SOME ASPECTS OF GROWTH IN THE FAMILY SALMONIDAE by ROBERT RAY PARKER B.S. i n Zoology, U n i v e r s i t y of Washington, 1°A6 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of ZOOLOGY We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1957 i . ABSTRACT Mathematical descriptions, of the growth of animals are reviewed i n the l i g h t of a p p l i c a b i l i t y to two species of the Family Salmonidae. No generalized growth equation i s found to accurately depict growth f o r the material discussed. Theoretical and p r a c t i c a l l i m i t a t i o n s of the use of age as a c l a s s i f i c a t i o n f o r r e l a t i n g growth rates are given. An hy-pothesis that r e l a t i v e growth rate declines with increase i n size but i s independent of age i s offered and explored. Data on steelhead from C h i l l i w a c k River, H i r i t i s h Columbia, are analysed with the use of s i z e - s p e c i f i c instantaneous growth rate regressions. Factors leading to observed v a r i -a t i o n and l i f e h i s t o r y events are discussed and the l i t e r a -ture reviewed. In a l l cases, s i z e i s determined to be a more r e l i a b l e c r i t e r i o n of p h y s i o l o g i c a l development than age. I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t 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 , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e . f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may b e g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e . I t i s u n d e r -s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . R o b e r t R . P a r k e r D e p a r t m e n t o f 7.r.oi ngy The 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 , V a n c o u v e r C a n a d a . Date A p r i l 16. 1957 ACKNOWLEDGEMENTS The author takes sincere pleasure i n acknowledg-ing the guidance of Dr. P.A. L a r k i n on the i n v e s t i g a t i o n of growth and development of the hypothesis of size-spec-i f i c instantaneous growth r a t e s . Dr. C.C. Lindsey c r i t i -c a l l y reviewed the manuscript and contributed m a t e r i a l l y to the query. V i r g i n i a E. Parker, wife of the author, c a r r i e d out typing of the manuscript i n i t s many dra f t s as w e l l as a s s i s t i n g i n processing the raw data. The B r i t i s h Columbia Game Commission, f o r use of steelhead and rainbow trout data, and the Alaska Department of F i s h -e r i e s f o r providing data on Chinook salmon as w e l l as r e -search funds, are g r a t e f u l l y acknowledged. i i • TABLE OF CONTENTS Page ABSTRACT i . LIST OF TABLES i v . LIST OF FIGURES v i . ACKNOWLEDGEMENTS v i i . INTRODUCTION 1. THE PHENOMENON OF GROWTH 2. De f i n i t i o n s 2. Mathematical Attempts f o r Growth Formulae . . . 3. Ultimate Size of F i s h 8. The V a l i d i t y of a General Growth Curve . . . . 11. P r a c t i c a l D i f f i c u l t i e s Encountered with F i s h . . 13. The Use of Age-specific Rates of Growth . . . . 14. HYPOTHESIS ON GROWTH OF FISH 17. THE TEST OF THE HYPOTHESIS . 18. Methods and Materials 18. Fresh Water Environment 25. Sex Differences 26. Differences Between Growth Years 26. L i f e H istory Groups 26. Discussion of Causative Factors . 31. S a l t Water Environment 35. Sex Differences 35. Differences Between Growth Years 36. Differences Between L i f e History Groups . . . . 36. SUMMARY REFERENCES i v . LIST OF TABLES Table Page I . L i f e h i s t o r y composition of samples of Chi l l i w a c k River steelhead used f o r growth analysis. 22. I I . Tests of s i g n i f i c a n c e of differences i n growth rate between sexes. C h i l l i w a c k River steelhead, f r e s h water 27. I I I . Tests of s i g n i f i c a n c e of differences i n growth rate between growth years. C h i l l i w a c k River steelhead, f r e s h water. . . . 28. IV. Regression equations f o r l i f e h i s t o r y groups. Chil l i w a c k River steelhead, f r e s h water 30. V. Mean ;size and standard deviation of l i f e h i s t o r y groups at completion of fre s h water annuli 32. VI. Tests of s i g n i f i c a n c e of differences i n growth rate between sexes. C h i l l i w a c k River steelhead, s a l t water 37. V I I . Tests of s i g n i f i c a n c e of differences i n growth rate between growth years. C h i l l i w a c k River Steelhead, s a l t water. . . 38. V I I I . Tests of s i g n i f i c a n c e of differences between l i f e h i s t o r y groups of the same marine h i s t o r y . C h i l l i w a c k River V . steelhead 40. IX. Regression equations f o r l i f e h i s t o r y groups. C h i l l i w a c k River steelhead, s a l t water. 41. X. Mean s i z e and standard deviation of l i f e h i s t o r y groups at the completion of s a l t water annuli 4 3 . v i , LIST OF FIGURES Figures Page 1. Walford transformation f o r Kamloops trout and Chinook salmon. 9. 2. A "Brody graphic s o l u t i o n of ultimate size, Chinook salmon. 10. 3. Scatter diagram of k on length, C h i l l i w a c k River steelhead. 24. 4. Regression l i n e s of k on length f o r each l i f e h i s t o r y group. 24. SOME ASPECTS OF GROWTH IN THE FAMILY SALMONIDAE INTRODUCTION Growth, of f i s h e s i s an important v i t a l s t a t i s t i c , yet i n w i l d populations the opportunity to d i r e c t l y measure growth of an i n d i v i d u a l i s seldom obtained. I t thus becomes necessary both to measure and to predict growth by s t a t i s t i -c a l inference. The problem has been approached both theo-r e t i c a l l y and e m p i r i c a l l y . Theorists have attempted gener-a l growth formulae that, given a series of observations at some stag© of l i f e , w i l l accurately extrapolate the series to predict growth at some future time. Other s c i e n t i s t s , working with empirical observations, have transformed the data by various methods to allow s t a t i s t i c a l a n a l y s i s . Pre-d i c t i o n s of si z e have been made on the basis of consistancy of past observations. Both approaches are e s s e n t i a l to understanding growth. Where growth i s measured, e i t h e r d i r e c t l y or i n d i -r e c t l y , a problem arises when a comparison i s made between i n d i v i d u a l s or groups or a p r e d i c t i o n of growth i s the ob-j e c t i v e . Most commonly, growth i s compared between groups of the same age, which implies that age i s considered to be a s i g n i f i c a n t determinant of growth. S i m i l a r l y , estimates 1. of future s i z e are based on growth with age. This t h e s i s i s concerned with reviewing the im-portant concepts of growth and discussing t h e i r a p p l i c a t i o n to representative species of Salmonidae. The concept of age as a determinant of growth i s examined and the use of size as an alternate explored. THE PHENOMENON OF GROWTH De f i n i t i o n s The term growth may have a broad connotation to many workers, i . e . i t may include d i f f e r e n t i a t i o n as w e l l as size increment (Hammett, 194-3). For the purposes of t h i s discussion growth i s r e s t r i c t e d by d e f i n i t i o n to mean increase i n s i z e . While growth of a f i s h i s i n three d i -mensions, and r e l a t i v e growth of parts may not be isometric, these a t t r i b u t e s may a l l be computed from length by appropri ate empirical formulae (Huxley, 1932; Martin, 194-9). Incre-ment of fork length, then, i s representative of growth of the whole animal and i s used throughout t h i s t h e s i s . Huxley (1932) l i s t s three e s s e n t i a l a t t r i b u t e s of growth: (a) i t i s a process of s e l f m u l t i p l i c a t i o n , (b) the r e l a t i v e rate i s retarded with increase i n size or age, and (c) growth rate i s affected by external environment. Fry (194-7) considers growth as one of the many " a c t i v i t i e s " of an animal and therefore dependent upon energies a v a i l a b l e i n excess of that required f o r sustenance. The sustenance requirement f o r any p a r t i c u l a r s i z e i s modified by p h y s i c a l , chemical, and b i o l o g i c a l factors of the environment. Thus, growth i s a r e s u l t of many complex, i n t e r a c t i n g f a c t o r s , few of which may be predictable or forecast except under laboratory conditions. Mathematical Attempts at Growth Formulae Many workers have attempted to describe growth mathematically, i . e . to formulate an equation that describes the course of growth throughout l i f e . Minot (1891), work-ing on the guinea p i g (Cavia cobaya), observed that abso-l u t e increment ( t o t a l increase i n weight per u n i t time) was r e l a t e d to the size of the animal. Relative increment, ex-pressed as a percentage of i n i t i a l s i z e f o r any short period of time, decreased with increase i n s i z e . He interpreted t h i s observation as implying a progressive loss of power of growth, beginning close to b i r t h . Growth during a f i n i t e , period of time was described by a percentage growth r a t e , W~ - W, K = 100 — . . . (1) W l where W-^ denotes weight at time 1, ^2 denotes weight at time 2, and K i s the percentage growth r a t e . Minot also suggested that average size during the time period should replace i n the denominator, i . e . assuming l i n e a r growth, W~ - W, K = 100 — ± . . . (2) (Wx + W2) / 2 This modification, while suggested, was not used as i t made l i t t l e improvement to the d e s c r i p t i o n . Robertson (1908) considered the course of growth throughout the l i f e of an animal to be l i k e a monomolecular, au t o c a t a l y t i c r e action i n which instantaneous v e l o c i t y of growth i s proportional not only to size attained, but also to s i z e yet to be attained. His formula, i n d i f f e r e n t i a l form, i s H - k W ( A - f ) . . . (3) where W denotes size at any i n s t a n t , A denotes adult or f i n a l s i z e , and k i s a v e l o c i t y constant. This equation, while intended to provide a t h e o r e c t i c a l de-s c r i p t i o n of the whole course of growth, has been c r i t i c i z e d by Brody (1945), Crozier (1926), and other workers as having l i t t l e s i m i l a r i t y to e m p i r i c a l l y derived growth curves. Robertson's equation describes a sigmoid curve with the point of i n f l e c t i o n occurring at the center, i . e . the curve i s , by d e f i n i t i o n , symmetrical. Observations, p r i n c i p a l l y on homoiotherms, have not shown such symmetry to be usual. Robertson's equation does e s t a b l i s h a fundamental aspect of growth i n that i t i d e n t i f i e s two simultaneously a c t i n g , opposing forces: (a) the capacity f o r growth as a finaction of s i z e , i . e . instantaneous "compound i n t e r e s t " at a constant r a t e , and (b) a decrease i n growth rate pro-p o r t i o n a l to increase i n s i z e , r e f l e c t i n g a progressive decrease i n metabolic e f f i c i e n c y . Attempts to modify Robertson's equation (3) (see Brody, 194-5) have l e d to p r a c t i c a l d i f f i c u l t i e s . To make a curve d e s c r i p t i v e of a process dependent upon many variables necessitates the use of several constants. The r e s u l t a n t curve thus becomes a m u l t i - i n f l e c t e d l i n e , f i t t e d to p a r t i c u -l a r empirical data. Such a formula has l i t t l e t h e o r e t i c a l s i g n i f i c a n c e unless the constants are meaningful and i d e n t i -f i a b l e w ith b i o l o g i c a l processes. Brody (1927a,b) was able to describe the course of growth f o r homoiotherms by considering Robertson's growth curve as encompassing two phases of growth. Accepting the hypothesis that the general growth curve i s sigmoid, Brody pointed to the d i f f i c u l t y i n p l a c i n g the point of i n f l e c t i o n . His s o l u t i o n was to write two equations, one f o r the " s e l f -a c celerating" phase where growth rate i s proportional to s i z e attained and the other for the " s e l f - i n h i b i t i n g " phase where growth rate i s proportional to the growth yet to be made. These formulae are: f o r the s e l f - a c c e l e r a t i n g phase i n d i f f e r e n t i a l form, and f o r the s e l f - i n h i b i t i n g phase, i n d i f f e r e n t i a l form, § - | - k 2 (A - W) . . . (5) The separation of the growth curve i n t o two component parts would seem to imply that during the s e l f - a c c e l e r a t i n g phase growth i s u n r e s t r i c t e d except by si z e ; at the point of i n -f l e c t i o n a second force (or sum of forces) begins to apply. Since i n f i s h i t i s generally conceded that the point of i n f l e c t i o n occurs close t o or wi t h i n the embryonic stage, the s e l f - a c c e l e r a t i n g phase may not be observable under f i e l d conditions. Ford ( 1 9 3 3 ) observed that i n herring (Clupea harengus) increment i n length measured between succeeding scale annuli, i . e . L^.^ - L^, was i n v e r s e l y correlated with L^. He determined a regression equation of the type = a + KL^ . . . ( 6 ) I t can be shown that a series of lengths calculated by equation ( 6 ) form a geometric progression when K i s greater or l e s s than u n i t y , and form an arithmetic progression when K equals u n i t y . As noted above, the usual case observed i s K < 1 , i . e . the s e l f - i n h i b i t i n g phase of Brody (equation 5 ) . Von Bertalanffy ( 1 9 3 8 ) approached the problem * Although empirical data may be observed to comply with a growth form dW/dt = K,W, t h i s cannot be distinguished from a growth form described by dW/dt = (k-, - ko )W , where k p i s negative and less than k-,. Hence, growth retarding process-es may act during the s e l f - a c c e l e r a t i n g phase and not be detected (see Gray, 1 9 2 9 ) . of growth from a p h y s i o l o g i c a l point of view, s t a t i n g that r e l a t i v e energy available f o r growth could be c a l c u l a t e d from the r e l a t i o n s h i p between surface and volume of a growing sphere. Since maintenance requirement i s r e l a t e d to mass, and the a b i l i t y to exceed t h i s requirement i s r e -l a t e d to absorptive area, growth rate of an organism ( i n three dimensions) w i l l n e c e s s a r i l y decline with increase i n s i z e . His formula f o r the growth curve i s equivalent to Brody's equation f o r the s e l f - i n h i b i t i n g phase and needs no further consideration here. His formula was shown to accurately describe the growth of the guppy (Lebistes r e -t i c u l a t u s (Peters)) under laboratory conditions. Walford (1946) has provided a graphic s o l u t i o n of a geometric progression where K < 1 by p l o t t i n g L^.+^ against L^ . and has pointed out that the r e s u l t i n g s t r a i g h t l i n e i n t e r s e c t s a 45° diagonal passing through the o r i g i n . The i n t e r s e c t i o n represents a s t a t i s t i c a l adult size of the a n i -mal, i . e . the average s i z e where .growth ceases (see Figure 1.). Walford*s growth transformation, Ford's regression (6), von Bertalanffy's equation, and Brody 1s equation ( 5 ) f o r the s e l f - i n h i b i t i n g phase are i n r e a l i t y equivalent solutions of a general growth curve where deceleration of r e l a t i v e growth rate i s constant and terminates at zero. Walford's graphic s o l u t i o n has the advantage of being much easier to use, but has a disadvantage of y i e l d i n g n - 1 8. points on the p l o t where n denotes age i n whole years. Im-p l i c i t i n a l l of these growth formulae i s the concept that the animal grows to a g e n e t i c a l l y predetermined ultimate s i z e . Ultimate Size of F i s h Ultimate s i z e , i n the case of the higher verte-brates, may he reached at maturity, past which point the animal may l i v e f o r several years (Brody, 194-5 ) . F i s h , how^ ever, u s u a l l y grow throughout l i f e (Jordan, 1 9 0 5 ) . Thus, i n f i s h e s , a progression of lengths can hardly he extrapolated to the point where growth ceases and r e t a i n any r e a l mean-ing . This c r i t i c i s m i s i l l u s t r a t e d as fo l l o w s . I f s i z e increment i n unit time i s a constant pro-po r t i o n of growth yet to he made, a series of lengths w i l l form a geometric progression having a common r a t i o of less than u n i t y . Ultimate size may be solved g r a p h i c a l l y by eithe r a Walford (194-6) graph or a Brody ( 1 9 2 7 a , 194-5) graph. Examples of these are provided i n Figures 1 and 2 . Data for Chinook salmon (One orhync hus tshawytscha) are taken from Parker and Kirkness ( 1 9 5 6 ) ; for rainbow trout (Salmo gaird-n e r i ) from L a r k i n , e t . a l . ( 1 9 5 7 ) . I t i s immediately apparent from the Walford growth transformation (Figure 1 ) that the c o e f f i c i e n t of regression i s close to unity. This means that an extrapolation of the o transformation l i n e e i t h e r w i l l not i n t e r s e c t the 4-5 d i -9 40 30 10 0^ ( 'A " V / d 0 10 20 30 40 Length at t n Figure I. Walford transformation for Kamloops trout and Chinook salmon. (I) Kamloops Lake, (2) Paul Lake, British Columbia. (Larkin, et. al in press.) Chinook salmon from Parker and Kirkness, (1956) . 10 2 Age Figure 2. A Brody graphic solution of ultimate s ize, Chinook salmon. 11. diagonal or w i l l do so only at some completely u n r e a l i s t i c "ultimate" s i z e . Figure 2 again i l l u s t r a t e s t h i s point. A series of t r i a l ultimate sizes are used to achieve a strai g h t l i n e i n a semi-logarithmic p l o t of A - L (f o r complete d i s -cussion, see Brody, 194-5 ) . I t i s seen that the higher the value of A chosen, the s t r a i g h t e r the series of points becomes and the more h o r i z o n t a l the slope, i n d i c a t i n g a .very large ultimate s i z e . I t must be concluded that f o r f i s h of these species and perhaps many others the concept of u l t i -mate s i z e has no r e a l meaning. The V a l i d i t y of a General Growth Curve Gray ( 1 9 2 9 ) proposed that growth rate of an embryo ( f i s h ) i s proportional to weight of the embryo (x) and concentration or amount of growth promoting substance ( y ) ; thus, f-f - k 0 0 y . . . ( 7 ) Gray states (p. 2 7 0 ) : " I f y decreases from a f i n i t e value to zero, i t follows that the integrated growth curve w i l l be sigmoidal quite independent of the manner i n which the decrease i n y occurs." Equation ( 7 ) becomes Robertson's basic formula under con-d i t i o n s where growth i s constantly proportional to s i z e , but modified by a constant decrease i n "growth promoting" substance. However, as Gray pointed out, there i s no a p r i o r i basis nor experimental evidence f or the precise manner i n which growth i s l i m i t e d ; thus, there i s no j u s t i -1 2 . f i c a t i o n f o r Robertson's d e r i v a t i o n . Gray's summation of t h i s argument i s worthy of quotation (p. 2 7 1 ) : "The known f a c t s of growth i n vivo and i n v i t r o seem to i n d i c a t e quite c l e a r l y that as an organism increases i n s i z e or age, the environment for growth becomes less favourable f o r those tissues s t i l l capable of growth. U n t i l the cause of t h i s phenomenon has been subjected to d i r e c t quantatative study, i t i s u n l i k e l y that we s h a l l f i n d an equation f o r any p a r t i c u l a r growth curve which i s more than an empirical representation of ob-served data." Other discussions on t h i s theme include that of Wilson ( 1934- ) , Bernstein ( 1934- ) , and Davenport ( 1 9 3 4 ) . The general shape of an absolute growth curve f o r f i s h need not necessarily be sigmoid, although t h i s i s a generally accepted r u l e . From the data already presented g r a p h i c a l l y (Figure 1 ) absolute annual increment might be described as a constant, i n which case the series i s a-r i t h m e t i c and a series of r e l a t i v e growth rates becomes a harmonic progression without l i m i t . Ricker (personal com-munication) has observed that f o r several l o n g - l i v e d northern f i s h e s a Walford l i n e tends to p a r a l l e l the diago-n a l , and suggests that while the general growth curve may be sigmoidal, the "point" of i n f l e c t i o n i s greatly pro-t r a c t e d , accupying the greater p o r t i o n of the l i f e span. In the l i g h t of von Bertalanffy's ( 1 9 3 8 , 194-9) and Robert-son's ( 1 9 2 3 ) arguments, t h i s would necessitate an increase i n metabolic e f f i c i e n c y w i t h increase i n mass. This has been experimentally shown to occur by Brown (194-6b), who noted that maintenance requirement of food per unit weight 13. of f i s h (Salmo t r u t t a ) decreased with increase i n weight. I t appears that a general mathematical equation has not been conceived that, through i t s constants, depicts the i n t e r a c t i o n of the many fac t o r s a f f e c t i n g rate of growth. Attempts, such as Robertson's, while valuable f o r t h e o r e t i -c a l comprehension, imply a single governing rea c t i o n , i . e . r Liebig's Law of the Minimum (Odum, 1953). That a l i m i t i n g r e a c t i o n governs the rate of growth i s not contested, but that a p a r t i c u l a r r e a c t i o n i s at a l l times throughout l i f e the l i m i t i n g f a c t o r has not been demonstrated. A mathemati-c a l equation, used to express growth r a t e , must be con-sidered as an empirical device, without general t h e o r e t i -c a l v a l i d i t y at the present l e v e l of knowledge. That rate of growth i s resultant from the i n t e r a c t i o n of two opposing forc e s , (a) the s i z e - s p e c i f i c capacity f o r growth, which i s progressively suppressed by (b) the e f f e c t s of growth, appears to be the only c l e a r l y established, general concept at t h i s time. P r a c t i c a l D i f f i c u l t i e s Encountered with F i s h The opportunity to d i r e c t l y measure growth of fi s h e s i s seldom obtained. This i s e s p e c i a l l y true where data on growth i n a natur a l environment are desired as op-posed to growth data obtained under laboratory conditions. As a r e s u l t of t h i s d i f f i c u l t y , growth studies are often based on the method of back-calculating the size of a f i s h 1 4 . at some previous stage of l i f e h i s t o r y as indicat e d hy mark-ings on scales or other bony pa r t s . Usually the end of the winter annulus or check i s taken as a reference point. This method precludes information on growth rate during the very ear l y ( f i r s t year) and sometimes very l a t e (ultimate) years of l i f e . The actual course of a growth curve obtained with-i n any one year would r e f l e c t the annual c y c l i c v a r i a t i o n of seasonal changes i n the surrounding environment. A growth curve r e l a t e d to some recurring event, i . e . the f o r -mation of the annulus, uses the sum of seasonal increment and the unit of time i n a l l cases i s taken as one year. P r i o r to and a f t e r the formation of the f i r s t and l a s t annu-l i , r e s p e c t i v e l y , absolute time cannot usually be computed. Thus, comparative growth rates f o r these periods are not obtainable. The Use of Age-specific Rates of Growth Age, as measured by solar time, i s not necessarily a causative f a c t o r of decrease i n growth rate. Brody (194-5) considered time only as a reference point and c r i t i c i z e d growth equations of Glaser (1938) and other workers as being functions of time and, therefore, u n r e a l i s t i c . Brown (1946a), on the other hand, e x p l i c i t l y states that f o r brown trout (Salmo t r u t t a ) f r y , age i s a s i g n i f i c a n t f a c t o r determining the deceleration of s p e c i f i c growth r a t e . She found no c o r r e l a t i o n between body weight and s p e c i f i c growth ra t e . Her conclusions were derived 1 5 . from c o n t r o l l e d laboratory experiments i n which ph y s i c a l and chemical environmental f l u c t u a t i o n s were held to a minimum. Under these conditions the inherent p h y s i o l o g i c a l e f f i c i e n c y of i n d i v i d u a l s would be p r i m a r i l y affected only by b i o l o g i c a l stresses such as a s o c i a l heirarchy i n t e r a c t i n g with a l i m i t -ed food supply. The f a c t that f i s h of the same absolute age but of d i f f e r e n t sizes grew at approximately the same r a t e s , v i f they occupied the same r e l a t i v e p o s i t i o n s i n d i f f e r e n t peck orders, does not necessarily preclude a s i z e - s p e c i f i c growth r a t e . Hiss Brown's f i s h were fed but once a day, a prac t i c e that would tend to favour growth i n larger i n d i -v i d u a l s . F i s h of d i f f e r e n t absolute ages were not compared. The experiment d i d , however, i s o l a t e some of the factors which cause the wide v a r i a t i o n observed between growth rates of i n d i v i d u a l s . For f i e l d data, the c l a s s i f i c a t i o n of f i s h accord-ing to age groups involves three averages. (1) Since f i s h do not a l l hatch out at the same time, absolute age at com-p l e t i o n of the f i r s t annulus i s v a r i a b l e . (2) The com-p l e t i o n of the annulus and commencement of spring growth does not take place at p r e c i s e l y the same time f o r a l l i n d i -v i d u a l s ; thus, another averaging procedure i s involved. (3) The capacity to grow i s quite v a r i a b l e between i n d i -v i d u a l s , even between progeny of the same parents (Brown, l°A6a,b) and a t h i r d averaging procedure i s involved i n age-specific growth rates of f i s h derived i n t h i s manner. 16. For f i s h e s with a long l i f e span, l i v i n g i n a f a i r l y constant environment, age-specific growth rates may y i e l d f a i r l y r e -l i a b l e growth curves with s u f f i c i e n t points to i n d i c a t e an average r e l a t i o n s h i p and trend. With f i s h e s such as the salmon (One orhynchus) and trout (Salmo) of the P a c i f i c Coast, the l i f e span i s r e l a t i v e l y short and environmental changes may occur eit h e r i n f r e s h water or as a consequence of anadromous habit s . The chinook salmon provide an example t y p i c a l of t h i s s i t u a t i o n . Individuals of t h i s species may spend from a few months to two years i n f r e s h water residence and then migrate to /s-ea. A f t e r a period from a few months to s i x years i n the ocean, they return to spawn and d i e . Depending upon the ultimate l i f e h i s t o r y , d i f f e r e n t average sizes may be c a l c u l a t e d f o r the end of each growth year. S t a r t i n g w ith data c o l l e c t e d from a spawning run and l a c k i n g knowledge of m o r t a l i t y r a t e s , i t i s quite impossible to c o r r e c t l y weight the obtained samples i n t o an average age-specific growth curve that i s representative of the population at any one time, or over any span of years (Parker and Kirkness, 1956). This lack of age-size r e l a t i o n s h i p i s borne out by the i n a b i l i t y to determine accurately year classes from a length frequency d i s t r i b u t i o n . This problem has been encountered by several workers. L a r k i n , e t . a l . (1957), suggested that an erroneous i n t e r p r e t a t i o n was made of the ef f e c t s of a known environ-17. mental change on the growth rate.of Kamloops trout (S. gaird-n e r i ) i n using age-specific growth r a t e s . They suggested that s i z e - s p e c i f i c , rather than age-specific, growth rates he used. In t h i s case a change of growth rate was shown to he the ef f e c t of a change i n Bood habits at a c r i t i c a l s i z e . Ford (1933) i n hi s herring studies at Plymouth, noted the large error attached to average lengths at each annulus and also a large v a r i a t i o n of absolute age at such a s p e c i f i c reference point. His procedure was to group the fi s h e s of each age i n t o c e l l s of length at the beginning of each growth year and use t h i s size-within-age-specific reference point f o r p r e d i c t i n g or characte r i z i n g annual increment. Moore (1934-) working on the barnacle, Balanus b a l -anoides, p l o t t e d the average growth rate (average percent increase i n sample population volume per ten days) against s i z e to show the eff e c t s of d i f f e r e n t environments upon the s i z e - s p e c i f i c growth r a t e . MacKay and Weymouth (1935) i n t h e i r studies of the crab, Cancer magister, were forced to r e l a t e growth at ecdysis to size i n describing the rate of growth as they were without any r e l i a b l e method f o r de-termining age. They obtained a size-age r e l a t i o n s h i p inde-pendent of the growth data and synthesized the two sets of data i n t o an average age-specific growth curve. HYPOTHESIS ON GROWTH OF FISH The foregoing discussion leads to the fol l o w i n g 18. hypothesis: In f i s h , r e l a t i v e growth rate declines with i n -crease i n size independent of age. Age i s simply a neces-sary event as growth takes place i n time. Passage of time i n i t s e l f exerts no l i m i t on the rate of growth. Environ-mental or b i o l o g i c a l changes which cause a change i n meta-b o l i c e f f i c i e n c y w i l l be r e f l e c t e d as a point of i n f l e c t i o n i n a growth curve. This concept implies that, f o r the species studied, size i s aomuch more r e l i a b l e i n d i c a t o r of ph y s i o l o g i c a l development than ,age. This hypothesis i s presently l i m i t e d to that period of l i f e susceptible to c a l c u l a t i o n by scale a n a l y s i s . THE TEST OF THE HYPOTHESIS Methods and Materials The hypothesis was tested i n d e t a i l , using a c o l l e c t i o n of data made avai l a b l e by the B r i t i s h Columbia Game Commission. Steelhead trout (S. gairdneri) were chosen as a species f o r study, p r i m a r i l y f o r two reasons. F i r s t , steelhead trout are anadromous and, therefore, a sudden and profound change occurs i n the environment. Second, a f a i r l y large c o l l e c t i o n of data, obtained from angler's catches, were ava i l a b l e that had been analyzed (Maher and L a r k i n , 1955). Dorsal-ventral diameters of annu l i , marked on cards from projected scale images., were made available to the author. For each f i s h considered, the size at the com-19. p l e t i o n of each annulus was estimated by back-calculation, using a d i r e c t proportion r a t i o between size of f i s h and siz e of scale. This method and i t s v a l i d i t y has been d i s -cussed by Smith (1955) f o r rainbow trout and the present study assumes the method has v a l i d i t y f or the same species of anadromous habits. The entire conversion of d o r s a l -v e n t r a l diameters to length, and to log-j^g length, was ob-tained i n one operation on a ten inch a r i t h - l o g s l i d e r u l e , y i e l d i n g three' s i g n i f i c a n t places i n the logarithm of s i z e . A l l t&sts of s t a t i s t i c a l s i g n i f i c a n c e were made by methods given by Snedecor (194-6). A growth year i s defined as the period of l i f e between the completion of an annulus at t = n to the completion of the subsequent annulus at t = n+1. This roughly coincides with the period from A p r i l to A p r i l f o r steelhead i n fresh water. The growth year i s desig-nated by the calendar year during which most of the growth occurs. Thus, growth year 1950 r e f e r s to the period ap-proximately corresponding to A p r i l 1950 to March 1951, i n -c l u s i v e . Prom the material available on Chilliwack River steelhead a sample of 152 i n d i v i d u a l s was drawn which con-formed to the foll o w i n g c r i t e r i a . 1. I n d i v i d u a l s were a l l maturing f o r the f i r s t time. This c r i t e r i o n eliminates any possible changes or d i s -placement of an annulus because of resorption during a previous spawning migration. About f i v e percent of the 20. ava i l a b l e t o t a l were discarded because they were repeat spawners. 2. Scale margins were sharply defined without apparent resorption at the s i t e of measurement. Resorption would cause an apparent greater length at each annulus than had a c t u a l l y been r e a l i z e d . While the extent of error from t h i s source has been minimized, i t has probably not been completely eliminated. 3. Only i n d i v i d u a l s that were e a r l y spring out-migrants were considered, i . e . the entrance i n t o s a l t water was ac-complished during or immediately a f t e r the completion of the winter annulus. Error may be inherent i n the placement of the edge of t h i s annulus, as f i s h that entered s a l t water before normal completion of the winter zone may show an im-mediate increase i n growth rate which would be interpreted as the point of annulus completion. 4-. The material considered was r e s t r i c t e d to those i n d i v i d u a l s that completed the ultimate annulus i n the 194-9 or 1 9 5 0 growth year. This r e s t r i c t i o n was imposed because of the p o s s i b i l i t y that environmental differences might e x i s t between growth years. A s u b s t a n t i a l error might be introduced i n t o the study by including small groups that could not be analyzed separately. With these c r i t e r i a the material cannot be considered as an unbiased sample of the entire population; however, t h i s i s not the objective of the study. Rather, the data were 21. chosen to avoid systematic error a f f e c t i n g the apparent growth r a t e . For the groups that are represented, the data presented are without known b i a s . A l l material used i s presented i n Table I , com-p i l e d by l i f e h i s t o r y and growth year groups. The termi-nology used i s descriptive of l i f e h i s t o r y events; 2/2/50 denoting a group or an i n d i v i d u a l that completed two annuli i n f resh water, two annuli i n s a l t water, and the l a s t annulus was completed at the close of the 1950 growth year. Thus, the animal was a member of the 194-7 year class and returned to f r e s h water to spawn i n 1951. I t was captured i n the C h i l l i w a c k River i n the 1951 growth year. The "50" of the symbol, r e f e r r i n g to the penultimate year of l i f e , i s the l a s t growth year bounded by completed annuli. While the exponential growth curve does not accu-r a t e l y describe the course of growth i n a time period, i t may be used as a convenient standard of comparison. The instantaneous growth rate k i s ca l c u l a t e d as the difference between log-^Q fork length at the beginning and end of the time period. Thus: k . l o s i o - l o s i o L t ... ( 8 ) t In a l l cases t i s un i t y , representing an entire growth year. This instantaneous growth r a t e , k, i s not to be confused with the constant of Brody*s equation (5) f o r the s e l f -Table I . L i f e h i s t o r y composition of samples of Chill i w a c k River steelhead used f o r growth a n a l y s i s , (G) = year of hatching; (FW) = fres h water; (SW) = s a l t water; (Sp) = year of spawning. L i f e h i s t o r y Number oV 9? , 19A6 1947 Growth 1948 year 1949 1950 1951 2/1/50 7 12 C FW SW Sp 2/1/49 13 9 C FW SW Sp 2/2/50 10 22! C FW SW SW Sp 2/2/49 11 9 C FW SW SW Sp 3/1/50 15 15 i C FW FW SW Sp 3/1/49 7 10 C FW FW SW Sp 3/2/50 4 8 C FW FW SW sw Sp 23. i n h i b i t i n g phase, but i s i d e n t i c a l with the constant k of formula (4-) f o r the s e l f - a c c e l e r a t i n g phase where growth i s calc u l a t e d separately f o r each time period. The successive values of k, the instantaneous growth r a t e , are observed to decrease with increase i n both t and L. I n d i v i d u a l k values were p l o t t e d against log-^Q of the length at the beginning of that growth year. These are presented as a scatter diagram i n Figure 3. P a r t i c u l a r notice should be made of the axes. Each c i r c l e represents the instantaneous growth rate observed during an entire growth year f o r a f i s h of a p a r t i c u l a r s i z e at the beginning of that time period. Three relationships.are immediately apparent. 1. The, scatter forms two d i s t i n c t clouds, one f o r growth i n f r e s h water, one f o r growth i n s a l t water. The clouds overlap considerably on the abscissa, i l l u s t r a t i n g the v a r i a t i o n i n size of seaward migrants. 2. Each cloud forms an approximately l i n e a r regression t y p i c a l f o r each environment. Regression l i n e s were f i t t e d to the scatter of points f o r each environment by the method of l e a s t squares. These are g r a p h i c a l l y demonstrated i n Figure 3. Further analysis of growth r a t e i s discussed r e l a t i v e to each environment. 3. There i s a w e l l defined proportional decline i n instantaneous growth rate k as the length increases. I t should be borne.in mind that the data shown i n Figure 3 24-. o o 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 I.I 1.2 1.3 1.4 Logarithm of initial size, L t Figure 3. Scatter diagram of k on length, Chilllwack River steelhead. 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 I.I 1.2 1.3 1.4 Logarithm of Initial size, L t Figure 4. Regression lines of k on length for each life history group. 25. comprise a mixture of f i s h of d i f f e r e n t lengths, l i f e histo-r i e s , sex, and growth years. The con t r i b u t i o n of each of these groups i s discussed below. Fresh Water Environment The regression l i n e f i t t e d to the scat t e r of points f o r a l l f i s h i n the f r e s h water environment i s de-scribed by the formula, Y = 0.4-308 - 0.3637 X, where Y i s the predicted value of k f o r any X, the log^o o £ i n i t i a l s i z e , L^. While the regression i s obviously s i g n i f i c a n t , the standard deviation from regression i s 0.9064-, i n d i -c ating a wide v a r i a t i o n between i n d i v i d u a l s . There i s the p o s s i b i l i t y of measurable differences between several groupings of these data. Groupings that may be tested f o r cont r i b u t i o n to the t o t a l variance are: (1) l i f e h i s t o r y types, (2) ages, (3) sexes, and (4-) growth years. Two or more of these groups may be correlated i n e f f e c t i n g the v a r i a t i o n . For example, i f the 194-8 growth year offered a much better opportunity f o r growth than the 194-9 growth year, and the 194-8 sample contained l a r g e l y males, a single t e s t by covariance would show a s i g n i f i c a n t difference be-tween the sexes i n respect to growth r a t e . Accordingly, the s i g n i f i c a n c e of differences between sexes should be determined w i t h i n each group. The plan followed i n the present analysis has been to proceed from the simple to the complex. 26. S e x D i f f e r e n c e s U s i n g c o v a r i a n c e , e a c h l i f e h i s t o r y g r o u p i n e a c h g r o w t h y e a r w a s t e s t e d f o r s t a t i s t i c a l d i f f e r e n c e s i n g r o w t h b e t w e e n t h e s e x e s . " F " r a t i o s w e r e a l l l e s s t h a n s i g n i f i c a n t a t t h e 0 . 0 5 p r o b a b i l i t y l e v e l ( T a b l e I I . ) . T h e c o n c l u s i o n i s , t h a t t h e s e x e s a r e n o t d i f f e r e n t i a l l y c o n t r i b u t i n g t o t h e v a r i a t i o n o f t h e t o t a l s a m p l e a n d n e e d n o t b e c o n s i d e r e d s e p a r a t e l y . D i f f e r e n c e s B e t w e e n G r o w t h Y e a r s T h e r e i s n o r e a s o n t o a s s u m e t h a t , e v e r y g r o w t h y e a r p r e s e n t s e q u a l o p p o r t u n i t y f o r g r o w t h t o t h e p o p u l a t i o n o f f i s h e s . D i f f e r e n c e s c a n b e v i s u a l i z e d , s t e m m i n g f r o m e i t h e r c l i m a t i c o r b i o l o g i c a l v a r i a t i o n . C o n s e q u e n t l y , t h e s e d a t a w e r e t e s t e d f o r d i f f e r e n c e s i n g r o w t h r a t e t h a t c o u l d b e a s c r i b e d t o v a r i a t i o n b e t w e e n g r o w t h y e a r s . T h e c o m p a r i s o n o f g r o w t h y e a r s f o r s i m i l a r l i f e h i s t o r y t y p e s a n d a g e s i s g i v e n i n T a b l e I I I . N o s i g n i f i c a n t d i f f e r e n c e s w e r e f o u n d b e t w e e n g r o w t h r a t e s o b t a i n e d b e t w e e n y e a r s 194-7 a n d 194-8 n o r b e t w e e n 194-8 a n d 194-9 . T h e y e a r s 194-7 a n d 194-9 c a n n o t b e d i r e c t l y c o m p a r e d , b u t c e r t a i n l y n o d i f f e r e n c e s a r e s u g g e s t e d . T h e c o n c l u s i o n i s r e a c h e d t h a t t h e r e a r e n o s i g n i f i c a n t d i f f e r e n c e s a p p a r e n t i n t h e s e d a t a a n d t h e g r o u p s n e e d n o t b e c o n s i d e r e d s e p a r a t e l y . L i f e H i s t o r y G r o u p s G r o w t h r a t e s o f d i f f e r e n t l i f e h i s t o r y g r o u p s Table II. Tests of significance of differences in growth rate between sexes. Chilliwack River steelhead, fresh water. Life history Age Growth year d . f . ( 1 ) "F" ratio Significance^) 2/1/50 2 194-9 1,16 0.45 P > 0.25 2/1/4-9 2 194-8 1,19 1.60 0.25 > P > 0.10 2/2/50 2 194-8 1,29 3.20 0.10 > P > 0.05 2/2/4-9 2 194-7 1,17 2.80 0.25 > P > 0.10 3/1/50 3 194-9 1,27 3.70 0.10 > P > 0.05 3/1/50 2 194-8 1,27 0.23 P > 0.25 3/1/4-9 3 194-8 1,14 2.80 0.25 > P > 0.10 3/1/4-9 2 194-7 1,14 0.47 P > 0.25 3/2/50 3 1948 1,9 0.37 P > 0.25 3/2/50 2 1947 • f : 0.02 P > 0.25 (1) Degrees of freedom. (2) In a l l tables, significance w i l l be given as the probability of obtaining a larger "F" ratio by chance. Table I I I , Tests of s i g n i f i c a n c e of differences i n growth rate between growth years. C h i l l i w a c k River steelhead, f r e s h water. Growth years L i f e h i s t o r y Age d.f. Significance compared groups r a t i o 1948 : 1 9 4 9 2 / 1 / 4 9 : 2/1/50 2 1 , 3 8 . 6 7 P > 0 . 2 5 1948 : 1 9 4 9 . 3 / 1 / 4 9 : 3 / 1 / 5 0 3 1 , 4 4 .26 P > 0 . 2 5 1 9 4 7 : 1 9 4 8 2 / 2 / 4 9 : 2 / 2 / 5 0 2 1 , 4 9 . 8 6 P > 0 . 2 5 1 9 4 7 : 1 9 4 8 3 / 1 / 4 9 : 3 / 1 / 5 0 2 1 , 4 9 . 7 6 P > 0 . 2 5 29. were compared, y i e l d i n g a highly s i g n i f i c a n t "F" r a t i o of 15.1, d.f. 3, 147. Apparently growth rate i s s i g n i f i c a n t l y associated with the eventual type of l i f e h i s t o r y pattern achieved. The test used (covariance) does not d i s t i n g u i s h between i n d i v i d u a l l i f e h i s t o r y groups; however, the r e -l a t i o n s h i p i s shown g r a p h i c a l l y i n Figure 4-. Equations f o r the regression l i n e s shown are given i n Table I V . In no case are the regression l i n e s extrapolated beyond the range of each l i f e h i s t o r y group. Three phenomena are c l e a r l y shown by these data. (1). growth rate declines with increase i n s i z e , inde-pendent of age. Each regression l i n e represents f i s h of i d e n t i c a l age and l i f e h i s t o r y . (2) Growth v e l o c i t y and time to maturity are i n v e r s e l y correlated. The regression l i n e f o r the group maturing as 3's ( i . e . 2/1) i s above those of groups maturing as 4-'s (2/2/ and 3/1) which are i n turn above that group maturing as 5's (3/2). (3) Older f i s h of the same l i f e h i s t o r y group have higher s i z e - s p e c i f i c instantaneous growth rates than the younger ones i n the same environment. This i s most c l e a r l y shown i n the two regression l i n e s depicting s i z e - s p e c i f i c Instantaneous growth rate of the 3/2 group f o r the second and t h i r d growth years i n f r e s h water. This increase i n growth v e l o c i t y appears to occur suddenly and i s associated with the time of seaward migration of other members of the population. A more complete explanation of t h i s observation w i l l be given Table IV. Regression equations for l i f e history groups. Chilliwack River steelhead, fresh water. Life history group Age Number Regression equation s y . x ( 1 ) 2/1 2 4-1 Y = .5582 - .5251 X .0562 2/2 2 52 Y = .4413 - .3535 X .0606 5/1 2 4-7 Y = .3971 - .3601 X .0642 3/2 2 12 Y = .4384 - .5278 X .0381 3/1 3 4-7 Y = .4745 - .4429 X .0437 3/2 3 12 Y = .3930 - .3450 X .0383 (1) Standard deviation from regression. 31. i n the following section. Table V presents a compilation of average size at the completion of each fre s h water annulus f o r i n d i v i d u a l l i f e h i s t o r y groups. V a r i a t i o n between i n d i v i d u a l s of each group;: i s large, as shown by standard deviation. What i s of s p e c i a l i n t e r e s t i s the apparent c r i t i c a l size f i s h must a t t a i n to respond to s t i m u l i that t r i g g e r out-migration. This siz e l e v e l i s approximately f i v e inches, fork length, regardless of age, i . e . s i z e i s a more r e l i a b l e i n d i c a t o r of p h y s i o l o g i c a l development than age. Discussion of Causative Factors The rate of growth of f i s h i s dependent upon two types of f a c t o r s . (1) A genetic capacity f o r growth pe-c u l i a r to i n d i v i d u a l s that together form a v a r i a b l e popu-l a t i o n i n any one area and (2) environmental opportunity which determines the degree of growth rate p o t e n t i a l at-tained. Genetic v a r i a t i o n between i n d i v i d u a l s i s a w e l l established f a c t and needs no f u r t h e r discussion. The environmental e f f e c t s upon growth are a p t l y demonstrated i n these data. A discussion on some of these factors w i l l c l a r i f y the observed phenomena. The work of Gray (1928a,b) has shown that the s i z e of a trout (S. f a r i o ) at the end of the embryonic stage i s l a r g e l y dependent upon two f a c t o r s : (a) the amount of yolk the egg contained and (b) the temperature at which Table V. Mean size and standard deviation of l i f e h i s t o r y groups at completion of f r e s h water annuli. Size given as fork length i n inches. 4 Group Number 1 Size at completion 2 of annulus 3 4 2 / 1 / 4 9 2 2 3 . 3 1 + . 7 8 8 6.41 ± 0 . 7 3 6 migrated 2 / 1 / 5 0 1 9 3 . 0 1 + .54-9 6 . 1 3 - 1.066 migrated 2 / 2 / 4 9 2 0 3.06 + . 7 7 2 5 . 5 6 i '1.260 migrated 2 / 2 / 5 0 3 2 2 . 8 3 + .611 5 . 5 7 - 1 . 2 2 2 migrated 3 / 1 / 4 9 1 7 2 . 4 5 + .412 4 . 3 6 ± 0 . 6 9 6 6 . 4 7 - 1 . 1 3 8 migrated 3 / 1 / 5 0 3 0 2.61 + .626 4 . 7 1 i 1 . 0 2 9 7 . 2 2 - 1 . 1 5 0 migrated 3 / 2 / 5 0 1 2 2 . 3 0 + . 4 5 4 3 . 9 9 - 0 . 5 8 9 6.08 i 0 . 6 6 9 migrated 3 3 . development took place. Under i d e n t i c a l incubating temper-atures eggs having larger yolk content w i l l produce larger f r y than smaller eggs. Under higher temperatures develop-ment w i l l be f a s t e r , but the r e s u l t i n g embryo w i l l be smaller due to a greater proportion of the ava i l a b l e food supply (yolk) being used f o r sustenance. This means that under w i l d conditions, eggs of the same s i z e , f e r t i l i z e d at the same time but i n d i f f e r e n t parts of the stream, may produce d i f f e r e n t sized f r y . Add to these, v a r i a t i o n be-tween egg s i z e , v a r i a t i o n i n time of actual egg f e r t i l i -z a t i o n , and the genetic v a r i a b i l i t y i n capacity f o r growth, and i t i s not s u r p r i s i n g that a population of steelhead f r y exh i b i t s considerable v a r i a t i o n i n i n d i v i d u a l s i z e . Brown (1946a) r a i s e d brown trout (S. t r u t t a ) f r y from hatching to eight months under experimental conditions where f l u c t u a t i o n s i n temperature, l i g h t , food, etc. were held to a minimum. She found that growth rate was highest during the f i r s t three weeks a f t e r beginning of feeding and declined thereafter. Although the experimental i n d i v i d u a l s were from a single p a i r of parents, and were incubated under i d e n t i c a l conditions, a large amount of v a r i a t i o n was r e -ported i n s i z e and i n growth ra t e . After i n i t i a l feeding a s o c i a l hierarchy was established i n each tank. The largest f i s h dominated the feeding habits and, therefore, the growth of the smaller i n d i v i d u a l s , so that the largest f i s h of each experimental l o t grew the f a s t e s t . In studying 34. t h e g r o w t h o f t w o y e a r o l d b r o w n t r o u t u n d e r c o n s t a n t t e m p e r -a t u r e B r o w n ( 1 9 4 6 b ) a g a i n s h o w e d t h e e x i s t e n c e o f a s o c i a l h i e r a r c h y . H o a r (1953> p . 4-77) s t a t e s : " P r o l o n g e d r e s i d e n c e o f j u v e n i l e s a l m o n a n d t r o u t i n s t r e a m b e d s d e p e n d s p r i m a r i l y o n t h e i r t e r r i t o r i a l b e h a v i o r . T h i s b e h a v i o r o f o c c u p y i n g a n d d e f e n d i n g t e r r i t o r i e s i s a s s o c i a t e d w i t h m i g r a t i o n i n t o s h a l l o w w a t e r a n d s e t t l i n g t o t h e b o t t o m t o r e m a i n i n a c t i v e a t n i g h t . " Newman (1956) o b s e r v e d s o c i a l s t r u c t u r e ( S a l v e l -i n u s f o n t i n a l i s , S a l m o g a i r d n e r i ) u n d e r w i l d c o n d i t i o n s a s w e l l a s i n a q u a r i a . Two o b s e r v a t i o n s a r e e s p e c i a l l y s i g -n i f i c a n t . ( 1 ) T h e f r e q u e n c y o f n i p p i n g w a s h i g h e r i n s m a l l e r , c o n f i n e d t a n k s t h a n i n l a r g e o n e s , w h i c h l e a d s t o t h e o b s e r v a t i o n t h a t c o n f i n e m e n t , s u c h a s p r o d u c e d b y l o w w a t e r c o n d i t i o n s o r b y d e n s e p o p u l a t i o n s , m a y i n t e n s i f y s o c i a l b e h a v i o r . T h i s c o n d i t i o n w o u l d s u p p r e s s g r o w t h r a t e s o f t h e d o m i n a t e d i n d i v i d u a l s . I n a n a t u r a l e n v i r o n m e n t t h e d o m i n a t e d i n d i v i d u a l s m a y b e e i t h e r y o u n g e r o r s l o w e r g r o w i n g o r b o t h . ( 2 ) A r o t a t i o n i n t h e p e c k o r d e r o f a s t r e a m w h e n d o m i n a n t f i s h w e r e a b s e n t f r o m t h e a r e a . T h i s s i t u a t i o n w o u l d , u n d e r c o n d i t i o n s o f l o w p o p u l a t i o n d e n s i t y , a l l o w f e e d i n g o f t h e s m a l l e r i n d i v i d u a l s ; h o w e v e r , i n a h i g h p o p u l a t i o n d e n s i t y t h e s m a l l e s t i n d i v i d u a l s m i g h t s t a r v e o r s u c c u m b t o o t h e r f o r m s o f m o r t a l i t y f r o m a w e a k e n e d c o n d i t i o n . I n s t e e l h e a d t h e m a s s o u t - m i g r a t i o n o f t h e l a r g e s t i n d i v i d u a l s i n t h e s p r i n g w o u l d b e e x p e c t e d t o r e s u l t i n a n 35. improved environment f o r the r e s i d u a l inhabitants, i . e . a sudden upward s h i f t i n a curve describing the s i z e - s p e c i f i c growth r a t e . Referring to Pigure 3, the observed discon-t i n u i t y i n the s i z e - s p e c i f i c growth curves between the second and t h i r d f r e s h water growth years has a r a t i o n a l explanation. S a l t Water Environment The migration of steelhead from f r e s h to s a l t water off e r s a s t r i k i n g example of the e f f e c t s of an en-vironmental change upon growth rate. The t o t a l s c a t t e r of points of s i z e - s p e c i f i c growth rates has been presented i n Figure 3. A regression l i n e f o r s a l t water growth i s de-scribed by the equation Y = 0.9592 - 0.6070 X. Standard deviation from regression i s 0.04-99 which, compared with 0.9064- obtained i n fr e s h water, r e f l e c t s considerably less v a r i a t i o n i n the growth rates of the i n d i v i d u a l s . The i n d i v i d u a l s , however, were not of the same age group, nor was the duration of s a l t water residence the same. Treat-ment of these data follows the pattern used f o r comparison of groups i n the f r e s h water environment. Sex Differences While no differences between growth rates of sexes were apparent i n fr e s h water, the p o s s i b i l i t y of a difference as the f i s h approach maturity was not overlooked. Each l i f e h i s t o r y group was tested by covariance. The r e s u l t s are 3 6 . presented i n Table VI. There i s no reason to suspect d i f f e r -e n t i a l growth between the sexes during that period of l i f e h i s t o r y studied. Differences Between Growth Years I t i s a common b e l i e f among f i s h e r i e s b i o l o g i s t s that the s a l t water environment may be considered as r e l a -t i v e l y constant i n a f f e c t i n g the v i t a l s t a t i s t i c s of anadro-mous f i s h (Neave, 1 9 5 3 ) . This postulate has not been f u l l y i n v e stigated, however, and i s s t i l l open to question. Growth years of steelhead i n the marine environment have been compared, using s i z e - s p e c i f i c growth r a t e s from groups having i d e n t i c a l l i f e h i s t o r i e s . The r e s u l t s of covariance te s t s are presented i n Table V I I . The consistency of growth opportunity w i t h i n the three years tested i s w e l l demon-str a t e d , provided only f i s h during t h e i r f i r s t s a l t water growth year are compared. Differences between the 194-9 and 1 9 5 0 growth years are s i g n i f i c a n t at the f i v e percent l e v e l when f i s h i n t h e i r second marine growth years are compared. There are several a l t e r n a t i v e explanations, one of which i s that those f i s h spending more time at sea wandered f a r t h e r , thus encountering more diverse environ-mental opportunity. Differences Between L i f e History Groups Differences i n growth during the f i r s t year of marine environment between l i f e h i s t o r y groups were tested. Table VI* Tests of significance of differences in growth rate between sexes. Chilliwack River steelhead, salt water. Life history Age Growth year d.f . "F" ratio Significance 2/1/50 3 1950 1,16 0.90 P > 0.25 2/1/4-9 3 1949 1,19 4.30 0.10 > P > 0.05 2/2/50 3 1949 1,29 0.29 P > 0.25 2/2/4-9 3 1948 1,17 3.80 0.10 > P > 0.05 2/2/50 4 1950 1,29 3.20 0.10 > P > 0.05 2/2/4-9 4 1949 1,17 2.30 0.25 > P > 0.10. 3/1/50 4 1950 1,27 1.10 P > 0.25 3/1/4-9 4 1949 1,14 0.00+ P > 0.25 3/2/50 4 1948 1,9 0.72 P > 0.25 3/2/50 5 1949 1,9 3.30 0.25 > P > 0.10 Table V I I . Tests of si g n i f i c a n c e of differences i n growth rate between growth years. C h i l l i w a c k River steelhead, s a l t water. Growth years compared L i f e h i s t o r y groups Age d.f. r a t i o Significance 1949 : 1950 • 2/1/49 : 2/1/50 3 1,38 0.18 P > 0.25 19A9 : 1950 • 3 / 1 A 9 :• 3/1/50 4 1,44 0.01 P > 0.25 1949 : 1950 • 2/2/49 : 2/2/50 4 1,4-9 5.20 0.05 > P > 0.025 1948 : 1949 2/2/49 : 2/2/50 3 1,4-9 0.06 P > 0.25 39. An "F" value of 11.4, d.f. 3, 147 i s s i g n i f i c a n t at .005; thus, there i s l i t t l e chance that the l i f e h i s t o r y groups were, growing at the same ra t e . A fu r t h e r test was c a r r i e d out comparing groups with the same marine h i s t o r y . These data are presented i n Table V I I I . Differences s i g n i f i c a n t at the f i v e percent p r o b a b i l i t y l e v e l are noted between the 2/1 and 3/1 groups. The comparisons between the 2/2 and 3/2 groups show no differences i n eit h e r the antipenultimate or penultimate years. Further, t h i s comparison shows f i s h of d i f f e r e n t ages to be growing at the same s i z e - s p e c i f i c growth r a t e . Noting that i n one case a difference s i g n i f i c a n t at the f i v e percent l e v e l e x i s t s , the growth years were nevertheless combined. Regression l i n e s were f i t t e d to the data f o r each year of marine residence and are presented i n Table IX. These data are g r a p h i c a l l y presented i n Figure 4. As was noted f o r f i s h i n f r e s h water, continued r e s i -dence i n s a l t water appears to increase the r e l a t i v e oppor-t u n i t y f o r growth with further increase i n s i z e . Rather than an abrupt change i n p o s i t i o n between regression l i n e s f o r f i r s t and second growth years, (2/2/ and 3/2) the process i s more gradual as.;, indicated by a change i n slope, i . e . the rate of deceleration of k on log-^QL i s l e s s . This could i n d i c a t e several f a c t o r s , i n c l u d i n g a s i z e - s p e c i f i c change i n environmental opportunity, perhaps a change from planktivorous to piscivorous habits, or a d i f f e r e n t Table V I I I . Tests of si g n i f i c a n c e of differences between l i f e h i s t o r y groups of the same marine h i s t o r y . C h i l l i w a c k River steelhead. L i f e h i s t o r y -groups Age Marine year d.f. "j7» r a t i o S ignificance 2/1 3/1 " 3 4 f i r s t 1,85 4.3 0.050 > P > 0.025 4/2 3/2 3 4 f i r s t 1,61 1.7 0.25 > ,P > 0.10 2/2 3/2 4 5 second 1,61 2.3 0.25 > P > 0.10 Table IX» Regression equations for l i f e history groups. Chilliwack River steelhead, salt water. Life history group Age Number Regression equation S y.x 2/1 3 41 Y = 1.0765 - .7215 X .0456 3/1 4 47 Y = 0.9562 - .5988 X .0321 2/2 3 52 Y = 1.0753 - .7950 X .0481 3/2 4 12 Y = 1.0293 - .7110 X .0404 2/2 4 52 t = 0.8202 - .4916 X .0372 3/2 5 12 Y = 0.7.982 - .4855 X .0390 4 2 . e n v i r o n m e n t e n c o u n t e r e d b y w a n d e r i n g f a r t h e r f r o m t h e n a t a l s t r e a m , o r p e r h a p s t h a t t h e g r o w t h y e a r c o n t a i n i n g m i g r a t i o n f r o m f r e s h w a t e r i s n o t c o m p l e t e l y i n s a l t w a t e r . T h e s e p o s t u l a t e s a r e p u r e s p e c u l a t i o n ; h o w e v e r , t h e f a c t r e m a i n s t h a t d i f f e r e n c e s e x i s t a n d t h e c h a n g e s o c c u r r e d i n a n o p p o -s i t e d i r e c t i o n t o t h a t e x p e c t e d i f g r o w t h d e c l i n e s w i t h a g e . T h e a c t s o f m a t u r i n g , l e a v i n g t h e s e a , a n d s p a w n -i n g a r e , l i k e t h e o u t - m i g r a t i o n f r o m f r e s h w a t e r , f u n c t i o n s o f p h y s i o l o g i c a l d e v e l o p m e n t . A g a i n s i z e i s a m o r e r e l i a b l e i n d i c a t i o n o f p h y s i o l o g i c a l d e v e l o p m e n t t h a n a g e . T h e r e -l a t i o n s h i p b e t w e e n s i z e , a g e , a n d m a t u r i t y i s p r e s e n t e d i n T a b l e X . Two g r o u p s o f f i s h e n t e r e d t h e s e a f r o m f r e s h w a t e r , t h o s e i n t h e i r t h i r d a n d f o u r t h g r o w t h y e a r s o f l i f e . E a c h g r o u p m a y b e s p l i t i n t o s l o w a n d f a s t g r o w i n g c o m -p o n e n t s . On t h e a v e r a g e , i f a f i s h g r e w t o a s i z e o f m o r e t h a n n i n e t e e n i n c h e s a t t h e e n d o f t h e f i r s t m a r i n e g r o w t h y e a r , i t m a t u r e d a n d r e t u r n e d t o s p a w n t h e f o l l o w i n g y e a r . O n t h e a v e r a g e , i f a s i z e o f n i n e t e e n i n c h e s w a s n o t a t -t a i n e d , t h e f i s h r e m a i n e d i n t h e s e a a n o t h e r y e a r , r e t u r n i n g t o s p a w n a t a m u c h l a r g e r s i z e t h a n , i t s f a s t g r o w i n g , b u t y o u n g e r , c o u n t e r p a r t . T h i s i s n o t t o s a y t h a t s i z e i n i t s e l f i s a c a u s a t i v e f a c t o r o f m a t u r i t y . S i z e i s , h o w e v e r , a f a i r l y r e l i a b l e m e a s u r e m e n t o f p h y s i o l o g i c a l d e v e l o p m e n t f o r t h e s e f i s h . T h e s i z e a t t h e e n d o f a g r o w t h y e a r h a s n o s i g n i f i c a n c e o t h e r t h a n a p o i n t t h a t c a n b e m e a s u r e d c o n v e n i e n t l y , a n d r e f l e c t s o r p r e d i c t s t h e p h y s i o l o g i c a l Table X. Mean size and standard deviation of l i f e h i s t o r y groups at the completion of s a l t water annuli. Size given as fork length i n inches. •> Size i n inches , at end of marine growth years Group Number Age f i r s t x i year S x Age second year -,± s x Age t h i r d year 2/1 41 3 19.8 ± 2 . 1 1 2 4 spawned 3/1 4 7 4 19.8 i 2 . 1 7 1 5 spawned 2/2 5 2 3 16 .9 * 1.982 4 27.6 ± 2 . 7 4 5 5 spawned 3/2 X. 1 2 4 18.2 ± 1.842 5 28.4 ± 2.008 6 spawned 4 4 . threshold of development that f i s h must a t t a i n to respond to migratory s t i m u l i . The foregoing discussion would appear to place an evolutionary advantage on r a p i d growth. However, r a p i d growth i s also associated with early maturity at a smaller ultimate s i z e . Scott (1956) has shown that egg number i s , i n part, a function of size o f the adult; thus, an evolution-ary advantage could also be ascribed to a slow growth ra t e . However, while large i n d i v i d u a l s produce many eggs, they also s u f f e r a greater t o t a l m o r t a l i t y with advanced age and se l e c t i v e advantage i s not tenable on the basis of growth rate alone. Evolutionary advantage i s apparent i n a system that insures against permanent damage from a catastrophe to any one year's spawning population. This i s accomplished by the d i v e r s i t y of l i f e h i s t o r i e s , i n c l u d i n g some second spawning of steelhead. This d i v e r s i t y , however, i s de-pendent on v a r i a t i o n of growth r a t e . Age i n i t s e l f cannot l o g i c a l l y be considered as an independent f a c t o r . The complete l i f e h i s t o r y and several f a c t o r s determining the course of events of any brood year of steelhead may be rec a p i t u l a t e d as f o l l o w s . Prom any given year's seeding the r e s u l t i n g emergent f r y w i l l e x h i b i t v a r i a t i o n from a mean i n respect to (1) i n h e r i t e d capaci-t y f o r growth, (2) s i z e , and (3) time of emergence. This v a r i a t i o n , coupled with a s o c i a l hierarchy, r e s u l t s - i n a 4-5. wide v a r i a t i o n between i n d i v i d u a l sizes and growth rates ca l c u l a t e d f o r the time corresponding to the second growth year. At the s t a r t of the t h i r d growth year, those i n d i -v iduals that have attained a p h y s i o l o g i c a l stage receptive to migratory s t i m u l i w i l l respond and leave f r e s h water. The r e s i d u a l population then assumes a p o s i t i o n of dominance formerly occupied by ,the larger i n d i v i d u a l s that migrated. The r e s i d u a l group grows at an improved average growthrate during the t h i r d growth year and responds to migratory s t i m u l i at the s t a r t of the fourth growth year. In s a l t water those i n d i v i d u a l s , composing the: earl y migrants (at the s t a r t of the t h i r d growth year) have var i a b l e c a p a c i t i e s f o r growth. Those that grow f a s t w i l l begin maturing and respond to migratory s t i m u l i . The slower growing i n d i v i d u a l s remain i n the sea, a t t a i n i n g maturity the following year. I d e n t i c a l marine l i f e h i s t o -r i e s are followed by the group that remained i n fr e s h water an a d d i t i o n a l year. The f i n a l product, i n terms of size of spawners, i s a heterogeneous s i z e d i s t r i b u t i o n . The whole course of l i f e h i s t o r y i s seen to be best describable i n terms of s i z e . Age i s not a r e l i a b l e i n d i c a t o r of either s i z e or p h y s i o l o g i c a l development under these natu r a l conditions. The course of growth during the f i r s t and u l t i -mate growth years cannot be approached through scale analy-s i s , and these periods constitute a gap i n ava i l a b l e knowledge of steelhead and salmon. E x i s t i n g growth curves are not s u f f i c i e n t l y d e s c r i p t i v e of the growth of these f i s h e s , even under conditions of an unchanging environment, and much remains to be done on t h i s problem. I t i s doubtful, however, that the growth of f i s h e s under changing environmental conditions can be described, hence predicted, by other than empirical formulations. SUMMARY The a b i l i t y to predict the s i z e of a f i s h i s considered e s s e n t i a l to f i s h e r i e s management. The accuracy of a p r e d i c t i o n necessitates knowledge of the causative factors of growth. Many attempts have been made to write general equations that describe the en t i r e course of growth throughout l i f e ; yet, i n f i n a l a n a l y s i s , growth i s the r e -s u l t of many Inte r a c t i n g f a c t o r s , many of which are not predic t a b l e . In the absence of a v a l i d general growth equation, the exponential growth formula i s used as a con-venient means of describing average annual growth rates f o r a comparison between i n d i v i d u a l s or groups. Instantaneous growth r a t e s , calculated as the differences i n logarithms of size at yearly i n t e r v a l s , are shown to decline with increase i n size and age. Thus, a comparison of growth rate between i n d i v i d u a l s or groups must be made at some point or l e v e l common to both groups. Age has been widely used by f i s h e r y workers, i . e . average 47. age-specific instantaneous growth rates are compared. The c l a s s i f i c a t i o n of i n d i v i d u a l s by age, however, lacks pre-c i s i o n and may lead to considerable anomaly unless a constant environmental opportunity can be postulated. An hypothesis i s advanced that growth r a t e , while n e c e s s a r i l y occurring i n time, i s independent of absolute age, at l e a s t during juve n i l e stages of development. Rather growth rate appears to be a function of s i z e . Steelhead (because of anadromous habits) provide an exceptional oppor-t u n i t y to explore the general hypothesis. Individuals are subject to a wide v a r i e t y of environmental stresses and s t i m u l i , each of which may contribute i n d i v i d u a l l y or through i n t e r a c t i o n i n a l t e r i n g the growth r a t e . The inference of siz e at previous times i n the l i f e h i s t o r y through the use of:;scales or other bony parts provides growth data only f o r the j u v e n i l e stages. 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