d e d i n the c a l c u l a t i o n E q . 3.10 u s i n g E q . 3.18 so tha t : Ua = Y,^i(&)Fp^\a)- (3-19) I O n c e th i s is done va gets u p d a t e s a u t o m a t i c a l l y w i t h changes w i t h F. T h e Pi<a m a t r i x n o w is c o m p u t e d as: Pia cx _ ' ; (3.20) a n d the r e d u c e d l i k e l i h o o d n o w i n c l u d i n g f i sh ing becomes : l „ L 4 o < f ^ ^ y (3.2!) l a \ Va ) 3.2.6 Simulations T o test the de r iva t i ons above I s i m u l a t e d d a t a u s i n g k n o w n pa rame te r s ( T a b l e 3.2.6). V a r i a t i o n i n pas t r e c r u i t m e n t a n o m a l i e s was i n c l u d e d as l o g - n o r m a l process er ror w i t h a m e a n of zero a n d s t a n d a r d d e v i a t i o n o f 1 m u l t i p l i e d by a coefficient o f v a r i a t i o n CVR. Chapter 3. Estimating Growth from Length At Age Data 63 I c o m p a r e d the pe r fo rmance of the s t a n d a r d F a b e n s (after R o t h c h i k l et a l . (1989)) m e t h o d t h a t a s s u m e s ' a r epresen ta t ive s a m p l e of numbers -a t -age a n d m i n i m i z e s the s u m of squares difference be tween p r e d i c t e d a n d obse rved lengths-a t -age to the four m o d e l s I de r ive above u s i n g s i m u l a t e d d a t a . I genera ted 100 d a t a sets w i t h no fishing (F = 0) , w i t h a su s t a inab l e f ishery (F = K) a n d a n overf i shed p o p u l a t i o n (F = 1). F i s h e r i e s where the fishing m o r t a l i t y has been s tab le for a l o n g t i m e are u n c o m m o n . U s i n g the same pa rame te r s ( T a b l e 3.2.6) a n d a fu l ly length-age s t r u c t u r e d s i m u l a t i o n m o d e l , I t es ted m o d e l s 3 a n d 4 w i t h s i m u l a t e d d a t a f rom s tocks where F i nc reased i n i n c r e m e n t s o f 0.1 pe r year for 5 years a n d where F was i nc reased i n i nc remen t s o f 0.1 per year for 10 years . F o r these cases, n e w r ec ru i t s each year were a s s u m e d to have a fu l l y r epresen ta t ive d i s t r i b u t i o n of i n d i v i d u a l a s y m p t o t i c l eng ths ( w i t h m e a n L^ ^ a n d va r i ance (Too c o m p u t e d w i t h e q u a t i o n 3.8 e v a l u a t e d at a n i n f in i t e age ). I n d i v i d u a l s o f specif ic a s y m p t o t i c l eng ths (Loo,i) across a l l ages were t h e n exposed to fishing m o r t a l i t y every year a c c o r d i n g to the size ( a n d hence v{) t hey were i n t ha t year . A s i n the s i m u l a t i o n s w i t h s t ab le f i sh ing m o r t a l i t y , n a t u r a l m o r t a l i t y was a s s u m e d c o n s t a n t a n d CVR was set to 0.5. T h e s e n s i t i v i t y of a l l of the m o d e l s to changes i n pa rame te r s u sed to s i m u l a t e d a t a were tes ted b y u s ing e x t r e m e p a r a m e t e r va lues . I c o n d u c t e d s i m u l a t i o n s w i t h : the l e n g t h at h a l f v u l n e r a b i l i t y 4 set to 0 .05*Loo a n d 0 .9*Loo, kn i fe -edged v u l n e r a b i l i t y (7 = 0.9 a n d w i t h l o w v a r i a b i l i t y i n l e n g t h at age (Ai set to 5) . F i n a l l y I tes ted the m o d e l s w i t h a sho r t l i v e d , fast Chapter 3. Estimating Growth from Length At Age Data 64 T a b l e 3.1: P a r a m e t e r s used to genera te fake d a t a . P a r a m e t e r NT V a l u e 1000 5 0.15 -0.25 0.2 0.6 0.1 Ax 16 A 2 0.5 CVR 0.5 g r o w i n g p o p u l a t i o n w i t h K = 0.7, M = 0.7. 3.2.7 G r o w t h p a r a m e t e r e s t i m a t i o n for n o r t h e r n p i k e m i n n o w I c o l l e c t e d d a t a for n o r t h e r n p i k e m i n n o w Ptychocheilus oregonensis f r o m M o o s e P a s t u r e l ake l o c a t e d o n the B o n a p a r t e P l a t e a u a p p r o x i m a t e l y 100 k m n o r t h of K a m l o o p s , B r i t i s h C o l u m b i a . I co l l ec t ed fish for age ing d u r i n g a d e p l e t i o n e x p e r i m e n t a i m e d at k i l l i n g a h i g h p r o p o r t i o n of the p o p u l a t i o n . F i s h were c a p t u r e d d u r i n g 6 b o u t s o f f i sh ing u s i n g four h o o p nets . T h r e e of these nets cons i s t ed of 6 m x 1 m f iberglass hoops covered i n 1 c m m e s h , 20 m center l ead , a n d 15 m side leads. T h e o ther cons i s t ed of 6 m x 0.7 m s teel h o o p s covered i n 0.5 c m m e s h , 15 m center l ead , a n d 10 m s ide leads. L a p i l l i o t o l i t h s were t a k e n f r o m each f ish a n d 945 were aged. I c u t l a rger o t o l i t h s a l o n g the v e n t r a l / d o r s a l ax i s u s i n g an I somet B u e l l e r s l o w speed Chapter 3. Estimating Growth from Length At Age Data 65 saw, b u r n e d a n d c o u n t e d a n n u l i . O t o l i t h s t oo s m a l l to c u t were b u r n e d a n d c o u n t e d d i r ec t l y . F o r fish o lder t h a n 5 years , f a i l i n g to c u t o t o l i t h s a l o n g the l o n g ax i s s o m e t i m e s r e su l t ed i n s ign i f i can t unde re s t ima te s of age. D u r i n g the three m o n t h s p r e c e d i n g the d e p l e t i o n (9-15 S e p t e m b e r 2002) , 1004 fish were t agged u s i n g 5 a n d 15 mm F l o y n u m b e r e d tags d u r i n g four b o u t s of m a r k - r e c a p t u r e c o n d u c t e d at a p p r o x i m a t e l y 2 week in t e rva l s . O n l y those fish t ha t were re leased i n perfect c o n d i t i o n are i n c l u d e d i n th i s ana lys i s . B e c a u s e the f u n c t i o n a l f o r m of the v u l n e r a b i l i t y - a t - l e n g t h is u n k n o w n for fyke nets a n d n o r t h e r n p i k e m i n n o w , I used these t a g g i n g d a t a to d i r e c t l y e s t i m a t e v u l n e r a b i l i t i e s - a t - l e n g t h . I d i v i d e d the fish i n t o 5 mm s ize b i n s a n d e s t i m a t e d the gear s e l e c t i v i t y for each b i n u s i n g the l i k e l i h o o d d e s c r i b e d b y M y e r s a n d H o e n i g (1997). I i n c l u d e th i s ana ly s i s b o t h to ensure t h a t the f u n c t i o n a l f o r m of the v u l n e r a b i l i t y - a t - l e n g t h has been spec i f i ed c o r r e c t l y a n d to c o m p a r e h o w w e l l the v u l n e r a b i l i t y f u n c t i o n e s t i m a t e d u s i n g o n l y the length-a t -age d a t a a n d the m u l t i n o m i a l l i k e l i h o o d ( s ) does r e l a t i ve to the d i r ec t e s t ima tes of v u l n e r a b i l i t y c o m p u t e d f r o m the t a g g i n g e x p e r i m e n t . 3.3 Results F o r the s i m u l a t e d d a t a w i t h no f i sh ing m o r t a l i t y K was o v e r e s t i m a t e d a n d Loo u n d e r e s t i m a t e d u s i n g F a b e n s m e t h o d ( F i g . 3.1). T h e s e biases were s m a l l (0 .20% for K a n d neg l i g ib l e for Loo). T h e r e was s t i l l the c o m m o n b ias of a large nega t ive to p a r a m e t e r w h i c h was u n d e r e s t i m a t e d b y a fac tor Chapter 3. Estimating Growth from Length At Age Data 66 of two . W i t h no f i sh ing m o d e l s 1,2,3 a n d 4 were u n b i a s e d for the g r o w t h , v u l n e r a b i l i t y pa r ame te r s b u t s l i g h t l y ove r -e s t ima ted M a n d i n the case of m o d e l 3 F . T h e pa r ame te r b ias u s i n g F a b e n s , m o d e l s 1 a n d 2 wo r sen ed w i t h increas- i n g F. W i t h the F a b e n s m e t h o d the bias was large a n d nega t ive for to, s m a l l for K a n d neg l ig ib le for L o o ( F i g . 3.1). M o d e l 1 a c c o u n t e d for the f i sh ing m o r t a l i t y by o v e r - e s t i m a t i n g the n a t u r a l m o r t a l i t y ( F i g . 3.2) b u t c o u l d not accoun t for the se lec t ive m o r t a l i t y o n h ighe r L ^ i n d i v i d u a l s caused b y f ish- i n g a n d so u n d e r e s t i m a t e d Loo- A l t h o u g h m o d e l 2 suffered f r o m the same b ias i n g r o w t h p a r a m e t e r e s t ima te s as m o d e l 1 d i d , m o d e l s 3 a n d 4 were u n b i a s e d . B i a s e s i n p a r a m e t e r e s t ima tes were m u c h worse where F — 1.0 for a l l b u t m o d e l s 3 a n d 4 ( F i g . 3.3). T h e b ias i n K, Loo a n d tQ was less severe for m o d e l s 1 a n d 2 bu t i n the same d i r e c t i o n as Fabens . W h e n f i sh ing m o r t a l i t y was l ow , the d i s t o r t i o n i n the s a m p l e caused b y F was c o m p e n s a t e d for b y h i g h es t imates ' o f M ( F i g . 3.2). T h i s was not the case w i t h h i g h F ( F i g . 3.3) . F i s h i n g m o r t a l i t y d i s t o r t e d the s a m p l e so m u c h t h a t the few o lder fish left were the s m a l l Loo,i ( s low g r o w i n g ) i n d i v i d u a l s . M o d e l s 3 a n d 4 c o r r e c t l y e s t i m a t e d the v o n B e r t a l a n f f y g r o w t h p a r a m - eters ( F i g . 1) at a l l levels o f s t ab le f i sh ing m o r t a l i t y . E v e n w i t h m o d e r a t e r e c r u i t m e n t anoma l i e s u sed to s i m u l a t e the d a t a ( C V r = 0 . 5 ) , F was over es- t i m a t e d . T h i s was the case at l o w F ( a l t h o u g h i t c a n n o t been seen due to the s c a l i n g of F i g . 3.1 a n d 3.2) a n d m u c h worse at h ighe r F ( F i g . 3.3). Chapter 3. Estimating Growth from Length At Age Data 67 (e) U K t 0 h X2 Y lh m F Figure 3.1: Proportional error in parameter estimates for each likelihood for- mulation with F = 0. (a) Fabens, (b) model 1, (c) model 2, (d) model 3, and (e) model 4, (circles represent outliers). Chapter 3. Estimating Growth from Length At Age Data 68 (e) 1 1 o o e O T o x I I I I I I I I I U K t 0 h ^2 1 lh m F F i g u r e 3.2: P r o p o r t i o n a l e r ror i n p a r a m e t e r e s t ima tes for each l i k e l i h o o d for- m u l a t i o n w i t h F = K. (a) F a b e n s , (b) m o d e l 1, (c) m o d e l 2, (d) m o d e l 3, a n d (e) m o d e l 4, (c i rc les represent ou t l i e r s ) . Chapter 3. Estimating Growth from Length At Age Data, 69 I I I I I I I I I U K t 0 h X2 J lh m F F i g u r e 3.3: P r o p o r t i o n a l error i n p a r a m e t e r e s t ima tes for each l i k e l i h o o d for- m u l a t i o n w i t h F = 1. (a) F a b e n s , (b) m o d e l 1, (c) m o d e l 2, (d) m o d e l 3, a n d (e) m o d e l 4, (c i rc les represent ou t l i e r s ) . Chapter 3. Estimating Growth from Length At Age Data 70 T h e p e r f o r m a n c e of m o d e l s 3 a n d 4 suffered w i t h va r i ab l e fishing. A l l the p a r a m e t e r s were e s t i m a t e d w e l l w i t h 5 years o f increased f i sh ing ( F i g . 3.4 a,c,e). B u t w i t h 10 years of i nc reased fishing, m o d e l 5 (F ig .3 .4 f) p e r f o r m e d as p o o r l y was F a b e n s ( F i g . 3.4 b) a n d m o d e l 4 was o n l y s l i g h t l y be t t e r ( F i g . 3.4 d ) . A t a l l levels o f f i sh ing , the m o d e l s 2 a n d 4 were less precise t h a n m o d e l s 1 a n d 3. M o d e l s 2 a n d 4 do no t a s sume a s t ab le age d i s t r i b u t i o n a n d so a d m i t t h a t m o r e p a r a m e t e r c o m b i n a t i o n s c a n e x p l a i n the da t a . T h e r e d u c e d l i k e l i h o o d s effect ively e s t i m a t e d r e l a t i ve r e c r u i t m e n t of each age a c o h o r t Rt — a. T h i s means a a d d i t i o n a l p a r a m e t e r s are e s t i m a t e d . W h i l e there is loss i n p r e c i s i o n of the pa r ame te r e s t ima tes , m o d e l s 2 a n d 4 a l l o w a m u c h m o r e hones t a c k n o w l e d g e m e n t of the u n c e r t a i n t y caused b y r e c r u i t m e n t v a r i a t i o n i n cases w h e r e a s t ab le age s t r u c t u r e is d o u b t f u l or u n k n o w n . A l l t he m o d e l s are sens i t ive t o l o w va lues of //,. A very s l o w l y s l o p i n g v u l n e r a b i l i t y (7 = 0.05) f u n c t i o n h a d the same effect. D i s t o r t i o n i n the d a t a of y o u n g e r age classes re la t ive to f u l l y represen ted ones needs to be present i n the d a t a for i t to be poss ib le t o reso lve the v u l n e r a b i l i t y pa r ame te r s . F o r e x a m p l e , w i t h no fishing, u s i n g the s ame g r o w t h pa rame te r s l i s t e d i n T a b l e 3.2.6 b u t w i t h lh is e q u a l to 0.05 of L^,, the d a t a d o not c o n t a i n a n y infor - m a t i o n a b o u t the v u l n e r a b i l i t y p a r a m e t e r s a n d the resul t is m e a n biases of 3 0 0 % for lh a n d 5 0 0 % for 7. M is c o n f o u n d e d w i t h the v u l n e r a b i l i t y p a r a m - eters a n d i t is u n d e r - e s t i m a t e d b y 0.28. F o r t u n a t e l y the g r o w t h p a r a m e t e r s K, Loo a n d to are w e l l e s t i m a t e d w i t h m e a n b ias o f less t h a n 5% bias . A s is Chapter 3. Estimating Growth from Length At Age Data 7 1 I I I I I I I I U K t 0 h \ 2 Y lh m F I I I I I I I I I U K t 0 h X2 Y lh m F F i g u r e 3.4: P r o p o r t i o n a l e r ror of F a b e n s (a ,b) , m o d e l 3 (c ,d) , m o d e l 4 (e,f), whe re F increases i n i n c r e m e n t s o f 0.1 to F = 0.5 (a,c,e) a n d to F — 1.0 (b ,d , f ) . F over t i m e was e s t i m a t e d b u t the p r o p o r t i o n a l b ias is no t i n c l u d e d here s ince the t rue F used to s i m u l a t e the d a t a changed a n n u a l l y . Chapter 3. Estimating Growth from Length At Age Data 72 e x p e c t e d where w i t h l i t t l e s ize se l ec t iv i ty , the F a b e n s m e t h o d a c t u a l l y per- forms as w e l l as l i k e l i h o o d s p resen ted here because there is no t s ign i f i can t d i s t o r t i o n i n length-age s amples f r o m e i ther f i sh ing or gear - se lec t iv i ty . W i t h no f i sh ing a n d p a r a m e t e r s aga in set to those l i s t e d i n T a b l e 3.2.6 b u t m a k i n g lh = 0.9, the p r o b l e m is t ha t there are no f u l l y represen ted age- classes i n the length-age s a m p l e . T h e pa rame te r s Loo , K, ^ 2 a n d lh are a l l w e l l e s t i m a t e d w i t h biases less t h a n 8%, b u t to, 7 a n d m are b i a sed b y 35, 21 a n d - 4 0 % respec t ive ly . A s l o n g as lh is an i n t e r m e d i a t e va lue , t h e n the m o d e l is robus t to s t eep ly s l o p i n g vi (7 = 0.9) T h e s i m u l a t e d es t ima tes were r o b u s t to d a t a s i m u l a t e d w i t h faster g row- i n g ( m o d e r a t e l y h i g h K = 0.5) a n d faster d y i n g (higher M = 0.6) p o p u l a t i o n . B u t i n p o p u l a t i o n s where K a n d M are greater t h a n a b o u t 0.7, f r a c t i ona l ages (ha l f or qua r t e r year) ages need to be used or the m o d e l p e r f o r m s b a d l y a n d e i ther unde re s t ima te s K or fai ls to converge at a l l . T h e s e m o d e l s b reak d o w n w h e n the shape of the v u l n e r a b i l i t y c u r v e is no t speci f ied cor rec t ly , i f f i sh ing m o r t a l i t y is t o o la rge or i f M is size or age-dependent , a n d w i t h s m a l l e r l e n g t h at age samples . If the a c t u a l v u l - n e r a b i l i t y f u n c t i o n is d o m e - s h a p e d b u t a n a s y m p t o t i c f u n c t i o n is a s s u m e d i n the ana lys i s , F is c o n f o u n d e d w i t h dec reas ing v u l n e r a b i l i t y o f o l d e r / l a r g e r fish a n d becomes b ia sed u p w a r d . V e r y h i g h F is ve ry d e s t r u c t i v e to the age s t r u c t u r e of the p o p u l a t i o n a n d no pa rame te r s c a n be e s t i m a t e d w e l l . W h e r e M is s ize or age dependen t (where M decreases over age for e x a m p l e ) , there is severe c o n f o u n d i n g of M a n d F w i t h the pa rame te r s t h a t desc r ibe vi. A t Chapter 3. Estimating Growth from Length At Age Data. 73 l o w s a m p l e sizes i t is poss ib l e to have no d a t a by r a n d o m chance f r o m e i ther the faster g r o w i n g younge r f ish ( tha t he lp resolve v{) or o lder f ish ( tha t re- so lve M a n d F). W i t h 25 age classes these m o d e l s w o r k e d v e r y p o o r l y w i t h fewer t h a n a p p r o x i m a t e l y 500 obse rva t ions . 3.3.1 Northern pikeminnow growth parameter estimates T h e five m o d e l fits to the n o r t h e r n p i k e m i n n o w d a t a are p l o t t e d i n F i g . 3.5. P a r a m e t e r s e s t ima tes are v e r y s i m i l a r for a l l o f the m o d e l s used . A s t hey s h o u l d , the l i k e l i h o o d f o r m u l a t i o n s t h a t i n c l u d e f i sh ing (mode l s 3 a n d 4) a c t u a l l y e s t ima te a s m a l l f i sh ing m o r t a l i t y i n th i s p o p u l a t i o n . M o d e l s 3 a n d 4 have a t e n d e n c y to ove r -es t ima te the f i sh ing m o r t a l i t y , b u t a non-ze ro va lue for t h i s p a r a m e t e r is no t as un reasonab le as i t m i g h t seem. T h e p o p u l a t i o n is exposed to a s m a l l scale f ishery f r o m l o c a l l odge owners t h a t have i n the pas t c o n d u c t e d a n n u a l t r a p p i n g p r o g r a m s d u r i n g the s p r i n g s p a w n . P a r a m e t e r e s t ima te s - f rom a l l four m o d e l s are ve ry s i m i l a r ( T a b l e 3.3.1). Since th i s p o p u l a t i o n was sub jec t to some f i sh ing i n the pas t b y f i sh ing lodge owners i n the a rea a n d because h o w s tab le r e c r u i t m e n t has been is u n c e r t a i n , the bes t m o d e l cho ice is the r e d u c e d l i k e l i h o o d w i t h f i sh ing . T h e v u l n e r a b i l i t y c u r v e e s t i m a t e d b y m o d e l five ( F i g . 6 ) is v e r y s i m i l a r to t h a t fit u s ing the m a r k r ecap tu re d a t a . F i t t i n g w i t h m o d e l 5 appears to over -es t imate the v u l n e r a b i l i t y at l e n g t h for sma l l e r s ize classes ( F i g . 3.6) Chapter 3. Estimating Growth from Length At Age Data 74 F i g u r e 3.5: G r o w t h curves fit to n o r t h e r n p i k e m i n n o w d a t a u s i n g a l l 5 m o d - els: so l i d= fabens , d a s h e d = f u l l l i k e l i h o o d , d o t t e d = r e d u c e d l i k e - l i h o o d , d o t d a s h = f u l l l i k e l i h o o d w i t h fishing, l o n g d a s h = r e d u c e d l i k e l i h o o d w i t h fishing. Chapter 3. Estimating Growth from Length At Age Data 75 T a b l e 3.2: E s t i m a t e d p a r a m e t e r values for each m o d e l P a r a m e t e r F a b e n s M o d e l # 1 2 3 4 LQO 179.61 162.06 179.77 166.46 188.10 K 0.12 0.19 0.14 0.18 0.14 to -1.95 -0.41 -0.00 -0.38 -0.00 A i 13.90 13.18 16.16 13.20 15.96 A 2 0.69 0.65 0.60 0.61 0.57 h - 0.45 0.49 0.44 0.47 r - 0.21 0.20 0.19 0.19 z - 0.38 - 0.26 - F - - - 0.18 0.15 b u t o the rwi se seems a reasonable a p p r o x i m a t i o n (note t ha t the p a r a m e t e r e s t ima tes for the v u l n e r a b i l i t y pa rame te r s i n t ab l e 3.3.1 were s i m i l a r for a l l m o d e l s ) . N o t e t ha t the v u l n e r a b i l i t y at l e n g t h for the la rger size classes is no t we l l def ined due to s m a l l s a m p l e sizes of t agged a n i m a l s i n those s ize b in s . 3.4 Discussion T h e e s t i m a t e d Loo of n o r t h e r n p i k e m i n n o w is s m a l l c o m p a r e d to o the r d o c - u m e n t e d p o p u l a t i o n s of th i s species.. W h i l e the v o n B e r t a l a n f f y g r o w t h pa - r ame te r (K) for' th i s p o p u l a t i o n of n o r t h e r n p i k e m i n n o w is s i m i l a r to- those p u b l i s h e d i n the l i t e r a tu re , the is m u c h sma l l e r . N o r t h e r n p i k e m i n n o w have been s t u d i e d ex t ens ive ly due to t h e i r p r e d a t i o n o n j u v e n i l e s a l m o n i d s i n a va r i e ty of sys tems such as C u l t u s L a k e B r i t i s h C o l u m b i a ( R i c k e r , 1941; S te igenberger a n d L a r k i n , 1974) a n d they are p resen t ly m a n a g e d i n Chapter 3. Estimating Growth from Length At Age Data 76 F i g u r e 3.6: P l o t of v u l n e r a b i l i t y c u r v e ( so l id l ine) for n o r t h e r n p i k e m i n n o w e s t i m a t e d u s i n g l i k e l i h o o d 3 a n d d i r ec t es t imates o f v u l n e r a b i l i t y u s i n g m a r k - r e c a p t u r e . Chapter 3. Estimating Growth from Length At Age Data 77 the C o l u m b i a b a s i n to reduce t he i r i m p a c t o n j u v e n i l e s a l m o n (Fr iesen a n d W a r d , 1999). T y p i c a l L M for th i s species are i n the o rder o f 400-600 mm F L ( P a r k e r et a l . , 1995) i n the C o l u m b i a r ive r b a s i n a n d i n I d a h o lakes the average r e p o r t e d size of a s e x u a l l y m a t u r e female a p p r o x i m a t e l y 440 mm T L (20 inches) for female a n d 300 mm (15 inches) for ma les J e p p s o n (1959). T h e s e values are w e l l above even the m a x i m u m sizes obse rved i n the s t u d y area. T h e reasons for t he i r s m a l l s ize are p resen t ly u n k n o w n a n d c o u l d be dens i t y o r e n v i r o n m e n t a l effects, b u t I h y p o t h e s i z e t h a t i t is m a i n l y due to the shor t g r o w i n g season ( three m o n t h s or so) t ha t these f ish exper ience . T h e s i m u l a t i o n s s h o w n here are no t u n u s u a l i n s h o w i n g the biases i n the v o n B e r t a l a n f f y g r o w t h p a r a m e t e r s ( a n d c o r r e s p o n d i n g y i e l d pe r r ec ru i t ana lyses) due to gear s e l e c t i v i t y a n d s ize-select ive m o r t a l i t y o n the e s t i m a t i o n of g r o w t h pa ramete r s . T h e s e p r o b l e m s are w e l l k n o w n ( D e r i s o et a l . , 1985; P a r m a a n d D e r i s o , 1990; S i n c l a i r et a l . , 2002b) . T h e m e t h o d s I present are o r i g i n a l i n u s i n g s i m u l a t i o n s tud ies t o show the biases i n e s t ima te s of b o t h the v o n Be r t a l an f fy pa rame te r s , the pa rame te r s d e s c r i b i n g s i ze - se lec t iv i ty , n a t u r a l a n d f i sh ing m o r t a l i t y a n d i n p r e sen t ing l i k e l i h o o d s t h a t m o d e l these effects. U n l i k e P a r m a a n d D e r i s o (1990) a n d S i n c l a i r et a l . (2002b) , I m a k e no effort to i n c l u d e e n v i r o n m e n t a l effects or i n the case of S i n c l a i r et a l . (2002b) , dens i t y dependen t g r o w t h . P a r m a a n d D e r i s o (1990) s h o w tha t i n c r e a s i n g the c o n t r i b u t i o n of e n v i r o n m e n t a l factors have l i t t l e effect o n the va r i ance i n size at age r e l a t i ve to s ize-select ive h a r v e s t i n g , a n d t h a t m o s t fisheries d a t a c o n t a i n l i t t l e i n f o r m a t i o n a b o u t such effects. S i n c l a i r et a l . Chapter 3. Estimating Growth from Length At Age Data 7 8 (2002b) also d e t e r m i n e d t h a t b y far the largest effect o n m e a n p r e d i c t e d L^ was s ize-select ive m o r t a l i t y . I have s h o w n i t poss ib l e u n d e r a r e s t r i c t ed set of a s s u m p t i o n s to es t i - m a t e the v o n B e r t a l a n f f y g r o w t h pa ramete r s , M, F a n d the v u l n e r a b i l i t y pa r ame te r s f r o m o n l y s ize-at-age d a t a w h e n o the r d a t a f r o m a f ishery are no t ava i l ab le . I c a u t i o n t h a t e s t ima tes of the v u l n e r a b i l i t y a n d m o r t a l i t y p a - ramete r s s h o u l d be c o n s i d e r e d v e r y u n c e r t a i n . U n f o r t u n a t e l y , the s e n s i t i v i t y of the m o d e l s to s t ab le f i sh ing m o r t a l i t y a n d k n o w n v u l n e r a b i l i t y shape re- s t r i c t s the a p p l i c a b i l i t y o f these m o d e l s . R e c a l l t h a t the m o d e l s are robus t to an i nc rea s ing f i sh ing ra te as l o n g as the f i sh ing m o r t a l i t y has no t g r o w n too r a p i d l y . W h i l e the F a b e n s m e t h o d p e r f o r m e d a l m o s t e q u a l l y as w e l l i n the case of g r o w i n g F i t d i d no t t e l l the researcher a n y t h i n g a b o u t M or the v u l n e r a b i l i t y f u n c t i o n vi. O f p a r t i c u l a r c o n c e r n is the b r e a k d o w n of the m o d e l s fo l l owing a v e r y r a p i d increase i n F. H a v i n g a c c u r a t e assessment of the t rue g r o w t h p a r a m e t e r s of the s tock is p a r t i c u l a r l y needed i n o rder t o assess the r e b u i l d i n g p o t e n t i a l of the s tock i n such s i t u a t i o n s . F o r t u n a t e l y , i n m a n y cases the reason for e s t i m a t i n g g r o w t h pa rame te r s i n the first p lace is t h a t i t is pa r t o f a la rger s tock assessment w h e r e F ( and s o m e t i m e s vi as i n v i r t u a l p o p u l a t i o n ana lys i s ) is a l r e a d y e s t i m a t e d . T h i s m e t h o d c o u l d be a p p l i e d i n m o r e c o m p l e x s tock assessments w h e r e n i a tables c a n be p r o v i d e d for a c o l l e c t i o n of s a m p l e years . F o r each such t ab le , the s tock assessment m o d e l p r o v i d e s a d d i t i o n a l i n f o r m a t i o n o n t i m e - v a r y i n g re- c r u i t m e n t s Rt-a a n d f i sh ing m o r t a l i t y rates F a n d i n some cases ( l ike v i r t u a l 1 Chapter 3. Estimating Growth from Length At Age Data 79 p o p u l a t i o n ana lys i s ) vi. A s s u m i n g the n^a d a t a are c o l l e c t e d i n d e p e n d e n t l y each year , the l o g - l i k e l i h o o d t e r m for each of these tab les c a n s i m p l y be a d d e d to the ove ra l l l o g - l i k e l i h o o d for the assessment m o d e l . T h e a c c o u n t i n g ( s u m or i n t eg ra t i on ) c a l c u l a t i o n s for each Zia ( c u m u l a t i v e m o r t a l i t y b y size a n d age) are w o u l d requ i re c a l c u l a t i n g the s u r v i v a l of those i n d i v i d u a l s g r o w i n g a l o n g each L ^ t r a j ec to ry , b u t m a y c a r r y v a l u a b l e i n f o r m a t i o n o n changes over t i m e i n F. A p o t e n t i a l l y i m p o r t a n t advan tage of t h i s a p p r o a c h w o u l d be to cor rec t the p r o b l e m t h a t has p l a g u e d some pas t l eng th -based s tock assessment m e t h o d s of i g n o r i n g c u m u l a t i v e effects o f f i sh ing o n l e n g t h d i s t r i - b u t i o n pa t t e rns . M e a n l e n g t h a n d v a r i a b i l i t y o f l e n g t h at age are e x p l i c i t l y va r i ab l e a n d d e p e n d e n t o n Ft i n m e t h o d 3 on ly , due to v a r i a t i o n i n Z^a. 3.5 Acknowledgements T h i s m a n u s c r i p t was g r e a t l y i m p r o v e d b y t h o r o u g h r ev i ews b y an a n o n y m o u s rev iewer a n d A n a P a r m a . I g r e a t l y app rec i a t e the h e l p of a n exce l len t f ie ld c r ew i n the c o l l e c t i o n of o t o l i t h s c o n s i s t i n g of S h a u n M c G l o u g h l i n , H a n n a h M u r p h y , L e w C o g g i n s , M i k e M e l n y c h u k , a n d E r i c P a r k i n s o n . I c o u l d n ' t have g o t t e n s t a r t e d w i t h o u t the expe r t adv i ce f r o m the D e p a r t m e n t o f F i she r i e s a n d Oceans age ing l a b 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 i n N a n a i m o , B . C . , or f in i shed w i t h o u t A n g e l a D a n y l u k w h o d i d the b u l k of the age ing . F i n a n c i a l s u p p o r t was p r o v i d e d b y an N S E R C o p e r a t i n g g r an t a n d P e w F e l l o w s h i p to C . W a l t e r s a n d b y a H a b i t a t C o n s e r v a t i o n T r u s t F u n d g ran t to E r i c P a r k i n - Chapter 3. Estimating Growth from Length At Age Data 8 0 s o n . Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 81 Chapter 4 Estimating movement and growth parameters given size-dependent spatial ontogeny Abstract I d e v e l o p e d a l i k e l i h o o d to s i m u l t a n e o u s l y e s t ima te g r o w t h , n a t u r a l m o r - t a l i t y , a n d gear s e l e c t i v i t y pa rame te r s u s i n g change i n l e n g t h f rom t a g g i n g d a t a . I c o m b i n e d th i s l i k e l i h o o d w i t h t w o others for m a r k - r e c a p t u r e a n d for l eng th-age d a t a to e s t ima te the v o n B e r t a l a n f f y g r o w t h pa ramete r s , n a t u r a l m o r t a l i t y , gear s e l e c t i v i t y a n d i n some cases l eng th -dependen t m o v e m e n t p a - ramete r s . U s i n g s i m u l a t i o n s tudies I s h o w e d t h a t i f a s t ab le r e c r u i t m e n t c a n be a s s u m e d i t is a lso poss ib le to e s t ima t e t a g loss b u t t ha t the a s s u m p t i o n s r e q u i r e d to d o so are ve ry l i m i t i n g . T h e c o m b i n e d l i k e l i h o o d was no t r o b u s t to la rge r e c r u i t m e n t v a r i a t i o n , measu remen t or age ing error . T h e advan tage of such a n a p p r o a c h however is t ha t i t p rov ide s a f r a m e w o r k to use a l l sources of d a t a to measu re p o p u l a t i o n pa rame te r s . 4.1 Introduction T h e r e are m a n y too l s at the d i s p o s a l of s t ock assessment sc ien t i s t s t o m e a - sure g r o w t h a n d m o r t a l i t y pa rame te r s p r o v i d e d s a m p l i n g is done represen- t a t ive ly . B u t represen ta t ive s a m p l i n g m a y be d i f f icu l t to acheive , e s p e c i a l l y i f f i sh m o v e a l o t . F i s h m o v e m e n t is i n v i s i b l e a n d c a n c o n t a m i n a t e s a m - p l i n g i n a n u m b e r of ways : the s p a t i a l d i s t r i b u t i o n of the p o p u l a t i o n m a y Chapter 4. Estimating movement a n d growth parameters given size-dependent spatial ontogeny 82 be u n k n o w n a n d s a m p l i n g done f r o m o n l y a p o r t i o n of the t rue range , i f s a m p l i n g is based o n an agency ' s j u r i s d i c t i o n r a the r t h a n the d i s t r i b u t i o n of the fish; or the s p a t i a l d i s t r i b u t i o n m a y be d y n a m i c (a f u n c t i o n o f the s t o c k ' s s ize or o c e a n o g r a p h i c c o n d i t i o n s ) . T h e n u m b e r of e x a m p l e s where f ish are d i s t r i b u t e d over la rger a rea t h a n p r e v i o u s l y t h o u g h t is i n c r e a s i n g i n b o t h a q u a t i c ( A n r a s et a l . , 1999; A r n e k l e i v a n d K r a a b o l , 1996) a n d m a r i n e sys tems ( H a i s t et a l , 1999; M c H i c h et a l , 2002; R o o k e r et a l . , 2003; B l o c k et a l . , 2005) . S u c h b ia sed s a m p l i n g w i l l c o n t a m i n a t e e s t ima tes of p o p u l a t i o n p a r a m e t e r s such as g r o w t h a n d m o r t a l i t y , p a r t i c u l a r l y i f the m o v e m e n t is size d e p e n d e n t a n d the age or s ize c o m p o s i t i o n differs be tween areas, f f la rger fish s w i m faster ( a n d hence fur ther ) t h e n s a m p l i n g at the m a r g i n s o f a s tock ' s d i s t r i b u t i o n w i l l be b iased for faster g r o w i n g fish, a n d s a m p l i n g i n the center of t he d i s t r i b u t i o n b i a sed for s lower g r o w i n g fish. F i n a l l y , the center o f a s t o c k ' s d i s t r i b u t i o n m a y also m o v e as o c e a n o g r a p h i c c o n d i t i o n s va ry . S u c h d y n a m i c s are present for e x a m p l e i n P a c i f i c H a k e ( B e n s o n et a l . , 2002) . E v e n where s a m p l i n g c a n be a s s ume d represen ta t ive i n the s p a t i a l sense, L a s l e t t et a l . (2002) s h o w g r o w t h p a r a m e t e r s m u s t be e s t i m a t e d s i m u l t a n e o u s l y w i t h n a t u r a l m o r t a l i t y a n d measu remen t e r ror for m a r k - r e c a p t u r e d a t a , f n C h a p - ter 3, I s howed u s i n g s i m u l a t e d length-age d a t a t h a t gear s e l e c t i v i t y m u s t a lso be cons ide red . So i n order t o p r o p e r l y e s t ima te g r o w t h pa rame te r s , i n some cases i t is a lso necessary to also e s t ima t e m o r t a l i t y , gear s e l e c t i v i t y a n d i n some cases m o v e m e n t m u s t be i n c l u d e d i n the s tock assessment . T h e fo rma t of m o s t m a r k - r e c a p t u r e d a t a is convenien t for e s t i m a t i n g sur- Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 83 v i v a l pa rame te r s at fine t i m e scale ( tha t of the m a r k - r e c a p t u r e e x p e r i m e n t ) a n d w h e n size i n f o r m a t i o n is i n c l u d e d w i t h obse rved r ecap tu res t h e n i t is also conven ien t for e s t i m a t i n g g r o w t h pa ramete r s . G r o w t h ana ly s i s o n l y re- qui res t h a t the I s a n d Os t y p i c a l l y u sed to denote obse rva t ions of i n d i v i d u a l l y m a r k e d f ish be r ep l aced w i t h s ize at t i m e . Rega rd le s s of t echn ique , e s t ima tes of g r o w t h a n d s u r v i v a l pa r ame te r s r e ly h e a v i l y o n a s s u m p t i o n s t h a t c a n r a r e l y be me t , or s h o w n to be me t , i n p rac t i ce . W i t h length-age d a t a the p r i n c i p a l c o n c e r n is age v a l i d a t i o n , t h a t is , s h o w i n g t h a t a n n u l i c o u n t e d o n a s t r u c t u r e represent a c t u a l years . B e a m i s h a n d M c F a r l a n e (1983) f o u n d t h a t o n l y 3.4% of 500 s tud ies c o n d u c t e d before 1982 were successful ly able to v a l i d a t e ages across the fu l l age range. T h e r e has been l i t t l e recent i m p r o v e m e n t i n th i s r a t i o , w i t h o n l y 1 5 % of s tud ies d o i n g so s ince t h e n ( C a m p a n a a n d T h o r r o l d , 2001) . M e a s u r e m e n t e r ror is of ten not even cons ide red i n assessments or worse, a s s u m e d to be ze ro a n d used to check the v a l i d i t y o f age ing ( P a r a g a m i a n a n d Beamesde r f e r , 2003) . F i n a l l y m a r k - r e c a p t u r e e x p e r i m e n t s r e ly o n a s s u m p t i o n s of no tag- loss , no t a g g i n g m o r t a l i t y a n d a l l tags b e i n g r e p o r t e d . S tud ie s t h a t e s t i m a t e tag- loss are i n vogue ( E b e n e r a n d C o p e s , 1982; P i e r c e a n d T o m c k o , 1993; S w a n s o n a n d S c h r a m , 1996; M c G l e n n o n a n d P a r t i n g t o n , 1997; J u l l i a r d et a l . , 2001; F e l d m a n et a l . , 2002; R i k a r d s e n et a l . , 2002; B r a t t e y a n d C a d i g a n , 2004) bu t i t is p r a c t i c a l l y ve ry d i f f icu l t to d o d u a l t ag s tudies a n d u s i n g i n t e r n a l tags is expens ive a n d l i m i t e d to r e l a t i v e l y la rge f ish. E v e n i f a d u a l t a g g i n g s t u d y c a n be done , i t c a n n o t be u sed to d e t e r m i n e t a g g i n g m o r t a l i t y . F u r t h e r m o r e , Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 84 d u a l t a g g i n g m a y a c t u a l l y increase the t a g g i n g m o r t a l i t y . It w o u l d be useful therefore to e s t ima te a c o m b i n e d tag- loss , t a g - m o r t a l i t y t e r m w i t h o u t u s i n g such s tudies . T h i s s t u d y consis ts o f three par t s . F i r s t I deve lop a l i k e l i h o o d ana logous to t h a t d e v e l o p e d i n C h a p t e r 3 t h a t c a n be used to e s t i m a t e g r o w t h p a r a m e - ters f r o m m a r k - r e c a p t u r e d a t a . T h e n I deve lop a n d e x p l o r e the pe r fo rmance of c o m b i n e d l i k e l i h o o d s for length-age , change i n l e n g t h a n d m a r k - r e c a p t u r e d a t a u n d e r two d i s t i n c t s i t u a t i o n s , w i t h a n d w i t h o u t l e n g t h dependen t move - m e n t s i m i l a r to tha t d e s c r i b e d i n C h a p t e r 2. U s i n g s i m u l a t i o n s tud ies , I test the pe r fo rmance of each at e s t i m a t i n g the v o n B e r t a l a n f f y g r o w t h p a r a m - eters, m o v e m e n t pa r ame te r s , m o r t a l i t y a n d tag-loss i n a range of scenar ios t ha t i n c l u d e m e a s u r e m e n t er ror , age ing er ror a n d t a g loss, f f i n d the per- fo rmance of the c o m b i n e d l i k e l i h o o d s g o o d b u t n o t r o b u s t to a s s u m p t i o n s a b o u t s t ab le h i s t o r i c a l r e c r u i t m e n t , a n d m e a s u r e m e n t e r ror . 4.2 Methods 4.2.1 Length-age likelihood T h e de ta i l s of the l i k e l i h o o d for the length-age d a t a are d i scus sed i n chap te r 3 so w i l l be o n l y b r ie f ly r ev i ewed here. I assume the d a t a ava i l ab le for ana lys i s cons is ts of a m a t r i x r i ; a w i t h e lements of n u m b e r s o f fish s a m p l e d at (discrete) l eng ths / a n d ages a, a n d t h a t th i s is a r a n d o m s a m p l e of the n u m b e r of v u l n e r a b l e f ish o f l e n g t h I a n d age a ava i l ab l e i n the p o p u l a t i o n to Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 85 be s a m p l e d . T h e gene ra l f o r m of the l i k e l i h o o d for n ; } Q g i v e n the p a r a m e t e r vec to r ( 9 ) is m u l t i n o m i a l , a n d the l o g l i k e l i h o o d a p r o d u c t of the d a t a n / i t t a n d the l o g of the p r e d i c t e d p r o p o r t i o n s p^a at l e n g t h I a n d age a: l o g L 1 ( n | 9 ) = ^ ^ n ( , a l n ( R a ) (4.1) ( a Pita is expressed as the p r o d u c t o f three fac tors : a s ize dependen t v u l n e r - a b i l i t y to gear vi t h a t depends o n size (bu t n o t age), r e l a t i ve a b u n d a n c e Na of age a f ish, a n d the c o n d i t i o n a l p r o b a b i l i t y P(l\a) o f b e i n g i n a d iscre te l e n g t h i n t e r v a l I g i v e n age a P l = ( 4 2 ) K a T,i EaviNaP(l\a)' [^Z) I a ssume v u l n e r a b i l i t y at l e n g t h vi a s , an i n c r e a s i n g f u n c t i o n of l e n g t h "(0 = T, ?7"TTT- ( 4 - 3 ) (1 + e - T C - W ) w i t h pa r ame te r s (//,) as the l e n g t h at 50 % v u l n e r a b i l i t y a n d a shape p a r a m - eter (7) t h a t desc r ibes the s lope of the c u r v e t h r o u g h lh ( D e r i s o et a l . , 1985) . A s s u m i n g s tab le r e c r u i t m e n t No, t h e n r e l a t i ve numbers -a t - age (Na) c a n be c a l c u l a t e d us ing : Na = Noe-W'-V. • , (4.4) E q u a t i o n 4.4 c o m p u t e s the e x p o n e n t i a l decay of o lde r cohor t s r e l a t ive to A^o i n d i v i d u a l s . T h e n a t u r a l m o r t a l i t y ra te M is t o be e s t i m a t e d a l o n g w i t h the Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 86 g r o w t h a n d v u l n e r a b i l i t y pa rame te r s u s i n g E q . 4 .1 . I a s sume v a r i a t i o n i n g r o w t h a m o n g i n d i v i d u a l s is caused v a r i a t i o n i n i n - d i v i d u a l a s y m p t o t i c l eng ths ( W a n g et a l . , 1995) , so t h a t the v o n B e r t a - lanffy p r e d i c t i o n for any i n d i v i d u a l i is L 0 0 j i / ( a ) where / ( a ) is sha red b y a l l i n d i v i d u a l s i. U s i n g the v o n B e r t a l a n f f y g r o w t h m o d e l th i s sha red effect is d e s c r i b e d b y : f{o) = l-e{--K{a-t°)\ (4.5) where K is the m e t a b o l i c g r o w t h p a r a m e t e r a n d tQ is the t h e o r e t i c a l t i m e of zero l e n g t h . A s s u m i n g t h a t i n d i v i d u a l s w i t h Loo,* present at the s t a r t of c o h o r t l i fe are d r a w n f r o m a n o r m a l d i s t r i b u t i o n w i t h m e a n L M , a n d va r i ance cr^,, an i n d i v i d u a l w i t h a specif ic L^i w i l l fo l low a g r o w t h t r a j e c t o r y d e t e r m i n e d b y the Lco.i t hey were b o r n w i t h . T h i s i m p l i e s t h a t the i n t e g r a l de f in ing P(l\a) for each age a s h o u l d be eva lua t ed w i t h m e a n la = Loaf(a) a n d v a r i a n c e i n m e a n l e n g t h at age CT2. 1 pl+d P(l\a) = 7 = / exp where I is the l e n g t h of the fish, d is h a l f the l e n g t h i n t e r v a l w i d t h , la is the m e a n leng th-a t -age , a n d CT2 is the va r i ance i n length-a t -age . I n m o s t fish species, the abso lu te va lue of CT2 increases w i t h age (cr 2 gets la rger as a increases) . T o a v o i d e s t i m a t i n g cr 2 for each age, I a s sume t h a t s t a n d a r d d e v i a t i o n at age oa c a n be expressed as a s i m p l e f u n c t i o n of the (la - If 2<7 2 dl (4.6) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 87 m e a n l e n g t h at age la. T h i s f u n c t i o n c a n be /„ m u l t i p l i e d b y some coefficient of v a r i a t i o n (CV) w h i c h is a s sumed to be cons t an t across a l l ages, or m o r e c o m p l i c a t e d func t ions c a n be used such as tha t of F o u r n i e r a n d S i b e r t (1991) as d e s c r i b e d i n E q . 4.7. I n th i s f o r m u l a t i o n p is the B r o d y g r o w t h coefficient (p = e ^ - 7 ^ ) , A, the n u m b e r o f ages, age a, Ai represents the m a g n i t u d e o f the s t a n d a r d d e v i - a t ions at age a — 1 a n d A2 d e t e rmines the l e n g t h dependen t t r e n d i n the s t a n d a r d d e v i a t i o n s ( i f A2=0, the s t a n d a r d d e v i a t i o n s are i n d e p e n d e n t o f l eng th ) ( F o u r n i e r a n d S i b e r t , 1991). T h i s f o r m u l a t i o n has the d i s a d v a n t a g e of a d d i n g two pa rame te r s r a the r t h a n one i f a\ is expressed as CV * la. T h e r a t i o n a l e for u s i n g i t however , is t h a t i t makes a less r e s t r i c t i ve a s s u m p t i o n a b o u t h o w aa changes as f ish g r o w ( ra ther t h a n a s s u m i n g a f ixed coeff icient m u l t i p l i e d b y l e n g t h at age). 4.2.2 Mark-Recapture Data I a s sume the d a t a cons is t of m a r k e d cohor t s R w i t h i n d i v i d u a l f ish of l e n g t h I t agged a n d released at t i m e t. E a c h i n d i v i d u a l % therefore has a c a p t u r e h i s t o r y c o n s i s t i n g o f lengths litt at m a r k i n g a n d subsequent r ecap tu re . T h e r e c a p t u r e h i s t o r y of the cohor t Rt t h e n is a m a t r i x w i t h e lements lt i f c a p t u r e d a n d 0 i f no t , rows of i n d i v i d u a l t a g n u m b e r s a n d c o l u m n s t w h e n s a m p l i n g (4.7) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 88 C o h o r t t a g tl *2 ts tk-1 tk Ri XXX k - k - - - x x x k k - k 4-1 — XXX k — - 4-i — XXX k - - - 4 R2 XXX k k - lk-1 - XXX k k - — — XXX k - ' k . - . - XXX k — - 4-i — XXX k k k — P a r a m e t e r s - - • •• capture probability Pt Pl Vi PA P5 survival 4>t fa 4>2 <t>3 <t>i <t>5 06 T a b l e 4 .1 : F o r m a t of m a r k - r e c a p t u r e d a t a b y c o h o r t R re leased a n d recap- t u r e d at t imes t a n d e s t i m a t e d pa rame te r s for s u r v i v a l <f>t a n d c a p t u r e p r o b a b i l i t y pt o c c u r r e d ( tab le 4.1) . T w o l i k e l i h o o d s are used for the m a r k - r e c a p t u r e da t a : the p r o b a b i l i t y of the obse rved sizes at c a p t u r e a n d r ecap tu re g i v e n the p r e d i c t e d age s t ruc - t u r e as w e l l as the p r o b a b i l i t y o f the c a p t u r e h i s t o r y g iven p r e d i c t e d s u r v i v a l over the m a r k - r e c a p t u r e t i m e p e r i o d . T h e first depends o n the g r o w t h , re- c r u i t m e n t a n d v u l n e r a b i l i t y p a r a m e t e r s t ha t l ed to the s i z e / a g e s t r u c t u r e of o b s e r v e d m a r k e d a n d r e c a p t u r e d a n i m a l s . T h e second d e p e n d s o n l y o n m o r t a l i t y pa r ame te r s over the course of the m a r k - r e c a p t u r e e x p e r i m e n t . I d i scuss f irst the l i k e l i h o o d for g r o w t h a n d second tha t for s u r v i v a l . Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 89 4.2.3 Mark-Recapture Likelihood for Growth T h e genera l f o r m of the l i k e l i h o o d for e s t i m a t i n g g r o w t h p a r a m e t e r s f r o m m a r k - r e c a p t u r e d a t a is a n a d a p t a t i o n of L a s l e t t et a l . (2002)'s f o r m u l a t i o n to i n c l u d e the effects of gear se l ec t iv i ty . It is the p r o d u c t o f t w o pa r t s : the j o i n t p r o b a b i l i t y of b e i n g m a r k e d at l e n g t h at t i m e of first c a p t u r e / c , pric a n d the j o i n t p r o b a b i l i t y h(lc,lr\a,l) o f b e i n g m e a s u r e d to have l eng ths lc at t i m e of m a r k i n g a n d at r ecap tu re lr after some t i m e i n c r e m e n t 5t l a te r . U s i n g d iscre te l eng ths I a n d ages a the l i k e l i h o o d is: whe re the d a t a niCiiT are the l eng ths at c a p t u r e a n d r ecap tu re , h(lc, lr\a, I) is the j o i n t dens i t y of lc a n d lr. I a s s u m e d the p r o b a b i l i t i e s o f obse rved l e n g t h at c a p t u r e a n d r ecap tu re to be i n d e p e n d e n t a n d n o r m a l l y d i s t r i b u t e d w i t h the t rue m e a n l e n g t h at m a r k i n g l\ a n d l e n g t h at r ecap tu re l2 r e spec t i ve ly l o g L 2 = ^ ^ " W r ^ E H P ^ M k . M a . O ] (4.8) lc , lr • l a h(lc, lr\a, I) = e' (4.9) where o20 is the m e a s u r e m e n t e r ror va r iance , lc a n d lr the m e a s u r e d l eng ths at m a r k i n g a n d r ecap tu re . I a s s u m e d each m a r k e d f ish fo l lows a n average g r o w t h t r a j ec to ry d e s c r i b e d b y some f u n c t i o n / ( £ ) , t h a t a l lows for i n d i v i d u a l Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 90 v a r i a t i o n i n each fish i so t h a t i t s t rue l e n g t h l\ at t i m e t a n d t rue age A is I a s su med tha t i n d i v i d u a l v a r i a t i o n i n l e n g t h at age comes f rom n o r m a l d is - t r i b u t i o n of i n d i v i d u a l w i t h m e a n u.^ a n d v a r i a n c e u2^ , A the age of fish a n d 9 a vec to r of g r o w t h pa rame te r s . U s i n g the v o n B e r t a l a n f f y m o d e l , we expec t the leng ths of fish m a r k e d at t\ a n d recovered at t2 to be func- t ions fl a n d / 2 ( respec t ive ly ) o f the m e t a b o l i c g r o w t h p a r a m e t e r (K) a n d the a m o u n t of t i m e 5t after m a r k i n g so t h a t l2 is the p r e d i c t e d l e n g t h at r ecap tu re c o m p u t e d as: S ince the t rue age A was u n k n o w n , for each c o m b i n a t i o n of age a a n d l e n g t h I i n E q . 4.8 f c o m p u t e d the i n d i v i d u a l L X i i t h a t w o u l d have p r o d u c e d the obse rved l e n g t h . I a s s u m e d th i s d i s t r i b u t i o n was n o r m a l w i t h the m e a n a s y m p t o t i c l e n g t h L M a n d va r i ance â ,. I n d i v i d u a l Look's were c a l c u l a t e d for each l e n g t h a n d age c o m b i n a t i o n u s i n g / ( a ) ( E q . 4 .5) : (4.10) l2 = L00,:f(t,A + 6ud) (4.11) Loo, = I/f(a) (4.12) T h e p r e d i c t e d p r o p o r t i o n s at l e n g t h a n d age for the m a r k - r e c a p t u r e s a m - Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 91 A d d i t i o n a l r ecap tu res are s i m p l y a d d e d to the l o g - l i k e l i h o o d of t h a t i n - d i v i d u a l ' s g r o w t h t r a j ec to ry . T h e v u l n e r a b i l i t y p a r a m e t e r s t h a t p r ed i c t vi, the g r o w t h pa rame te r s t ha t p r ed i c t h(lc, lT\a, I) c o m b i n e d w i t h M to p r e d i c t priiC are e s t i m a t e d i n the l i k e l i h o o d . I t r ea t ed the obse rved lengths as c o m i n g f r o m a d i s t r i b u t i o n w i t h a m e a n t rue l e n g t h I a n d a measu remen t e r ror t e r m a s s u m e d n o r m a l l y d i s t r i b u t e d w i t h m e a n zero a n d s t a n d a r d d e v i a t i o n o\. I a s s u m e d the d i s t r i b u t i o n of measu remen t errors was the same for m a r k i n g a n d r ecap tu re . F o r each ob- served l e n g t h at e i ther m a r k i n g or r ecap tu re , I c o m p u t e a range of poss ib le t rue l eng ths lrng = lc or lr ± 2o0. T h i s f o rma t does n o t p e r m i t e s t i m a t i n g the m e a s u r e m e n t e r ror . T h i s m u s t be a s s u m e d or done e m p i r i c a l l y where poss ib le by q u e r y i n g the l eng ths of f ish m a r k e d at sho r t t i m e in te rva l s (say one day) a p a r t a n d c o m p u t i n g the m e a n difference b e t w e e n those t w o t imes . 4.2.4 Mark-Recapture Likelihood for Survival with no Movement I used the m e t h o d r e v i e w e d i n L e b r e t o n et a l . (1992) for e s t i m a t i n g s u r v i v a l . T h e d a t a a n d p a r a m e t e r s used are of the f o r m d e s c r i b e d i n t ab l e 4.1 bu t i n s t e a d of l ' s t y p i c a l l y used to denote r e c a p t u r e d f ish I use size obse rva t ions pie have a s i m i l a r f o r m to the length-age d a t a ( E q . 4 .2) : (4.13) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 92 lt > 0 where fish were obse rved a n d lt = 0 where no t . C a l c u l a t i n g the l i k e l i h o o d o f each i n d i v i d u a l i c a p t u r e h i s t o r y i nvo lves three steps: d e t e r m i n i n g the t i m e w h e n each fish was las t obse rved a l i ve r ; c o m p u t i n g the p r o b a b i l i t y of each lt o b s e r v a t i o n for t i m e t < T g i v e n the fish was a l ive ; a n d c o m p u t i n g the p r o b a b i l i t y the fish was n o t obse rved for t i m e t > T. T h e p r o b a b i l i t y of the d a t a at a l l t i m e p o i n t s t < r is s i m p l y the p r o d u c t of s u r v i v a l 4>t a n d the c a p t u r e p r o b a b i l i t y pt i f the fish was obse rved a n d i f no t , the p r o d u c t (frt a n d the c o m p l i m e n t of the c a p t u r e p r o b a b i l i t y qt = l-pt: where pitt = vtpt. T h e c o m p u t a t i o n is m o r e c o m p l e x for the p r o b a b i l i t y of obse rva t ions at t i m e t > rt. H e r e the p r o b a b i l i t y of each o b s e r v a t i o n is the s u m of the fish m a y no t have been obse rved due to any c o m b i n a t i o n o f d y i n g a t any t i m e t > T or no t b e i n g de tec ted even t h o u g h a l ive . F o r t u n a t e l y these p r o b a b i l i t i e s c a n be c a l c u l a t e d b y b a c k w a r d s r e c u r s i o n . If Xt is the p r o b a b i l i t y of no t b e i n g obse rved a g a i n g i v e n release a l ive at t = r a n d the las t s a m p l i n g t i m e p o i n t t = k t h e n Xk is b y d e f i n i t i o n 1. A c c o r d i n g to C o r m a c k (1968) Xi is c a l c u l a t e d as: (4.14) p r o b a b i l i t i e s t ha t c o u l d have l ed to the f ish n o t b e i n g obse rved . I n d i v i d u a l 1 + Xi = M1 ~ Qi+iXi+i) (4.15) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 93 T h e l o g - l i k e l i h o o d of each c a p t u r e h i s t o r y is m u l t i n o m i a l w i t h the pre- d i c t e d p r o b a b i l i t y e q u a l to the p r o d u c t of the p r o b a b i l i t i e s o f a l l the t i m e t obse rva t ions . S u p p o s e for e x a m p l e , a n i n d i v i d u a l was m a r k e d at t = 1 at 120 mm, no t obse rved at t = 2, m e a s u r e d a g a i n at t = 3 at 123 m m ; t h e n no t obse rved aga in i n two a d d i t i o n su rveys c o n d u c t e d at t imes t = 4 a n d t = 5. I ts c a p t u r e h i s t o r y is: 120 0 123 0 0. T h e l i k e l i h o o d Li o f i n d i v i d u a l i ' s c a p t u r e h i s t o r y is the p r o d u c t of the p r o b a b i l i t i e s of each o f o b s e r v a t i o n at t i m e t: , Li-= <p2q2<f>3P3X3 - • ( 4 -16) T h e t o t a l l o g - l i k e l i h o o d o f a l l d a t a t h e n is the s u m of the l i k e l i h o o d s o f each i n d i v i d u a l of the i n d i v i d u a l c a p t u r e h i s to r i e s i. l og L 3 = ] T L / (4.17) i T h e c a p t u r e p r o b a b i l i t i e s pt m a y be e s t i m a t e d i n the l i k e l i h o o d b u t are g i v e n b y the c o n d i t i o n a l m a x i m u m l i k e l i h o o d es t ima te : P t = (4.18) where rt is the r ecap tu re of i n d i v i d u a l i (e i ther 1 or 0) v^i is the gear s e l e c t i v i t y of i n d i v i d u a l i a n d N[ti is the p r e d i c t e d s u r v i v o r s h i p of t h a t i n d i v i d u a l . U s i n g the c o n d i t i o n a l m a x i m u m l i k e l i h o o d e s t ima tes o f the c a p t u r e p r o b a b i l i t i e s is conven ien t p a r t i c u l a r l y i f the c a p t u r e p r o b a b i l i t i e s are low , a n d / o r i f m a n y Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 94 a n i m a l s are never obse rved a g a i n after m a r k i n g (for such d a t a there is v e r y l i t t l e i n f o r m a t i o n a b o u t the c a p t u r e p r o b a b i l i t i e s ) . C a l c u l a t i n g vi requires p r e d i c t i n g the l e n g t h of each i n d i v i d u a l at t i m e li.t a n d c a l c u l a t i n g i t s v u l n e r a b i l i t y v^i u s i n g E q . 4 .3 . I p r e d i c t e d kit at A i t i m e after first m a r k i n g tc, ltc+At as ktc+M = lc,i + ( L 0 0 - l c , i ) ( l - e - K ^ ) (4.19) u s i n g the v o n B e r t a l a n f f y g r o w t h p a r a m e t e r s e s t i m a t e d w i t h E q s . 4.8 a n d / o r 4 .1 . 4.2.5 Mark-Recapture Likelihood for estimating survival parameters and movement T o e s t ima t e m o v e m e n t pa r ame te r s I depa r t f r om the t r a d i t i o n a l m a r k - r e c a p t u r e m e t h o d d e s c r i b e d above a n d i n s t e a d a d o p t the s ta te-space a p p r o a c h of D e V a l p i n e a n d H a s t i n g s (2002) to f o r m u l a t e a l i k e l i h o o d f u n c t i o n . H e r e I suppose a t i m e series c o n s i s t i n g o f l e n g t h obse rva t ions y\.y2, •••VT u n t i l some m a x i m u m t i m e T. I deno te a l l obse rva t ions Y u n t i l t i m e t as Yt. T h e l i k e l i h o o d is c a l c u l a t e d r e c u r s i v e l y w i t h the p r o b a b i l i t y o f a l l t he d a t a at t i m e t g i v e n the pa rame te r s P(Yt) expressed as the p r o d u c t o f the p r o b a - b i l i t y o f the d a t a t h r o u g h t — 1 a n d the p r o b a b i l i t y of the la tes t o b s e r v a t i o n Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 95 P(Yt) = PiY^PiytlY^) (4.20) P(yt\Yt-i) is expressed as: (4.21) St where St represents a l l poss ib l e fish s tates (a l ive i n a rea 1, a l i ve i n a rea 2, e tc . a n d dead) . P(yt\st,Yt-i) is the p r o b a b i l i t y of the o b s e r v a t i o n g i v e n the s tate , or s i m p l y the c a p t u r e p r o b a b i l i t y . F o r e x a m p l e , i f a f ish is obse rved i n a rea 1 at t i m e t t h e n the p r o b a b i l i t y o f t h a t o b s e r v a t i o n is s i m p l y the c a p t u r e p r o b a b i l i t y i n t h a t s ta te pSjt. T h e p r o b a b i l i t y of i t b e i n g obse rved i n any of the o ther s tates (a l ive i n o the r areas, or dead) g i v e n i t was c a p t u r e d i n a r ea 1 is therefore zero. P(st\Yt) is u p d a t e d a t each t i m e s tep u s i n g B a y e s t heo rem so P(st\Yt) is e q u a l to the p r i o r P(st\Yt-i) m u l t i p l i e d b y the p r o b a b i l i t y o f the d a t a g i v e n the s ta te ( the l i k e l i h o o d p(yt\st)) d i v i d e d b y the s u m of a l l poss ib le c o m b i n a t i o n s of p r i o r s a n d l i k e l i h o o d s ( the m a r g i n a l ) . W h e r e there is a n o b s e r v a t i o n i n one of the l o c a t i o n s ta tes , the pos t e r io r p r o b a b i l i t y of b e i n g ' i n t h a t s ta te is s i m p l y 1. T h e p r io r s at the subsequent s tep P(st+i\Yt) are the p r o d u c t o f the pos t e r io r s ta te p r o b a b i l i t i e s P(st\Yt) a n d the s ta te t r a n s i t i o n m a t r i x MSliSl+1 w h i c h is a square m a t r i x w i t h rows P(st\Yt) = P(st\Yt_l)p(yt\st)lY.Pist\Yt-Myt\st) (4.22) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 96 Area 1 (Nursery) F i g u r e 4 .1 : M o v e m e n t m o d e l used to s i m u l a t e d a t a . F i s h enter the m o v e m e n t p o o l at the l eng th -dependen t m o v e m e n t ra te p,i f r om the nu r se ry a rea t h e n d i v i d e i n t o areas 2 a n d 3 w i t h t he p r o p o r t i o n p2 g o i n g to a rea 2, l — p2 g o i n g to area 3, a n d 1 — s t a y i n g i n the nurse ry area. Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 97 St+i a n d c o l u m n s St w i t h e lements s u r v i v a l ra te 4> a n d m o v e m e n t p r o b a b i l i t i e s ps. T a k i n g P(st\Yt) as a c o l u m n vec tor w i t h rows for each s tate , P(st+1\Yt) = MatiSt+lP{st\Yt). (4.23) T h e t r a n s i t i o n p r o b a b i l i t y of g o i n g f r o m any l o c a t i o n s ta te to the d e a d s ta te is s i m p l y 1 — 4>, a n d f rom the d e a d s ta te to the d e a d s ta te 1. 4.2.6 Movement Model T h e r e is cons ide rab l e f l e x i b i l i t y to m o d e l c o m p l i c a t e d m o v e m e n t pa t t e rn s u s i n g the above m e t h o d o l o g y . S ince the p a r t i a l o b j e c t i v e of th i s s t u d y was to s i m u l a t e the e s t i m a t i o n of g r o w t h a n d m o v e m e n t p a r a m e t e r s for a s t ock w i t h a s p a t i a l s t r u c t u r e l i ke tha t d e s c r i b e d i n C h a p t e r 2 a n d for s i m p l i c i t y , I s i m u l a t e a s t ock w i t h t w o life h i s t o r y types : a m o v i n g t y p e w h i c h undergoes a s ingle l eng th -dependen t m o v e m e n t f rom the n u r s e r y area , a n d a res ident t y p e tha t r e m a i n s i n the nu r se ry a rea i ts en t i re life ( F i g . 4 .1) . F i s h are a s s u m e d no t to r e t u r n to nu r se ry a rea after d i s p e r s i n g . F o r conven ience I s u b s c r i p t each a rea a c c o r d i n g to F i g . 4 .1 . T h e p r o p o r t i o n of f ish at l e n g t h I i n s i te s is ipitS. I a s sume t h i s p r o b a b i l i t y to be the p r o d u c t of the t o t a l p r o p o r t i o n at l e n g t h l e a v i n g the nu r se ry a rea piti a n d a l e n g t h dependen t m o v e m e n t p r o b a b i l i t y f u n c t i o n a s s umed to be n o r m a l l y d i s t r i b u t e d , w i t h m e a n l e n g t h at m o v e m e n t lyt a n d s t a n d a r d d e v i a t i o n o^ so t h a t the p r e d i c t e d p r o p o r t i o n at l e n g t h i n the nu r se ry a rea is: Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 98 T h e p r o p o r t i o n at l e n g t h i n s i te 2 is ipit2 = (1 — ipi,i)P2 a n d ipit3 — ipifii^- — P2) f ° r s i te 3. F o r e x a m p l e , w i t h the t o t a l p r o p o r t i o n m o v i n g pn set to 0.70 a n d n.2 set to 0.5 the p r e d i c t e d p r o p o r t i o n at l e n g t h i n a l l areas is i l l u s t r a t e d i n F i g . 4 .2 . B e c a u s e a n y l eng th -dependen t m o v e m e n t . w i l l also affect the length-age s t r u c t u r e i n each si te , ipitS t e rms for s i te m u s t be i n c l u d e d to the p r e d i c t e d p r o p o r t i o n s at l e n g t h a n d age i n E q . -4.13 a n d E q . 4.2. I n the m o v e m e n t case, E q . 4.13 becomes 2 ^M = ( l - x x O C i - exp — dl) (4.24) (4.25) and E q . 4.2 Pi,a,s --= ipi,sviNaP{l\a) (4.26) J2i EaEsipsviNaP(l\ay so t h a t t he l i k e l i h o o d L2 ( E q . 4.8) becomes l o g L m 2 = £ £ £ n i < ; S ] , i . J o . g [ £ £ £ p ^ i S h ( / C ) S , / r ^ | a , / i s ) ] (4.27) 5 lc,s lr,s I C S Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 99 F i g u r e 4.2: P r o p o r t i o n o f the p o p u l a t i o n i n each a rea as a f u n c t i o n of l e n g t h ipi, i n a rea 2 (red, 1P2) a n d 3 (green ip3). Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 100 a n d L\ ( E q . 4.1) becomes l o g - L m i ( n i ] Q ] 5 | 9 ) = J2J2J2ni;a,sm(Pi^) (4-28) ( a s 4.2.7 Combined Likelihoods T h e w a y m o v e m e n t is m o d e l e d here requi res t ha t g r o w t h , m o r t a l i t y a n d m o v e m e n t l i k e l i h o o d s be c o m b i n e d . W i t h p r a c t i c a l s a m p l e sizes, l eng th-age or s i ze -a t - cap tu re a n d r e c a p t u r e d a t a d o n o t c o n t a i n e n o u g h i n f o r m a t i o n to e s t ima t e the pa rame te r s of the m o v e m e n t p r o b a b i l i t y f u n c t i o n ( E q . 4 .24) . A l s o , the s u r v i v a l l i k e l i h o o d s ( w i t h or w i t h o u t m o v e m e n t ) r equ i re e i the r as- s u m p t i o n s , or es t imates of g r o w t h to e s t ima te the c a p t u r e p r o b a b i l i t i e s u s i n g E q . 4.18 (since ijj 's are needed) a n d o b v i o u s l y the l eng th -dependen t move - m e n t p r o b a b i l i t y f u n c t i o n ( E q . 4 .24) . T h e s e f o r m u l a t i o n s have cons ide rab l e f l e x i b i l i t y w i t h respect t o h o w sur- v i v a l a n d m o r t a l i t y are m o d e l e d . T h e e s t ima t e of M i n the g r o w t h l i k e l i h o o d s ( E q s . 4.1 a n d 4.8) assumes s tab le r e c r u i t m e n t . I test h o w r o b u s t E q . 4.8) is to th i s a s s u m p t i o n be low. S u r v i v a l a n d m o v e m e n t m a y be m o d e l e d as t i m e d e p e n d e n t (fit = e~MAt at fine scale (at each t i m e s tep i n the m a r k - r e c a p t u r e e x p e r i m e n t ) , as d i s t i n c t for the m a r k e d cohor t , or a s s um e d the same as the h i s t o r i c a l M t h a t gave rise to the age s t r u c t u r e represented i n E q s . 4.1 a n d 4.8. S i n c e pa r t of the pu rpose o f t h i s s t u d y was to exp lo re i f a c o m b i n e d t a g - l o s s / t a g - m o r t a l i t y p a r a m e t e r c a n be e s t i m a t e d w i t h o u t d u a l m a r k i n g , I Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 101 a s s u m e d t h a t the n a t u r a l m o r t a l i t y e x p e r i e n c e d by the m a r k i n g cohor t ( s ) M was the same as the M t h a t gave r ise to the age s t r u c t u r e so tha t the difference i n the appa ren t m o r t a l i t y expe r i enced b y the m a r k e d c o h o r t m u s t be due to a c o m b i n e d t a g - l o s s / t a g - m o r t a l i t y t e r m . 4.2.8 Simulation Stock-Assessment Using Combined Likelihoods with No Movement I tes ted the p e r f o r m a n c e of the l i k e l i h o o d s u s i n g s i m u l a t e d d a t a . T h e l i ke - l i h o o d used for the l eng th-age d a t a (L\ E q . 4.1) was tes ted ex t ens ive ly i n chap te r 3; L 3 for s u r v i v a l d a t a has a lso been used a n d tes ted ex t ens ive ly (re- v i e w e d i n L e b r e t o n et a l . (1992)) a n d E q . 4.20 l ikewise for a n i m a l m o v e m e n t ( Jonsen et a l . , 2003, 2005) so t he i r i n d i v i d u a l p e r f o r m a n c e was n o t eva lu - a t ed here. I tes ted: the p e r f o r m a n c e of the m a r k - r e c a p t u r e l i k e l i h o o d for g r o w t h i nc remen t s ( E q . 4.8) across a range of r e c r u i t m e n t a n d m e a s u r e m e n t er ror values; a n d the a b i l i t y o f the c o m b i n e d l i k e l i h o o d s ( E q . 4 .1 , 4 .8, a n d 4.16) t o c a p t u r e tag- loss i n s i m u l a t e d d a t a w i t h a n d w i t h o u t s u p p l i m e n t a r y leng th-age d a t a . I e x p l o r e d the f o l l o w i n g scenar ios: a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g n o t a g loss u s i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L 2 ( E q . 4.8) b) d a t a genera ted w i t h t a g loss a n d fit a s s u m i n g no t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4.17) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 102 c) d a t a genera ted w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4.17) d) d a t a genera ted w i t h t a g loss a n d e s t i m a t i n g th i s t a g loss u s ing l e n g t h - age (Li), g r o w t h i n c r e m e n t ( L 2 ) a n d t a g s u r v i v a l l i k e l i h o o d s (L3) ( E q s . 4.8, 4.17 a n d 4 .1) . T a b l e 4.2: P a r a m e t e r s used to genera te fake d a t a for c o m b i n e d l i k e l i h o o d s P a r a m e t e r V a l u e s a m p l e s ize NT 1000 log a s y m p t o t i c l e n g t h InLoo 5.5 mm v o n Be r t a l a n f fy g r o w t h p a r a m e t e r K 0.15 yr'1 n a t u r a l m o r t a l i t y M 0.2 yr'1 f r ac t ion of at h a l f v u l n e r a b i l i t y k 0.5 mm se l ec t i v i t y s lope 7 0.1 s t a n d a r d d e v i a t i o n i n l e n g t h at age 1 Ar 16 mm age s t a n d a r d d e v i a t i o n sca la r A 2 0.5 t a g loss U 0:3 yr-1 measu remen t e r ror Om 5 mm . I r a n three sets of s i m u l a t i o n s for the c o m b i n e d l i k e l i h o o d s w i t h p a r a m e t e r values l i s t e d i n t ab l e 4.2.8. F o r the f irst , r e c r u i t m e n t v a r i a t i o n was a s su m ed to be 0, m e a s u r e m e n t a n d age ing er ror set to zero a n d t a g loss set to 0.3. F o r the second set, I i n c l u d e d v a r i a t i o n i n pas t r e c r u i t m e n t a n o m a l i e s as l o g - n o r m a l process er ror w i t h a m e a n of zero a n d s t a n d a r d d e v i a t i o n of 1 m u l t i p l i e d b y a coefficient o f v a r i a t i o n CVR of 0.2, a n d m e a s u r e m e n t er ror of 5 mm. F o r the f ina l series, age ing er ror was i n c l u d e d i n the s i m u l a t e d length-age d a t a (see b e l o w ) . Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 103 A g e i n g e r ror m a y be e i ther measu remen t e r ror clue to s t ruc tu res s h o w i n g different n u m b e r s o f a n n u l i ( B e a m i s h a n d M c F a r l a n e , 1983) or er ror a r i s i n g f rom the sub j ec t i ve a s s ignmen t of r ings o n s t ruc tu re s to a n n u l i . T h e former is genera l ly no t n o r m a l l y d i s t r i b u t e d , a n d i n s t e a d t ends to be n e g a t i v e l y b iased , r e s u l t i n g i n u n d e r - a g e i n g of o lder fish ( C a m p a n a a n d T h o r r o l d 2001, S h a y n e M a c C l e l l a n D e p a r t m e n t of F i she r i e s a n d Oceans . N a n a i m o . C a n a d a , pers. comm.). T h i s e r ror s t r u c t u r e occu r s because the first s p a w n often appears as a check o n the o t o l i t h w h e n fish s top g r o w i n g . U n d e r - a g e i n g is ve ry c o m m o n . S ince the a m o u n t o f t i ssue l a i d d o w n - o n each ear b o n e gets sma l l e r w i t h age, m a n y a n n u l i c a n be compres sed together . If the o t o l i t h is sec t ioned a l o n g the shor t ax i s , these c o m p r e s s e d r ings m a y appea r as a s ingle r i n g . F u r t h e r m o r e , the p r e p a r a t i o n o f o t o l i t h s for r e a d i n g u s u a l l y i nvo lves b u r n i n g t h e m so th i s same outer layer c a n be c o m p l e t e l y c h a r r e d d u r i n g th i s process . I m o d e l e d the s i m u l a t e d age ing er ror a c c o r d i n g l y , a s s u m i n g readers cor- r e c t l y e s t i m a t e d ages w i t h a c e r t a i n p r o b a b i l i t y C o f b e i n g cor rec t where the cor rec t age is e s t i m a t e d a n d o the rwise m a k i n g a n o r m a l l y d i s t r i b u t e d er ror w i t h m e a n size a * a a n d s t a n d a r d d e v i a t i o n 0.1 * a. I m o d e l e d a as a s i g m o i d a l f u n c t i o n ( F i g . 4.2.8) h a v i n g a p o s i t i v e d o m a i n a t ages unde r some in f l ec t i on age a,- a n d a nega t ive d o m a i n for o lder fish so tha t : (4.29) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 104 o o o o m o ° o o o o o o o o o o o o o o o o o o o o r o T T I 25 5 10 15 20 age (years) 30 F i g u r e 4 .3: P l o t of a used to s i m u l a t e age ing er ror Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 105. a n d the e s t i m a t e d age a i n the s i m u l a t e d d a t a : a = N(aa,0.1o) (4.30) w h e r e a was a n o r m a l l y d i s t r i b u t e d r a n d o m n u m b e r w i t h m e a n a * a a n d s t a n d a r d d e v i a t i o n 0.1 * a. F o r s i m u l a t i o n s C = 0.7 a n d a* = 8. I i n i t i a l l y s i m u l a t e d d a t a w i t h 1000 length-age a n d m a r k - r e c a p t u r e s a m - ples . T h e c a p t u r e p r o b a b i l i t i e s at a l l t i m e steps i n the s i m u l a t e d d a t a were set to 0.2. F o r subsequent s i m u l a t i o n s w i t h o u t v a r y i n g a n n u a l r e c r u i t m e n t ( a n d hence es t ima tes of g r o w t h a n d m o r t a l i t y ) , a n d w i t h m e a s u r e m e n t a n d / o r age ing e r ror the s i m u l a t e d n u m b e r of m a r k e d fish was 300. T h i s was done to exp lo re m o r e r ea l i s t i c s a m p l e sizes, a n d also for c o m p u t a t i o n a l efficiency. C a l c u l a t i n g L2 is c o m p u t a t i o n a l l y in t ens ive because of h a v i n g to in t eg ra t e across ages, l eng ths ( E q . 4.8) a n d m e a s u r e m e n t errors (<r 0 )(Eq. 4 .9) . T h i s issue is no t t r i v i a l , the n u m b e r of f u n c t i o n eva lua t ions of E q . 4.8 needed for each s i m u l a t i o n t r i a l is a m u l t i p l e o f the n u m b e r of obse rva t ions , ages, l eng th -b in s , a n d the range of m e a s u r e m e n t errors . 4.2.9 Simulation of growth parameter estimates with length-dependent movement G i v e n the d i f f i cu l ty o f m a r k i n g s m a l l f ish i n m a r k - r e c a p t u r e p r o g r a m s , i t is no t p r a c t i c a l to m o d e l , or even a t t e m p t to cha rac t e r i ze any s ize -dependen t m o v e m e n t process of j u v e n i l e f ish. Never the les s such m o v e m e n t w i l l have a n Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 106 effect o n the size-age s t r u c t u r e where s a m p l i n g is l i m i t e d to e i ther nu r se ry or o u t l y i n g areas. I e x p l o r e d p o t e n t i a l biases f r o m u s i n g the leng th-age l i ke - l i h o o d ( E q . 4.1) w h e n each a rea is t r ea t ed as an i n d e p e n d e n t s t o c k h a v i n g i ts o w n g r o w t h a n d m o r t a l i t y pa rame te r s . T h e m a i n pu rpose o f these s i m - u l a t i o n s was to d e t e r m i n e w h e t h e r or no t i t is necessary to m o d e l a l l of the m o v e m e n t d y n a m i c s i n o rde r to c o r r e c t l y e s t ima te g r o w t h a n d m o r t a l i t y pa - ramete r s . F o r c o m p u t a t i o n a l eff ic iency I chose E q . 4.1 for these s i m u l a t i o n s . 4.2.10 Effects of Gear Selectivity and Capture Probability on Mortality and Movement Parameters W h e n there are m a r k - r e c a p t u r e d a t a ava i l ab le , m o v e m e n t ra tes m a y be es- t i m a b l e . T w o th ings are r e q u i r e d to d o so: fish m u s t be c a p t u r e d a n d m a r k e d at sizes s m a l l enough t h a t s u c h m o v e m e n t c a n be de tec t ed ( the r a t i o of the l e n g t h a t h a l f s e l e c t i v i t y to the gear to the m e a n l e n g t h at w h i c h m o v e m e n t takes p lace lh/1^ s m a l l ) , a n d t h e y m u s t be r e c a p t u r e d i n suff icient n u m b e r s ( h i g h c a p t u r e p r o b a b i l i t y ) . I therefore tes ted the p e r f o r m a n c e o f E q . 4.20 across a range o f c a p t u r e p r o b a b i l i t i e s a n d ra t ios o f m e a n l e n g t h at m o v e m e n t to the l e n g t h at h a l f s e l e c t i v i t y to the gear lh (l^/lh)- F o r these s i m u l a t i o n s I set the reference m o d e l 1^ : lh to 0.16, 1.16 a n d 1.83 a n d c a p t u r e p r o b a b i l i - t ies pt at a l l t i m e steps e q u a l to 0.05, 0.35 a n d 0.55. I r a n 100 s i m u l a t i o n s of for each c o m b i n a t i o n of pt a n d l^ : lh- Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 107 G r o w t h pa rame te r s were e s t i m a t e d u s i n g E q . 4.13 a s s u m i n g no mea- su remen t er ror a n d v a r i a t i o n i n pas t r e c r u i t m e n t a n o m a l i e s was i n c l u d e d as l o g - n o r m a l process er ror w i t h a m e a n of zero a n d s t a n d a r d d e v i a t i o n of 1 m u l t i p l i e d by a coefficient of v a r i a t i o n CVR = 0.2. E a c h s i m u l a t e d da tase t cons i s t ed of a s ingle m a r k e d c o h o r t of 1000 ( the a p p r o x i m a t e t o t a l n u m b e r m a r k e d i n D a d ' s a n d M o o s e P a s t u r e lakes over the s u m m e r of 2001) i n d i v i d - ua ls m a r k e d i n the nu r se ry area , w i t h r ecap tu re s a m p l i n g o c c u r r i n g every 2 m o n t h s for two years . 4.3 Results 4.3.1 Estimation Trials with No Movement E s t i m a t e s of g r o w t h p a r a m e t e r s were u n b i a s e d a n d w i t h l o w va r i ance w h e n la rge datasets (1000 g r o w t h i n c r e m e n t observa t ions ) were s i m u l a t e d w i t h no r e c r u i t m e n t v a r i a b i l i t y , no t a g loss a n d nei ther m e a s u r e m e n t no r age ing er ror ( F i g . 4.4 (a)) . W h e n d a t a were gene ra t ed w i t h t a g loss ( i j ) , b u t i t was n o t e s t i m a t e d , M was p o s i t i v e l y b i a sed . T h e g r o w t h i nc remen t d a t a p r e d i c t e d the cor rec t M a n d the a d d i t i o n of the L$ t e r m to the t o t a l l i k e l i h o o d d r a g g e d the e s t ima te of M u p b y 15 % ( F i g . 4.4 (b ) ) . T h e m o d e l s were no t r o b u s t to v i o l a t i o n s i n the a s s u m p t i o n o f s t ab le re- c r u i t m e n t or to s m a l l e r m a r k - r e c a p t u r e cohor t s . E v e n s m a l l a n n u a l v a r i a b i l - i t y i n r e c r u i t m e n t (CVR = 0.2) caused h i g h va r i ance i n g r o w t h a n d m o r t a l i t y Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 108 ( a ) i — i — i — i — r K h X2 y l h M tl (b) " i — i — i — i — i — i i r U K h ^ 2 7 lh M tl (c) (d) ; f - - LT) _ O - * V , * -L. * + o i n o - o ' i L , K ^ 1 ^ 2 7 lh M tl 1 — I — I — I — I — I — I — T L. K ^ 1 h 7 lh M tl F i g u r e 4.4: B o x p l o t s o f p r o p o r t i o n a l b ias ((true — estimate)/true) of 100 g r o w t h a n d m o r t a l i t y p a r a m e t e r e s t ima tes for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss u s i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b ) d a t a genera ted w i t h t a g loss a n d fit a s s u m i n g no t a g loss u s i n g the g r o w t h i n - c remen t 1/2 a n d t a g s u r v i v a l l i k e l i h o o d s L3 ( E q s . 4.8 a n d 4.17) , c) d a t a gene ra t ed w i t h t a g loss a n d e s t i m a t i n g t h i s t a g loss u s i n g the g r o w t h i n c r e m e n t L 2 a n d t a g s u r v i v a l l i k e l i h o o d s L3 ( E q s . 4.8 a n d 4 .17) , a n d d) d a t a genera ted w i t h t a g loss a n d es t ima t - i n g th i s t a g loss u s i n g length-age ( l a ) , g r o w t h i n c r e m e n t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s ( L 3 ) ( E q s . 4 .8, 4 .17 a n d 4.1) w i t h CVR — 0, no m e a s u r e m e n t or age ing e r ror . Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 109 pa rame te r s w h e n o n l y the m a r k - r e c a p t u r e d a t a were used ( F i g . 4.5 pane ls a, b , a n d c ) . D u e to h i g h covar i ance o f pa rame te r s , p o o r es t imates o f one resu l t ed i n p o o r es t ima tes o f the others . W h e n t a g loss was n o t fit ( F i g . 4.4 (b)) b u t d a t a genera ted w i t h i t , M was p o s i t i v e l y b i a sed b u t the es t ima tes of the g r o w t h pa rame te r s a n d K were a lso b i a sed . T h i s b ias was r e d u c e d w h e n t a g loss was fit ( F i g . 4.5 c ) , but o n l y m a r g i n a l l y . T h e a d d i t i o n o f length-age d a t a r e d u c e d the bias a n d the v a r i a n c e o f p a r a m e t e r e s t ima tes c o n s i d e r a b l y ( F i g . 4.5 d) b u t o n l y w h e n age ing e r ro r was zero. T h e a b i l i t y o f the length-age d a t a to c o m p e n s a t e for measu remen t errors ( in L 2 ) i n the c o m b i n e d l i k e l i h o o d was c o m p r o m i s e d w h e n a g i n g er ror was i n c l u d e d . B e c a u s e o f the f u n c t i o n tha t was used to genera te the age ing er ror , ( the t e n d e n c y of y o u n g fish be over -aged a n d o lde r f ish to be under-aged) M was p o s i t i v e l y b i a sed (there were few " o b s e r v a t i o n s " of o l d fish) a n d K nega t ive ly b i a sed . T h e p a r a m e t e r s used to descr ibe the va r i ance i n l e n g t h at age (A] a n d A 2 ) were p o o r l y e s t i m a t e d a l l scenar ios excep t the first whe re there was no r e c r u i t m e n t v a r i a t i o n a n d large s a m p l e s ize. W i t h few g r o w t h i n c r e m e n t samples , there was l i t t l e i n f o r m a t i o n a b o u t the d i s t r i b u t i o n of l eng ths at each age. I n genera l Ai a n d A 2 were the m o s t sens i t ive to d a t a s i m u l a t e d w i t h measu remen t e r ror . T h e r e were also the m o s t p o o r l y b e h a v e d d u r i n g f i t t i ng , of ten r e s u l t i n g i n the m o d e l s f a i l i n g to converge . T h i s was also the case for es t imates o f CV\a w h e n oa was def ined m o r e s i m p l y as a p r o d u c t of l e n g t h at Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 110 (a) " i — i — i — i i i r L. K h h 1 lh M tl (b) "i i i i i i r U K h >-2 Y lh M tl (c) i — i — i — i — i — i — i — r I™ K h ^-2 J lh M tl (d) " i — i — i — i — i — i i r L. K h h y lh M tl Figure 4.5: Boxplots of proportional bias ((true — estimate)/true) of 100 growth and mortality parameter estimates for scenarios a) data generated with no tag loss and fit assuming no tag loss using only the growth increment likelihood L 2 (Eq. 4.8). b) data generated with tag loss and fit assuming no tag loss using the growth in- crement 1/2 and tag survival likelihoods L 3 (Eqs. 4.8 and 4.17), c) data generated with tag loss and estimating this tag loss using the growth increment L 2 and tag survival likelihoods L 3 (Eqs. 4.8 and 4.17), and d) data generated with tag loss and estimat- ing this tag loss using length-age (Li), growth increment (L2) and tag survival likelihoods (L3) (Eqs. 4.8, 4.17 and 4.1) with CVR = 0.2, no ageing error, measurement error= 5mra. Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 111 (a) i — i — i i i i i r U K l i ^2 T lh M tl (b) i — m — ¥ — i — i — i — r L_ K h ^2 Y lh M tl (C) i™ K 2̂ y ih M ti ( d ) n — i — i — i — i — i — i — r U K h h y lh M ti F i g u r e 4.6: B o x p l o t s o f p r o p o r t i o n a l b ias ((true — estimate)/true) o f 100 g r o w t h a n d m o r t a l i t y p a r a m e t e r e s t ima tes for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss u s i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b) d a t a gene ra t ed w i t h t a g loss a n d fit a s s u m i n g no t a g loss u s i n g the g r o w t h i n - c remen t 1/2 a n d t a g s u r v i v a l l i k e l i h o o d s L3 ( E q s . 4.8 a n d 4 .17) , c) d a t a genera ted w i t h t a g loss a n d e s t i m a t i n g t h i s t a g loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4.17) , a n d d) d a t a genera ted w i t h t a g loss a n d e s t ima t - i n g th i s t a g loss u s i n g length-age (L\), g r o w t h i n c r e m e n t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s (L3) ( E q s . 4.8, 4 .17 a n d 4.1) w i t h CVR = 0.2, age ing er ror , m e a s u r e m e n t e r r o r = 5 m m . Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 112 age a n d a coefficient of v a r i a t i o n i n l e n g t h at age ( Z a C V / a ) . I n some cases, the s i m u l a t e d d a t a c o u l d best be e x p l a i n e d b y m a k i n g the va r i ance i n l eng th-a t - age ve ry large. T h o u g h f i x i n g these pa rame te r s a lways i m p r o v e d the s t a b i l i t y of the m o d e l i t o n l y i m p r o v e d , the b ias i n p a r a m e t e r e s t ima tes s i g n i f i c a n t l y for scenar io d ) . ( F i g . 4 .7) . 4.3.2 S i m u l a t i o n o f g r o w t h p a r a m e t e r e s t i m a t i o n w i t h l e n g t h - d e p e n d e n t m o v e m e n t W h e n each a rea was t r ea t ed as a separa te s tock w h i l e the s i m u l a t e d d a t a c a m e f r o m a s tock w i t h on togene t i c m o v e m e n t f rom area 1 to a r ea 2, the m a i n effect was t h a t g r o w t h p a r a m e t e r s were u n b i a s e d b u t gear s e l e c t i v i t y p a r a m e t e r s (4 a n d 7) , a n d M were b i a sed ( F i g . 4.8). I n areas 2 a n d 3 the m o d e l ' s aw ' the fa i lure to observe s m a l l f ish as, a gear effect, so 42 a n d 43 h a d m e a n p r o p o r t i o n a l biases of 200%. T h i s was the ' co r rec t ' i n t e r p r e t a t i o n of gear s e l e c t i v i t y i n a n y case, s ince o v e r a l l s e l e c t i v i t y c a n be v i e w e d as the p r o d u c t o f b o t h the gear effects a n d s p a t i a l d i s t r i b u t i o n effects. T h e s m a l l fish d i d no t appea r v u l n e r a b l e to the gear because t hey were no t there. M o v e m e n t ou t of a rea 1 ( the nu r se ry area) appears as a m e a n 50 % bias i n es t ima tes M. T h e v o n B e r t a l a n f f y g r o w t h pa rame te r s were u n b i a s e d across a range of s m a l l e r values b u t once b e c a m e large, the b ias i n M g r e w large or the m o d e l of ten c o u l d no t converge at a l l . I n the nu r se ry area , M was c o n f o u n d e d Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 113 (a) ~ \ — i — i — i i i i r U K ^2 Y lh M ti (c) d i—i—i—i—T—n-1—r U K ^1 ^2 1 lh M tl (b) i—i—i—i—i—i—i—r L. K h >-2 y lh M tl (d) " i — i — i — r — i — i — i — r L. K h h y lh M tl F i g u r e 4.7: B o x p l o t s o f p r o p o r t i o n a l b ias ((true — estimate)/true) of 100 g r o w t h a n d m o r t a l i t y pa r ame te r e s t ima tes for scenar ios a) d a t a genera ted w i t h no t a g loss a n d fit a s s u m i n g no t a g loss u s i n g o n l y the g r o w t h i n c r e m e n t l i k e l i h o o d L2 ( E q . 4 .8) , b) d a t a genera ted w i t h t a g loss a n d fit a s s u m i n g no t a g loss u s i n g the g r o w t h i n - c remen t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4 .17) , c) d a t a gene ra t ed w i t h t a g loss a n d e s t i m a t i n g th i s t ag loss u s i n g the g r o w t h i n c r e m e n t L2 a n d t a g s u r v i v a l l i k e l i h o o d s L 3 ( E q s . 4.8 a n d 4 .17) , a n d d) d a t a genera ted w i t h t a g loss a n d e s t ima t - i n g t h i s t a g loss u s i n g length-age ( I a ) , g r o w t h i n c r e m e n t (L2) a n d t a g s u r v i v a l l i k e l i h o o d s ( L 3 ) ( E q s . 4 .8, 4 .17 a n d 4.1) w i t h va r i ance i n l e n g t h at age pa rame te r s ( A i a n d A 2 f ixed at t he i r t rue va lues) Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 114 b y an appa ren t d o m e - s h a p e d gear s e l e c t i v i t y process (clue to m o v e m e n t ) . M was ove r - e s t ima t ed i n the nu r se ry area , whe re fish m o v e m e n t to o u t l y - i n g areas inc reased the appa ren t m o r t a l i t y . T h i s b ias decreased as the t o t a l p r o p o r t i o n r e m a i n i n g i n the nurse ry a rea Lin i nc reased a n d as the r a t i o of Ih/lfi inc reased . W h e n the t o t a l p r o p o r t i o n m o v i n g pi was h i g h , the bias i n the nu r se ry M\ was a lso h ighe r b u t i t d e p e n d e d a lso o n the r a t i o of lh to ZM a n d o n <7M. If m o v e m e n t was c o m p l e t e at sizes s m a l l e r t h a n the gear was ca - pab le of d e t e c t i n g ( s m a l l ZM a n d CTm), t h e n there was l i t t l e b ias i n the samples t a k e n f rom each area. W h e n the s i m u l a t e d gear was ab le to c a p t u r e sma l l e r a n d sma l l e r f ish, the s amples at y o u n g ages b e c a m e i n c r e a s i n g l y d i s t o r t e d , a n d the b ias i n M g r ew p r o p o r t i o n a t e l y larger i n the nu r se ry area. 4.3.3 Effects of Gear Selectivity and Capture Probability on Mortality and Movement Parameters A c r o s s a range of c a p t u r e p r o b a b i l i t i e s a n d gear s e l e c t i v i t y values , M was w e l l e s t i m a t e d ( F i g . 4.9) for m o d e l s t h a t i n c l u d e d m o v e m e n t . V a r i a n c e i n es t imates of M i nc reased as c a p t u r e p r o b a b i l i t y decreased, bu t the bias was neg l ig ib l e (1-3 %) a n d nega t ive . Ho wev e r , the p a r a m e t e r s t h a t def ined m o v e m e n t were o n l y w e l l e s t i m a t e d i n those cases where c a p t u r e p r o b a b i l i t i e s were r e l a t i v e l y h i g h (greater the 30 %) a n d where Ih/lhn was a p p r o x i m a t e l y 1. Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 115 o co l a "co c g ti o Q. o CM H I I I I I I I I I I I I I I I I I I I I I m1m2m;M-~J-"3Ki K2K3h,hfafafafa3\M l„2'h3 Yi Y2 Y3 F i g u r e 4.8: B o x p l o t s o f p r o p o r t i o n a l b ias ((true — estimate)/true) of 100 g r o w t h (LQO, -K\ A i , A 2 ) , m o r t a l i t y ( M ) , l e n g t h at h a l f gear se- l e c t i v i t y (//(), a n d gear s e l e c t i v i t y f u n c t i o n s lope (7) p a r a m e t e r s w h e n each a rea is a s s u m e d to be separa te s tock , w h i l e s i m u l a t e d d a t a come f rom a s tock w i t h on togene t i c m o v e m e n t f r o m a rea 1 to areas 2 a n d 3. Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 116 T h e r e are severa l i m p o r t a n t caveats . E v e n w i t h r e l a t i v e l y h i g h c a p t u r e p r o b a b i l i t i e s , lk/l/Ht set to 0.16 a n d 1000 f ish m a r k e d , the n u m b e r o f m a r k e d fish t h a t a c t u a l l y move over a two year p e r i o d is r e l a t i v e l y s m a l l ( a p p r o x - i m a t e l y 160) a n d those t agged f ish are d i s t r i b u t e d be tween two areas. So , even w i t h r e l a t i v e l y h i g h c a p t u r e p r o b a b i l i t i e s , the n u m b e r of obse rva t ions t h a t c a n be used to define the m o v e m e n t pa r ame te r s is s m a l l even w h e n a large p r o p o r t i o n o f the p o p u l a t i o n is l e a v i n g the nu r se ry a rea (70%) . W h e n lh/lhn = 1-16, the n u m b e r of m a r k e d fish t h a t are a c t u a l l y obse rved m o v i n g is m u c h s m a l l e r ( approx . 15-20). I n the case o f h i g h lh/hin = 1-83, p2 is no t e s t i m a b l e at a l l , or c o r r e c t l y e s t i m a t e d to be s m a l l , because there s h o u l d t y p - i c a l l y be no obse rva t ions of fish g o i n g t o t h a t area . A d d i t i o n a l l y , here a g a i n I a s s u m e d the same M for the m a r k e d c o h o r t a n d the h i s t o r i c a l age s t r u c t u r e s a m p l e so the e s t i m a t e d va lue o f M is r o b u s t to lower c a p t u r e p r o b a b i l i t i e s i n w a y s i t w o u l d not o the rwise be h a d the o n l y i n f o r m a t i o n a b o u t M been f r o m the m a r k - r e c a p t u r e d a t a . F i n a l l y , regardless o f w h e t h e r or no t p a r a m - eters de f in ing l eng th -dependen t m o v e m e n t c a n be e s t i m a t e d , a d m i t t i n g the p o s s i b i l i t y o f m o v e m e n t i n the m o d e l makes a b i g difference to v a r i a n c e o f the e s t ima t e o f M, s ince m a n y c o m b i n a t i o n s o f c a p t u r e p r o b a b i l i t y a n d n a t u r a l m o r t a l i t y c a n e x p l a i n the obse rved d a t a . Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 117 Ihg/lhm = 0.16 "i 1 1 1 r M Ihm Om Mn M2 Ihg/lhm =1.16 ~i 1 1 1 r M Ihm O m Mn M2 Ihg/lhm - 1-83 i 1 1 1 r M Ihm Om Mn M2 M Ihm "rn ~ i — i — i — ~ i — T M Ihm O m Mn M2 i — i — i — r M Ihm Om Mn M2 M Ihm O, T I I i r M Ihm O m Mn M2 t t _i_ _i_ ° M Ihm O m Mn M2 F i g u r e 4.9: B o x p l o t s of p r o p o r t i o n a l b ias ((true — estimate)/true) i n 100 es- t ima te s of M a n d m o v e m e n t pa ramete r s w i t h c a p t u r e p r o b a b i l i t y (rows) set to 0.05, 0.35, 0,55 a n d w i t h r a t i o of l e n g t h at h a l f gear s e l ec t i v i t y to the m e a n l e n g t h at m o v e m e n t / ^ / ^ set t o 0.16, 1.16 a n d 1.83. Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 118 4.4 Discussion T h e su i te of g r o w t h , s u r v i v a l a n d m o v e m e n t l i k e l i h o o d s I p resen ted here per - m i t s i m u l t a n e o u s ana ly s i s o f severa l processes u s i n g d a t a c o m m o n l y co l l ec t ed i n m a n y a p p l i e d eco logy p r o g r a m s . T h i s is p a r t i c u l a r l y usefu l because these pa rame te r s are n e a r l y a lways o f in teres t i n a p p l i e d eco logy b u t a l so because b o t h b i o l o g i c a l a n d o b s e r v a t i o n processes m e a n these p a r a m e t e r s m u s t be e s t i m a t e d together . C o n s i s t e n t w i t h the obse rva t ions of E v e s o n et a l . (2004) , different types of d a t a c o n t a i n m o r e i n f o r m a t i o n a b o u t some processes t h a n o thers . F o r e x a m p l e , o n l y w i t h v e r y la rge s a m p l e sizes (greater t h a n 100 000) c o u l d the length-age d a t a be used to e s t ima t e m o v e m e n t rates u s i n g s i m u l a t e d d a t a . T h e p r o b l e m is tha t u s i n g p r a c t i c a l s a m p l e sizes, e s t i m a t i n g M u s i n g l e n g t h - age d a t a requi res es t ima tes o f m o v e m e n t rates, a n d l i kewi se , i f m o v e m e n t ra tes are a f u n c t i o n of s ize, t h e n cor rec t es t imates of g r o w t h are a lso r e q u i r e d . O n e p o t e n t i a l l y ser ious p r o b l e m w i t h c o m b i n i n g a l l d a t a toge ther is t h a t some d a t a m a y bias p a r a m e t e r e s t ima tes due to i m p r o p e r l y m o d e l e d effects (for e x a m p l e m a r k - r e c a p t u r e d a t a w i t h a lo t of measu remen t e r ror , a s s u m e d t o have none) . M o r e d a t a a n d m o r e c o m p l i c a t e d l i k e l i h o o d s d o n o t necessar i ly m e a n be t t e r p a r a m e t e r es t imates , therefore the processes u sed to co l l ec t s u c h d a t a s h o u l d be e x a m i n e d v e r y careful ly . R a t h e r t h a n assume s m a l l measu remen t a n d age ing er rors as w e l l as c o n - ven ien t d i s t r i b u t i o n s for s u c h errors , I have t r i e d to s i m u l a t e the p e r f o r m a n c e Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 119 of the l i k e l i h o o d s u n d e r the wors t r a the r t h a n best s i t u a t i o n s . T h e biases i n pa r ame te r es t imates s h o w n here are therefore conse rva t ive , a n d worse t h a n m i g h t be e x p e c t e d i n m a n y m a r k - r e c a p t u r e a n d / o r age ing p r o g r a m s . M e a s u r e m e n t e r ror t ends to bias g r o w t h p a r a m e t e r e s t ima tes d i s p r o p o r - t i o n a t e l y i n sma l l e r , s lower g r o w i n g fish, fn th i s ana ly s i s , m e a s u r e m e n t er ror was set at 5 mm because i n the f ield large m e a s u r e m e n t errors o c c u r w h e n fish t a i l s are d a m a g e d f r o m s p a w n i n g , or w h e n la rger r u l e i n c r e m e n t s are m i s - r e a d (fish l e n g t h is r eco rded as 235 r a the r t h a n 230 mm for e x a m p l e ) . It is i n s t r u c t i v e to t h i n k o f the measu remen t e r ror r e l a t i v e to the a n n u a l i n - crement of the f ish. I n the s i m u l a t i o n s p e r f o r m e d here a 5 mm measu remen t er ror is la rger t h a n the a n n u a l i n c r e m e n t of f ish grea ter t h a n age 12, less t h a n h a l f the m a x i m u m age. T h e m a g n i t u d e a n d d i r e c t i o n of the s i m u l a t e d age ing e r ror was cons ider - able . T h e cho ice o f s u c h a f u n c t i o n to represent th i s e r ro r was based o n the rev iew of C a m p a n a (2001) w h o shows t h a t v e r y few age ing p r o g r a m s v a l i d a t e the i r age ing c o r r e c t l y or even at a l l . M u c h age ing c a n r e a s o n a b l y be a s s u m e d cor rec t , or to have n o r m a l l y d i s t r i b u t e d er ror p u r e l y f r o m c o u n t i n g . H o w - ever, the r ea l i t y of m o s t s t o c k assessment p r o g r a m s is t h a t a l l these sources o f er ror are present a n d there are s y s t e m a t i c biases t o w a r d s u n d e r - a g i n g o lder f ish. It is un reasonab le to assume m a r k - r e c a p t u r e p r o g r a m s for size a n d fish s u r v i v a l are no t sub jec t to some v i o l a t i o n o f a s s u m p t i o n s a b o u t cons t an t r e c r u i t m e n t , l a ck o f m e a s u r e m e n t er ror , no tag- loss e tc . The re fo re , the choice Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 120 of m e t h o d s for e s t i m a t i n g g r o w t h pa rame te r s u s i n g m a r k - r e c a p t u r e is a cho ice be tween the least of ev i l s . O n one h a n d , t r a d i t i o n a l m e t h o d s ignore n a t u r a l m o r t a l i t y , gear s e l e c t i v i t y a n d measu remen t e r ror a l toge ther . M e t h o d s such as L a s l e t t et a l . (2002) a n d E v e s o n et a l . (2004) d o no t accoun t for s ize- se lec t iv i ty , so over -es t ima te K a n d of the t o t a l p o p u l a t i o n , an issue tha t is i r re levan t i f the s t o c k assessment sc ient i s t wishes o n l y to desc r ibe the g r o w t h of the p o p u l a t i o n b e i n g ha rves t ed . O n the o ther , the m e t h o d I d e v e l o p e d here is d a t a in tens ive , m e a n s t o l e r a t i n g at least a 5 — 1 0 % bias i n K a n d p o o r l y e s t i m a t e d p a r a m e t e r s d e s c r i b i n g the va r i ance i n length-a t -age . Ho wev e r , the d i r e c t i o n o f the b ias i n K a n d M is the m o s t conse rva t ive . S t o c k assessments u s i n g u n d e r e s t i m a t e s o f K a n d M p r e d i c t s m a l l e r t h a n a c t u a l y i e l d - p e r - rec ru i t a n d cu r r en t b i o m a s s . F u r t h e r , the b ias does n o t m a t t e r i f the ob jec t i ve is s i m p l y to c o m p a r e the g r o w t h of one s tock to ano the r . C o m b i n i n g length-age , g r o w t h i n c r e m e n t a n d m a r k - r e c a p t u r e d a t a c a n o n l y be used to e s t i m a t e o f tag- loss w h e n r e c r u i t m e n t is r ea sonab ly cons tan t over t i m e . I n cases w h e r e r e c r u i t m e n t is v a r i a b l e , noise caused b y the re- c r u i t m e n t v a r i a t i o n makes M uns tab le , hence u n r e l i a b l e as a resource base for d e t e c t i n g tag- loss . A l s o , s ince the M of the p o p u l a t i o n is w h a t is o f in ter - est i n some cases, m a k i n g such an a s s u m p t i o n defeats the pu rpose of d o i n g the m a r k - r e c a p t u r e i n the first p lace . H o w e v e r there is a cons ide rab le l i t e r a - tu re d e v e l o p i n g for e s t i m a t i n g tag-loss ( E b e n e r a n d C o p e s , 1982; P i e r c e a n d T o m c k o , 1993; S w a n s o n a n d S c h r a m , 1996; M c G l e n n o n a n d P a r t i n g t o n , 1997; J u l l i a r d et a l . , 2001; F e l d m a n et a l . , 2002; R i k a r d s e n et a l . , 2002; B r a t t e y a n d Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 121 C a d i g a n , 2004) so such i n f o r m a t i o n c o u l d be used to genera te p r io r s for the tag-loss . B u t none o f th i s l i t e ra tu res addresses p r o b l e m s w i t h l o n g - t e r m tag- g i n g m o r t a l i t y or t a g u n d e r - r e p o r t i n g . A d m i t t i n g a range o f poss ib le tag-loss values is i m p o r t a n t for p r o p e r l y a d m i t t i n g u n c e r t a i n t y a b o u t m o r t a l i t y es- t i m a t e s s ince the t rade-off be tween tag- loss a n d m o r t a l i t y is one- to-one a n d u n c e r t a i n t y a b o u t w h a t the t rue tag-loss is p ropaga te s t h r o u g h the es t ima tes of a l l the o the r pa rame te r s . A s s u m i n g t h a t cons t an t r e c r u i t m e n t so tag- loss c a n be e s t i m a t e d is ob - v i o u s l y i nco r r ec t . Never the less w i t h e x t e r n a l tags i t is be t t e r t h a n m a k i n g the s t i l l worse a s s u m p t i o n of no tag-loss , no u n d e r - r e p o r t i n g , a n d no t ag - m o r t a l i t y . T h i s is p a r t i c u l a r l y t rue w h e n e x t e r n a l tags are used. W h e r e the m a g n i t u d e of the t a g - l o s s / t a g - m o r t a l i t y is large , the b ias i n M ( a n d the c o r r e s p o n d i n g p o s i t i v e b ias i n es t ima tes o f the p o p u l a t i o n size where a p p l i - cable) p r o d u c e d b y s u c h a s s u m p t i o n s f a i l i n g is cons ide rab l e a n d also i n the least conse rva t ive d i r e c t i o n ( o v e r - e s t ima t i n g M a n d hence the p o p u l a t i o n s ize) . F o r e x a m p l e , tag-loss for d a r t tags has been r e p o r t e d b y M c G l e n n o n a n d P a r t i n g t o n (1997) at O.OOOGcT 1 a n d for a n c h o r tags a t 10 - 2 0 % y r ~ 1 ( E b e n e r a n d C o p e s , 1982). E v e n i n the case o f i n t e r n a l tags, pass ive i n d u c e d t r a n s p o n d e r t a g ( P I T ) fa i lure has been r e p o r t e d i n sha rks as h i g h as 1 2 % y r _ 1 ( F e l d m a n et a l . , 2002) . T h e s e biases are a lso i n the least conse rva t ive d i r ec - t i o n w i t h respect to e x p l o i t a t i o n ra te p r e d i c t i o n s . E s t i m a t i n g h igher t ha t a c t u a l n a t u r a l m o r t a l i t y means p r e d i c t i n g h i g h e r t h a n o p t i m a l e x p l o i t a t i o n rates. Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 122 T h e s i m u l a t i o n s were u n r e a l i s t i c i n a s s ign ing fixed nu r se ry a n d n o n - n u r s e r y b o u n d a r i e s . W h e n s tocks have s u c h a s p a t i a l s t r uc tu re , fishing a n d s u r v e y s a m p l i n g are l i k e l y to ove r l ap each a rea to a c e r t a i n ex ten t . Neve r the l e s s a n u m b e r o f fisheries are d i v i d e d a l o n g s i m i l a r l ines w i t h a n onshore sector t a r g e t i n g younge r fish a n d a n offshore sector t a r g e t i n g different fishes, e.g. P a c i f i c H a k e or Y e l l o w f i n t u n a . In s u c h s i t u a t i o n s separa te gear a n d s p a t i a l effects need to be cons ide red for d a t a c o m i n g f r o m each fishing sector i n any case (onshore , offshore e tc . ) , because i n a d d i t i o n to s p a t i a l effects, t he gear used a lso differs. T h i s is no t the first pape r to use the s ta te-space m e t h o d s l ike D e V a l p i n e a n d H a s t i n g s (2002) w i t h m a r k - r e c a p t u r e d a t a . R i v o t et a l . (2004) u sed th i s m e t h o d a n d m a r k - r e c a p t u r e d a t a to e s t ima t e u p s t r e a m m i g r a t i o n of a d u l t s a n d d o w n s t r e a m m i g r a t i o n of j u v e n i l e s i n A t l a n t i c s a l m o n . C l a r k et a l . (2005) use a h i e r a r c h i c a l B a y e s i a n m o d e l to e s t ima t e m a t u r a t i o n age, s u r v i v o r s h i p , a n d p o p u l a t i o n g r o w t h i n s i m u l a t e d a n d r ea l d a t a , a n d J o n s e n et a l . (2003) used s ta te space approaches to c o m b i n e i n f o r m a t i o n f rom m u l t i p l e i n d i v i d u a l m o v e m e n t t ra jec tor ies w i t h m i s s i n g d a t a . F i n a l l y s ta te space m e t h o d s have been used to e s t ima te g r o w t h p a r a m e t e r s for p h y s i o l o g i c a l l y based i n d i v i d - u a l g r o w t h m o d e l s w i t h size t r a j e c t o r y d a t a ( F u j i w a r a et a l . , 2005) . T h e m e t h o d used i n th i s s t u d y is no t fu l ly a s ta te space f o r m u l a t i o n because o f the p r e d i c t e d g r o w t h t ra jec tor ies are m o d e l e d d e t e r m i n i s t i c a l l y u s i n g the v o n B e r t a l a n f f y g r o w t h m o d e l , b u t i t is the first to c o m b i n e g r o w t h i n f o r m a t i o n w i t h m o v e m e n t d a t a to e s t ima te a s i ze -dependen t m o v e m e n t f u n c t i o n . U n f o r - Chapter 4. Estimating movement and growth parameters given size-dependent spatial ontogeny 123 t u n a t e l y the mode l s p resen ted here requ i re a lo t of d a t a , (several 100 m a r k e d a n d r e c a p t u r e d f ish, a p p r o x i m a t e l y 1000 length-age obse rva t ions , a n d i n the case o f m o v e m e n t severa l m a r k e d fish obse rved to have m o v e d ) a n d are no t robus t to e i ther measu remen t or age ing error . S ince da tase ts used to measu re g r o w t h a n d m o r t a l i t y m a y n o t c o n t a i n e n o u g h i n f o r m a t i o n to e s t ima t e p a r a m e t e r s such as gear s e l e c t i v i t y a n d m o r - ta l i ty , i n t e g r a t i n g the i n f o r m a t i o n f r o m a l l ava i l ab le d a t a sources to e s t ima t e g r o w t h pa rame te r s s h o u l d be e x p a n d e d to the ent i re s t ock assessment process for m a n y c o m m e r c i a l f isheries. S t o c k assessments t y p i c a l l y c o n t a i n i n f o r m a - t i o n a b o u t the f i sh ing m o r t a l i t y a n d gear s e l e c t i v i t y a n d often have m a n y years o f length-age , or l eng th - f r equency or m a r k - r e c a p t u r e d a t a . S e v e r a l years of th i s d a t a c o u l d be i n c o r p o r a t e d i n t o m u l t i p l e l eng th-age a n d m a r k - r e c a p t u r e tab les to t r ack changes i n n a t u r a l m o r t a l i t y a n d g r o w t h over the t i m e of a fishery. Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 124 Chapter 5 Predicted and Observed Ecosystem Responses to Fishing Abstract I used a s i m p l e ecosys t em m o d e l a n d c o m p a r e d the p r e d i c t i o n s to obse rved responses f o l l o w i n g e x p e r i m e n t a l f i sh ing i n a two fish l ake s y s t e m w i t h r a i n - b o w t r o u t a n d n o r t h e r n p i k e m i n n o w . C o n s i s t e n t w i t h the m o d e l ' s p r ed i c - t ions , g r o w t h a n d m o r t a l i t y o f j u v e n i l e r a i n b o w t r o u t was h igher r e l a t i ve to the c o n t r o l i n lakes where n o r t h e r n p i k e m i n n o w were r e m o v e d w h i l e a d u l t r a i n b o w t r o u t s u r v i v a l r e m a i n e d u n c h a n g e d . V i s u a l s u r v e y ind ices o f n o r t h - e r n p i k e m i n n o w fry i n d i c a t e d s u r v i v a l o f 1 + fish w or se ne d a n d 2 + i m p r o v e d f o l l o w i n g f i sh ing . C o n s i s t e n t w i t h the m o d e l ' s p r e d i c t i o n s no o b v i o u s m o r - t a l i t y or g r o w t h responses were obse rved i n n o r t h e r n p i k e m i n n o w . W h i l e the agreement be tween the m o d e l a n d observa t ions was e n c o u r a g i n g , f ie ld t e s t i ng such a h y p o t h e s i s was f raught w i t h d i f f icul ty . T h e p r o b a b i l i t y d i s t r i b u t i o n s of the pa rame te r s of in teres t were v e r y b r o a d a n d the m o d e l p r e d i c t s m a n y of the i m p o r t a n t d y n a m i c s , i n p a r t i c u l a r b e h a v i o r m e d i a t e d v u l n e r a b i l i t y ex- change rates, to o c c u r i n f ish s ize classes a n d groups o f z o o p l a n k t o n t h a t are d i f f icu l t to observe. keywords: non- t a rge t species response to f i sh ing , c u l t i v a t i o n - d e p e n s a t i o n , n o r t h e r n p i k e m i n n o w , m o v e m e n t m o r t a l i t y e s t i m a t i o n Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 125 5.1 Introduction J u v e n i l e s u r v i v a l is u s u a l l y a s s u m e d to i m p r o v e at l o w s tock size so as to m a k e r e c r u i t m e n t m u c h m o r e sens i t ive to s tock s ize t h a n w o u l d be the case i f s u r v i v a l were cons t an t . T h e r e is g o o d ev idence to s u p p o r t th i s a s s u m p t i o n ( M y e r s et a l . , 1999, 1995b) . G i v e n the fa i lure of a n u m b e r of o v e r e x p l o i t e d s tocks ( S h e l t o n a n d H a r l e y , 1999) to recover f o l l o w i n g co l lapse , there has recen t ly been cons ide rab l e c o n c e r n a b o u t w h e t h e r or no t r e c r u i t m e n t de- creases at l o w s tock s ize (depensa t ion ) . M y e r s et a l . (1995b) c o n c l u d e d t h a t o n l y 3 / 1 2 8 s tocks showed s ign i f i can t d e p e n s a t i o n . Never the less , cons ide rab le w o r k fo l lowed the i r a n a l y s i s w i t h p a r t i c u l a r a t t e n t i o n d e v o t e d to d e t e r m i n i n g w h e t h e r or no t m o d e l s p a r a m e t e r i z e d w i t h d e p e n s a t i o n fit the d a t a be t t e r t h a n those w i t h o u t i t ( L i e r m a n n a n d H i l b o r n , 1997, 2001) a n d i f depensa- t i o n c o u l d be de t ec t ed at a l l i n co m p lex es o f m u l t i p l e ' sub- s tocks ' , each w i t h d i f fer ing p r o d u c t i v i t e s ( F r a n k a n d B r i c k m a n , 2000) . I n a l l these cases, the depensa to ry d y n a m i c s were a s su med s t a t i o n a r y i n a s t a t i s t i c a l sense, where the pa rame te r s d e s c r i b i n g the r e l a t i o n s h i p are a s s u m e d t i m e - i n v a r i a n t . C h a n g e s i n e c o s y s t e m p r o d u c t i v i t y a n d the process o f f i sh ing i t se l f l i k e l y a l te r r e c r u i t m e n t d y n a m i c s of fish s tocks over t i m e , s ince they a l te r f o o d a n d p r e d a t i o n reg imes . F o r a g i n g a r ena t heo ry ( W a l t e r s a n d Juanes , 1993; W a l t e r s a n d K o r m a n , 1999) p red ic t s t h a t as the r a t i o of p r e d a t i o n r i sk to food p r o d u c t i o n changes over t i m e , t hen so t o o w i l l r e c r u i t m e n t . A b r u p t ecosys tems s ta te t r a n s i t i o n s have been obse rved i n a q u a t i c sys tems (Scheffer Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 126 et a l . , 2001b; Scheffer a n d C a r p e n t e r , 2003) . W a l t e r s a n d K i t c h e l l (2001) pos tu l a t e a specif ic hypo thes i s t e r m e d " C u l t i v a t i o n - D e p e n s a t i o n " e x p l a i n i n g h o w such shif ts m i g h t h a p p e n i n response to f i sh ing , a n d w h a t obse rva t ions s h o u l d be obse rved i n the field i f they are. I f t he i r e x p l a n a t i o n is cor rec t , the c u l t i v a t i o n - d e p e n s a t i o n h y p o t h e s i s is t h a t i f a d o m i n a n t s tock is r educed , there w i l l be a r e d u c t i o n i n the extent to w h i c h i t " cu l t i va t e s" m o r e favor- able c o n d i t i o n s for i t s j u v e n i l e s by r e d u c i n g a b u n d a n c e o f c o m p e t i t o r s a n d preda tors . C u l t i v a t i o n - d e p e n s a t i o n effects ar ise i n E c o s i m I I ( W a l t e r s et a l . , 2000) m o d e l s t h o u g h the f o l l o w i n g sequence of events ( W a l t e r s a n d K i t c h e l l , 2001) . F i s h i n g reduces the a d u l t p o p u l a t i o n size o f a fish species a n d hence, the t o t a l n u m b e r of j u v e n i l e s i n p r e d a t i o n refuges. J u v e n i l e s reduce feeding t i m e or t i m e spent at b o d y sizes s m a l l e n o u g h to be v u l n e r a b l e to p r e d a t i o n r i sk . J u v e n i l e m o r t a l i t y t h e n decreases so t h a t the net n u m b e r of r ec ru i t s s tays n e a r l y cons t an t even t h o u g h fewer j uven i l e s are b e i n g p r o d u c e d . H o w e v e r , i f there is p r e d a t i o n be tween the a d u l t f ish a n d a p r e d a t o r or c o m p e t i t o r o f the juven i l e s (a "forage" fish) t h e n as a d u l t d e n s i t y is r e d u c e d , the forage f ish is re leased to increase i n a b u n d a n c e . T h e n one or t w o nega t ive effects c a n occu r . I f the forage fish p r e y d i r e c t l y o n juven i l e s , t h e n p r e d a t i o n m o r t a l i t y is d i r e c t l y inc reased . If the forage fish a n d j u v e n i l e s are c o m p e t i t o r s , inc reased forage fish a b u n d a n c e leads to r e d u c e d f o o d d e n s i t y a n d hence, inc reased j u v e n i l e fo rag ing t i m e a n d genera l p r e d a t i o n r i sk . T h e s e d y n a m i c s c a n be represented w i t h a t r o p h i c t r i ang le such as t h a t i n F i g . 1.1. Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 127 I used f ie ld d a t a co l l ec t ed i n 2001-2003 to c o n s t r u c t e d a s i m p l e ecosys t em m o d e l o f s m a l l lakes i n n o r t h e r n B r i t i s h C o l u m b i a C a n a d a (see S e c t i o n 2.2.1) u s i n g E c o p a t h w i t h E c o s i m ( W a l t e r s a n d C h r i s t e n s e n , 2004) . T h e s e lakes h a d two p r e d a t o r y fish species, r a i n b o w t r o u t (Onchorhynchus mykiss) a n d s t u n t e d n o r t h e r n p i k e m i n n o w (Ptychocheilus oregonensis). T h e s t u d y s y s t e m h a d the fo rag ing a r e n a s t r u c t u r e d e s c r i b e d above w i t h j u v e n i l e r a i n b o w t r o u t a n d n o r t h e r n p i k e m i n n o w ( in a l l age classes) conf ined to the m a r g i n s o f the lake d u r i n g the d a y (Sec t ion 5.2.2), whereas a d u l t r a i n b o w • t r o u t were d i s t r i b u t e d m a i n l y i n the center o f the lakes . I s a m p l e d i n the s y s t e m a n d m e a s u r e d the g r o w t h a n d s u r v i v a l response of the t w o fish c o m m u n i t i e s to d e p l e t i o n f i sh ing (where a large p r o p o r t i o n o f the p o p u l a t i o n was fished i n a short, series of fishing bou t s ) o f b o t h r a i n b o w t r o u t a n d n o r t h e r n p i k e m i n n o w . I found t h a t cons i s t en t w i t h m o d e l p r e d i c t i o n s , s u r v i v a l a n d g r o w t h of s m a l l r a i n b o w t r o u t decreased i n lakes where n o r t h e r n p i k e m i n n o w were r e m o v e d a n d t h a t no changes i n g r o w t h or s u r v i v a l for a d u l t a d u l t n o r t h e r n p i k m e i n n o w c o u l d be de t ec t ed a n d i t was no t pos s ib l e to e s t ima t e g r o w t h a n d s u r v i v a l p a r a m e t e r s due to l o w s a m p l e sizes for a d u l t r a i n b o w t r o u t . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 128 5.2 Methods 5.2.1 Ecosim Mode l of Predicted Observations T h e de ta i l s of the E c o p a t h - E c o s i m m o d e l i n g a p p r o a c h are d i scussed ex t en - s ive ly i n W a l t e r s et a l . (1997, 2000) a n d W a l t e r s a n d C h r i s t e n s e n (2004) so w i l l o n l y be br ie f ly d i scussed here. E c o p a t h is used to define the i n i t i a l ecosys- t e m b i o m a s s s ta te t ha t is m a s s - b a l a n c e d , i .e. where e s t i m a t e d t o t a l b i o m a s s loss ra tes Zi for each m o d e l e d b i o m a s s g r o u p i are p a r t i t i o n e d a m o n g as- s u m e d s t a t i c p r e d a t i o n ra te c o m p o n e n t s a n d u n a c c o u n t e d losses. I n E c o s i m m o d e l s , these s t a t i c flows are t u r n e d i n t o d y n a m i c , t i m e - v a r y i n g p r e d i c t i o n s b y a s s u m i n g t h a t flows C f r o m p rey i t o p r e d a t o r j g roups are m e d i a t e d b y v u l n e r a b i l i t y exchange rates vitj be tween " v u l n e r a b l e " a n d n o n - v u l n e r a b l e p rey p o o l s ( W a l t e r s et a l . , 2000): c >•,.,<>,., (5. |) + i ,.j'iKjPj where a ; is the effective search r a t e , o f . p reda to r s , B t he b i o m a s s a n d • the exchange ra te f r o m the v u l n e r a b l e p o o l b a c k t o the n o n - v u l n e r a b l e p o o l , a s s u m e d to be e q u a l to vitj. T h e v u l n e r a b i l i t y exchange ra tes ^ j s ' s d e t e r m i n e the ra te at w h i c h p r e y enter e i ther a v u l n e r a b l e s ta te j ( w h i c h is ava i l ab le to be ea ten b y p reda to r s ) f r o m a n i n v u l n e r a b l e s ta te i ( a s sumed n o t to be v u l n e r a b l e to p r e d a t o r s ) . T h e s e d y n a m i c s are a s sumed to o c c u r o n a m u c h faster t i m e scale t h a n o the r Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 129 p o p u l a t i o n d y n a m i c s such as p r e d a t i o n a n d m o r t a l i t y ( W a l t e r s a n d Juanes , 1993; A b r a m s a n d W a l t e r s , 1996) a n d thus reach an e q u i l i b r i u m v u l n e r a b l e p o o l o f p r e y V tha t is ava i l ab l e to p reda to r s ( W a l t e r s et a l . , 1997) . T h e b e h a v i o r a l i n t e r p r e t a t i o n of w h a t Vifs are c a n best be t h o u g h t o f as any b e h a v i o r (avoidance , f ish s c h o o l i n g , h a b i t a t refuges etc.) t h a t l i m i t s the access of the prey to the p reda to r s . S m a l l Vij's m e a n t h a t a lower p r o p o r t i o n of the t o t a l p r e y p o p u l a t i o n is i n the v u l n e r a b l e s ta te at a n y g i v e n t i m e , a n d v i c e versa . T h e s e ra tes therefore have a v e r y large inf luence o n the p o p u l a t i o n d y n a m i c s p r e d i c t e d b y E c o s i m . S m a l l vitj's i m p l y a lo t o f f o r a g i n g a r e n a s t r u c t u r e ( W a l t e r s a n d Juanes , 1993), whereas large ra tes i m p l y c l a s s i ca l t y p e II (Ffo l l ing 1959) p r e d a t i o n d y n a m i c s . O v e r a l l b iomass was s i m u l a t e d for pe l ag ic z o o p l a n k t o n , c h a o b o r u s l a rvae , ben thos , p h y t o p l a n k t o n a n d d e t r i t u s s ince d a t a to e s t ima te these were u n - ava i l ab l e . S i m p l i f i c a t i o n o f the s y s t e m i n t o these g roups was done t o a l l o w a focus o n specif ic hypo theses a b o u t s ize-dependent p r e d a t i o n a n d c o m p e - t i t i o n i n t e r ac t i ons i n v o l v i n g the t w o fish species. C h a o b o r u s l a rvae were s i n g l e d o u t as a p a r t i c u l a r l y i m p o r t a n t g r o u p because t h e y are the m a i n d ie t i t e m of (70%) of p i k e m i n n o w b u t were v i r t u a l l y absent i n r a i n b o w t r o u t s t o m a c h contents . P i k e m i n n o w u n d e r g o d a i l y offshore m i g r a t i o n s t h a t are c o n c u r r e n t w i t h the n i g h t l y r ise of c h a o b o r u s (Tab le 5.2.1, D a v e O ' B r i e n un- published data). T h e d ie t m a t r i x was p a r a m e t e r i z e d u s i n g s t o m a c h con ten t d a t a c o l l e c t e d over 2001 a n d 2002 ( D a v e O b r i e n unpublished data). I u sed the m u l t i - s t a n z a a p p r o a c h ( W a l t e r s a n d C h r i s t e n s e n , 2004) for Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 130 m o d e l i n g fish species i n the s y s t e m , w i t h pa r ame te r s l i s t e d i n T a b l e 5.2.1. T h e m u l t i - s t a n z a ve r s ion of E c o s i m a l lows for the d i v i s i o n of a species i n t o age-size g roups (s tanzas) a s s u m e d to share s i m i l a r m o r t a l i t y a n d d ie t c o m - p o s i t i o n . It assumes g r o w t h fo l lows the v o n B e r t a l a n f f y (von Ber t a l an f fy , 1934) g r o w t h curve . T o i n i t i a l i z e the p o p u l a t i o n s t a n z a age s t r u c t u r e , i t is a s s u m e d t h a t r e c r u i t m e n t a n d m o r t a l i t y have been s tab le for l o n g e n o u g h for the p o p u l a t i o n to be at a s t ab le age d i s t r i b u t i o n . L e a d i n g values for m o r - t a l i t y are needed for a l l s t anzas , w h i l e a n n u a l c o n s u m p t i o n per u n i t b i o m a s s Q/B a n d b i o m a s s are needed for one l e a d i n g g roup . T h e b i o m a s s a n d Q/B of the r e m a i n i n g g roups are c a l c u l a t e d u s ing age-dependent we igh t wa a n d s u r v i v o r s h i p la. T h e i n i t i a l p o p u l a t i o n g r o w t h co r r ec t ed p r o p o r t i o n of a f ish la is m o d e l e d i n E c o p a t h as: whe re Z is th i s case is the i n s t an t aneous a n n u a l n a t u r a l m o r t a l i t y ( i n years yr~l) T h e la for any g i v e n age is the s u m of Zs is over a l l ages u p t o a, a n d B A / B t e r m represents the effect o n re la t ive n u m b e r s at age of the p o p u l a t i o n g r o w t h ra te ( W a l t e r s a n d C h r i s t e n s e n , 2004) . T h e r e l a t ive b iomass of o the r s t anzas re la t ive to the l e a d i n g s t a n z a is i n i t i a l i z e d u s i n g r e l a t ive b i o m a s s p r o p o r t i o n s bs, whe re for any s t a n z a s: 7 - p-l2aZa-aBA/B (5.2) a (5.3) Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 131 ( W a l t e r s a n d C h r i s t e n s e n , 2004) . T h e re l a t ive we igh t s at age wa are a s sumed to fo l low the v o n B e r t a l a n f f y p r e d i c t i o n : wa = (l- eKaf. (5.4) where K is the v o n B e r t a l a n f f y g r o w t h p a r a m e t e r e s t i m a t e d for b o t h f ish species u s i n g the m e t h o d s d e s c r i b e d i n S e c t i o n 5.2.6. Q / B es t imates for n o n - l e a d i n g s t anzas are c a l c u l a t e d w i t h a s i m i l a r a p p r o a c h , a s s u m i n g t h a t feeding rates v a r y w i t h age as the 2 / 3 power of b o d y we igh t ( W a l t e r s a n d C h r i s t e n s e n , 2004) . C o n s u m p t i o n per u n i t b i o m a s s r a t io s for o ldes t s t anza ' s were a s sumed to be 1.5 for n o r t h e r n p i k e m i n n o w a n d 5 for r a i n b o w t r o u t . I d i v i d e d n o r t h e r n p i k e m i n n o w ( N P M ) i n age i n t o 4 l i f e -h i s to ry s tanzas deno t ed by the age a at w h i c h the s t a n z a b e g a n . T h i s s t a n z a d i v i s i o n was chosen s ince n o r t h e r n p i k e m i n n o w are m a r k e d l y different i n sizes for o n l y the first four years . R a i n b o w t r o u t ( R B T ) were d i v i d e d i n t o t w o s tanzas , 0-1 a n d 2 + years . R a t h e r t h a n p a r a m e t e r i z e the fish g roups i n abso lu t e b iomass , t hey were p a r a m e t e r i z e d r e l a t i ve to each o ther . W h e r e the b i o m a s s of the 4 + n o r t h e r n p i k e m i n n o w a n d the 2 + r a i n b o w t r o u t were a s sumed e q u a l t h e y were b o t h set to 1. E c o p a t h was used to c a l c u l a t e i nve r t eb ra t e b iomasses needed s u p p o r t the base e s t i m a t e d c o n s u m p t i o n ra tes caused b y these r e l a t ive b iomasses , a s s u m i n g reasonable e c o t r o p h i c efficiencies ( T a b l e 5.2.1, e c o t r o p h i c efficiency is p r o p o r t i o n of Zi e x p l a i n e d b y m o d e l e d p r e d a t i o n ) . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 132 Star t Rela t ive Instantaneous N a t u r a l C o n s u m p t i o n per A g e yr~l Biomass M o r t a l i t y (Z yr~l) unit biomass yr~l Northern pikeminnow 1 0.002 3 13.033 2 0.009 0.5 5.362 3 0.022 0.3 3.5 4+ 1 0.2 1.5 Rainbow trout 0 0.061 3 16.491 2 1 0.7 5 T a b l e 5.1: P a r a m e t e r s for m u l t i - s t a n z a r ep re sen t a t i on of n o r t h e r n p i k e m i n n o w a n d r a i n b o w t r o u t p o p u l a t i o n s I p r e d i c t e d changes i n m o r t a l i t y , b o d y g r o w t h , p o p u l a t i o n s ize a n d feed- i n g t i m e f o l l o w i n g a ve ry shor t pu l se o f in tense ' d e p l e t i o n ' f i sh ing F = 1 a p p l i e d for one year . I e x p l o r e d the s e n s i t i v i t y of the m o d e l to a range of v u l n e r a b i l i t y exchange rates (vij) for the f ish a n d z o o p l a n k t o n g roups . I e x p l o r e d h o w differences i n r e l a t ive f ish b i o m a s s a n d v u l n e r a b i l i t y exchange ra tes the m o d e l w o u l d or w o u l d no t p r o d u c e C u l t i v a t i o n - D e p e n s a t i o n effects, a n d i n p a r t i c u l a r two e q u i l i b r i a w i t h o n l y one f ish g r o u p d o m i n a n t at each. I n search for p a r a m e t e r c o m b i n a t i o n s t h a t w o u l d p r o d u c e m u l t i p l e e q u i l i b r i a , the two fish b iomasses were set to 1.0, so as to represent a p o t e n t i a l l y u n - s tab le e q u i l i b r i u m p o i n t be tween the t w o s tab le e q u i l i b r i a . W h e n t w o s tab le s tates exis t , a n y f i sh ing d i s t u r b a n c e tends over t i m e to one of the b iomasses b e i n g d o m i n a n t . T a b l e 5.2: D i e t c o m p o s i t i o n m a t r i x for E c o p a t h m o d e l . E a c h c o l u m n is the d ie t c o m p o s i t i o n of a p a r t i c u l a r p r eda to r , as a p r o p o r t i o n of t o t a l a n n u a l b iomass food in take Z o o P h y t o D e t . P r e y P r e d R B T 2 + R B T 1 N P M 4 + N P M 3 N P M 2 N P M 1 C h a o b B e n R B T 2 + R B T 1 0.049 0.02 0.091 N P M 4 0.00001 N P M 3 0.00005 N P M 2 0.0001 0.00049 N P M 1 0.0005 0.009 C h a o b 0.665 0.686 0.27 B e n 0.909 .0.1 0.19 0.196 0.27 0.1 Z o o 0.091 0.9 0,095 0.098 0.36 0.9 1 P h y t o 0.05 D e t . 0.95 T a b l e 5.3: B a s i c p a r a m e t e r i n p u t s for E c o p a t h M o d e l B i o m a s s P r o d u c t i o n per u n i t b iomass yr~l C o n s u m p t i o n per u n i t b iomass yr~ 1 E c o t r o p h i c efficiency U n a s s i m i l a t e d C o n s u m p t i o n R B T 2 + 1 0.7 5 0.2 R B T 1 0.0613 3 16.491 0.2 N P M 4 1 0.2 1.5 0.2 N P M 3 0.0219 0.3 3.5 0.2 N P M 2 0.00865 0.5 5.362 0.2 N P M 1 0.0019 3 13.033 0.2 C h a o b 2 6 0.8 0.2 B e n 3 15 0.3 0.2 Z o o 5 20 0.8 0.2 P h y t o 30 0.4 D e t . 100 Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 135 5.2.2 E x p e r i m e n t a l f i sh ing I n the s u m m e r of 2001 1 d e p l e t i o n fished two lakes c a l l e d M o m ' s a n d C h e r y l (see F i g . 2.1) i n two separa te d ra inages on the B o n a p a r t e P l a t e a u n o r t h o f K a m l o o p s i n s o u t h c e n t r a l B r i t i s h C o l u m b i a . I set one lake i n each d ra inage as ide as a c o n t r o l ( D a d ' s a n d M o o s e P a s t u r e ) . E a r l y obse rva t ions showed n o r t h e r n p i k e m i n n o w are conf ined to the shore l ine d u r i n g the d a y b u t per- f o r m c r e p u s c u l a r m i g r a t i o n s offshore f r o m nearshore h i d i n g spo ts . T h i s be- h a v i o r was used to se lec t ive ly r emove t h e m b y se t t i ng g i l l ne t s a l o n g the ent i re sho re l ine of the e x p e r i m e n t a l lakes . T h i s same b e h a v i o u r was used t o selec- t i v e l y dep le te r a i n b o w t r o u t i n W i l d e r n e s s a n d N e s t o r lakes i n 2001 a n d 2002, by s e t t i n g g i l l ne t s m i d - l a k e r a the r t h a n p a r a l l e l to shore ( O ' B r i e n unpublished data). D u r i n g J u n e a n d J u l y of 2001 n o r t h e r n p i k e m i n n o w dep l e t i ons were c o n - d u c t e d i n two or three b o u t s of severa l (3-5) consecu t ive n i g h t s fishing. D u r - i n g each b o u t , the l e n g t h of g i l l n e t used was sufficient to c o m p l e t e l y s u r r o u n d M o m ' s L a k e a n d a b o u t 8 0 % of the p e r i m e t e r o f C h e r y l L a k e , f r o t a t e d net pane ls w i t h different ba r meshes a r o u n d each even ing to ensure each a r ea was e xpos e d to a l l meshes. S u m m a r i e s of the d e p l e t i o n effort b y da te a n d b a r m e s h are c o m p i l e d i n T a b l e 5.4 for C h e r y l L a k e a n d i n T a b l e 5.2.2 w i t h a p l o t o f the p r o p o r t i o n o f m e s h sizes used i n figure 5.1. I m e a s u r e d the f o r k - l e n g t h ( F L ) o f every fish c a p t u r e d a n d sac r i f i ced 285 f r o m C h e r y l lake a n d 264 f r o m M o m ' s L a k e for age ing . G i v e n the nur se ry s t r u c t u r e d i scussed i n C h a p t e r 2, I d e t e r m i n e d after Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 136 T a b l e 5.4: T o t a l l e n g t h a n d p r o p o r t i o n s by ba r l e n g t h (cm) C h e r y l L a k e Proportion of bar mesh by cm Date Total (m) 1.25 1.5 1.9 2.5 3.1 3.75 26-Jun-01 1200 0.06 0.06 0.08 0.57 0.11 0.11 27-Jun-01 1200 0.06 0.06 0.08 0.57 0.11 0.11 28-Jun-01 1200 0.06 0.06 0.08 0.57 0.11 0.11 2-Jul-01 1300 0.06 0.06 0.10 0.57 0.10 0.10 3-Jul-01 1300 0.06 0.06 0.10 0.57 0.10 0.10 15-Jul-01 1300 0.06 0.06 0.10 0.57 0.10 0.10 16-Jul-01 1300 0.06 0.06 0.10 0.57 0.10 0.10 17-Jul-01 1300 0.06 0.06 0.10 0.57 0.10 0.10 T a b l e 5.5: T o t a l l e n g t h a n d p r o p o r t i o n s by bar l e n g t h (cm) M o m ' s L a k e P r o p o r t i o n of bar mesh by c m Date T o t a l (m) 1.25 1.5 1.9 2.5 3.1 3.75 18-Jun-01 1150 0.06 0.06 0.08 0.57 0.11 0.11 19-Jun-01 1150 0.06 0.06 0.08 0.57 0.11 0.11 20-Jun-01 1150 0.06 0.06 0.08 0.57 0.11 0.11 9-Jul-01 1135 0.06 0.06 0.10 0.57 0.10 0.10 10-Jul-01 1135 0.06 0.06 0.10 0.57 0.10 0.10 l l - J u l - 0 1 1135 0.06 0.06 0.10 0.57 0.10 0.10 Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 137 1.25 1.56 1.87 2.5 3.12 3.75 mesh size (cm) F i g u r e 5.1: P r o p o r t i o n of g i l l ne t meshes u sed o n a l l dep le t ions . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 138 c a r r y i n g o u t the C h e r y l a n d M o m ' s L a k e dep le t i ons t ha t i n order to observe a n o r t h e r n p i k e m i n n o w r e c r u i t m e n t response , a nu r se ry lake h a d to be m a - n i p u l a t e d as w e l l . I n la te A u g u s t a n d ea r ly S e p t e m b e r of 2002 I f ished the eas te rn d r a i n a g e nu r se ry lake c a l l e d M o o s e P a s t u r e ( F i g . 2.1). F i s h were c a p t u r e d d u r i n g 6 b o u t s of d a i l y f i sh ing u s i n g 4 h o o p nets . T h r e e o f these nets cons i s t ed o f 6 x 1 m fiberglass hoops cove red i n 1 cm m e s h , 24 m center l ead , a n d 15 m s ide leads. T h e o ther cons i s t ed o f 6 x 0.7 m s teel hoops cov- ered i n 0.5 cm m e s h , 15 m center l ead , a n d 10 m s ide leads. L a p i l l i o t o l i t h s were t a k e n f r o m each n o r t h e r n p i k e m i n n o w a n d 945 of these were aged of 3682 fish caugh t i n M o o s e P a s t u r e . U s i n g the s ame gear, a n a d d i t i o n a l 1082 n o r t h e r n p i k e m i n n o w were c a p t u r e d a n d aged f r o m D a d ' s L a k e i n S e p t e m b e r 2003. A d d i t i o n a l d e p l e t i o n f i sh ing of r a i n b o w t r o u t was c o n d u c t e d i n W i l d e r n e s s L a k e i n 2001 a n d N e s t o r L a k e i n the s u m m e r o f 2002 ( D a v i d O ' b r i e n unpub- lished data. A m a p s h o w i n g the lakes, a n d w h a t r emova l s (e i ther n o r t h e r n p i k e m i n n o w or r a i n b o w t rou t ) is s h o w n i n F i g . 5.2. 5.2.3 Fish ageing T o age the fish I cu t L a p i l l i o t o l i t h s a l o n g the v e n t r a l / d o r s a l ax i s u s i n g a n Isomet B u e l l e r s low speed saw, b u r n e d a n d c o u n t e d a n n u l i . O t o l i t h s t oo s m a l l to c u t were b u r n e d a n d c o u n t e d d i r e c t l y . F o r fish o lder t h a n 5 years , f a i l i ng to c u t o t o l i t h s a l o n g the l o n g ax i s r e su l t ed i n s ign i f i can t under -age ing . Mom's Lake (NPM depletion Nestor Lake (RBT depletion 2002) Moose Pasture Lake (NPM Depletion 2002) Iderness L a k e ^ ^ Wil r (RBT Depletion 2001) Cheryl Lake (NPM depletion 2001) F i g u r e 5.2: M a p of e x p e r i m e n t a l lakes s h o w i n g the l o c a t i o n of r a i n b o w t r o u t dens i t y r educ t ions ( R B T dep le t i on ) , a n d n o r t h e r n p i k e m i n n o w d e n s i t y r educ t ions ( N P M dep le t i on ) . 9 CD CD CL o CD i CL ft .8 ft) o o tr 3' Crq 00 Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 140 5.2.4 Depletion Experiments P o p u l a t i o n sizes a n d percen t r e m o v a l were e s t i m a t e d u s i n g the m e t h o d ou t - l i n e d i n S c h n u t e (1983). T h e ana ly s i s cons is t s of a p o p u l a t i o n m o d e l desc r ib - i n g the n u m b e r s r e m a i n i n g (Nt) a n d an o b s e r v a t i o n m o d e l d e s c r i b i n g the p r e d i c t e d n u m b e r caugh t Ct. Ct was p r e d i c t e d as p r o p o r t i o n of the p o p u l a - t i o n r e m o v e d by the fishing gear each n i g h t (q) a n d the n u m b e r s r e m a i n i n g a l i ve at t i m e t (Nt): Nt = N 0 - £ c t t = 0 (5.5) Ct = qNt T h e o b s e r v e d catches at t i m e t i n l e n g t h b i n I were fit to the p r e d i c t e d catches i n E q . 5.5 u s i n g a P o i s s o n l o g l i k e l i h o o d . I g n o r i n g a l l cons tan t s t h a t d o no t d e p e n d o n the e s t i m a t e d pa ramete r s , the p o i s s o n l o g p r o b a b i l i t y of the d a t a (Ct) g i v e n the e s t i m a t e d pa rame te r s (q,N0) is: P(Ct\Noh m) c< Ct,i In (qiNu) - qiNtJ. (5.6) T h e p a r a m e t e r qt was e v a l u a t e d at i t s c o n d i t i o n a l m a x i m u m l i k e l i h o o d es t i - m a t e : q=^. (5.7) t I u sed 10 mm l e n g t h b ins . S i n c e there were tagged a n i m a l s i n M o o s e P a s t u r e L a k e w h e n dep le t i ons were c o n d u c t e d i t was poss ib le to use these d a t a to e s t ima te d e p l e t i o n a lso . I Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 141 used f ish m a r k e d i n the two weeks p r e c e d i n g remova ls to o b t a i n a p o p u l a t i o n e s t ima t e ( a s s u m i n g no t a g loss or m o r t a l i t y i n t h a t t i m e i n t e r v a l ) . T h e log - l i k e l i h o o d was c a l c u l a t e d as: L = Ri \og(Pn) + Utlog(l - Pn) (5.8) where Ri is the n u m b e r o f r ecap tu res at l e n g t h , Ui the n u m b e r of m a r k e d a n i m a l s a n d Pri the p r e d i c t e d p r o b a b i l i t y of c a p t u r i n g a m a r k e d a n i m a l . Pri was the r a t i o o f t agged r ecap tu res to the n u m b e r of t agged f ish at r i sk to c a p t u r e (or the r a t i o of t o t a l cap tu res (MiUi) to t o t a l N at r i sk , N0j). I t is t y p i c a l i n d e p l e t i o n e x p e r i m e n t s for each b o u t of seve ra l days f i sh ing to resu l t i n a n u n d e r e s t i m a t e of N, clue to some fish no t b e i n g v u l n e r a b l e d u r i n g a n y s h o r t - t e r m b o u t . I h o p e f u l l y co r r ec t ed for th i s effect b y u s i n g m o r e t h a n one b o u t o n each l ake , a n d the d a i l y catches over a l l b o u t s ( F i g . 5.11) s u p p o r t t h i s hope . 5.2.5 Visual Surveys I c o n d u c t e d v i s u a l f ry surveys i n a l l s t u d y a n d c o n t r o l lakes i n 2002 to c o n f i r m the presence or absence of fry a n d to generate a q u a n t i t a t i v e i n d e x of fry a b u n d a n c e . A second series o f v i s u a l obse rva t ions was o n a p p r o x i m a t e l y the s ame dates i n 2003. D u e to a n e a r b y forest fire o n l y one set o f obse rva t ions was poss ib l e i n 2003. T h e su rveys were c o n d u c t e d o n s u n n y days be tween 9 : 00 A . M . a n d 3 : 00 P . M . b y e i ther w a l k i n g or r o w i n g as close as poss ib l e Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 142 a l o n g the shore l ine . W h e r e fry were present ( i n M o o s e P a s t u r e a n d D a d ' s lake) I r eco rded es t imates of the n u m b e r of 0 + fry, age 1 + , a n d age 2 + n o r t h e r n p i k e m i n n o w obse rved a l o n g w i t h the G P S p o s i t i o n s of each s c h o o l s p o t t e d . I c a l c u l a t e d c rude s u r v i v a l ra tes b y c a l c u l a t i n g the r a t i o of the 2 + i n d e x i n 2003 to the 1 + i n d e x i n the p r e v i o u s year , a n d l ikewise the 1 + i n d e x i n 2003 t o the 0 + i n d e x i n 2002. T h e s e s u r v i v a l e s t ima tes are p l o t t e d for the m a n i p u l a t e d l ake ( M o o s e Pas tu r e ) a n d the u n m a n i p u l a t e d lake ( D a d ' s ) i n F i g . 5.15. 5.2.6 Estimation of Survival and Growth Parameters F o r n o r t h e r n p i k e m i n n o w g r o w t h , I used m a r k - r e c a p t u r e m e t h o d s to m e a - sure the g r o w t h a n d s u r v i v a l responses f o l l o w i n g m a n i p u l a t i o n s . A t a p p r o x - i m a t e l y w e e k l y in te rva l s , I s u r v e y e d a l l the lakes u s i n g the gear d e s c r i b e d i n S e c t i o n 5.2.2, r e c o r d e d the fork l e n g t h o f a l l m a r k e d a n d u n m a r k e d a n i - m a l s , a n d m a r k e d new a n i m a l s . S ince the o v e r w h e l m i n g m a j o r i t y o f n o r t h - e rn p i k e m i n n o w m a r k e d were greater t h a n 90 mmFL (or a p p r o x i m a t e l y 4 + ) , t h e y are t r ea t ed as a s ing le a d u l t " s t anza" a n d a s s u m e d to be sub j ec t t o same n a t u r a l m o r t a l i t y . I d i v i d e d m a r k e d r a i n b o w t r o u t i n t o two g roups : those greater or sma l l e r t h a n 200 mm. A l l d a t a used for t h i s ana ly s i s c o m e f r o m fish c a p t u r e d i n fyke nets a n d m a r k e d f o l l o w i n g e x p e r i m e n t a l dep le t ions i n each lake . I e s t i m a t e d n o r t h e r n p i k e m i n n o w s u r v i v a l a n d m o v e m e n t pa r ame te r s i n the eas te rn a n d wes te rn d r a i n a g e lakes u s i n g the c o m b i n e d l i k e l i h o o d s de- T a b l e 5.6: T o t a l n u m b e r of m a r k e d a n d r e c a p t u r e d n o r t h e r n p i k e m i n n o w b y dra inage , lake a n d t r ea tmen t . N P M = n o r t h e r n p i k e m i n n o w , R B T = r a i n b o w t rou t a n d d e p = d e p l e t i o n N u m b e r of Tota l number Tota l recaptures from Treatment Drainage Lake marked cohorts marked all cohorts/t imes Moose 7 343 153 N P M dep East Cheryl 10 613 216 N P M dep Wilderness 7 580 143 R B T dep Dad's 11 2024 667 Control West Mom's 11 597 428 N P M dep Nestor 9 629 155 R B T dep Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 144 T3 a 3 o IS I o _Q fl ' S -n i-i fl D H 03 • O CD i-1 3 *•< S v. g • 6-5 in $ O TT X ri o ao p CN « b ^ « r~ 12 ; Is E! Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 145 s c r i b e d i n S e c t i o n 4.2.5 ( E q s . 4.20, 4.27 a n d 4 .28) . F i s h m a r k e d f o l l o w i n g e x p e r i m e n t a l m a n i p u l a t i o n s were m a r k e d a n d r e c a p t u r e d i n a p p r o x i m a t e l y w e e k l y in te rva l s , w i t h the n u m b e r o f m a r k e d cohor t s (groups o f a n i m a l s m a r k e d i n any p a r t i c u l a r s a m p l i n g b o u t ) , the n u m b e r of fish m a r k e d i n each c o h o r t a n d the t o t a l n u m b e r of r ecap tu res f r o m a l l cohor t s at a l l t i m e s i n each l ake s u m m a r i z e d i n tables 5.2.6 a n d 5.2.6. I d i d n o t assume a n o r m a l d i s t r i b u t i o n of m e a n l e n g t h at m o v e m e n t ( E q . 4.24) s ince i t is r e s t r i c t i ve a b o u t the shape of m o v e m e n t p r o b a b i l i t y dens i ty . Ins t ead , I represented the c u m u l a t i v e p r o b a b i l i t y o f m o v i n g at l e n g t h I as the p r o d u c t o f the m a x i m u m p r o p o r t i o n m o v i n g f r o m the nur se ry a rea U\ a n d an i n c o m p l e t e b e t a d i s t r i b u t i o n . T h e l e n g t h dependen t c u m u l a t i v e m o v e m e n t p r o b a b i l i t y f u n c t i o n became: where a. a n d (3 are the shape p a r a m e t e r s a n d pn the m a x i m u m p r o p o r t i o n m o v i n g . I set a lower b o u n d o n the p a r a m e t e r a of 2 for f i t t i n g s ince at va lues a p p r o a c h i n g 1 i t was poss ib le for the c u r v e t o p r e d i c t 100 % of f ish m o v e d before 50 mm F L . G e a r s e l ec t i v i t y pa ramete r s ( E q . 4.3) were f ixed w i t h 4 = 0.45 a n d 7 = 0.2 for a l l areas a n d b o t h fish s ince t h e y were n o t e s t imab le . T h e a s s u m e d gear s e l e c t i v i t y pa rame te r s are b a s i c a l l y the same as those e s t i m a t e d b y the length-age l i k e l i h o o d ( C h a p t e r 3 T a b l e 3.3.1) . (5.9) o Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 146 F o r r a i n b o w t rou t , I a s s u m e d no s t r u c t u r e d on togene t i c m o v e m e n t a n d e s t i m a t e d the r a i n b o w t r o u t g r o w t h a n d s u r v i v a l pa rame te r s u s i n g the c o m - b i n e d l i k e l i h o o d s de sc r ibed i n S e c t i o n 4.2.4. It was no t poss ib l e to e s t ima t e the h i s t o r i c a l n a t u r a l m o r t a l i t y for r a i n b o w t r o u t < 200 mm so I f ixed these va lues at the m e a n va lue of the p r i o r for n a t u r a l m o r t a l i t y for j u v e n i l e r a i n - b o w t r o u t where M — 1.78 (see S e c t i o n 5.2.7 b e l o w ) . 5.2.7 Prior Distributions I n a l l e s t i m a t i o n p rocedures for b o t h f ish species I used B a y e s i a n p r i o r s for a l l m o r t a l i t y , g r o w t h a n d tag-loss pa rame te r s . I n the case o f r a i n b o w t r o u t , the t a g loss was a h y p e r - p a r a m e t e r a n d a s sumed sha red across a l l the s t u d y lakes . A n a l y s i s of the n o r t h e r n p i k e m i n n o w d a t a was t oo m e m o r y - i n t e n s i v e to a l l o w p a r a m e t e r es t imates for a l l s ix s t u d y lakes to be r u n at once . T h e a n a l y s i s was done i n s t ead b y d r a i n a g e where tag-loss was a s s u m e d e q u a l across the d ra inage . T h e p r i o r o n n o r t h e r n p i k e m i n n o w n a t u r a l m o r t a l i t y M a n d the m o r t a l i t y of t he t agged cohor t s b y lake Mt was n o r m a l N~(p = 0.30, a = 0.19) a n d b u i l t f r o m 7 es t imates o f n a t u r a l m o r t a l i t y i n the C o l u m b i a R i v e r ( R i e m a n a n d Beamesde r fe r , 1990). G r o w t h p a r a m e t e r p r i o r s come f rom 2 obse rva t ions i n M o n t a n a lakes a n d s t reams ( C a r l a n d e r , 1969; Pe te r s , 1964) a n d f r o m R i e m a n a n d Beamesde r f e r (1990). F o r log^^) the p r i o r was N~(p = 6.23, cr = 0.1) a n d for the v o n Be r t a l an f fy K p a r a m e t e r N~(p = 0.14,CT = 0.08) . T h e p r i o r for age 1 r a i n b o w t r o u t n a t u r a l m o r t a l i t y c o m e f r o m P o s t et a l . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 147 (1999) 's 47 obse rva t ions of age 1 r a i n b o w t r o u t s u r v i v a l across a range of r a i n b o w t r o u t densi t ies . T h i s p r i o r was n o r m a l N ~ (fi = 1.78, cr = 1.95). P r i o r s for the r a i n b o w t r o u t v o n B e r t a l a n f f y g r o w t h p a r a m e t e r s a n d for a d u l t m o r t a l i t y come f rom 7 e s t ima tes i n ( R u i z - C a m p o s et a l . , 1997; P i d g e o n , 1981; K w a i n , 1981). F o r K th i s p r i o r was N~ (LI = 0.53, a = 0 .1) , for i t was N ~ (p, = 6.0, o = 0.2) l a c k i n g i n f o r m a t i o n o n M, the p r i o r for M was set to the same as for K. T h e p r i o r for anchor t a g loss for b o t h species comes f r o m s tud ies t h a t e s t i m a t e d the tag-loss rates for f i sh of c o m p a r a b l e sizes u s i n g F l o y t y p e an- chor tags ( E b e n e r a n d C o p e s , 1982; E b e n e r , 1982; M u o n e k e , 1992; P i e r c e a n d T o m c k o , 1993; S w a n s o n a n d S c h r a m , 1996; M c G l e n n o n a n d P a r t i n g t o n , 1997; J u l l i a r d et a l , 2001; R i k a r d s e n et a l . , 2002; B r a t t e y a n d C a d i g a n , 2004) . T h i s p r i o r was aga in a s s u m e d to be n o r m a l l y d i s t r i b u t e d N~(p = 0.33, a = 0.27) 5.2.8 Markov Chain Monte Carlo Sampling for parameter uncertainty I expressed pa r ame te r u n c e r t a i n t y by s a m p l i n g the pos t e r i o r p r o b a b i l i t y d i s - t r i b u t i o n s of each e s t i m a t e d p a r a m e t e r u s i n g the MCMC a l g o r i t h m b u i l t i n t o A D M o d e l B u i l d e r (a C + + software, O t t e r R e s e a r c h L t d . S i d n e y , B . C . , C a n a d a ) , w h i c h a l lows fast m a x i m i z a t i o n of the l i k e l i h o o d s of c o m p l e x m o d - els because a n a l y t i c de r iva t ives are a u t o m a t i c a l l y c a l c u l a t e d . F o u r M a r k o v cha in s were r u n for each ana ly s i s ( adu l t n o r t h e r n p i k e m i n n o w , r a i n b o w t r o u t Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 148 sma l l e r t h a n 200 mm) u n t i l the m u l t i v a r i a t e p o t e n t i a l scale r e d u c t i o n factor ( G e l m a n et a l . , 1995) was s m a l l e r t h a n 1.05. 30 000 samples o f the pos t e r io r were t aken f rom each c h a i n f o l l o w i n g convergence . C o n v e r g e n c e d i agnos t i c s were p e r f o r m e d u s i n g the CODA w i t h the R s t a t i s t i c a l sof tware package (http://www.r-project.org). 5.3 Results 5.3.1 Predicted responses to experimental fishing of using Ecosim T h e m o d e l showed t h a t i t is poss ib l e to p r o d u c e c u l t i v a t i o n - d e p e n s a t i o n ef- fects i n the e x p e r i m e n t a l s y s t e m a n d t h a t i t was poss ib l e to p r o d u c e a f l ip f r om e i ther a r a i n b o w t r o u t d o m i n a t e d s y s t e m to a n o r t h e r n p i k e m i n n o w d o m i n a t e d one a n d v i c e - v e r s a ( F i g s . 5.4 t h r o u g h 5.10). T h e s e p r e d i c t i o n s were ve ry sens i t ive to changes i n the v u l n e r a b i l i t y exchange rates . F l i p s were not p r e d i c t e d w h e n a l l v u l n e r a b i l i t y exchange rates be tween p r e y a n d p reda - tors were set to 2 ( i m p l y i n g a m a x i m u m m o r t a l i t y ra te o n p r e y at v e r y h i g h p r eda to r a b u n d a n c e o f 2x t he E c o p a t h base rate) for a l l g roups . I n o rder to p r o d u c e f l ips b y n o r t h e r n p i k e m i n n o w d e p l e t i o n f i sh ing , t h e v u l n e r a b i l i t y ex- change rates be tween z o o p l a n k t o n a n d the i r p reda to r s , as w e l l as c h a o b o r u s a n d 2 + , 3 + , 4 + n o r t h e r n p i k e m i n n o w h a d to be 3 or greater a n d the v u l - n e r a b i l i t y exchange ra te be tween z o o p l a n k t o n a n d c h a o b o r u s greater t h a n Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 149 10. W h e n v u l n e r a b l e exchange rates were h i g h e n o u g h to p r o d u c e flips, the m a i n p r e d i c t e d changes i n the s y s t e m f o l l o w i n g n o r t h e r n p i k e m i n n o w b iomass r e d u c t i o n ( F i g . 5.4) o p e r a t e d t h r o u g h the c h a o b o r u s a n d z o o p l a n k t o n d y - n a m i c s . A s 4 + n o r t h e r n p i k e m i n n o w d e c l i n e d , c h a o b o r u s was released f rom p r e d a t i o n . W h i l e i t s t o t a l p r e d a t i o n m o r t a l i t y d e c l i n e d ( F i g . 5.4), the b iomass o f c h a o b o r u s d i d no t increase ( F i g . 5.3) s i g n i f i c a n t l y s ince at the same t i m e i ts o w n f o o d supp ly , z o o p l a n k t o n , was dec reas ing because o f i n - creases i n r a i n b o w t r o u t 2 + dens i t y a n d la rge increases i n g r o w t h by the r e m a i n i n g 2, 3, a n d 4 + n o r t h e r n p i k e m i n n o w a n d 2 + r a i n b o w t r o u t ( F i g . 5.5). B e c a u s e of decreased z o o p l a n k t o n dens i ty , p r e d i c t e d r e l a t ive feeding t i m e of b o t h the j u v e n i l e r a i n b o w t r o u t a n d n o r t h e r n p i k e m i n n o w inc reased . In te res t ingly , the p r e d i c t e d response o f the r a i n b o w t r o u t p o p u l a t i o n was for the t o t a l b i o m a s s to increase a n d be c o m p r i s e d o f fewer, b u t larger f ish. W h i l e the m o r t a l i t y of the juven i l e s inc reased , the a d u l t s were larger ( F i g . 5.5) a n d so the p r e d i c t e d b i o m a s s of r a i n b o w t r o u t h igher . P r o d u c i n g flips b y r a i n b o w t r o u t d e p l e t i o n f i sh ing o c c u r r e d o n l y w h e n v u l n e r a b i l i t y exchange ra tes be tween 2 + , 3 + a n d 4 + n o r t h e r n p i k e m i n n o w a n d 2 + r a i n b o w t r o u t were 5 ( F i g s . 5.8 to 5.10) or greater . A s was the case i n p r o d u c i n g f l ips w i t h n o r t h e r n p i k e m i n n o w dep le t i ons above , the v u l n e r a b i l i t y exchange rates of z o o p l a n k t o n to chaoborus needed a lso h a d to be greater t h a n 10 i n order to p r o d u c e flips. T h e m o d e l s were r e l a t i v e l y insens i t ive to changes i n the re la t ive fish s ta r t - Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 150 i n g b iomasses a n d w o u l d s t i l l p r o d u c e a f l ip f r o m one d o m i n a t e d s ta te to ano the r i n b o t h cases where r a i n b o w t r o u t b i o m a s s is h a l f the n o r t h e r n p i k e m i n n o w b i o m a s s a n d v ice -versa . In genera l , y o u c o u l d move the u n - s tab le s t a r t i n g p o i n t a r o u n d a lo t , w i t h o u t e l i m i n a t i n g the two s t ab le p o i n t s where a l t e rna t e e q u i l i b r i a ex is t at a l l . 5.3.2 Estimated Depletion T h e d e p l e t i o n es t ima tes here are those of the v u l n e r a b l e (ac t ive) p o p u l a t i o n . T h e d e p l e t i o n es t ima tes i n F i g . 5.12 a n d the u p p e r p a n e l of F i g . 5.13 are ve ry h i g h , i .e. are o p t i m i s t i c a b o u t the i m p a c t o f the r e m o v a l f i sh ing . G i l l - nets are pass ive gear a n d so fish m u s t be ac t ive i n o rder to be c a p t u r e d i n t h e m . F u r t h e r m o r e , i n c o m p l e t e dep le t ions i n a p a r t i c u l a r gear t y p e m a y be due to l ea rned gear avo idance (after an unsuccess fu l c a p t u r e encoun te r ) . T h e d e p l e t i o n es t ima tes based o n the t agged a n i m a l s (F ig .5 .13 ) showed the deple- t i o n to be o n average 7 0 % across size classes r a t he r t h a n the 100% e s t i m a t e d u s i n g E q . 5.6. B y c a t c h m o r t a l i t y o f r a i n b o w t r o u t was neg l i g ib l e d u r i n g dep le t i ons i n M o o s e P a s t u r e (s ince t r a p gear was used) a n d M o m ' s L a k e . Howeve r , there was cons ide rab l e b y c a t c h i n C h e r y l L a k e o f r a i n b o w t r o u t where 1257 m a i n l y s m a l l ( < 200 mm) were c a p t u r e d . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 151 Rbt2+ Rbt 1 '8 **»*«*»» *»»»»»B**«iS*»B?»9S>i NPM 4+ NPM 3 NPM 2 Chaoborus NPM 1 Zoo F i g u r e 5.3: P r e d i c t e d re la t ive b i o m a s s (B) changes after d e p l e t i o n f i sh ing of 4 + n o r t h e r n p i k e m i n n o w . T h e b i o m a s s of 2+ R B T a n d 4 + N P M have been a r b i t a r i l y set to 1 a n d the o the r g r o u p s sca l ed acco rd ing ly . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 152 Rbt 2+ NPM 4+ NPM 2 Chaoborus Rbt1 NPM 3 NPM 1 Zoo F i g u r e 5.4: P r e d i c t e d changes i n M after s i m u l a t e d d e p l e t i o n f i sh ing o f 4 + n o r t h e r n p i k e m i n n o w . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 153 Rbt 2+ Rbt1 NPM 4+ NPM 3 NPM 2 NPM 1 Chaoborus Zoo year F i g u r e 5.5: P r e d i c t e d b o d y weight changes (kg) after 4 + n o r t h e r n p i k e m i n n o w d e p l e t i o n f i sh ing . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 154 Rbt2+ NPM 4+ Rbt 1 NPM 3 NPM 2 NPM 1 Chaoborus Zoo F i g u r e 5.6: P r e d i c t e d changes i n re l a t ive feeding t i m e after 4 + n o r t h e r n m i k e m i n n o w d e p l e t i o n fishing. Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 155 Rbt 2+ Rbt 1 NPM 4 NPM 3 NPM 2 Chaoborus NPM 1 Zoo F i g u r e 5.7: P r e d i c t e d r e l a t ive changes i n b i o m a s s B f o l l o w i n g 2 + r a i n b o w t r o u t d e p l e t i o n f i sh ing . T h e b i o m a s s o f 2 + R B T a n d 4 + N P M have been a r b i t a r i l y set to 1 a n d the o the r g roups sca led a c c o r d - i n g l y . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 156 Rbt 2+ Rbt1 NPM 4 10 20 NPM 2 Chaoborus NPM 3 NPM 1 Zoo F i g u r e 5.8: P r e d i c t e d changes i n M f o l l o w i n g 2 + r a i n b o w t r o u t d e p l e t i o n f i sh ing . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 157 Rbt 2+ NPM 4 NPM 2 10 20 30 year 40 50 Chaoborus Rbt1 NPM 3 NPM 1 20 30 Zoo F i g u r e 5.9: P r e d i c t e d changes i n weight ( i n kg) after r a i n b o w t r o u t d e p l e t i o n f i sh ing . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 158 Rbt 2+ Rbt 1 NPM 4 NPM 3 NPM 2 I 1 r - 20 30 40 Chaoborus NPM 1 Zoo F i g u r e 5.10: P r e d i c t e d r e l a t ive changes i n feeding t i m e after r a i n b o w t r o u t d e p l e t i o n f i sh ing . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 159 Cheryl Lake 2001 o ° _ i u — ra _ O o -o - CM Jun 27 Jul 02 1 Jul 07 Date 1 Jul 12 Jul 17 Mom's Lake 2001 Jun 22 Jun 27 Jul 02 Jul 07 Jul 12 Date Moose Pasture Lake 2002 o Sep 09 Sep 10 Sep 11 Sep 12 Sep 13 Sep 14 Sep 15 Sep 16 Date F i g u r e 5.11: D e p l e t i o n ca tches of n o r t h e r n p i k e m i n n o w ( i n n u m b e r s ) b y da te for C h e r y l l ake i n 2001 ( top) , M o m ' s l ake i n 2001 ( m i d d l e ) a n d M o o s e P a s t u r e l ake i n 2002 ( b o t t o m ) . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 160 Cherl Lake o CN Mom's Lake o o c o oj -o o o o 50 "i r 100 150 200 o "S3 CP "D C O O o o o "i r 50 100 150 200 FL (mm) FL (mm) F i g u r e 5.12: E s t i m a t e d n o r t h e r n p i k e m i n n o w v u l n e r a b l e n u m b e r s ( iV) a n d pe rcen t d e p l e t i o n es t imates b y l e n g t h for C h e r y l a n d M o m ' s lake . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 161 Depletion Estimates 50 100 150 200 FL (mm) Mark-recapture Estimates FL (mm) Q- "D co o -3- o CM O FL (mm) FL (mm) F i g u r e 5.13: N o r t h e r n p i k e m i n n o w p o p u l a t i o n a n d percen t d e p l e t i o n es t i - m a t e s b y l eng th , V represent 95 percen t C I . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 162 50 100 150 200 FL(mm) F i g u r e 5.14: F i t o f p r o p o r t i o n n o r t h e r n p i k e m i n n o w l e a v i n g the nu r se ry a r ea f u n c t i o n by l e n g t h for each d ra inage . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 163 5.3.3 Visual Surveys T h e change i n the v i s u a l su rvey i n d e x shows t h a t s u r v i v a l o f f ish f r o m 0 + to 1 + was be t t e r i n the unf i shed lake t h a n the f ished one (0.06 i n D a d ' s lake b u t o n l y 0.03 i n M o o s e P a s t u r e ) f o l l o w i n g e x p e r i m e n t a l f i sh ing ( F i g . 5.15). I n con t ras t , the s u r v i v a l ra te f r o m 1 + to 2 + was m u c h i m p r o v e d f o l l o w i n g f i sh ing of a d u l t s i n M o o s e P a s t u r e r e l a t i v e to the unf i shed lake ( F i g . 5.15). A ser ious p r o b l e m w i t h i n t e r p r e t i n g these resu l t however , is t h a t t h e y c o m e f r o m a s ingle pa i r of obse rva t ions so are n o t re l i ab le . 5.3.4 Northern pikeminnow growth, mortality and movement parameter estimates T h e n o r t h e r n p i k e m i n n o w i n each d r a i n a g e have a p p r o x i m a t e l y the same g r o w t h curves ( F i g . 5.16). I n b o t h d ra inages , the obse rved l eng ths a t age i n the n o n - n u r s e r y lakes t ended to be h i g h e r t h a n the nur se ry lakes sugges t i ng e i ther t ha t la rger fish m o v e u p s t r e a m to the head -end lakes, or t h a t g r o w t h is be t t e r i n these lakes. N o r t h e r n p i k e m i n n o w m o v e m e n t differed be tween the eas te rn a n d wes t e rn d ra inages i n two ways . I n the eas te rn d ra inage , there was a t e n d e n c y for f ish to m i g r a t e i n t o the headwa te r lakes at s m a l l e r sizes ( F i g . 5.14). F o r e x a m p l e , age 2 + N P M were absent f r o m the wes te rn d ra inage ( F i g . 5.16 u p p e r pane l ) b u t present i n the eas te rn d ra inage ( F i g . 5.16 lower pane l ) . T h i s o b s e r v a t i o n was a lso cons is ten t w i t h the p o p u l a t i o n es t ima tes ( F i g . 2.3) s h o w i n g the Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 164 F i g u r e 5.15: Pe rcen t change i n v i s u a l survey i n d e x i n D a d ' s (b lue) a n d M o o s e P a s t u r e ( red) . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 165 F i g u r e 5.16: F i t o f v o n B e r t a l a n f f y g r o w t h cu rve t h r o u g h length-age d a t a i n wes te rn ( top) a n d eas te rn ( b o t t o m ) d a t a . J i t t e r a d d e d t o be t t e r see over lay . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 166 presence of 1 a n d 2 + fish i n C h e r y l lake, b u t n o t i n M o m ' s or N e s t o r lakes. A l s o , the t o t a l p r o p o r t i o n m o v i n g f rom the nu r se ry a r ea pn a p p e a r e d to be lower i n eas te rn d r a i n a g e t h a n i n the wes te rn ( F i g . 5.18). T h e b r o a d pos t e r io r p r o b a b i l i t y d i s t r i b u t i o n s m e a n t there were no c lear differences i n g r o w t h or s u r v i v a l pa rame te r s i n n o r t h e r n p i k e m i n n o w greater t h a n 90 mm be tween the eas te rn a n d wes te rn d r a i n a g e ( F i g . 5.17). 5.3.5 Rainbow trout growth and mortality estimates I t was no t pos s ib l e to e s t i m a t e g r o w t h pa rame te r s for r a i n b o w t r o u t > 200 mm. T h e r e were v e r y few d a t a , so the g r o w t h l i k e l i h o o d w o u l d no t converge a n d o n l y Mt was e s t i m a b l e u s i n g o n l y E q . 4 .17. I n a d d i t i o n , no f ish m a r k e d fo l l owing the e x p e r i m e n t a l m a n i p u l a t i o n s i n N e s t o r L a k e were r e c a p t u r e d so i t was no t poss ib l e to e s t ima t e Mt i n tha t l ake at a l l . T h e r e d i d a p p e a r to be some effect of the r a i n b o w t r o u t d e p l e t i o n f i sh ing i n W i l d e r n e s s l ake a n d to the c o m b i n e d n o r t h e r n p i k e m i n n o w ( a n d acc iden - ta l ) r a i n b o w t r o u t d e p l e t i o n i n C h e r y l l ake ( F i g . 5.20). H o w e v e r , w h i l e the pos t e r io r m o d e s of these d i s t r i b u t i o n s are a different, the pos te r io r s are t o o b r o a d to con f iden t l y a rgue a difference was obse rved . T h e e s t i m a t e d v o n Be r t a l an f fy K for j u v e n i l e r a i n b o w t r o u t was the same be tween a l l t r e a t e d a n d un t r ea t ed lakes. T h e r e were differences i n the Zog(Loo) be tween t r e a t e d a n d un t r ea t ed lakes, ( F i g . 5.21), w i t h f ish appear - i n g to be s t u n t e d i n those lakes where n o r t h e r n p i k e m i n n o w were r e m o v e d ( M o o s e P a s t u r e , C h e r y l a n d M o m ' s ) . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 167 5.10 5.15 5.20 5.25 5.30 5.35 5.10 5.15 5.20 5.25 5.30 5.35 log(L_) log(L_) 1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0 F i g u r e 5.17: P o s t e r i o r samples of g r o w t h p a r a m e t e r s ( / o c / ( L 0 0 ) , K), h i s t o r i c a l n a t u r a l m o t a l i t y M, a n d t a g loss tl for unf i shed wes te rn (left c o l u m n ) a n d fished eas te rn d r a i n a g e ( r igh t c o l u m n ) . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 168 J 10 15 20 - r - 25 - 1 30 i — i 10 . iJlTrriT-E*. I 1 1 1 15 20 25 30 F i g u r e 5.18: P o s t e r i o r samples of m o v e m e n t pa r ame te r s ( m a x i m u m p r o p o r - t i o n l e a v i n g the nu r se ry a rea p,n, p r o p o r t i o n of the m o v i n g p o o l g o i n g to lake 2 p2 ( C h e r y l a n d M o m ' s ) , a n d the b e t a d i s t r i - b u t i o n pa r ame te r (3 for the unf i shed wes te rn (left c o l u m n ) a n d f ished eas te rn d ra inage . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 169 Dad 0.0 0.2 0.4 0.6 0.8 1.0 1.2 r Moose tun ~i 1 r 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 mil Mom Cheryl s i "i 1 1 r ~\ 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 I 1 1 1 1 1 1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 m t 2 m,2 Nestor o 0.0 0.2 0.4 0.6 0.8 1.0 1.2 mt3 Wilderness o o o 0.0 0.2 0.4 0.6 0.8 1.0 1.2 mt3 F i g u r e 5.19: P o s t e r i o r samples of n o r t h e r n squawf ish t agged c o h o r t m o r t a l i t y Mt b y lake . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 170 F i g u r e 5.20: P o s t e r i o r samples of Mt for r a i n b o w t r o u t grea ter t h a n 200 mm b y lake . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 171 Moose Dad's T 1 1 4.5 5.0 5.5 6.0 6.5 l o g ( U ) I—-—I 1 1 1 4.5 5.0 5.5 6.0 6.5 l o g ( U ) Cheryl Mom's I 1 1 1 1 4.5 5.0 5.5 6.0 6.5 l o g ( U ) I 1 1 1 1 4.5 5.0 5.5 6.0 6.5 l o g ( U ) Wilderness Nestor g- N -I c <D O 3. ° cr o a) o T 1 1 1 4.5 5.0 5.5 6.0 6.5 I 1 1 1 1 4.5 5.0 5.5 6.0 6.5 l o g ( U ) log(L-) F i g u r e 5.21: P o s t e r i o r s ample s of the log a s y m p t o t i c l e n g t h /Joc>(Loo for r a i n - b o w t r o u t s m a l l e r t h a n 200 mm b y lake . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 172 F i g u r e 5.22: P o s t e r i o r s amples o f the v o n B e r t a l a n f f y K for r a i n b o w t r o u t s m a l l e r t h a n 200 mm by lake . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 173 I n sp i t e of the very large pos t e r io r p r o b a b i l i t y in t e rva l s , Mt for the r a i n - b o w t r o u t was h ighe r i n those lakes where" n o r t h e r n p i k e m i n n o w we're f i shed ( M o o s e P a s t u r e , C h e r y l , a n d M o m ' s F i g . 5.23). T h e lowest m o r t a l i t y was obse rved i n D a d ' s lake , where there was .very h i g h n o r t h e r n p i k e m i n n o w den - si ty. 5.4 Discussion I c a n n o t say w h e t h e r or no t the e x p e r i m e n t a l m a n i p u l a t i o n s of e i ther r a i n b o w t r o u t or n o r t h e r n p i k e m i n n o w w i l l e v e n t u a l l y resu l t i n a l t e rna te s tab le s tates . T h e r e is some agreement be tween the obse rved resu l t s a n d f rom m o d e l p r e d i c - t ions w i t h p a r a m e t e r c o m b i n a t i o n s i m p l y i n g s t r o n g c u l t i v a t i o n - d e p e n s a t i o n effects. B u t , to m a k e a case t h a t the e x p e r i m e n t a l f i sh ing p r o d u c e d a n a l - te rna te s tab le s ta te t h r o u g h c u l t i v a t i o n - d e p e n s a t i o n effects w o u l d r equ i r e a) obse rved changes i n r e l a t ive feeding t i m e of 1+ n o r t h e r n p i k e m i n n o w a n d 1 + r a i n b o w t rou t ; b) obse rved changes i n z o o p l a n k t o n a n d c h a o b o r u s dens i t ies ; a n d c) a l o n g series of observa t ions f o l l o w i n g the m a n i p u l a t i o n s s h o w i n g t h a t any r e c r u i t m e n t responses were no t t r a n s i t o r y . E v e n i n the case o f m o r t a l - i t y a n d p a r t i c u l a r l y g r o w t h of 1 + r a i n b o w t r o u t , t he pos t e r io r p r o b a b i l i t y d i s t r i b u t i o n s for g r o w t h a n d m o r t a l i t y p a r a m e t e r s showed the d a t a c a n be e x p l a i n e d b y a la rge range of p a r a m e t e r c o m b i n a t i o n s , i n c l u d i n g some c o n - t r a r y t h a t w o u l d no t i m p l y s t r o n g c u l t i v a t i o n - d e p e n s a t i o n effects a c c o r d i n g to E c o s i m . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 1 7 4 Figure 5.23: Posterior samples of the instantaneous annual mortality of tagged fish by lake for rainbow trout smaller than 200 mm. Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 175 M e a s u r i n g the n o r t h e r n p i k e m i n n o w response to e x p e r i m e n t a l r e m o v a l to e i ther r a i n b o w t rou t or n o r t h e r n p i k e m i n n o w was m u c h m o r e p r o b l e m a t i c t h a n s i m p l y w i d e p r o b a b i l i t y d i s t r i b u t i o n s for response pa rame te r s . B e c a u s e of d i s p e r s a l a m o n g lakes of n o r t h e r n p i k e m i n n o w i n the s t u d y s y s t e m , the e x p e r i m e n t a l u n i t was effect ively a d r a inage . There fo re , the o n l y re levant c o m p a r i s o n for n o r t h e r n p i k e m i n n o w responses to n o r t h e r n p i k e m i n n o w fish- i n g were be tween the f ished a n d un f i shed nu r se ry lakes ( M o o s e P a s t u r e a n d D a d ' s r e spec t ive ly ) . E v e n i g n o r i n g the p r o b l e m t h a t s a m p l e s ize for the m a n i p u l a t i o n s , was one lake , the f low of fry f rom lakes above the t r e a t ed ( M o o s e P a s t u r e ) a n d c o n t r o l lake ( D a d ' s ) c o u l d have been affected b y f i sh ing c o n d u c t e d i n those u p s t r e a m lakes . F o r t u n a t e l y , the m a n i p u l a t i o n s i n lakes above D a d ' s a n d M o o s e P a s t u r e were i d e n t i c a l , offer ing the p o s s i b i l i t y of l o n g t e r m c o m p a r i s o n s . I n the case of m e a s u r i n g the effects o f r a i n b o w t r o u t r e m o v a l , no 1 + a n d 2 + n o r t h e r n p i k e m i n n o w p a r a m e t e r s c o u l d have been measu red , s ince there are no f ish of those size classes i n those lakes . T h e n o n - n u r s e r y lakes were p r o b a b l y reasonable e x p e r i m e n t a l u n i t s insofar as m e a s u r i n g the response of r a i n b o w t r o u t to f i sh ing of n o r t h e r n p i k e m i n n o w s ince l i t t l e i n t e r a c t i o n be tween 1 a n d 2 + n o r t h e r n p i k e m i n n o w a n d r a i n b o w t r o u t r ec ru i t s was e i ther p r e d i c t e d i n the m o d e l here or obse rved i n the field. T h e r e was a t rade-off be tween n o r t h e r n p i k e m i n n o w dens i ty a n d r a i n - b o w t r o u t g r o w t h a n d m o r t a l i t y ( F i g s . 5.23 a n d 5.21 (Pos t et a l . , 1999). I n E c o s i m , th i s t rade-off opera tes t h r o u g h the effects of n o r t h e r n p i k e m i n n o w o n Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 176 c h a o b o r u s w h i c h i n t u r n affects the d e n s i t y of r a i n b o w t r o u t f o o d s u p p l y ( the z o o p l a n k t o n a n d ben thos F i g s 5.21, 5.22, a n d 5.5). H o w e v e r , s ince rainbow- t r o u t were no t m a r k e d u n t i l t hey were at least 100 mm, changes o c c u r r i n g i n g r o w t h a n d s u r v i v a l of these f ish before t h a t p o i n t were i n v i s i b l e . W h e r e n o r t h e r n p i k e m i n n o w were f ished, j u v e n i l e r a i n b o w t r o u t d e n s i t y c o u l d have inc reased for e x a m p l e i f n o r t h e r n p i k e m i n n o w p r e d a t i o n was r e d u c e d resul t - i n g i n s lower g r o w t h a n d h ighe r m o r t a l i t y s i m i l a r to the p a t t e r n obse rved by P o s t et a l . (1999). D i s t i n g u i s h i n g be tween the t w o h y p o t h e s i s is s i m p l y a m a t t e r o f o b s e r v i n g the s y s t e m over a few more years . T h e i m p o r t a n t t h i n g to measure is h o w r e c r u i t m e n t ( i n b iomass ) has c h a n g e d before a n d s ince the m a n i p u l a t i o n s . O n t o g e n e t i c m o v e m e n t of n o r t h e r n p i k e m i n n o w severe ly con founds any m e a s u r e m e n t of m o r t a l i t y a n d g r o w t h response. I m p l i c i t i n the ana ly s i s s h o w n here was a la rge a n d u n l i k e l y a s s u m p t i o n t h a t m o v e m e n t ra tes re- m a i n e d cons tan t over t i m e . R e c a l l i n chap te r 4.3.3 t h a t I c o m b i n e d the leng th-age a n d t a g g i n g d a t a to s i m u l t a n e o u s l y e s t ima t e g r o w t h a n d move - m e n t pa ramete r s . T h i s a p p r o a c h i m p l i c i t l y assumes t h a t the h i s t o r i c a l move - m e n t ra tes l e a d i n g to the obse rved length-age s t r u c t u r e ( i n t h i s case c o l l e c t e d before any m a n i p u l a t i o n s ) was the same f o l l o w i n g e x p e r i m e n t a l r emova ls . T h i s was necessary i n o rder to a c c u r a t e l y e s t ima te the g r o w t h pa rame te r s i n the nu r se ry lakes needed to p r e d i c t g r o w t h t ra jec to r ies o f the m a r k e d fish (used i n t u r n to p r e d i c t the p r o b a b i l i t y of m o v e m e n t ) . T h i s a s s u m p t i o n w o u l d be v i o l a t e d i n the l i k e l y case t h a t m o v e m e n t b e i n g dens i t y -dependen t . Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 177 T h e ve ry h i g h effective dens i t i es o f n o r t h e r n p i k e m i n n o w i n the nu r se ry lakes (chapter 2, F i g . 2.5) suggest these lakes are ve ry c r o w d e d . I f the cue for fish to move u p s t r e a m is v e r y h i g h dens i ty i n the nu r se ry area , t hen dens i t y r e d u c t i o n s i n the nu r se ry a rea w o u l d resul t i n less m i g r a t i o n a n d p o s s i b l y no change i n m o r t a l i t y ra tes . A n a d d i t i o n a l p r o b l e m is t h a t m o v e m e n t of n o r t h e r n p i k e m i n n o w c o u l d have o c c u r r e d to lakes where n o s a m p l i n g c o u l d have de tec ted . I n the eas te rn lakes, fish c o u l d leave M o o s e P a s t u r e l ake b y the ou t f l ow creek, a n d i n the case of D a d ' s , to b o t h T a s h a l ake above i t a n d the ou t f low creek b e l o w i t ( F i g . 2.1) . T h e es t imates of any m o v e m e n t pa rame te r s c o u l d be g ross ly inco r rec t . T h e s i m u l a t i o n s tud ies i n chap t e r 4.3.3 show t h a t i n cases w i t h l o w c a p t u r e p r o b a b i l i t i e s a n d w h e r e m o v e m e n t occurs at sizes s m a l l e r t h a n the s e l e c t i v i t y of the gear (low Ih/hpi), the t o t a l p r o p o r t i o n of the p o p u l a t i o n l e a v i n g the nu r se ry a rea (pi) is ove r - e s t ima ted . W h i l e the m o v e m e n t . p r o b a b i l i t y f u n c t i o n used i n the ana lys i s o f the f ie ld d a t a was different, the e s t i m a t e d m o v e m e n t func t ions show t h a t m o v e m e n t l i k e l y occu r s i n s ize classes t o o s m a l l to be c a p t u r e d w i t h s t a n d a r d h o o p nets , m e a n i n g we s h o u l d expec t a p o s i t i v e b ias i n es t imates of the t o t a l p r o p o r t i o n l e a v i n g the n u r s e r y a rea p\. H o w e v e r , these same s i m u l a t i o n s tud ies showed tha t the e s t ima t e o f m o r t a l i t y of the t agged cohor t Mt was s t i l l u n b i a s e d . O n t o g e n e t i c m o v e m e n t does present an i n t e r e s t i n g o p p o r t u n i t y for n o r t h - e rn p i k e m i n n o w c o n t r o l i n th i s s y s t e m . B y p r e v e n t i n g n o r t h e r n p i k e m i n n o w f r o m r e t u r n i n g to head -end lakes u s ing d a m s , p o p u l a t i o n s i n those lakes Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 178 w o u l d e v e n t u a l l y dec l ine . S ince the j u m p i n g a b i l i t y of r a i n b o w t r o u t is m u c h greater t h a n n o r t h e r n p i k e m i n n o w , such ba r r i e r s need no t prevent the i r ac- cess to h e a d w a t e r lakes. O n l y a s ingle c o n s t r u c t i o n event w o u l d be needed to b u i l d these bar r ie r s w i t h regu la r m a i n t e n a n c e t o p reven t s t r eams c u t t i n g a r o u n d the s t r e a m b a n k s a r o u n d t h e m . T h i s w o u l d be c o n s i d e r a b l y less ef- fort t h a n large-scale p r e d a t o r r e m o v a l . U n f o r t u n a t e l y , the effect of the clams m i g h t t ake severa l years to be felt s ince n o r t h e r n p i k e m i n n o w are r e l a t i v e l y l o n g l i v e d , a n d have been k n o w n to s p a w n i n the m a r g i n s o f lakes ( J eppson , 1959). O n the o the r h a n d , efforts to e rad ica te n o r t h e r n p i k e m i n n o w i n any lake lower i n the d r a i n a g e w i l l be a lmos t en t i r e ly frui t less s ince there w i l l be a cons t an t f low of fry f r o m lakes u p s t r e a m . C o m p a r i n g m e a s u r e d a n d p r e d i c t e d e x p e r i m e n t a l responses of ecosys t em to f i sh ing has severa l advantages . F i r s t , i t gets away f r o m a t t e m p t i n g to i n t u i t ecosys tem responses to f i s h i n g . . T h e r e is l i t t l e d i s p u t e t h a t f i sh ing w i l l have c o m m u n i t y w i d e effects a n d t h a t the i n t e r ac t i ons effects are no t l i k e l y s i m p l e . It is o p t i m i s t i c to t h i n k any "expec ted" (as d i scussed b y S i h et a l . (1985)) effects o f s u c h r emova l s c o u l d c o m e f rom a n y t h i n g o the r t h a n an ecosys t em m o d e l . E c o s y s t e m responses to f i sh ing m a y o c c u r i n severa l different species , at severa l different t r o p h i c levels a n d have d y n a m i c s m e d i a t e d b y change i n p r e y b e h a v i o r ( v u l n e r a b i l i t y exchanges ra tes) . I n a d d i t i o n , some of the e x p e c t e d response va r i ab le s such as j u v e n i l e r a i n b o w t r o u t s u r v i v a l r e s p o n d are l i k e l y to change i n h i g h l y coun te r i n t u i t i v e ways ( s u r v i v a l dec reas ing b u t ove ra l l b i o m a s s of a d u l t r a i n b o w t rou t i n c r e a s i n g over t i m e ) . T h a t s a id , the Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 179 E c o s i m m o d e l I used here m i g h t requ i re a m o r e d e t a i l e d d e s c r i p t i o n of the p o p u l a t i o n d y n a m i c s (more g roups to desc r ibe z o o p l a n k t o n for e x a m p l e ) to r e a l i s t i c a l l y desc r ibe p o p u l a t i o n d y n a m i c s . M y resul t s were s i m i l a r to those of V a n d e r Z a n d e n et a l . (2005) i n i d e n - t i f y i n g the p o t e n t i a l i m p o r t a n c e of the b e n t h i c - z o o p l a n k t o n l inkage i n pre- d i c t i n g the o u t c o m e of p r e d a t o r r e m o v a l f r o m lakes . T h e m o d e l i n g a p p r o a c h used here is s i g n i f i c a n t l y different i n t h a t I a s s u m e d the d y n a m i c s were m i t - i g a t e d by b e h a v i o r ( v u l n e r a b i l i t y exchange processes) a n d , t h a t m o d e l pre- d i c t i o n s were v e r y sens i t ive to a s s u m p t i o n s a b o u t those d y n a m i c s . E v e n t h o u g h s i m p l e p r e d a t o r p r e y m o d e l s are k n o w n to p r o d u c e p a r a d o x i c a l be- h a v i o r ( A b r a m s a n d W a l t e r s , 1996), l a rger scale ecosys t em m o d e l s w i t h the same flaws are s t i l l b e i n g p r o d u c e d ( V a n d e r Z a n d e n et a l . , 2005; M a n g e l a n d L e v i n , 2005) w i t h appa ren t d i s rega rd to the p r o b l e m s of the s i m p l e m o d e l s . T h i s s t u d y ident i f ies some d a u n t i n g p r a c t i c a l chal lenges w i t h m e a s u r i n g h o w ecosys tems m i g h t r e s p o n d to fishing ( e x p e r i m e n t a l l y or o the rwi se ) . T h e m a j o r p r o b l e m s were f i r s t l y the s p a t i a l o r g a n i z a t i o n of the s tock a n d secondly , t h a t d y n a m i c s p r e d i c t e d to be the m o s t i m p o r t a n t to the response to fishing are those o c c u r r i n g i n s ize classes t oo s m a l l to measure . I n the case of m a r i n e fisheries these d i f f icu l t ies are l i k e l y to be worse . S p a t i a l d y n a m i c s i n m a r i n e sys tems are a r g u a b l y m u c h m o r e c o m p l e x , a n d m o r e p o o r l y u n d e r s t o o d t h a n lakes. M a n y m a r i n e sys t ems are also l i k e l y to b y a l r e a d y affected b y fishing ( F i s h e r a n d F r a n k , 2004) , a n d d a t a o n non- t a rge t species at any s ize or t r o p h i c l eve l are even more l i m i t e d for mos t m a r i n e ecosys tems . T h e m o d e l Chapter 5. Predicted and Observed Ecosystem Responses to Fishing 180 p r e d i c t i o n s a n d the field exper i ence shows the m o s t i m p o r t a n t d y n a m i c s are those tha t o c c u r i n prec i se ly those y o u n g age g roups a n d / o r s m a l l s ize classes for w h i c h there is ve ry p o o r i n f o r m a t i o n even for the target species of m o s t fisheries. Chapter 6. General Conclusions 181 Chapter 6 General Conclusions 6.1 The difficulty of properly estimating growth and mortality parameters G r o w t h a n d m o r t a l i t y s h o u l d be r e l a t i v e l y s i m p l e pa rame te r s to measu re i n response to h a r v e s t i n g b u t I have s h o w n here t h a t i t is no t easy to e s t ima t e these pa rame te r s c o r r e c t l y even w i t h l i k e l i h o o d s t h a t c o r r e c t l y a c c o u n t for the s a m p l i n g process . T h i s is a ser ious c o n c e r n s ince g r o w t h pa rame te r s are used i n v i r t u a l l y every s tock assessment to p r e d i c t size at age, y i e l d per r ec ru i t , a n d of ten even as p rox ies for n a t u r a l m o r t a l i t y i t se l f ( P a u l y , 1980; Jensen , 1997) . T r a d i t i o n a l m e t h o d s , such as the F a b e n s m e t h o d are b i a s e d i n the wor s t poss ib l e d i r e c t i o n (o ve r - e s t i ma t i ng the m e t a b o l i c g r o w t h p a r a m e t e r K a n d n a t u r a l m o r t a l i t y M). T h i s b ias w i l l l e a d to o v e r - e s t i m a t i n g the. o p t i m a l e x p l o i t a t i o n ra te . T h e biases i n t r a d i t i o n a l m e t h o d for e s t i m a t i n g g r o w t h p a r a m e t e r s have been k n o w n for some t i m e ( P a r m a a n d D e r i s o , 1990) b u t s o l v i n g the p r o b l e m has p r o v e n very di f f icul t even w i t h t echn iques d e v e l o p e d i n th i s thesis a n d Chapter 6. General Conclusions 182 elsewhere L a s l e t t et a l . (2002); E v e s o n et a l . (2004) . T h e l i k e l i h o o d s deve l - o p e d here ( C h a p t e r s 4 a n d 3) are no t ve ry r obus t to t he i r a s s u m p t i o n s a n d c o u l d no t be used i n m a n y fisheries. C o n s i d e r for e x a m p l e t h a t the length-age l i k e l i h o o d fails to e s t ima t e p a r a m e t e r s c o r r e c t l y w h e n the h i s t o r i c a l f i sh ing ra te has been va r i ab l e (chap . 3, F i g . 3.4) m e a n i n g t h a t these m e t h o d s c o u l d o n l y be a p p l i e d i n a ve ry r e s t r i c t e d n u m b e r of cases. O f p a r t i c u l a r c o n c e r n is t h a t g r o w t h pa rame te r s b ias is wor s t i n the c o m m o n s i t u a t i o n where e x p l o i t a - t i o n ra te increases r a p i d l y before a col lapse . U n f o r t u n a t e l y , t h i s is w h e n i t is m o s t i m p o r t a n t to be able to e s t ima te the cor rec t t a rge t e x p l o i t a t i o n rate , a n d to c o r r e c t l y p ro jec t the b i o m a s s for r e b u i l d i n g . E s t i m a t i n g g r o w t h p a r a m e t e r s needs to be i n c l u d e d i n the s tock assess- m e n t itself, r a the r t h a n t r e a t i n g g r o w t h pa rame te r s as ' k n o w n ' va lues exter - n a l to the mode l s , the i r e s t i m a t i o n c o u l d be i n c l u d e d w i t h p a r a m e t e r s ( such as p r o d u c t i v i t y , etc.) t h a t are u s u a l l y e s t i m a t e d i n such m o d e l s . N a t u r a l m o r t a l i t y , gear s e l e c t i v i t y a n d f i sh ing m o r t a l i t y are often a l r e a d y m o d e l e d i n m o s t s tock assessment m o d e l s so p r e d i c t i n g a m a t r i x of v u l n e r a b l e n u m b e r s at l e n g t h a n d age (pi, a E q . 4.6) for every year w o u l d be r e l a t i v e l y s i m p l e . W h e n there are t i m e series of length-age d a t a , m a r k - r e c a p t u r e d a t a m a n y years of such tab les c o u l d be i n c l u d e d as t i m e series to e s t i m a t e the effects of f i sh ing o n the size a n d age s t r u c t u r e of the s tock . M a n y s u c h tab les c o u l d p o t e n t i a l l y p r o v i d e i n f o r m a t i o n a b o u t t i m e - v a r y i n g g r o w t h a n d r e c r u i t m e n t . Chapter 6. General Conclusions 183 6.2 Evaluating Ecosystem Impacts of Fishing T h e d y n a m i c s E c o s i m p r e d i c t e d to have the greates t effect o n a n ecosys tem's response to f i sh ing are also those mos t c h a l l e n g i n g to s t u d y : the v u l n e r a b i l i t y exchange rates, a n d j u v e n i l e fish s u r v i v a l . M e t h o d s to e s t ima t e s u r v i v a l at least ex is t b u t there are cons ide rab l e d i f f icul t ies c a t c h i n g s m a l l f ish a n d m a r k - i n g t h e m once c a p t u r e d . T h e v u l n e r a b i l i t y exchange rates have the greatest effect o n p r e d i c t e d d i r e c t i o n a n d m a g n i t u d e of the response to f i sh ing . E s - t i m a t i n g v u l n e r a b i l i t y exchange rates is t y p i c a l l y done i n E c o s i m b y f i t t i n g t i m e series; a n a l y s i s of change i n p rey m o r t a l i t y w i t h changes i n p r e d a t o r a b u n d a n c e ; e x a m i n a t i o n of l o n g - t e r m changes i n p r e d a t o r a b u n d a n c e a n d c a l c u l a t i o n s based o n m o v e m e n t / e x c h a n g e - r a t e d a t a ( W a l t e r s a n d M a r t e l l , 2004) . S ince I d i d n o t have m u l t i p l e years o f d a t a o n l y d i r ec t c a l c u l a t i o n of m o v e m e n t a n d exchange ra te d a t a w o u l d have been poss ib le . S ince the m o s t i m p o r t a n t d y n a m i c s o c c u r i n s m a l l f ish, the cha l l enge here is to deve lop m e t h o d s measure t h i s exchange ra te d i r e c t l y or i n d i r e c t l y i n j u v e n i l e f ish . If t h i s s t u d y is c a r r i e d f o r w a r d for severa l years i t w i l l be poss ib l e to e s t ima t e the r e c r u i t m e n t i n the years t ha t f o l l o w i n g d e p l e t i o n f i sh ing once those rec ru i t s b e c o m e fu l ly v u l n e r a b l e to f i sh ing year u s i n g a s t a n d a r d s tock- assessment m o d e l . H o w e v e r , w i t h o u t obse rva t ions of changes i n the v u l n e r a - b i l i t y exchange rates (or some p r o x y of fo rag ing t i m e ) i t w i l l n o t be poss ib le to say a n y t h i n g a b o u t w h e t h e r C u l t i v a t i o n - D e p e n s a t i o n effects were p ro - Chapter 6. General Conclusions 184 duced. While agreement between observed and predicted response variables were encouraging, the true test of whether or not cultivation-depensation was produced will be to actually observe an alternate stable state with lower recruitment over several years and the changes in foraging behavior that produced that state. While Mangel and Levin (2005) may be right saying we have no excuse for not shifting to a community paradigm in fisheries, the data requirements to practically do so may be considerable. Consider the study system. To monitor and manage the community effects of fishing in this case f had to consider the dynamics of one species with two life-history types; one with large-scale density dependent spatial dynamics (northern pikeminnow) and rainbow trout on a more localized scale. Considering the relatively closed nature of this system and the iarge quantity of data - measuring growth and mortality responses should have been relatively simple. In many (especially marine) fisheries the data are poorer; the spatial dynamics are more complex; and the dynamics are further complicated by fast changing variables such as fishing effort. My study shows that simple growth and mortality variables may respond to fishing in very counter-intuitive directions. Consider for example, our modeling and field results showed that juvenile rainbow trout mortality was actually higher following northern pikeminnow removals. The model predicts this response but at the same time predicts an overall increase in rainbow biomass related to improved growth. The number of juvenile rainbow trout Chapter 6. General Conclusions 185 s u r v i v i n g m i g h t have i n d e e d been lower i n n u m b e r s , b u t the fewer r e m a i n i n g r a i n b o w t rou t c o u l d have g r o w n be t te r , l i v e d longer a n d p r o d u c e m o r e re- c ru i t s t h a t m a n y sma l l e r fishes w o u l d have. 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