"Science, Faculty of"@en . "Zoology, Department of"@en . "DSpace"@en . "UBCV"@en . "Tautz, A. F."@en . "2011-06-07T21:58:41Z"@en . "1970"@en . "Master of Science - MSc"@en . "University of British Columbia"@en . "For a variety of stock-recruit systems in which environmental variability is simulated by random normal deviates used as multipliers or divisors Ricker (1958) and Larkin and Ricker (1964) demonstrated the benefits of complete stabilization of escapement as opposed to removal of a fixed proportion of the stock each year. Part I is primarily concerned with the response of these same systems to a pattern of stochastic modification which is more regular in form, a pattern such as might be imagined to result from long-term trends in environmental conditions. In addition, some mathematical properties of these systems are discussed.\r\nPart II considers the stock-recruit relationship from a more reductionist or mechanistic point of view. Evidence for differential utilization of spawning areas is presented and spawner distributions in three different environments are compared. These results are discussed in terms of their relevance to existing stock-recruit theory. Also, observations on egg retention and social facilitation are presented."@en . "https://circle.library.ubc.ca/rest/handle/2429/35271?expand=metadata"@en . "S O M E A S P E C T S O F E N V I R O N M E N T A L V A R I A B I L I T Y I N R E L A T I O N TO S T O C K R E C R U I T M E N T S Y S T E M S by A R T H U R F R E D E R I C K T A U T Z B . S c . , U n i v e r s i t y of B r i t i s h Columbia , 1968 A THESIS 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 M A S T E R O F S C I E N C E in the Department of Zoology We accept this thesis as conforming to the r equ i r ed standard 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 August, 1970 In p resent ing t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree t h a t permiss ion fo r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t t e n p e r m i s s i o n . Depa rtment The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date A B S T R A C T F o r a va r i e ty of s t o c k - r e c r u i t systems in which environmenta l v a r i a -b i l i t y i s s imula ted by r andom n o r m a l deviates used as m u l t i p l i e r s or d i v i s o r s R i c k e r (1958) and L a r k i n and R i c k e r (1964) demonstrated the benefits of c o m -plete ' s t ab i l i za t ion of escapement as opposed to r e m o v a l of a f ixed propor t ion of the stock each year . P a r t I is p r i m a r i l y concerned with the response of these same systems to a pattern of s tochast ic modi f ica t ion which is more regular i n fo rm, a pattern such as might be imagined to r e su l t f r o m long -t e r m trends in envi ronmenta l condit ions. In addition, some mathemat ica l proper t ies of these systems are d i scussed . P a r t II cons iders the s t o c k - r e c r u i t re la t ionship f r o m a more reduc-t ionis t or mechanis t ic point of v iew. Evidence for dif ferent ia l u t i l i za t ion of spawning areas is presented and spawner d is t r ibut ions i n three different environments are compared . These resu l t s are d i scussed i n t e rms of their re levance to exis t ing s t o c k - r e c r u i t theory. A l s o , observat ions on egg retent ion and s o c i a l fac i l i t a t ion are presented. i i i T A B L E O F C O N T E N T S | Page T I T L E P A G E ; i A B S T R A C T i i T A B L E O F C O N T E N T S i i i L I S T O F F I G U R E S . . . i v L I S T O F T A B L E S v G E N E R A L I N T R O D U C T I O N ' 1 P A R T I 4 The B a s i c Systems 4 S imula t ion P rocedure 8 D e t e r m i n i s t i c S in Effects 11 The Effect of Cycle Length and Ampl i tude Modi f ica t ions 14 Stochast ic Modi f ica t ions 18 The Nature of the Modi f ica t ions 20 D i s c u s s i o n . . . 25 P A R T II 28 Introduct ion 28 Site Selec t ion and Ex t rapensa to ry M o r t a l i t y 32 The Study A r e a s , 33 I F o u r M i l e Creek 33 Me thods . . . . . . . . 34 R e s u l t s . \"... 37 P h y s i c a l c h a r a c t e r i s t i c s of the sections 37 The spawning run 39 S t r e a m mig ra to ry behavior 42 Egg retention \u00E2\u0080\u009E.' ~ 44 II P inkut and Weaver Creeks 45 I M P L I C A T I O N S O F T H E S T U D I E S 50 C O N C L U S I O N S 54 A C K N O W L E D G E M E N T S 56 B I B L I O G R A P H Y 57 i v L I S T O F F I G U R E S F i g u r e Page 1 Stock rec ru i tment curves A , B , C of R i c k e r (1958) in wh ich z = w e a ( 1 - w ) for a- = 1.000, 2.000, and 2.678 r e s p e c t i v e l y . . . \u00E2\u0080\u009E , 5 2 - Stock rec ru i tment curves F , G, H of R i c k e r (1958). See text for explanation 7 3 Catch i n de t e rmin i s t i c s imula t ion of a f ixed percentage f i shery on curve C systems with 12- and 24-year s in wave cycles for amplitude scal ing factor P=2.0 15 4 Catch i n de t e rmin i s t i c s imula t ion of a f ixed percentage f i shery on a curve C s y s t e m with a 12-year s in cyc le for ampli tude sca l ing factor at two levels , P = 0.5 and P .= 2.0 \"... 1 7 5 Catch i n de t e rmin i s t i c s imula t ion of a complete ly s tab i l i zed f i shery on curve A and curve B systems with a 12-year s in cyc le and amplitude sca l ing factor P = 2.0 19 6 Re la t ionsh ip between mean catch (c) and standard deviat ion of catch (a c) in complete ly s tab i l i zed f i sher ies for 200 year s imula t ions for curves A , B , and C for which envi ronmenta l effects at var ious l eve l s were s imula ted by scaled random n o r m a l deviates used in the method of R i c k e r (1958) 26 7 Stock r ec ru i tmen t curve A and average curve when the sy s t em i s exposed to stochastic va r i a t ion A ' 30 8 F o u r M i l e Creek showing loca t ion of g r ids A - J and the meter ing site (*) 36 9 T e m p o r a l d i s t r ibu t ion of spawning run and a re la t ive m e a -sure of changes i n d ischarge 40 10 R e g r e s s i o n l ines fitted to mean number of sightings per g r i d plotted against the depth and ve loc i ty of the g r i d 41 11 M e a n depth of the redds i n g r i d A plotted against per cent of m a x i m u m spawner density (18 redds) 43 1 2 D a i l y number of f i sh plotted against a c ross sect ion of the upper g r i d at P inkut Creek 47 LIST O F T A B L E S Table ' \u00E2\u0080\u00A2 ' Page I Mean catch and escapement i n de te rmin i s t i c models of s ix stock r e c r u i t re la t ionships 12 II - M e a n catch and escapement i n 200 year s imulat ions of f ixed percentage exploi tat ion for each of s ix reproduct ive curve systems, with l o n g - t e r m environmental fluctuations, represented by s in modi f ie r s , at cycle lengths of 6, 11, 12 and 24 years , and at two leve ls of ampli tude. See text for explanation 13 III Mean catch and escapement i n 200 year s imulat ions of a f i she ry with complete ly s tab i l i zed escapement for each of s ix reproduct ive curve systems, when l o n g - t e r m env i ron -, mental fluctuations are represented by s in modi f ie r s , at cyc le lengths of 6, 11, 12, and 24 years and at two l eve l s of ampli tude. See text for explanation IV P h y s i c a l c h a r a c t e r i s t i c s of g r ids A - J wi th pe rmeab i l i t y index expressed as per cent of sample passing through a l . l 9 n a m sieve. 38 1 G E N E R A L I N T R O D U C T I O N j The es tabl ishment of l eve ls of exploitat ion consistent with opt imal u t i l i za t ion of stocks of c o m m e r c i a l l y important species r emains as a p r i -m a r y focus of contemporary f i sher ies b iology. Th i s p rob lem of m a x i m u m sustained y i e l d i s , i n essence, a p r o b l e m of population ecology, and it i s not su rp r i s i ng therefore that f i sher ies and population theory have fol lowed s i m i l a r , though dis t inguishable, courses of evolut ion. A s i d e f r o m the fact that f i she r ies biology is concerned with fishes, i t is best cha rac t e r i zed by i t s pragmat ic , i f perhaps inelegant, nature. Thus, many management p r o -g rams are l a r g e l y concerned wi th the co l l ec t ion of catch and escapement s ta t i s t ics which, when added to previous records , should provide some insight into opt imal leve ls of escapement. Given enough of this type of informat ion , one has a reasonable expectation of successful management, p rovided that the va r i a t ion in r ec ru i tment of a stock of a g iven size i s not excess ive . Unfortunately, the s t o c k - r e c r u i t data which is now avai lable indicates that this v a r i a t i o n i s considerable and therefore h i s t o r i c a l approaches can only meet wi th l i m i t e d success . Thus, the development of better management p rograms would seem dependent on the incorpora t ion of r ec ru i tmen t va r i a t i on into management theory and a corresponding ana lys i s of the sources of this va r i a t ion . R i c k e r (1958) showed the i n i t i a l in teres t in this problem, and developed a conceptual f ramework and n u m e r i c a l model which s imula ted the behaviour of s t o c k - r e c r u i t systems when exposed to randomly-f luc tuat ing envi ronments . The bas ic model was de r ived e a r l i e r (1954) f r o m a cons idera t ion of the effects of predation and cann iba l i sm on numbers , the resu l t of which was the w e l l -. I i known s t o c k - r e c r u i t or reproduct ion cu rves . L a r k i n and R i c k e r (1964) con-f i r m e d e a r l i e r conclusions concerning the behavior of these systems by the use of computer techniques. The reproduc t ion curve i s dome-shaped which, i n theory, resu l t s f r o m an increase in the number of predators to a degree such that the abso-lute number of prey s u r v i v o r s i s decreased. Though one may jus t i f iably object to predat ion as the cont ro l l ing mechan i sm for some specif ic situations, the dome-shaped curve seems to be a reasonable fit for many f i she r ies (e.g, G a r r o d , 1966), and may be taken as one general f o r m of parent-progeny re la t ionships given density dependent mechanisms of regulat ion. The bedraggled debate oi density dependent versus density independent mor t a l i t y which occupied much of the ecologis t s ' t ime, never became a c r i t i c a l p r o b l e m in f i she r ies biology. It was c lear f r o m the outset that weather and c l imate played an important ro le i n influencing product ion of most s tocks. Consequently, the addi t ion of s tochast ic va r i a t i on to a sy s t em which was b a s i c a l l y density dependent i n form, was not considered as an outrageous d i s to r t ion of r e a l i t y . A t this l e v e l of invest igat ion one further attribute of the sys t em was i n need of study, namely, the effects of long t e r m trends in density independent mor t a l i t y fac tors . Many environmenta l var iab les ; e.g., cur rent patterns, tempera tures , etc., s eem to fol low a more regular pat tern of va r i a t i on than a r andom model would suggest. Thus, i t was of in teres t to determine i f the addit ion of these long t e r m phenomena would marked ly affect previous con-elusions concerning the gross behavior of these sys tems, Th is d i s cus s ion compr i s e s P a r t I of the fol lowing thesis . 1 While the above d iscuss ions provide a useful f r amework for the fo rmula t ion of genera l management pol icy , their value i s l i m i t e d for specif ic s i tuat ions. One cannot, for example, determine the c a r r y i n g capacity of a given s t r e a m and consequently a stock unit cannot be defined. Thus, a different l e v e l of inves t igat ion is r equ i red and a p r e l i m i n a r y study consistent wi th this approach i s desc r ibed i n P a r t II, which d iscusses some aspects of the spawning behavior of sockeye salmon, Oncorhynchus ne rka . A t the specif ic l eve l one must investigate those aspects of the population and environment relevant to the defini t ion of c a r r y i n g capaci ty. One need ask, for example, which areas of a s t r e a m are suitable for spawning, whether qual i ta t ive differences exis t i n the areas which are u t i l i zed , which factors influence neares t neighbor distances, and others . The pa r t i cu la r p r o b l e m invest igated in P a r t II i s , i n rea l i ty , pertinent to both leve ls of invest igat ion. A t the general l eve l i t cons iders the effect of env i ronmenta l v a r i a b i l i t y operating in a density dependent manner while, at the speci f ic l e v e l i t presents evidence for the mechan i sm of site se lect ion and the ab i l i ty of spawners to d i s t ingu ish habitats of different qual i ty. 1 P a r t I has been published as \"Some effects of s imulated l o n g - t e r m e n v i r o n -mental fluctuations on m a x i m u m sustained y i e ld\" , in the J . F i s h . R e s . B d . Canada, 26: Z71 5-Z726. P A R T I The B a s i c Sys tems The curves used in the present s imulat ions are iden t i ca l to those desc r ibed by R i c k e r (1958). Curves A , B and C are member s of the exponential f ami ly Z t = we a ( 1 ~ w ) where Z t = product ion i n year t w = spawning stock size ^ \" a \" i s a parameter de te rmin ing m a x i m u m production and, consequently, the shape of the reproduct ion curve . F o r curves A , B and C the p a r a -meter \" a \" assumes a value of 1.000,2.000, and 2.678 respec t ive ly (F ig . Curve A desc r ibes the situation -where m a x i m u m product ion occu r s at the e q u i l i b r i u m pos i t ion w = 1.000 = Z m a x . D i sp lacements to the. left of e q u i l i b r i u m (w < 1.0) resu l t i n a \" c l i m b i n g \" of the ascending l i m b of the curve . D i sp lacemen t s to the r ight of e q u i l i b r i u m (w > 1.0) resu l t in an immedia te compensation, the stock being depressed to a l e v e l below e q u i l i b r i u m density to which i t gradual ly re turns . Curve B . In this case the m a x i m u m product ion i s associa ted wi th a stock density of approx imate ly one- th i rd that of e q u i l i b r i u m densi ty . Compar ing Curve B with A , product ion per spawner at any g iven stock density i s greater in Curve B for 0 1. A r b i t r a r y d isp lacement f r o m e q u i l i b r i u m resu l t s in the p roduc-t ion of a damped o s c i l l a t i o n of abundance which re turns the stock to the e q u i l i b r i u m pos i t ion . Curve C i s a more extreme v e r s i o n of B i n that product ion rate are greater and compensat ion i s more severe . The sys tem i s unstable i n the sense that d isp lacements f r o m the e q u i l i b r i u m posi t ion resul t in the product ipn of permanent o sc i l l a t i ons and there i s no tendency for the stock to re turn to the e q u i l i b r i u m of w = 1. C u r v e s F , G and H ( F i g . 2) each belong to a different f ami ly of cu rves . Curve H represents the converted B ever ton-Holt re la t ionsh ip as desc r ibed i n R i c k e r (1958), whi le Curves F and G are cont r ived equations representat ive of the remain ing types of s t o c k - r e c r u i t sys tem Curve F i s cha rac t e r i zed by an ascending l i m b which conforms to Curve B for 0 w D = 0 , Z t < w B Zt+1 = W \u00C2\u00BB e a ( 1 \" W m ) , Z t - w B > 0 where wm = escapement assoc ia ted wi th m a x i m u m e q u i l i b r i u m catch (m. e. c. ) The computer s imulat ions conducted were a l l run for 200 s imulated y e a r s for a l l combinat ions of: (1) four l o n g - t e r m cyc le lengths: 6, 11, 12, 24 yea r s . (2) S ix stock r e c r u i t curves : A , B, C, F , G, H . (3) Two l eve l s of random effects. (4) Two l eve l s of l o n g - t e r m effects. (5) Three patterns of f i sh ing: f ixed percentage, pa r t i a l and complete s tab i l iza t ion of escapement ( R i c k e r 1958). (6) Three patterns of envi ronmenta l effects: s in effects only, s in plus random, s in t imes random. 11 D e t e r m i n i s t i c S in Effects In the s imula t ions using the _sin wave modif ier and a fixed percentage f i shery , the catch pattern was i n i t i a l l y one of e r r a t i c changes in abundance. Wi th in a few generations a repeatable pattern of catch and escapement was evident, the values o sc i l l a t i ng in phase wi th the sin modi f i e r but at lower ampl i tudes . (The i n i t i a l pe r iod of ins t ab i l i t y was a resu l t of s tar t ing the s imulat ions with the stock at i t s e q u i l i b r i u m density (w = 1). Two l e v e l s of ampli tude ( P = . 5, P = 2.0) were used i n conjunction with four cycle lengths and the resu l t ing mean catch and escapement values for two hundred s imulated y e a r s are s u m m a r i z e d in Table II, which can be compared with the s imple de t e rmin i s t i c case (Table I). F o r curves A , B and C, the tabulated escapement values differ only s l ight ly f r o m the de t e rmin i s t i c values assoc ia ted wi th m a x i m u m e q u i l i b r i u m catch (m. e. c . )* The differences a re at tr ibutable to the i n i t i a l pe r iod of ins tab i l i ty and the f ixed 200 year pe r iod of s imula t ion which did not a lways end on a year complet ing a cyc le . F o r curve F , the mean catch i s s l ight ly l e s s than the de t e rmin i s t i c mode l and curve G goes to ext inct ion under conditions of f ixed percentage The de t e rmin i s t i c values of m . e. c. i n Table I are de te rmined by setting the f i r s t der iva t ive of w t e ^ a _ w t ) -w t equa l to zero and solving for w. 12 T A B L E T. M e a n catch and escapement in de t e rmin i s t i c models of six s t o c k - r e c r u i t re la t ionsh ips . C U R V E C A T C H E S C A P E M E N T A 0.330 0.433 B 0.935 0.361 C 1.656 0.314 F 0.760 0.210 G 0.330 0.433 H 0.520 0.240 13 T A B L E II. M e a n catch and escapement in 200 year s imula t ions of f ixed percentage exploi ta t ion for each of s ix reproduct ive curve systems, wi th l o n g - t e r m envi ronmenta l fluctuations, represented by sin modi f ie r s, at cyc le lengths of 6, 11, 12 and 24 year s, explanation. and at two l e v e l s of ampli tude. See text for > C Y C L E 6 yea r s 11 year s 12 year s 24 year s Curve L e v e l Ca tch Escap , Catch E scap Catch E scap Catch E scap. A 1 2 .3 33 .338 .436 .442 .333 .338 .436 .442 .336 .346 .440 .453 .340 .358 .445 .469 B 1 2 .937 .948 .360 .365 .936 .945 .360 .364 .940 .956 .362 .368 .949 .981 .365 .377 C 1 2 1.657 1.673 .313 .316 1.656 1.673 .313 .316 1.660 1.684 .314 .318 1.676 1.723 .316 .325 F ' 1 2 .739 .746 .204 .206 .728 .711 .201 .197 .731 .742 .202 .20 5 .724 .750 .200 .208 G * 1 2 .0 13 .014 .018 .099 .019 .026 .024 .034 .0 20 .028 .026 .037 .037 .057 .049 .075 H 1 2 .543 .686 .250 .317 .550 .752 .254 .347 .553 .766 .255 .3 54 .562 .823 .259 .380 Cu rve G goes to ext inct ion i n a few generat ions under condit ions of f ixed percentage exploi ta t ion. exploi ta t ion. Curve H i s the only sys tem which responds favorably to the combinat ion of sin modi f ica t ion and fixed percentage exploi ta t ion. Curve H i s s i m i l a r to A in that m a x i m u m product ion i s assoc ia ted wi th a stock size much l a rge r than the stock size which provides m a x i m u m catch, but differs in that there i s no compensation at the higher stock dens i t ies . Since the catch i s p ropor t iona l to product ion in the f ixed percentage f i shery , gains are to be expected. Table III s u m m a r i z e s the resu l t s of s imula t ions using the same amplitude and cyc le length modi f ica t ions but with a s tab i l ized f i shery . Compar ing these resu l t s with Table I, i t i s apparent that a s tab i l ized f i shery re su l t s in an inc reased y i e l d in a l l cases . The Effect of Cyc l e Length and Ampl i tude Modi f i ca t ions In the prev ious section it was shown that the mean catches for curves A , B and C are unchanged with the combinat ion of sin m o d i f i -cat ion and f ixed percentage exploi ta t ion. Never the less , the pattern of the catch responds to both changes in cycle length and ampli tude. F i g u r e 3 compares , for curve C, the pattern of a 12-year cyc le with that of a 24-year cycle , while F i g u r e 4 shows the effect of va ry ing the ampli tude of the s in modifier\". F o r the fixed percentage exploi tat ion, va r i a t i on in cycle length has a lmost no effect on the standard deviat ion of catch ( c r 0 ), and serves only to increase the length of the se r i e s of 4 u u u 0 B y\u00C2\u00BBor eye* [1 24 y w r eyelt I 2 3 4 9 6 7 8 9 0 II 12 13 Generation * B 6 17 \u00C2\u00AB 19 20 * 22 23 24 F i g u r e 3 . C a t c h i n d e t e r m i n i s t i c s i m u l a t i o n o f a f i x e d p e r c e n t a g e f i s h e r y o n c u r v e C s y s t e m s w i t h 1 2 - a n d 2 4 - y e a r s i n w a v e c y c l e s f o r a m p l i t u d e s c a l i n g f a c t o r P = 2 . 0 . 16 i I T A B L E III. Mean catch and escapement i n 200 year s imula t ions of a f i she ry with complete ly s tab i l ized escapement for each of six reproduct ive curve systems, when l o n g - t e r m e n v i r o n -mental f luctuations a re represented by sin modi f i e r s , at cyc le lengths of 6, 11, 12 and 24 yea rs and at two l eve l s of ampli tude. See text for explanation. C Y C L E \u00E2\u0080\u00A2 6 year s 11 yea r s 12 year s 24 yea r s Curve L e v e l Catch E scap. Ca tch E scap. Catch E scap. Catch E scap. 1 .368 .433 .367 .433 .369 .433 .375 .433 A 2 .624 .370 .643 .351 .649 .348 .686 .330 1 .994 .361 . .994 .361 .996 .361 1.007 .361 JD 2 1.422 .361 1.436 .361 1.442 .361 1.482 .361 1 1.744 .314 1.744 .314 1.748 .314 1.765 .314 2 2.392 .314 2. 414 .314 2.424 .314 2.487 .314 TP 1 .837 .210 .837 .210 .839 .210 .847 .210 Jc 2 1.169 .210 1.179 .210 1.184 .210 1.214 .210 1 .368 .433 .367 .433 .369 .433 .375 .433 C j 2 .394 .322 .312 .250 .311 .243 .236 .174 T T 1 .557 .240 .556 .240 .558 .240 .564 .240 r i 2 .811 .240 .817 .240 .821 .240 .843 .240 o o o L k i B Lw ompntuO* 0 Miflh ompNtudt I 2 3 4 1 6 7 8 9 O II 12 13 14 6 16 Generation 17 M 20 21 22 23 24 F i g u r e 4. Catch i n de te rmin i s t i c s imula t ion of a f ixed percentage f i shery on a curve C sys tem with 12-year s in cycle for ampli tude sca l ing factor at two leve ls , P = 0.5 and P = 2.0. good and poor catches. A s might be expected, o\"c responds to ampli tude modif icat ions , i nc reas ing as the ampli tude becomes l a r g e r . F o r the s tab i l ized f i shery two s l ight ly different catch patterns were evident. In the systems which had a r e l a t ive ly high product ion per spawner at low stock dens i t ies (Curves B and C), the product ion never dropped below w, and consequently the stocks a lways reproduced at an op t imal rate (F ig . 5). In the l e s s responsive systems (Curves A and G) the catch pat tern is t yp i ca l ly a ser ies of r e l a t i ve ly good catches fol lowed by a se r i e s of zero catches, the length of the se r ies i nc reas ing as a function of the ampli tude of the mod i f i e r s . Stochast ic Modi f i ca t ions The de t e rmin i s t i c s in modif ica t ions desc r ibed above were s tochas t i s ized by either additive or mu l t ip l i ca t ive super impos i t ion of random n o r m a l deviates. A l g e b r a i c a l l y , the modif ica t ions (R) m a y b e represented as: Add i t i ve Effects R = (1 + Q + RND) for Q + R N D > 0 \u00C2\u00B0 ( I + Q ' + M T O ) for Q + RND < 0 i Curve A Q Curve 8 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 Generation F i g u r e 5 . Catch i n de te rmin i s t i c s imula t ion of a completely s t ab i l i zed f i shery on curve A and curve B systems with a 1 2 - y e a r s in cycle and ampli tude sca l ing factor P = 2 . 0 . 20 M u l t i p l i c a t i v e Effects = (1 + Q) (1 + RND) = ( l +Q) ( \u00E2\u0080\u0094 ) \ 1 + R N D / U 4 ( - i ) \1 +QJ \ 1 .+ R N D / for Q > 0, R N D > 0 for Q > 0, R N D < 0 for Q< 0, R N D < 0 for Q < 0, R N D < 0 where Q = scaled s in modi f ie r R N D = scaled random modi f i e r In general , the addit ion of the stochastic mod i f i e r s serves only to accentuate the bas ic patterns desc r ibed for the de t e rmin i s t i c s in effects, the frequency of ze ro catches becoming greater for the s tab i l ized f i shery , and cre becoming l a r g e r for f ixed percentage exploi ta t ion. The catches for the s tab i l ized f i shery are l a rge r as a function of o\"0 whi le no changes are observed for f ixed percentage exploi ta t ion. The Nature of the Modi f i ca t ions F r o m the preceding resu l t s three genera l conclus ions per taining to curves A , B and C are evident. (1) F o r a s tab i l ized f ishery, an increase in y i e l d over the de t e rmin i s t i c m a x i m u m i s apparent for a l l systems subjected to stochastic modi f ica t ions , and this inc rease i s commensurate wi th the va r i ance of the m o d i f i e r s . (2) The addi t ion of stochastic mod i f i e r s to a sys tem undergoing f ixed percentage exploi tat ion has no effect on the mean catch, i t s value remain ing the same as the de te rmin i s t i c m a x i m u m . (3) The pattern of modi f ica t ion ( i . e . , s inoidal , random, etc.) i s unimportant r e la t ive to the var iance of the modif ica t ions . The inc reased y i e ld s for the s tabi l ized f i shery can, i n a sense, be at t r ibuted to the technique of stochastic modi f ica t ion . Augment ing by one the absolute value of the random var ia te and subsequently using i t as a m u l t i p l i e r or d i v i s o r , has the effect of mul t ip ly ing product ion by an average modi f i e r which i s greater than 1. A l g e b r a i c a l l y , i f X i s a s y m m e t r i c a l l y d is t r ibu ted var iab le with mean 0, the frequency of a pa r t i cu l a r pos i t ive var ia te Xl i s the same as the frequency of the cor responding negative value. The appropriate mod i f i e r s would be 1 + X . for the fo rmer and ^r\u00E2\u0080\u0094\u00E2\u0080\u0094i for the la t te r . ' 1 1 It i s ea s i ly demonstrated that the mean of a pa i r of these m o d i f i e r s i s greater than 1, f r o m which i t fo l lows that the mean of a se r i e s of these mod i f i e r s (R) i s a lso grea ter than 1. F o r example, i f X t = + 1, the cor responding m u l t i p l i e r = 2, and for X t = -1 , the appropr ia te m u l t i p l i e r = \ , F u r t h e r m o r e , since (1 +X) + ^ ^ \YL \} i s 2 an inc reas ing function of X , and since inc reas ing the standard deviat ion ( i s independent of any 30 I STOCK F i g u r e 7. Stock rec ru i tment curve A and average curve when the s y s t e m is exposed to stochastic va r ia t ion A 1 . 31 var i ab le envi ronmenta l influence, and consequently no p r o v i s i o n would seem to be made for environmental changes to operate i n a density dependent manner . Thus, the sys tem now envisaged is one in which the c a r r y i n g capaci ty i s cons idered to be a r andom var iab le ; that i s , e q u i l i b r i u m density changes f r o m year to year and the compensatory response of the stock i s in r e l a t i on to that pa r t i cu la r condit ion ra ther than to an average value. Since , for most c o m m e r c i a l l y impor tant species, compensat ion is assumed to occur i n the reproduct ive and ea r ly stages of the l i fe h i s to ry , i t was felt that the above condition could be best demonstrated by examining the mechan i sms assoc ia ted with spawning and s u r v i v a l of f ry . Th i s , then, would a l l ow one to hypothesize the nature of the curve re la t ing s u r v i v a l of f ry (production) to stock size, and by an understanding of the re levant mechanisms, to suggest the nature of the v a r i a b i l i t y about that curve . F u r t h e r m o r e , a stock r e c r u i t curve would be suggested f r o m this re la t ionship , i f one assumes that the number of r e c r u i t s is some constant propor t ion of the number of fry, i .e . , that the density dependent effects are confined to a l i fe h i s to ry stage for wh ich the c a r r y i n g capacity of the assoc ia ted environment i s s m a l l , r e la t ive to the lake and oceanic life h i s to ry stages. T h i s i s , to some degree, erroneous and it would be su rp r i s i ng indeed if r ec ru i tment was found to be a constant p ropor t ion of the number of f ry produced. However , for some situations (e.g., Skeena R ive r ) i t serves as a reasonable approximat ion . E v e n i f i t were shown that l i m i t a t i o n was a proper ty of the lake and/or ocean environments , the above re la t ionsh ip would r e m a i n as an important management tool since fry product ion must s t i l l be de termined so as to opt imize the number of ind iv idua ls 32 entering the l i m i t i n g l i fe h i s t o r y stage. Spec i f i ca l l y , then, the purpose of this paper i s : (1) to descr ibe some of the behav io ra l mechan isms operating during spawning; (2) to develop the concept of p r e f e r r ed and m a r g i n a l habitats for spawning f ish; and (3) to con-s ider how this m e c h a n i s m would influence the exis t ing s t o c k - r e c r u i t model . Site Se lec t ion and Ext rapensa to ry M o r t a l i t y D u r i n g spawning aggress ive behavior i s m a x i m a l , there is obvious c o m -pet i t ion for space, and the eggs, when deposited i n the g rave l , are sensi t ive to environmenta l change. F lood ing , e ros ion , and dry ing up of ce r ta in areas often resul t i n severe egg mor ta l i ty ( Neave, 1953 ) and, consequently, the mechan i sms responsib le for the pattern of nest locat ion are of considerable in teres t . It i s evident that wi th respect to a given source of mor ta l i ty , ce r ta in a reas of the s t r e a m constitute m a r g i n a l habitates; e.g., shal lower areas are m o r e susceptible to dry ing up than deeper ones. It is a lso poss ib le that under different sets of c i r cums tances shal lower areas may be considered as opt imal habitats and deeper areas m a r g i n a l . Thus, over a la rge number of generations, the p robab i l i t i e s of s u r v i v a l assoc ia ted wi th phys ica l ly different areas of the s t r e a m may be s i m i l a r to one another, and therefore the mor ta l i ty rate assoc ia ted with var ious environmenta l changes may be density independent in the manner desc r ibed by R i c k e r (1958). T h i s i s not the only way that the con-di t ions of the R i c k e r formula t ion are fu l f i l led , however, since i t i s poss ible 33 that ce r ta in areas of the s t r eam are consis tent ly better than others, yet the adult spawners may not have the capacity to differentiate between these a reas . T h i s , too, would resul t i n a si tuation where mor ta l i ty rate was, on the average, independent of the density of the stock. Therefore , given either of these two situations, one might anticipate that the d i s t r ibu t ion of eggs would be random wi th respect to any measurable phys i ca l var iab le , since there would be no select ive p r e s su re which would influence the choice of a s i te . A n al ternat ive hypothesis would be one which would predic t that the \" o p t i m a l \" a reas of a s t r e a m would be colonized i n i t i a l l y and marg ina l a reas would only be used in the event of h igh stock dens i t ies . Th i s would suggest that the order of c o l o n i -zat ion would cor respond to some measurable phys ica l va r i ab l e . Therefore , f ie ld studies were conducted in an attempt to determine which patterns cha rac te r i zed the behavior of na tura l populations. The Study A r e a s I Fou r M i l e Creek The f i r s t study was conducted at F o u r - M i l e Creek, an inlet s t r eam of the Babine Lake system, which has been desc r ibed in deta i l by Hanson (1964). A se r i e s of pools along the length of the creek (depths of up to 1.5 metres) serve as res t ing areas for the f i sh during thei r mig ra t ion ups t ream. These a re i n t e r spe r sed wi th shal lower areas suitable for spawning. A wate r fa l l 1.8km ups t ream f r o m the lake confines the run to the lower area of the s t r eam and, under conditions of low discharge, mig ra t ion is further r e s t r i c t e d at 550in ups t r eam f r o m the lake due to a t r i fu rca t ion in the creek and resu l t ing shallowness 34 of the f low. The creek is heav i ly shaded throughout i ts length and contains a good representa t ion of the range of conditions i n 'wh ich sockeye are l i k e l y to spawn. The run in F o u r - M i l e Creek appears to be a d is t inc t stock in the sense that i t i s c l e a r l y separated in both space and t ime f r o m other segments of the Babine run. It i s one of the ea r l i e s t runs to a r r i v e and averages 2300 i n d i v i -duals per year (Hanson, 1964). Methods The 550m section of the creek below the t r i fu rca t ion was enclosed using two b r o o m st ick fences, the lower fence being equipped wi th a V t rap and a holding f ac i l i t y to aid i n counting, measur ing and tagging the sa lmon. Th i s pa r t i cu l a r a rea was chosen because most of the good spawning grounds are found below the t r i fu rca t ion and, i f the run were sma l l , i t could eas i ly be observed . It was also des i rab le because a natura l b a r r i e r to mig ra t ion per iod i c a l l y occurs at the t r i fu rca t ion . The conditions, however, were not idea l s ince i t was necessa ry to have enough ind iv idua l s in the study a rea to ensure co loniza t ion of the m a r g i n a l areas , yet not severe ly damage product ion by overc rowding the spawners . Th i s proved to be a dif f icul t s i tuation since neither the total s ize of the run, nor the t empora l d i s t r ibu t ion , could be e s t i -mated in advance. The run was l a rge r than ant icipated and, consequently, the upper fence had to be removed p e r i o d i c a l l y when la rge numbers of spawners accumulated at this loca t ion . With in the lower section ten f a i r l y un i fo rm areas, which differed f r o m one another, were selected for intensive observat ion ( F i g . 8). E a c h a rea was approx imate ly 7 m in length and was divided into l m s t r ips ac ross the width of the s t ream; e.g., i f the s t r eam were 5m wide, five l x 7 m g r i d s would be fo rmed . The contours, depths and gradients were determined using o r d i -na ry surveying techniques and ve loc i t i e s were taken using a Gur l ey flow mete r . The ve loc i t i e s were measured a standard distance f r o m the bot tom (10cm) in order to determine the range of ve loc i t i es a spawner would be sub-jected to, rather than de termining the average ve loc i ty of the s t r eam sect ion. F o r each of the 1x7m sections, nine measurements of depth and ve loc i ty were made, ' three measurements ac ros s the top of the section, three ac ross the middle , and three ac ros s the bot tom. G r a v e l samples in each of the sections were a lso taken using a core sampler and analyzed using the v o l u m e t r i c technique desc r ibed by M c N e i l (1964). Samples could not be obtained in a l l a reas since the grade was too coarse , but photographs of a l l g r id s were taken wi th the a id of a p lex ig lass -bo t tomed box and a wide angle lens . Staff gauges were ins ta l l ed i n each of the ten sections and an addi t ional staff gauge was set up as indicated i n F i g u r e 8, which served as a standard meter ing si te. These measurements were taken in the three-week per iod p r i o r to the onset of the run, the ve loc i t i e s being taken las t (July 22-23). It i s therefore neces sa ry to assume that the re la t ive differences in depth and ve loc i ty r emained constant during the spawning per iod, which is probably not quite true for a l l of the cases cons idered . However , this method was more des i rab le than the a l ternat ive of making da i ly measurements during the spawning pe r iod 36 F i g u r e 8 . F o u r M i l e C r e e k s h o w i n g l o c a t i o n of g r i d s A - J a n d the m e t e r i n g s i t e . (*)\u00E2\u0080\u00A2 as d a i l y d i s t u r b a n c e s w o u l d p r o b a b l y i n f l u e n c e t h e n o r m a l p a t t e r n o f c o l o n i z a -t i o n a n d e g g s u r v i v a l . E a c h d a y d u r i n g t h e s p a w n i n g r u n a l l o f t h e f i s h t r a p p e d d u r i n g t h e p r e v i o u s 2 4 - h o u r p e r i o d w e r e c o u n t e d a n d a r e p r e s e n t a t i v e s a m p l e o f t h e f e m a l e s p a w n e r s w a s t a g g e d , m e a s u r e d a n d c h e c k e d f o r s t a t e o f m a t u r i t y . T h e l a t t e r p r o c e d u r e i n v o l v e d g e n t l y s q u e e z i n g t h e b e l l y o f t h e f e m a l e s a n d , i f e g g s w e r e e x p e l l e d , t h e f i s h e s w e r e c o n s i d e r e d t o b e m a t u r e . P r i o r t o t h i s , e a c h d a y , t h e s p a w n e r s i n e a c h o f t h e g r i d s w e r e c o u n t e d a n d t h e i r p o s i t i o n r e c o r d e d o n m a p s o f t h e a r e a s . T h u s , e a c h d a y ' s e s c a p e m e n t w a s g i v e n a 1 5 - 2 0 h o u r p e r i o d t o d i s t r i b u t e i n t h e s t r e a m w i t h o u t b e i n g d i s t u r b e d b y o b s e r v a t i o n s o r b y n e w f i s h e n t e r i n g t h e s t r e a m . R e s u l t s P h y s i c a l c h a r a c t e r i s t i c s o f t h e s e c t i o n s . T h e d e p t h s , v e l o c i t i e s , a n d a n i n d e x o f s u b s t r a t e p e r m e a b i l i t y f o r e a c h o f t h e t e n s e c t i o n s d e s c r i b e d p r e v i o u s l y , a r e p r e s e n t e d i n T a b l e I Y \u00E2\u0080\u00A2 T h e p e r -m e a b i l i t y i n d e x i s e x p r e s s s e d a s a p e r c e n t a g e o f t h e c o r e s a m p l e p a s s i n g t h r o u g h a 1 . 1 9 m m s e i v e . T h i s w a s s l i g h t l y d i f f e r e n t f r o m t h e t e c h n i q u e d e s c r i b e d b y M c N e i l ( 1 9 6 4 ) i n t h a t h i s c a l c u l a t i o n s a r e e x p r e s s e d a s a p e r -c e n t a g e p a s s i n g t h r o u g h a 0 . 8 8 3 m m s e i v e . T h u s , t h e s e c a l c u l a t i o n s p r o b a b l y u n d e r e s t i m a t e a c t u a l p e r m e a b i l i t y , b u t e v e n i g n o r i n g t h i s d i s c r e p a n c y , a l m o s t all o f t h e a r e a s w o u l d b e c l a s s i f i e d a s m e d i u m t o h i g h i n p e r m e a b i l i t y ( c o e f f i c i e n t o f p e r m e a b i l i t y a s s o c i a t e d w i t h 10 p e r c e n t o f f i n e m a t e r i a l i s 38 "Thesis/Dissertation"@en . "10.14288/1.0102299"@en . "eng"@en . "Zoology"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "Some aspects of environmental variability in relation to stock recruitment systems"@en . "Text"@en . "http://hdl.handle.net/2429/35271"@en .