UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Growth and mortality in relation to maximum yield in pounds of chinook salmon (Oncorhynchus tshawytscha) Parker, Robert Ray 1959

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1959_A1 P2 G7.pdf [ 6.5MB ]
Metadata
JSON: 831-1.0106514.json
JSON-LD: 831-1.0106514-ld.json
RDF/XML (Pretty): 831-1.0106514-rdf.xml
RDF/JSON: 831-1.0106514-rdf.json
Turtle: 831-1.0106514-turtle.txt
N-Triples: 831-1.0106514-rdf-ntriples.txt
Original Record: 831-1.0106514-source.json
Full Text
831-1.0106514-fulltext.txt
Citation
831-1.0106514.ris

Full Text

Wqt Pmtestig of ^rtttstf Qlolitntbta Faculty of Graduate Studies P R O G R A M M E O F T H E FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ROBERT RAY PARKER B. S. University of Washington, 1946 M. A. University of British Columbia, 1957 IN ROOM 187A, BIOLOGICAL SCIENCES BUILDING TUESDAY, APRIL 14, 1959 at 3:30 p.m. C O M M I T T E E I N C H A R G E DEAN W. H. GAGE, Chairman P. A. LARKIN E . BLACK W. A. CLEMENS I. MoT. COWAN C. C. LINDSEY H. B. HAWTHORN A. J. WOOD External Examiner: Dr. W. E. RICKER Fisheries Research Board of Canada GROWTH AND MORTALITY IN RELATION.TO MAXIMUM YIELD IN POUNDS OF CHINOOK SALMON (Oncorhynchus tshawytscha) ABSTRACT Life history events of chinook salmon preclude determination of a critical size for this species by established methods. The use of size, rather than age, as a basic correlate of growth rate is discussed and compared to analagous treatment of physiological rates described in literature. Ecological opportunity and physiological opportunity are visualized as the two inter-acting components that determine growth, both of which are related to size attained. Growth opportunity occurs in stanzas which are entered at 'threshold' sizes. The function, dw/dt = kw x is developed into a growth equation for linear dimensions, It + 1 = a + 1|, and three methods of fitting this equation to growth data are demonstrated. Application is explored and discussed using steelhead trout and chinook salmon as examples. Significant differences in growth rate were found between life history types and sexes. The chinook data were then treated on a l t + i , l t plot and it was shown how an apparent fit of the von Bertalanffy type growth equation can result from selectively fishing for the larger fish of any brood year. Accordingly, life history sub-groups of a year class must either be treated separately or weighted accord-ing to relative abundance in determining critical size. The former alter-native is followed in lieu of necessary weighting data. Natural mortality of a chinook population is estimated from the pat-tern of tag recoveries, taking advantage of the fact that maturity occurs at different ages for individuals of a year class and that the fishery operated mainly on maturing individuals. Annual instantaneous natural mortality was estimated to lie in the range 0. 3 to 0. 4. The growth equation was then transformed to a length-specific average annual instantaneous growth (weight) rate and critical size was observed to occur at maturity for each life history type. Since fishing is presently allowed on the immature stock, a size limit protecting the older life history types causes a loss in yield from the younger life history types. This loss might be offset, depending on the relative abundance of life history types in the stock, provid-ing mortality due to hooking and releasing is negligible. Capture by trolling was found to subject feeding coho and chinook salmon to hyperactivity which may lead to a distressed condition or death, and death cannot be predicted from examination of individual fish at time of capture. Mortality of coho was estimated to be in the 0. 95 confidence interval of 34 percent and 52 percent; of chinook in the 0. 95 confidence interval of 40 percent and 71 percent. Time of maximum death rate is shown to coincide with the period of maximum blood lactate response. Survival occurred either when blood lactate did not reach critical levels (above 125 mg%) or reached critical levels and subsequently subsided. Holding salmon in a live box for 8-14 hours before release did not improve tag recovery, suggesting additional indiscriminate stress was caused at release. Adult coho in freshwater did not appear capable of lethal hyper-activity. This led to the hypothesis that cessation of feeding during spawn ing migration has adaptive significance for survival of Pacific salmon. The combination of natural mortality, mortality from hooking injur and delayed mortality from fatigue gave a total instantaneous first year mortality rate (exclusive of fishing) greater than 1. 0 and possibly as high as 2. 5. This mortality rate results in a critical size of not more than 22. 5 inches and most likely about 15. 0 inches fork length. It is thus concluded that for maximum yield in pounds (1) fishing for chinook should be restricted to their ultimate year (maturity) and (2) the use of non-selective gear should be encouraged. These recommendations are opposite to present practices. If fishing is to be allowed on the imma-ture stock, size limits should be abolished. G R A D U A T E S T U D I E S Field of Study: Zoology Population Dynamics Marine Field Course -Biology of Fishes . P . A . Larkin .P. A . Dehnel C . C . Lindsey Other Studies: Fisheries Hydraulics E.S. Pretious Fisheries Anthropology H . B. Hawthorn Introduction to Dynamic Oceanography. . . . . G . L . Pickard Introduction to Synoptic Oceanography G . L . Pickard Advanced Synoptic Oceanography. G. L. Pickard Chemical Oceanography J . D . H . Strickland P U B L I C A T I O N S Larkin, P. A . , J . G . Terpenning andR.R. Parker. 19S7. Size as a determinant of growth rate in rainbow trout, Salmo gairdneri. Trans. Am. Fish. Soc. , 86: 84-96. Parker, Robert R. 1955. Two proposed methods of estimating animal populations. Proc. 7th Alaska Science Conference. Parker, Robert R. and Walter Kirkness. 1951. Biological investiga-tions. Alaska Dept. Fish., Ann. Rept. No. 2, 1950: 25!-42. Parker, Robert R. and Walter Kirkness. 1954. Estimates of popula-tion of spawning king salmon in the Taku River, Alaska, for the year 1951. Proc. 3rd Alaska Sci. Confer., pp. 179-191. Parker, Robert R. and Walter Kirkness. 1956. King salmon and the ocean troll fishery of Southeastern Alaska. Alaska Dept. Fish. , Res. Rept.No. 1, 64 pp. Parker, Robert R. and Robert E. Vincent. 1956. Progress report on research studies at the Kitoi Bay Research Station. Alaska  Dept. Fish., Ann. Rept. No. 7, 1955. pp. 25-67. Parker, Robert R. and Edgar C . Black. 1959. Muscular fatigue and mortality in troll-caught chinook salmon (Oncorhynchus  tshawytscha). J_. Fish. Res. Bd. Canada. 16(1): 95-106. Parker, Robert R . , Edgar C . Black and Peter A. Larkin. 1959. Fatigue and mortality of Pacific salmon (Oncorhynchus). h Fish- Res. Bd. Canada. In press. Parker, Robert R. and P. A . Larkin. 1959. A concept of growth of fishes. Submitted toJ_. Fish. Res. Bd. Canada. GROWTH AND MORTALITY IN RELATION TO MAXIMUM YIELD IN POUNDS OF CHINOOK SALMON (Oncorhynchus tshawytscha) by Robert Ray Parker B.S. i n Zool., University of Washington, 194-6 M.A., University of B r i t i s h Columbia, 1957 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy ,in the Department of Zoology We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Ap r i l , 1959 i i ABSTRACT Li f e history events of chinook salmon preclude determi-nation of a c r i t i c a l size for this species by established methods. The use of size, rather than age, as a basic cor-relate of growth rate i s discussed and compared to analagous treatment of physiological rates described i n l i t e r a t u r e . Ecological opportunity and physiological opportunity are visualized as the two interacting components that determine growth, both of which are related to size attained. Growth opportunity occurs i n stanzas which are entered at "threshold" sizes. The function, dw/dt = kwx i s developed into a growth equation for linear dimentions, 1^_+^  = ^ ' and three methods of f i t t i n g this equation to growth data are demon-strated. Application i s explored and discussed using steel-head trout and chinook salmon as examples. Significant differences i n growth rate were found between l i f e history types and sexes. The chinook data were then treated on a 1 +^-^, 1^ plot and i t was shown how an apparent f i t of the von Bertalanffy type growth equation can result from selectivly fishing for the larger f i s h of any brood year. Accordingly 1, l i f e history subgroups of a year class must either be treated separately or weighted according to relative abundance i n determining c r i t i c a l size. The former alternative i s followed i n l i e u of necessary weighting data. Natural mortality of a chinook population i s estimated from the pattern of tag recoveries, taking advantage of the fact that maturity occurs at different ages for individuals of a year class and that the fishery operated mainly on maturing individuals. Annual instantaneous natural mortality was e s t i -mated to l i e i n the range 0.3 to 0.4. i i i The growth equation was then transformed to a length-specific average annual instantaneous growth (weight) rate and c r i t i c a l size was observed to occur at maturity for each l i f e history type. Since fishing i s presently allowed on the immature stock, a size limit protecting the older l i f e history types causes a loss i n y i e l d from the younger l%fe history types. This loss might be offset, depending on the relative abundance of l i f e history types i n the stock, providing mor-t a l i t y due to hooking and releasing i s negligible. Capture by t r o l l i n g was found to subject feeding coho and chinook salmon to hyperactivity which may lead to a d i s r tressed condition or' death, and death cannot be predicted from examination of,individual f i s h at time of capture. Mortality of coho was estimated to be i n the 0.95 confidence interval of 34 percent and 52 percent} of chinook i n the 0.95 confidence interval of 40 percent and ,71 percent. Time of maximum death v rate i s shown to coincide with the period of maximum blood lactate, response. Survival occurred either when blood lactate did not reach c r i t i c a l levels (above 125 mg%) or reached c r i t i -c a l levels and subsequently subsided. Holding salmon i n a l i v e box for 8-14 hours before release^ did not improve tag recovery, suggesting additional indiscriminant stress was caused at release. Adult coho i n freshwater did not appear capable of lethal hyperactivity. This led to the hypothesis that ces-sation of xfeeding during spawning migration has adaptive sig-nificance for survival of Pacific salmon. The combination of natural mortality, mortality from hooking injury and delayed mortality from fatigue gave a t o t a l instantaneous f i r s t year mortality rate (exclusive of fishing) greater than 1.0 and possibly as high as 2.5".' This mortality rate results i n a c r i t i c a l size of not more than 22.5 inches and most l i k e l y about 15.0 inches fork length. i i i i It i s thus concluded that for maximum y i e l d i n pounds (1) fishing for chinook should he restricted to their u l t i -mate year (maturity) and (2) the use of non-selective gear should be encouraged. These recommendations are opposite to present practices. If fishing i s to be allowed on the imma-ture stock, size limits should be abolished. " 2 % pnfceraitg of ^rtttsl| Ololumbta Faculty of Graduate Studies P R O G R A M M E O F THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ROBERT RAY PARKER B. S. University of Washington, 1946 M. A. University of British Columbia, 1957 IN ROOM 187A, BIOLOGICAL SCIENCES BUILDING TUESDAY, APRIL 14, 1959 at 3:30 p.m. C O M M I T T E E I N C H A R G E DEAN W. H. GAGE, Chairman P. A. LARKIN E . BLACK W. A. CLEMENS I. McT. COWAN C. C. LINDSEY H. B. HAWTHORN A. .1. WOOD External Examiner: Dr. W. E. RICKER Fisheries Research Board of Canada GROWTH AND MORTALITY IN RELATION TO MAXIMUM YIELD • IN POUNDS OF CHINOOK SALMON (Oncorhynchus tshawytscha) ABSTRACT Life history events of chinook salmon preclude determination of a critical size for this species by established methods. The use of size, rather than age, as a basic correlate of growth rate is discussed and compared to analagous treatment of physiological rates described in literature. Ecological opportunity and physiological opportunity are visualized as the two inter-acting components that determine growth, both of which are related to size attained. Growth opportunity occurs in stanzas which are entered at 'threshold1 sizes. The function,, dw/dt '= kw x is developed into a growth equation for linear dimensions, It + 1 = a + 1£, and three methods of fitting this equation to growth data are demonstrated. Application is explored and discussed using steelhead trout and chinook salmon as examples. Significant differences in growth rate were found between life history types and sexes. The chinook data were then treated on a l t + i , l t plot and it was shown how an apparent fit of the von Bertalanffy type growth equation can result from selectively fishing for the larger fish of any brood year. Accordingly, life history sub-groups of a year class must either be treated separately or weighted accord-ing to relative abundance in determining critical size. The former alter-native is followed in lieu of necessary weighting data. Natural mortality of a chinook population is estimated from the pat-tern of tag recoveries, taking advantage of the fact that maturity occurs at different ages for individuals of a year class and that the fishery operated mainly on maturing individuals. Annual instantaneous natural mortality was estimated to lie in the range 0. 3 to 0. 4. The growth equation was then transformed to a length-specific average annual instantaneous growth (weight) rate and critical size was observed to occur at maturity for each life history type. Since fishing is presently allowed on the immature stock, a size limit protecting the older life history types causes a loss in yield from the younger life history types. This loss might be offset, depending on the relative abundance of life history types in the stock, provid-ing mortality due to hooking and releasing is negligible. Capture by trolling was found to subject feeding coho and chinook salmon to hyperactivity which may lead to a distressed condition or death, and death cannot be predicted from examination of individual fish at {time, of capture. Mortality of coho was estimated to "be in the 0.'.95»c6nfidenc'e-interval of 34 percent and 52 percent; of chinook in the 0. 95 confidence interval of 40 percent and 71 percent. Time of maximum death rate is shown to coincide with the period of maximum "blood lactate response. Survival occurred either when blood lactate did not reach critical levels (above 125 mg%) or reached critical levels and subsequently subsided. Holding salmon in a live box for 8-14 hours before release did not improve tag recovery, suggesting additional indiscriminate -stress was caused at release. Adult coho in freshwater did not appear capable of lethal hyper-activity. This led to the hypothesis that cessation of feeding during spawn ing migration has adaptive significance for survival of P acific salmon. The combination of natural mortality, mortality from hooking injun and delayed mortality from fatigue gave a total instantaneous first year mortality rate (exclusive of fishing) greater than 1. 0 and possibly as high as 2. 5. This mortality rate results in a critical size of not more than 22. 5 inches and most likely about 15.0 inches fork length. It is thus concluded that for maximum yield in pounds (1) fishing for chinook should be restricted to their ultimate year (maturity) and (2) the use of non-selective gear should be encouraged. These recommendations are opposite to present practices. If fishing is to be allowed on the imma-ture stock, size limits should be abolished. G R A D U A T E S T U D I E S Field of Study: Zoology Population Dynamics P . A . Larkin Marine Field Course. P. A . Dehnel Biology of Fishes C . C . Lindsey Other Studies: Fisheries Hydraulics E. S. Pretious Fisheries Anthropology H . B . Hawthorn Introduction to Dynamic Oceanography. . ... . G. L. Pickard Introduction to Synoptic Oceanography G . L . Pickard Advanced Synoptic Oceanography. G . L . Pickard Chemical Oceanography J. D. H. Strickland P U B L I C A T I O N S Larkin, P . A . , ]. G. Terpenning and R. R. Parker. 1957. Size as a determinant of growth rate in rainbow trout, Salmo gairdneri. Trans. Am. Fish. S o c , 86:84-96. Parker, Robert R. 1955. Two proposed methods of estimating animal populations. Proc 7th Alaska Science Conference. Parker, Robert R. and Walter Kirkness. 1951. Biological investiga-tions. Alaska Dept. Fish., Ann. Rept. No. 2, 1950: 25-42. Parker, Robert R. and Walter Kirkness. 1954. Estimates of popula-tion of spawning king salmon in the Taku River, Alaska, for the year 1951. Proc. 3rd Alaska Sci. Confer., pp. 179-191. Parker, Robert R. and Walter Kirkness. 1956. King salmon and the ocean troll fishery of Southeastern Alaska. Alaska Dept. Fish., Res. Rept.No. 1, 64 pp. Parker, Robert R. and Robert E. Vincent. 1956. Progress report on research studies at the Kitoi Bay Research Station. Alaska  Dept. Fish. , Ann. Rept. No. 7, 1955. pp. 25-67. Parker, Robert R. and Edgar C . Black. 1959. Muscular fatigue and mortality in troll-caught chinook salmon (Oncorhynchus  tshawytscha). J. Fish. Res. Bd. Canada. 16(1): 95-106. Parker, Robert R. , Edgar C . Black and Peter A . Larkin. 1959. Fatigue and mortality of Pacific .salmon (Oncorhynchus). ]_. Fish. Res. Bd. Canada. In press. Parker, Robert R. and P. A . Larkin. 1959. A concept of growth of fishes. Submitted to_£. Fish. Res. Bd. Canada. In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the'University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for f i n a n c i a l gain s h a l l not be allowed without, my written permission. Robert Ray Parker Department of Zoology  The University of B r i t i s h Columbia, Vancouver Canada. Date March 20 , 1959  V TABLE OF CONTENTS Page Abstract i i Lis t of; tables v i i Li s t of figures i x Acknowledgments x i i Introduction • . . . . . . . . 1 A concept of growth, i n fishes 4 Introduction 4 Materials 8 Mathematical derivation 11 Application 20 Discussion 33 Summary and conclusion 42 Natural mortality of chinook salmon 44 C r i t i c a l size 48 Muscular fatigue and mortality i n troll-caught Pacific salmon 54 Introduction 54 Methods and materials 58 Ocean study 58 Freshwater study 62 vii TABLE OF CONTENTS (Continued) Page Sub-mature coho i n sea water 64 Comparison of lactate of blood of heart and caudal vein 64 Blood lactate levels • , 64 Mortality 66 Recapture of. tagged f i s h 70 Adult coho i n freshwater . * 72 Ocean chinook 75 Summary of-results . 78 Discussion 79 The v a l i d i t y of size r e s t r i c t i o n for a stock of chinook 90 General summary 95 References 97 Appendix 106 v i i LIST OF TABLES Table No. Page I . L i f e history groups of steelhead and chinook used i n growth analysis 12 I I . Summary of s ta t i s t i c s re lat ive to optimum z as found by i t era t ion 21 I I I . Values of z and accompanying s ta t i s t i c s found for sub-groups of chinook 23 IV. S ta t i s t i c s leading to solution (by Alwac H I E computer) of optimum z for the .0/4 group of oMnoo*. - a • ! « 25 V. Analysis of variance on steelhead and chinook for growth differences between l i f e history groups and sexes 31 V I . Average growth (measured by a ) for groupings of steelhead and chinook showing s ignif icant differences 32 VII • Average size at age for l i f e history groups of chinook salmon, as estimated by direct proportion back calculat ion 39 VIII . Average size at ultimate annulus mean o (z = 1.3) and f i d u c i a l intervals for chinook l i f e history groups. Data from Tables VI and VII 51 v i i i LIST OF TABLES (Continued) Table No. Page IX. Average annual size-specific instantaneous growth rates and 0 . 9 5 f i d u c i a l intervals for each l i f e history type 52 X. Repeated determinations of blood lactate levels from the caudal vein and heart of each of eleven coho caught by t r o l l i n salt water 65 XI. Blood lactate levels of troll-caught coho salmon which died during post-exercise period . 67 XII. Mortality of coho salmon during post-exercise rest period 68 XIII. Blood lactate levels of coho salmon during post-exercise period i n freshwater 73 XIV. Blood lactate (mg%) of 16 troll-caught ocean chinook which were sampled more than once 77 XV. Comparison of delayed mortality observations on troll-caught salmon 81 i x LIST OP FIGURES Figure No. Page 1. Plot of 1^ + 1 on 1^ for hypothetical f i s h growing from 2 to 30 units (length) i n four years, using different exponents(z). 1. represents exponential growth 15 2. Nomograph for establishing axes i n making graph paper with 1 scales ,. 18 3 . Plot of relationship between relative standard deviation of a and t r i a l value of z for 0/4 chinook data 24 4. Plot of l t + 1 on l t and 1°*^ on l£* 6, 2/1 l i f e history group of steelhead i n freshwater 26 5. Plot of l t + 1 on l t and 1°*^ on 1°* 6, 2/2 l i f e history group of steelhead i n freshwater. . . . 26 6. Plot of l t + 1 on l t and on 1°* 6, 3/1 l i f e history group of steelhead i n freshwater. . . . 27 7. Plot of l t + 1 on l t and 1°*^ on 1°* 6, 3/2 l i f e history group of steelhead i n freshwater. . . . 27 8. Plot of l t + 1 on l t for 2/1 and 3/1 l i f e history groups of steelhead i n salt water. . . . 28 9. Plot of l t + 1 on l t for 2/2 and 3/2 l i f e history groups of steelhead i n salt water. . . . 28 X LIST OF FIGURES (Continued) Figure No. Page 10 . P l o t of l t + 1 on l t and l£*^ on l £ # ^ f o r 0/2 l i f e h i s t o r y group of chinook i n s a l t water 29 11. P l o t of l t + 1 on l t and 1 ^ on l £ # 5 f o r 0/3 l i f e h i s t o r y group of chinook i n s a l t water 29 12. P l o t of l t + 1 on l t and on l ^ * 5 f o r 0/4 l i f e h i s t o r y group of chinook i n s a l t water. . . . . . 30 13. P l o t of l t + 1 on l t and l j ' ^ on l * * 5 f o r 0/5 l i f e h i s t o r y group of chinook i n s a l t water 30 14. Two treatments of data by "Walford trans-formation" leading to d i f f e r e n t conclusions. Chinook, s a l t water. See text f o r explanation. . 40 1 5 . Length-specific average annual instantaneous growth (weight) rates of l i f e h i s t o r y groups of chinook salmon compared with zone of instantaneous n a t u r a l m o r t a l i t y rate 53 16. Coho blood l a c t a t e (expressed as mg% l a c t i c acid) response i n time from hooking 69 x i LIST OF FIGURES (Continued) Figure No. Page 1 7 . Length-specific average annual instantaneous growth (weight) rates of l i f e history groups of chinook salmon compared with zone of "size limit mortality". 92 x i i ACKNOWLEDGMENTS It i s a pleasure to acknowledge Ingvold Ask for ac-commodations and working space provided free of charge aboard his fishing vessel Scenic. Miss Anne Robertson, Research Assistant of the Department of Physiology, University of Briti s h Columbia, assisted with the bio-chemical analysis. Drs. S.W. Nash, Department of Mathematics, W.N. Holmes, C.C. Lindsey and W.A. Clemens, Department of Zoology, Uni-versity of Br i t i s h Columbia, have contributed as consultants and constructive c r i t i c s . Dr. W.E. Ricker of the Biological Board of Canada has contributed constructive c r i t i c i s m . The use of the Alwac H I E computer was provided by the National Research Council of Canada, and Messers. H. Dempster and C. Newberry were essential i n designing the programs for treat-ment of the data. Financial support for the study and oppor-tunity for procurement of data were provided by the Alaska Department of Fish and Game, Juneau, Alaska. Additional funds were provided by the National Research Coundil of Canada and the B r i t i s h Columbia El e c t r i c Company. The physiological study was made under the help and guidance of Dr. E.C. Black, Department of Physiology, University of B r i t i s h Columbia. The synthesis of physiology and populations dynamics iixto the solution of the main theme of this thesis was done at the sug-gestion of and under the direction of Dr. P.A. Larkin, Director of the Institute of Fisheries, University of B r i t i s h Columbia. GROWTH AND MORTALITY IN RELATION TO MAXIMUM YIELD IN POUNDS OF CHINOOK SALMON (Oncorhynchus.tshawytscha) INTRODUCTION The theory of size limits has been discussed by Allen (1953, 1954), Ricker (194-5), and Beverton and Holt (1957) and applications of this theory by regulation to maximize the yie l d of various populations of fishes have been explored. The population models used portray a population structure i n which a year class, f u l l y recruited to the fishable stock, i s subjected to an approximately constant natural mortality rate while growth rate i s a declining function of, age... It ,is shown that a c r i t i c a l size results from these two rates, defined by Ricker (1958, p.209) as "•' . . . the size at which the instan-taneous rates of growth and natural mortality are equal. At that time and size the year class has i t s maximum bulk". Ricker (194-5, 1958) presents arguments for maximising y i e l d by a minimum size regulation consistent with a given rate of fishing where fishing starts prior to attainment of c r i t i c a l size i n l i e u of the a b i l i t y of a fishery to crop a year class instantaneously. Life history events of chinook salmon, how-ever, exclude this species from such a simple model. Chinook are anadromous, and any particular race i s widely distributed i n the marine environment (Milne, 1957, Parker and Kirkness, 2 1956; Kauffman, 1951; Fry and Hughes, 1951; Neaye, 1951). During the immature stage some fraction of the population i s susceptible to present fishing methods. Year classes are re-cruited annually, thus f i s h of a l l sizes and ages may be present. With approaching maturity members of each particu-lar race migrate from oceanic feeding grounds to the an-cestral r i v e r and thus become increasingly concentrated and vulnerable to fishing, particularly by t r o l l gear along migration routes and by g i l l net fisheries i n the river estuaries or within the river i t s e l f . Individuals die after spawning and consequently do not re-enter the fishable stock. Other features of chinook,life history further compli- \ cate their populations dynamics. Maturity may occur within any given year class at several ages. For example, entering adult runs of Taku River chinook contained f i s h of ages 1+ to 5+ years (1 to 5 scale annuli) and of length groups from 10.0 to 4-7.5 inches (Anon., 1951). A size r e s t r i c t i o n , or gear r e s t r i c t i o n designed to accomplish a maximum y i e l d should consider the spawning loss of small but mature f i s h from the fishable stock. A chinook year class, then, at f i r s t i s susceptible while immature to protracted fishing (both spatial and tempo-ral ) and then f i n a l l y to highly intensive fishing during a short period of approaching maturity. Each l i f e history type 3 i s subject to natural mortality from disease, predation, etc. while immature and then to complete mortality after spawning. Thus a population model must either consider l i f e history types separately or include appropriate methods of weighting. While a l l elements necessary to construct a population model are not at present known, certain questions can be discussed and answered from somewhat less complete infor-mation. C r i t i c a l size for each l i f e history type may be determined from natural mortality and growth rates, and, from knowledge of c r i t i c a l size, methods of fishing to produce maximum y i e l d may be deduced. While chinook are used i n the present study, other species of Oneorhynchus show simil a r i t y to varying degrees i n respect to l i f e history events. Any general conclusions regarding management principles gained from a study of chinook may be of value i n considering these other related types,. The questions of c r i t i c a l size and maximum y i e l d are in themselves important i n view of present oceanic salmon fisheries ( Anon., 1957) a n d the desire to enter these fisheries expressed by North American fishermen. The determi-nation of c r i t i c a l size and i t s application i n management constitutes the main objective of this thesis. Material for each phase of the study has been organized and presented separately. 4-A. A CONCEPT OF GROWTH IN FISHES 1 INTRODUCTION Prediction of growth i n natural populations of fishes i s an important facet of many applied problems of fisheries management. It might be expected that age would be an ade-quate c r i t e r i o n of size and growth potential. However, i t is well known that growth rates of fishes are influenced by environmental conditions such as f o o d abundance and popu-latio n . Age i s thus only a reliable index of size or growth rate i n re l a t i v e l y constant environments. However, even under a given set of physical conditions opportunity for growth of the individual f i s h may not be, related to age. Brown (194-6), Stringer and Hoar (1955), Newman (1956), and Kalleberg (1958) describe size hierarchies i n groups of fishes which might influence their growth rates. Larkin, Terpenning and Parker (1957) suggest that size, rather than age, gives a better indication of ecological opportunity for growth i n rainbow trout (Salmo gairdnerii). They also suggest size "thresholds" which, when crossed, provide the individual with new growth opportunities. Parker, R.R. and P.A.Larkin. 1959. A concept of growth i n fishes. Submitted to J. Fish. Res. Bd. Canada.> Feb. 1959. 5 Physiologists have long recognized that size i s the "better c r i t e r i o n of physiological opportunity for growth. Brody (1937. 194-5) indicates that chronological age may not re f l e c t physiological age. Ptitter (1920), Brody (1945) and yon Bertalanffy (1938) developed growth equations i n which size and the difference between size and an "ultimate size" determines the growth rate. These equations have been applied to studies of natural populations of f i s h (Beverton and Holt, 1957). However, there are instances i n which growth of fishes i s not adequately described by these systems (Ricker, 1958). Some f i s h do not appear to be growing to an "ultimate size". Many species may change their ecological niche as they grow larger, thus revising the "ultimate size" to which they are growing (Larkin, Terpenning and Parker, 1957). Many species of salmonoids undergo marked physiological transformations (Hoar, 1939, 1957; Hoar and B e l l , 1950; Green, 1926; Mislin, 194-1) at different periods of their l i f e history and these transformations may also be related to a size "threshold" (Aim, 1949; Elson, 1957; Parry, 1958). Growth of f i s h may thus be visualized as a series of growth stanzas (Brody, 1945) which are entered by ecological and physiological size thresholds, and within which size i s the basic determinant of both ecological and physiological opportunity for growth. 6 The question of mathematical technique for de-scribing growth i s highly controversial. Arbitrary curve f i t t i n g may result i n growth equations which combine dis-similar growth stanzas, thus "smooth out" important aspects of growth processes. Within each growth stanza, curves of "best f i t " may result i n growth equations i n which the con-stants have no biological meaning or at best are of vague and complex significance (Gray, 1 9 2 9 ) . Alternatively, i f equations are used which have been derived from physiolo-gical premises (and for which presumably the constants have physiological meaning) there i s the r i s k that empirically determined values of these constants w i l l r e f l e c t the combi-nation of physiological processes with other factors i n f l u -encing growth i n natural environments, hence w i l l not actu-a l l y describe accurately the physiological processes from which they were deduced.. Under such circumstances i t would seem appropriate to choose a method of depicting growth which £ 1 ) summarizes the complex of interacting factors i n each stage of growth into a minimum number,of constants which reflect the combined effects of both ecological and physiolo-gical factors, ( 2 ) chooses as a basic premise the widely ac-cepted view that size i s the major correlate of growth. Assuming that size i s the basic correlate of growth the " simplest mathematical expression to describe growth would be: dw/dt = f(w) . . (A.l) 7 where growth rate (weight/time) i s some function of weight attained. A widely used f i r s t approximation containing one- v a r i -able i s : dw/dt = kw . (A . 2 ) i . e . ,r exponential growth as derived from.Minot's (1891) growth equation by Brody. ( 1927) . Since growth i n weight i s rarely observed to be exponential, a modified function i n -volving two variables i s : dw/dt = kwx , (A.3) where k establishes the coordinates of,the system and x i s a fractional exponent of weight less than unity. This type of equation appears a particularly suitable choice because i t parallels empirical description of the re-lationship between weight and various physiological processes. In these instances also, the mechanisms involved may be com-plex and incompletely understood but the mathematical ex-pression adequately describes the end result. For example, i t has been abundantly demonstrated (Brody, 194-5; Adolph, 194-9) for mammals that standardized physiological rates are size-specific and can be adequately represented by the para-bolic equation: dE/dt = Awx (A.3a) where dR/dt denotes a physiological rate and A i s a pro-portion constant. Why equation (A.3a) should adequately 8 represent so many "body functions i s not understood (Weymouth, Fieldv and Kleiber, 1942; Pirozynski and von Bertalanffy, 1951; von Bertalanffy and Pirozynski, 1953; von Bertalanffy and Estwick, 1953, 1954) hut i s well established as empirical fact through many observations. As far as i s known, equation (A.3a) describes physiological rates for f i s h , v i z . oxygen uptake at standard resting and active conditions (Pry, 1957; Job, 1955), oxygen uptake being interpreted to indicate meta-bolic rate. The\present study has as a main objective the de-scription of growth of fishes, using the theoretical premise that growth rate may also be described by a parabolic equation. This p o s s i b i l i t y has apparently not been previously explored. MATERIALS Steelhead trout (Salmo gairdnerii), the anadromous form of rainbow trout, and chinook salmon (Oneorhynchus  tshawytscha), offer an opportunity for study of the growth problem. They have highly variable l i f e histories (Maher and Larkin, 1955; Parker and Kirkness, 1956; see Wilimovsky and Freihofer, 1957, for entrance to literature on chinook), and show greatly differing growth rates i n their freshwater and marine environments. Accordingly, f i s h of several ages and l i f e history patterns but of the same size can be com-pared i n similar environments at the same time. 9 Material for this study was selected from data de-2 scribed for Chilliwack River steelhead by Maher and Larkin (1955) and for chinook salmon^ by Parker and Kirkness (1956). It i s noted that steelhead used were a l l mature. The chinook sample contained some immature specimens; however, the sample as a whole was calculated to include more than 80 percent of f i s h i n their ultimate year of l i f e (Parker and Kirkness, 1956), and were of mixed r a c i a l origin. A l l o r i g i -nal measurements were i n inches fork length. Length at previous age was estimated from scale measurements by direct proportion. For steelhead dorso-ventral diameters of scale and scale annuli were used. The use of direct proportion back calculation seemed j u s t i f i e d for this species from the,findings of Smith (1955) and of Mottley (1942). Direct proportion between fork length and anterior r a d i i of, scale and scale annuli was assumed for chinook. Pre-liminary examination of this assumption was made using a sample of 93 chinook selected to provide maximum range i n size (18.5 to 41.0 inches). The equation Y = ax b was f i t t e d to the regression of anterior scale radius (Y) on the fork length (x). In log form the regression was obviously linear, with 2 ; A tributary of the Fraser River 60 miles above salt water, i n Br i t i s h Columbia. ^Of mixed origin caught by commercial t r o l l off the coast of.Southeastern Alaska between Sitka and Cross Sound, 57 to 58° N Lat. 10 slope b = 0.9731, SJ = 18.0863 X 10 . If b i s tested against unity, t = 0.63, d . f . 9 1 , 0.6 > P > 0.5. Accordingly, the use of direct proportion for back calculat ing length, at age of chinook,xannot introduce serious error. A l l data were selected to conform to the following c r i t e r i a : 1. Scale margins were c l ear ly defined, showing no apparent resorption associated with sexual maturity. 2. Steelhead used were "f irst spawners", eliminating any error i n back calculat ion from scale resorption of a previous spawning. 3. Steelhead had gone to sea during the early spring. The " f a l l migrants" of Maher and Larkin were eliminated. Freshwater growth of chinook was not considered i n the present analysis . 4. Scales used were regularly shaped and without apparent previous damage or regenerated parts . 5. A l l individuals completed the last annulus i n the 1949 or 1950 growth year. A growth year i s here defined as that portion of l i f e history bounded by the completion of two adjoining annul i . 6. Growth i n the year of maturity i s not considered i n the present analysis . 7. Chinook used were res tr ic ted to the "ocean type".(Fraser, 1917; Rich, 1925), i . e . those f i s h that migrated to the 11 sea "before the formation of the f i r s t annulus. The " l i f e history type" or combination of freshwater and salt water annuli on the scales of each f i s h i s indicated as, for example, 1/3, which denotes one annulus i n freshwater and three i n salt water, etc. Table I presents the data used i n the present study grouped according to sex (steelhead) and l i f e history types. MATHEMATICAL DERIVATION The basic relationship describing growth i n mass i s taken as: dw/dt = kw" x (A .3) Integrating: w. w"x dw = k / dt 0 and: w. (1-x) - (1-x) kt + w r(l-x) 0 U - 4 ) t Since there i s no knowledge of size except at the com-pletion of each annulus, t must be considered i n whole units of one year each. If we set t = 1, i . e . , only consider growth 12 Table I. L i f e history of steelhead and chinook used i n growth analysis. L i f e history Sex Total number type of f i s h d* 9 2/1 20 21 41 ;teelhead 2 / 2 2 1 51. 52. 3/1 22 25 47 3/2 4 8 12 Total 67 85 152 0/2 27 Chinook ° / 5 " 150 ^ 0/4 60 0/5 8 Total 245 13 from time t to t+1, the relationship becomes a regression of w^^x^ on w^1~x\ with intercept k(l-x) and slope always equal to unity, thus: w t i l x ) = k ( 1 - x > + w t 1 _ x ) ( j U 5 ) Equation (A.5) holds for a l l values of w^  without regard to absolute age. Assuming the weight length relationship to be ade-quately described by the expression: w = q l y (A. 6) and substituting for w i n (A . 5 ) the general equation i n terms of length becomes: which may be further simplified to: ! t + l • a - t . l f (A.8) where, for convenience: andi z = y(l-x) 14 Thus a i s an : abstract constant unit expressing annual growth in length when the length axes are adjusted by the exponent z. Graphically, i f i s plotted on the ordinate and 1^ on the abscissa, points formed from a length progression 1^, l£, 1^, etc. w i l l l i e a distance above a 45° diagonal originating at 0,0. Thus, a expresses length increment i n a manner which i s comparable regardless of size or age. It has the same u t i l i t y as instantaneous relative growth rate would have i n the case of an animal growing exponentially (equation (A.2)). Some characteristic curves (for relationships charac-terized by values of z = 0.5, 1.0, 1.5) axe plotted on un-5 1 5 modified axes i n Figure 1. Two of the curves, \ " and 1 # > represent extremes that have been met with. Thus, i n plotting against l ^ , i f the trend appears to diverge from the 4-5° diagonal, the value of z probably l i e s between 0.5 and 1.0. Conversely, i f the data appear to approach the 4-5° diagonal, z i s l i k e l y to l i e between 1.0 and 1.5. If the data appear linear and p a r a l l e l to the diagonal, the value of z w i l l be close to 1. Assuming no progressive change i n shape Exponential growth (Brody,1927, 1945) i s a. limiting case of (A.3) where dw/d-T = kw x = 1 and the axes are transformed by logarithms. 15 32 0 4 8 12 16 20 24 Figure 1. Plot of 1^ + 1 on 1^ for hypothetical f i s h growing from 2 to 30 units (length) i n four years, using different exponents (z). 1. represents exponential growth. 16 (isometry) weight may "be described by the equation: w - q l ' - 0 and the corresponding diff e r e n t i a l s for growth are as follows: z « 0 . 5 , dw/dt = kw 5 / 6 z = 1 .0 , dw/dt * kw2^5 z = 1 .5 , dw/dt = kw1/2. Since i n (A.8) both a and z are presumably unknown,, z i s found using t r i a l values and seeking a minimum relative 5 variance of oL . If a computer i s unavailable the tedium of determining z may be considerably reduced i n the following manner. Length at previous age data C-i^., l ^ i 1^, etc*) are transformed to 1 £ 5 , l ^ 5 , l ^ 5 , etc. and l ^ * 5 , l ^ * 5 , l j * 5 , etc., giving three sets,with z values of 0 . 5 , 1 .0 , and 1 .5 , re-spectively. J?or each set compute mean a (<i) and the v a r i -2 ance (S^). The square root of the relative variance r 2 -i 2 a J 1/2 or relative standard deviation, S_, was found r ^An Alwac H I E computer was used. The program i s on f i l e at the Computing Centre, university of Br i t i s h Columbia, Canada. Copies may be obtained upon request. 17 to.be related to z approximately as a quadratic function: p B S ^ J a + bz + cz (A.9). Having three sets of values of S-^  and z, (A.9) can be solved using simultaneous equations. Optimum z (the value of z giving minimum relative variance) i s obtained when the de-rivative of (A.9) i s zero, thus: 2 cz - b = 0 and z « — . . (A.10). 2c This method has given values of optimum z accurate to two places. A graphic approximation can also y i e l d usable estimates of both z and at • As stated by Brody (1945) the eye i s quite sensitive to deviations from a straight line and i f data are r e c t i f i e d by suitable alteration of the axis l i n e a r i t y w i l l be apparent. Scales for converting axis for z values of 0,1 to 2,0 are presented i n Figure 2. Graph paper can be made using these scales, length data converted to a hundred unit scale (so a l l Length values are more than one and less than 100) and plotted directly as 1^ + 1 on 1^ .. A straight l i n e f i t t e d by "eye" to the data and with a slope of 4-5° can be used to judge goodness of f i t . For best accuracy, i n l i e u of a computer, i t i s sug-18 19 gested that the treatment of data be f i r s t approached graphi-call y , then solved by use of the quadratic method, choosing two values to bracket and a third to approximate the desired optimum. With an optimum value of z the length at age data are then converted to 1^, l | , 1^, etc. Significance of d i f f e r -ences i n growth between any desired grouping or populations can then be decided using analysis of variance on the o values for individual f i s h . Certain precautions are necessary when determining z for any group of data. When 1^.+^ i s plotted against 1^ a single point, representing growth as distance above the 4-5° diagonal i s obtained. At optimum z growth i s given as , an abstract unit, which i s an appropriate s t a t i s t i c for a l l sizes and/or ages provided the assumption of constant en-vironmental and physiological conditions i s approximated. However, natural variation i n a b i l i t y to grow- (genotypic) as well as variation i n growth dictated by environmental opportunity and social interaction (phenotypic) i s typical of f i s h populations. To some degree fast growing individu-als and slow growing individuals maintain their relative status throughout l i f e . For any group of f i s h i n which a l l Devalues are close, i . e . , i n the same order of magnitude, the plot of points with coordinates 1. , 1. n w i l l be biased 20 i f the relative size position of f i s h i n a population tends to remain stationary. Under these conditions a fast growing member i s always larger, and the resulting line w i l l have a steeper slope than the average growth of the group warrants. This error may be visualized from a consideration of Figures 4,5,8, and 10. For this reason z has been determined only from series of lengths containing three or more successive values for each f i s h (two or more complete growth years). In the foregoing treatment, a l l of the variation i n a sample has been ascribed to a . z was treated as an inde-pendent variable, determined without error, thus f a c i l i t a t i n g direct comparison of growth rates without regard to size or age, provided average growth i n the compared groups i s ade-quately described by the same z value. The v a r i a b i l i t y of z values i s further explored i n the following section. APPLICATION Optimum z was determined for the freshwater phase of l i f e history for the 5/1 steelhead group (Fig. 6 ) . The 2/2 group was used to compute z for steelhead i n salt water (Fig. 9 ) . For chinook, z was independently computed for the 0/3, 0/4, and 0/5 groups (Fig. 11-13). Table II summarizes the s t a t i s t i c a l results. To gain some appreciation of the v a r i a b i l i t y of z, two Table II. Summary of s t a t i s t i c s relative to optimum z as found by iteration. Species Li f e history Number of z "Mean" Variance Relative type f i s h difference s 2 OL variance 5. S 2/a 2 Steelhead 3/1 47 0.59 0.69536 0.0374-9 0.07752 2/2 52 1.00 11.14231 3.59302 0.02894 0/3 150 1.32 31.64658 30.59787 0.03055 Chinook 0/4 60 1.30 27.57002 28.54040 0.03755 0/5 8 1.11 12.56085 8.58274 0.05440 22 of the chinook groups were subdivided. For the 0/4 group (60 fish) the f i r s t and last 30,were treated separately. For the 0/3 group (150 fish) the f i r s t 30, second 31,. t h i r d 43, and remaining 46 f i s h were treated separately. The pertinent s t a t i s t i c s are presented i n Table III. z i s observed to vary between 1.25 to 1.46 when calculated from sub-groups of ap-parently random c l a s s i f i c a t i o n . The parabolic relationship between values of z and- the relative standard deviation of <x are demonstrated i n Figure 3, the 0/4 chinook group was used i n this example (Table IV). Optimum z l i e s close to 1.3. A parabolic solution gave z = 1.33. From Figure 3, a change of .05 i n either direction from optimum z i s seen to effect a change of only approxi-mately 0.001 i n relative standard deviation. Thus the at-tachment of significance beyond the f i r s t decimal place i n z i s unarranted. Accordingly, the entire data (Table I) were treated as follows: Pi fi Steelhead, freshwater, 1^ +T_ = A + Steelhead, marine, ^t+l = a + ^ t 1.3 _ „ . -.1.3 2 i Z n Z Chinook, marine, ^t+l ~ a + "*"t Values of 1 , lzy i , etc. and oc-^ , a23» e - f c c» were computed for each individual. These transformations are presented. 23 Table III . Values of z and accompanying s t a t i s t i c s found for sub-group of chinook. Sub-group Number of z a n S a 2 2 3 / a f i s h 0/4 30 1.36 36.14174 33.35864 0.02550 30 1.26 24.17668 27.27589 0.04666 43 1.42 43.60381 52.53047, 0.02763 . 0/3 46 1.25 24.26675, 16.95653 0.02879 30 1.30 31.19169 35.49098 0.03648 31 1.46 53.29454 78.56134- 0.02766 Table IV. Sta t i s t i c s leading to solution (by Alwac H I E computer) of optimum z for the 0/4 group of chinook, Xt+I = a + lz z a s 2 • a, •-• (S/a) 2 S/a 1.00000 8.75056 4.15228 O.05423 0.23287 ' 0.50000 1.04882 0.18507 0.16824 0.41017 I.5OOOO 57.65691 14-5.3,5886 O.04373 0.20912 1.25000 22.79004 19.75700 0.03804 0.19504 1.37500 36.34871 50.71640 0.03839 0.19593 1.31250 28.80405 31.16188 0.03756( 0.19380 1.28125 25.62648 24.71367 0.03763 0.19398 1.29688 2747020 27.7234-2. 0.03755 0.19378 1.30469 27.97554 , 29.38511 0.03755 0.19378 1.30078 27.50020 28.54040 6.03755 0.19378 Figure 3. Plot of relationship between relative standard deviation of a and t r i a l value of z for 0/4 chinook data. 25 graphically for each major grouping of f i s h i n Figures 4 - 1 5 . Differences between a. values for l i f e history groups and sexes were tested by analysis of variance, with appropriate correction for disproportionality i n sample size (Snedecor, 1946). Results are presented i n Tables V and VI. From these results the following conclusions for steel-head may be drawn: 1. In freshwater, male and female steelhead grow at approxi-mately the same rate. In salt water males grow s i g n i f i -cantly faster than females. 2. Growth rate i s inversely related to eventual l i f e history events i n both fresh and salt water. Slow-growing steel-head f a i l e d to become smolts at completion of the second growth year and remained an additional year i n freshwater. Fast-growing individuals migrated at the completion of the second growth year. 5. In salt water, the two freshwater growth groups further subdivided into fast and slow-growing fractions. The faster-growing fraction of the former slow-growing group matured following the f i r s t ocean growth'year. The slow-growing fraction matured after two ocean growth years. The same subdivision took place i n the freshwater fast-growing group. These results are i n part substantiated by observations of Aim (1949) and by Elson (1957) for Salmo salar. and of Parry (1958) for S. salar, S. trutta, and S. gairdnerii. 26 10.0 8.0 6.0 4.0 2 0 0 o o o o 08 o o o o 40 _ o 0 o 4.0 J " 3.0 2.0 o < °° / ' o / Oj / •>/ ° / o / ° 0 yf i O / o co o %° 7 2 0 A 4.0 6.0 2.0 3.0 Figure 4-. Plot of , 1 ^ on l t and 1 ° ^ o n l j ' 6 - , 2/1 l i f e history group/of steelhead i n freshwater, 10.0 8.0 6.0 4.0 2.0 o o 0 o o o oo o o 8 o ° o o / ° o , t ? o o o o o&> 0 o 20 4.0 6.0 A Figure 5 r Plot,of l t + 1 on 1^ and 1 ° ' ^ on I 0 / 6 , 2/2 l i f e history group of steelhead i n freshwater. 27 10.0 / 8.0 6.0 4.0 2.0 o o ° 0 o 3 o o 0 o j j O o r P /? ft ° o o o o ° 0 ° o o o o o o o Q ° ° 8 o o e c° °o° c?o°t> * O o * 0 o / 1 / O / n o o 2.0 40 6.0 0 1.0 2.0 3.0 ' A' Figure 6. Plot of l t + 1 on l t and on 1 ° * 6 , 3/1 l i f e history group of steelhead i n freshwater. 10.0 A. 80 60 4.0 2.0 6 o ° > o o o . <p ° o CO o / o 3 ° / o / o / 2.0 4.0 6.0 A A' lo 3/2 l i f e history group of steelhead, i n freshwater. Figure 7. P t of l t + 1 on 1 and 1°*^ on l£' 6, 28 35 h i 30 25 20 c CD ° O % ° y O o 2/l 35 4 25 20 o c 7§ ° ><8feo 10 It 20 o- 20 i f Figure 8. Plot,of l t + 1 on l t for 2/1 and 3/1 l i f e history groups of steelhead i n salt water. 35 k i 30 25 20 o c ° o o 0 o o ° Vo ° o / ° ° ° 8 / 0 ° °6 c r 2/2 35 1*1 30 25 20 ° V s o / 0 / o o o °/ O •o o o 3/2 20 10 4 -4 20 Figure 9. Plot of l t + 1 on l t for 2/2 and 3/2 l i f e history groups of steelhead i n salt water. 29 40 30 20 10 3 eg °8 <P o ° c o o o 10 20 30 A Figure 1G. Plot of l t + 1 on l t and l£^| on l£* 5 for 0/2 l i f e history group of chinook i n salt water. 40 30 20 o m o o o S o * 8 J T / o o ^ ^ c ? co^wT o O " ° 0 O y 10 20 30 A jr Figure 11. Plot of l t + 1 on . l t and on lj»3 for 0/3 l i f e history group of chinook i n salt water. 30 ^'U.3 t 0/4 l i f e history groups of chinook i n salt water. Figure 12. Plot of l t + 1 on l t and l j * ^ on 7 5 for 40 30 20 10 o o :u- - 0 o ... °o<*> ° o o =p / %°° o ft ° %° o / o o o o 10 20 30 A A o: 0/5 l i f e history groups of chinook i n salt water Figure 13. Plot f l t + 1 on l t and on l j ' 5 for 3 L Table V. Analysis of variance on steelhead and chinook for growth differences between l i f e history groups and sexe^s. Environment x Grouping Degrees "F" r a t i o Probability freedom Freshwater Life history 3 35.8 P <k 0.005 steelhead Sexes 1 , 0.4 -P~ > 0.250 Interaction 3 1.4 P > 0.250 Error 203 • Salt water Li f e history 3 17.4 P < 0.005 steelhead Sexes 1 9 .7 P < 0.005 , • 1 • 1 Interaction 3 0 .7 P > 0.250 , Error 208 Salt water ' Life history 3 13 .0 P < 0 .005 chinook Error 538 3? Table VI. Average growth (measured by ot ) for groupings of steelhead and chinook, showing significant differences. Environment Lif e history Mean QL type Steelhead 2/1- 1.02 (both sexes) Freshwater 2/2 0.90 z = 0.6 3/1 0.73 3/2 0.65 Steelhead o* 9 Salt water 2/1, 13.63 13.34 z = 1.0 2/2 11.73 10.75 3/1 13.05 12.54 3/2 12.20 10.68 Chinook .0/2 34.10 (both sexes) Salt water 0/3 29.82 z = 1.3 0/4 27.49 0/5 25.89 33 For chinook salmon, "both sexes were lumped. As i n the steel-head i n salt water, the fastest growing f i s h matured at the earliest age. DISCUSSION Growth of steelhead and chinook has been described using the basic premise that gtowth rate (dw/dt) increases ! proportionally to weight raised to a power (w , where x varies between 0 . 5 and 1 . 5 approximately). No experimental evidence has been offered to j u s t i f y the use of this relationship, how-ever empirical growth data for those species considered were approximately linear after transformation by a suitable choice of the length exponent z . In this manner these data are ade-quately described by the hypothesis. Equation (A.3) has analo-gy with empirical expressions of other physiological rates, summarized as equation (A.4). Adolph ( 1 9 4 - 9 ) l i s t e d 33 physi-ological rates ( O 2 uptake, -Hg excretion, ventilation, etc.) that appear (for mammals) adequately described by the general equation (A.4), i . e . that the rates are proportional to w . Zeuthen ( 1 9 5 3 ) and Weymouth, et a l . ( 1 ° A 2 ) extended these ob-servations to respiration of various individual organs. This parallelism underlines the coordinated aspect of a l i v i n g system (Haldane, 1 9 3 6 ) . Various physiological rates are not independent but correlated. That growth rate i s also part of the correlated system appears to be a tenable hypothesis. Barrett (Fry, 1 9 5 7 ) demonstrated for rainbow trout ( 5 - 7 5 34 grammes) i n freshwater and under standard conditions that the rate of O2 consumption increases i n proportion to wx ~ It was shown.in a previous section that juvenile steelhead i n freshwater grew proportional to l z " Q , ^ # Assuming that weight 5 - 6 i s proportional to 1 , then growth rate i n terms of weight 3C—O ft was proportional to w " * , This similarity of exponents suggests the p o s s i b i l i t y that values of x or z for growth equations may be derived from a comparative study of standard metabolic rate over a range of sizes. Data are not at present available to make such a comparison. The phenomenon of 'stanzas" i s characteristic both of metabolic rates and growth rates. Anadromous salmon and trout experience at least two rather abrupt physiological transfor-mations (Hoar, 1939, 1957; Hoar and B e l l , 1950:.; Green, 1926), one at parr-smolt transformation, the other at maturity. While published data.have not been found describing,.^ he re-lation of standard metabolic rate to weight for f i s h i n each stage of l i f e history, certain analogies may be drawn from other groups of animals. For mammals, Brody (1945) has de-scribed discontinuities or "breaks" i n weight-specific meta-bolic rate curves and he directed attention to similar breaks i n growth curves. He has suggested a direct connection be-tween metabolic rate and growth rate. Zeuthen (1953, 1955) 35 extended these observations to include several poikilotherms. Martin (194-9) has demonstrated sharp breaks i n relative growth lines for several species of f i s h and related these disconti-nuities to ossification and maturity. Hiatt (194-7) demon-strated a sharp break i n relative growth of gut length of Chanos chanos occurring at approximately 100 mm body length. Available data suggest that increase i n growth rate i s pro-portional to increase i n standard metabolic rate as measured by ©2 consumption. The exponent x may be primarily establish-ed for each growth stanza by the endocrine control system and the proportion constant k perhaps has meaning as environmental opportunity. The analogy has the limitation that growth stanzas may be delimited by ecological as well as physiologi-cal thresholds. Thus within any physiological growth stanza (within which x may be constant) there may be more than one ecological growth stanza, each characterized by a particular k, or perhaps progressive sh i f t of k from a low to a high value or vice versa. A growth equation currently popular i n fisheries science i s that of von Bertalanffy (1938, 1949, 1957). It i s equivalent to the "s e l f - i n h i b i t i n g " growth equation of Brody (1945) which is„much used on mammals; to the modified expo-nential of Croxton and Cowdan (194-6) and to the graphic trans-formation presented by Walford (194-6). Bertalanffy considers growth to be the net result of an open system of supply and demand of resources which can be metabolized. Since material 36 must enter the organism through a surface, and maintenance demand i s proportional to mass, given isometric growth the organism w i l l eventually reach a size where supply and mainte-nance demand are i n equilibrium. Bertalanffy 1s basic equation i s therefore: dw/dt « HS - kw . (A.ll ) where S denotes surface of some limiting membrane, w denotes mass, and H and k are proportion constants. With isometric growth and constant density a surface i s proportional to the square of the length while mass i s pro-portional to length cubed. Introducing equation (A.6) for mass, and le t t i n g : S.= pl? equation ( A . l l ) takes the form: dl/dt » a->31 . . (A.12) HP /, k where a = and/? = | Integrated, equation (A.12) depicts growth as a process in which f i r s t differences of a length series 1^, l£, 1^, etc. decrease by a constant percentage, i . e . on a arithmetic plot of 3-t+l against 1^, points f a l l on a line which intercepts a 4-5° diagonal with origin 0,0 (Walford, 194-6),. Bertalanffy• s equation has found practical application i n y i e l d equations by Beverton and Holt (1957). 37 There are several assumptions inherent i n von Bertal-anffy* s growth equation that need to be examined. F i r s t l y , emphasis i s placed on the "two-thirds" rule or surface rule (see Brody, 194-5) which states that standard metabolism, as measured by rate of (X, consumption, increases as the 2/3 power of weight. Brody,(194-5), Adolph (194-9), Prosser (1950), Zeuthen (1953), von Bertalanffy (1957), and others have i n d i -cated that, more accurately, metabolic rate increases approxi-mately as the 0.73 power of weight. Further, these obser^rti vations have been based on interspecific comparisons of adult animals (mouse to elephant) and do not reflect the weight specific metabolic rate of any single organism throughout l i f e . Secondly, as pointed out by Cohn and Murray (1927), there i s no reason for growth of internal surfaces to be iso-metric. Szarski et a l . (1956) have found the absorptive area of the gut of Abramis brama to grow approximately proportional-ly to the weight by means of infolding. Elust (1939, 194-0) and Al Hussaini (194-9) have demonstrated ontogenetic increase in relative gut length and/or relative absorptive surface i n cyprinids. Hiatt (194-7) demonstrated a relationship between allometric growth of the gut of Ghanos chanos and a size-specific change i n dietary habit. Price (1931) demonstrated 0 785 ) positive allometry i n growth of g i l l surfaces (G = 8.65w *' ^' of Micropterus dolomieui. It would appear to be the unusual case where a surface membrane r e s t r i c t s growth i n the manner 38 of equation (A.11). The apparent f i t of a von Bertalanffy equation or Walford line to growth data may i n some; cases he forced as a result of the method of sampling or combining the data. Aver-age lengths at the completion of an annulus for the several groups of chinook are used as an example.(Table VII). In Figure 14 these data are graphically transposed from an aver-age size at age plot (right side) to a l t + 1 on 1^ plot ( l e f t side). Two treatments have been used. The f i r s t represented by so l i d lines i n both sides of the figure, considers the l i f e history groups separately. The dashed line i n both sides of the figure represents the case where only f i s h captured i n their fourth growth year are used to compute average size at age III, etc. This l a t t e r method reflects "Lee's phenomenon" (Lee, 1920) which can be accounted for by the growth r a t e - l i f e history relationship previously demonstrated (Table V), by selectivity of the fishing gear for larger f i s h , and by shoaling of chinook according to stage of maturity (Neave,, 1951> Parker and Kirkness, 1956) or by a direct correlation between growth rate and mortality rate (Gerking, 1957). These two methods of treatment lead to diverse conclusions. By con-sidering each l i f e history group separately growth i s seen to approach parallelism with the 45° diagonal. The second treat-ment depicts growth rate as gradually decreasing and forms an approximately linear plot (Walford line) which w i l l inter-39 Table VII. Average size at age for l i f e history groups of chinook salmon, as estimated by direct proportion back calculation. Life history Number of Size at end of annulus - type f i s h 1 2 . 3 4 5 0 / l a 4 10 .9 0/2 27 9 .0 20.8 0/3 150 .7 .5 19 .1 27 .7 0/4 60 7 .0 17.4 25.5 33 .3 0/5 8 5.0 15 .1 22 .5 2 9 . 9 37.6 Sample of four f i s h captured i n t h e i r second year of l i f e , not included i n Table I or pr e v i o u s l y considered. 40 ? * 8 8 m CVJ 8 Figure 14. Two treatments of data by "Walford transformation" leading to different conclusions. Chinook;, salt water. See text for explanation. 41 cept the 4-5° diagonal. Thus the l a t t e r treatment depicts growth as a von Bertalanffy equation. In the present case the l a t t e r method leads to a serious underestimation when predicting future increment to the stock ifrom growth. Thus far, growth of the average individual of sub-groups of the population has been presented. For chinook, the von Bertalanffy equation i s shown to oversimplify and underestimate the growth of a hypothetical "average" f i s h i n the entire population. Each component group should be weighted according to i t s actual abundance i n the population, a proposition necessitating a schedule of mortality rates which are related to growth rates. Considering that approximately 95 percent of steelhead (Maher and Larkin, 1956) and substantially a l l chinook (for possible exceptions see Robertson, 1957) die at f i r s t spawning, and considering selectivity of fishing gear for larger f i s h , the relative magnitudes of growth rate and t o t a l mortality rate i n these populations are undoubtedly directly correlated (see Gerking, 1957, for comment on other species). This aspect of populations dynamics has been l i t t l e explored and presents a necessary f i e l d for study before the average growth of a population can be depicted from a consideration of growth of individuals. 4-2 SUMMARY AND CONCLUSION Growth, i n fishes has here "been visualized as a series of stanzas within each of which the growth rate i s propor-tional to a constant multiplied by a fractional power of weight, i . e . dw/dt = kwx . This approach implies that i n each growth stanza the incre-ment of weight can be related to the weight i n the same way as various physiological rates are related to weight. In both of these instances a complex of processes may be involved which are best summarized mathematically i n the r e l a t i v e l y simple parabolic equation. However, the interpretation attached to the constants k and x i s complicated i n the case of growth rate because both ecological and physiological factors act as determinants. The similarity i n x, the exponent of weight for meta-bolic rate and growth rate suggests that x measures the complex of physiological processes while k measures ecological opportunities. Whether or not this i s true does not alter the usefulness of the equation i n describing growth processes. This equation can be considered as an example of General Systems Theory approach of von Bertalanffy (1950, 1951) . In addition growth stanzas may be delimited both by ecological and by physiological thresholds. Fi n a l l y growth of the i n d i -43 vidual or Qf a group of individuals may be characterized by different values of the constants k and x, necessitating separation of a population into " l i f e history" groups, etc. These groups may be characterized by mortality rates associ-ated with their respective growth rates. The prediction of growth increment i n a population thus requires: 1. Separation into l i f e history groups (and possibly sex), each characterized by particular growth rates. 2. Determination for each group and for each growth stanza of appropriate value of the constant k for an average exponent x. 3. Determination for each group and each growth stanza of appropriate t o t a l mortality rate. 4. Summation of the increments to each group with correction for mortality. Sampling data of a population obtained through a selective fishery cannot be used per se to depict "average individual", and detailed mortality studies, as related to size and growth rate are needed. A relationship between growth rate and metabolic rate i s suggested as a means of independently establishing one basic parameter of the growth equation. These two approaches constitute profitable f i e l d s of research for agencies engaged i n fisheries management. 44 NATURAL MORTALITY OF CHINOOK SALMON The rate of natural mortality i s perhaps the most elusive parameter to determine. A widely used approach i s by the analysis of catch curves (Ricker, 1958), bub the peculiarities of the chinook l i f e history omit this method from consideration. It i s , however, possible to compute natural mortality of a chinook population using data from tagging. This method was summarily published by the author (Parker and Kirkness, 1956), but i s included here i n ex-panded form. A population of N tagged f i s h are released during the year 0. As long as these f i s h remain immature they are sub-ject to a negligable fishing rate. N Q, N ^ Ng, etc. denotes the number of f i s h tagged belonging to groups which w i l l mature during years 0,1,2, respectively, and RQ, R^ , R£, etc. denote the number of tags recovered and turned i n during the subscript years. It has been assumed that: 1. The annual expectation of death from fishing (u) i s constant, 2. annual mortality rate from natural causes (n) i s constant, and natural survival rate, denoted by s, i s s = (L-n), 3. that loss of tags from structural failure i s not pro-gressive, 45 4 . t h a t t h e n u m b e r s o f t a g s t u r n e d i n i s a c o n s t a n t f r a c t i o n ( X ) o f t h o s e t a g g e d f i s h r e c a p t u r e d , 5 . t h a t m o r t a l i t y d u e t o t a g g i n g i s c o m p l e t e w i t h i n a s h o r t t i m e o f t a g g i n g . J d e n o t e s t h e f r a c t i o n s u r v i v i n g t h i s m o r t a l i t y , 6 . t h a t n a t u r a l m o r t a l i t y r a t e i s t h e s a m e f o r t a g g e d a n d u n t a g g e d f i s h . T h e b a s i c r e l a t i o n s h i p b e t w e e n t h e t a g g e d p o p u l a t i o n , a n d r e c o v e r y o f t a g s i s d e f i n e d b y t h e e q u a t i o n : R ± = . N j J X u s 1 ( B . l ) w h e r e i d e n o t e s a n y y e a r o f m a t u r i t y a f t e r t a g g i n g . P o r t h e y e a r o f t a g g i n g ( B . l ) b e c o m e s : a Q = N Q J X u s G . . ( B . 2 ) a n d t h e s u r v i v a l t e r m b e c o m e s 1 . W h e n > t h e s t o c k m a t u r e s o v e r a s e r i e s o f y e a r s , R . E N . . J X U = e - i ( B . 3 ) s 1 a n d w h e r e , t a g r e c o v e r y e x t e n d s o v e r j y e a r s , R l R p R - i N J X u - R 0 + - ± . + - £ + . . . - 4 - ( B . 4 ) 1 2 j s s s ° 46 also: NJXu R J D = E i s ( d ~ 1 ) + R 2s ( d"" 2 ) + . . . R.jS0 . .(B.5) and: NJXu R, R ns R 0s (0-2) - . . R. = 0 .(B.6) JXu can be estimated from the recovery during year 0 of f i s h known to be mature. Appropriate data presented by Parker and Kirkness (1956) from tagging studies conducted along the coast of Southeastern Alaska are: JXu was estimated from the recovery of f i s h tagged and re-leased i n their 5th ?and 6th years of l i f e . From 215 of these f i s h tagged, 44 were recovered (42 during year 0). Thus: MM. JXu = — = .205 215 and substituting the above data i n equation (B.6) the re-lationship becomes: N = 918 918(.205) - l ioj s 3 - 55s2 -78s3 - 35s2 - l i s - 1 = 0, l i s - 1 = 0, the approximate solution of which gives: s = 0.681. 4? Since not a l l the 4+ and 5+ year old f i s h were mature, further consideration of JXu i s necessary. Following above reasoning: 1 R l JXu => ± . -± + R N s u and JXu = — • — - — + 42 = 0.209 215 0.681 which value i s substituted into equation (B.6) and the second estimate,of s i s : s = 0.659* Further i t e r a t i o n does not affect the third decimal place of s. The problem of variance of s has not been considered. It i s appreciated that a difference of one unit i n the second decimal place of JXu causes a change of approximately five units i n the second decimal place of s; thus, s i s c r i t i c a l l y affected by error i n estimating JXu. The assumptions given are also not completely s a t i s -f i e d . A small number of f i s h tagged were recaptured while yet immature. Fishing mortality rate may vary from year to year. Annual natural mortality may not be constant. No evidence of progressive tag loss has been found i n the Alaskan experiment, yet Calhoun, et a l . (1951) report high incidence of progressive tag failure (the same type tags were used) i n the California studies. As w i l l be shown i n a later section and from observations reported by Milne (1956) mor-t a l i t y from tagging- would appear to be over or negligible 48 within a few days. Perhaps the most c r i t i c a l assumption of a l l i s that tagged f i s h are representative of the untagged population. It i s at present impossible to establish the v a l i d i t y of this assumption. A l l assumptions appear to be reasonable s a t i s f i e d i n the population studied (Parker and Kirkness, 1956); however, no significance i s placed beyond the f i r s t decimal place. The best available estimate of annual natural mortality rate i s then given as i n the magni-tude of 0.5 to 0.4. The instantaneous natural mortality rate (q) i s estimated to be of the magnitude 0.36 to 0.51. C. CRITICAL SIZE For any particular l i f e history group the average size specific annual growth (length) rate i s described by the equation: ^I - A+ A • • • • <A-8> and the relationship: w » q l y also defines 1 as a function of w, thus: (A.6) 49 Substituting (C.l) into (A.8): z 7 - a + 11 , z ^t w^+1 = q y ( a + 1 Z ) , and w t + l = q ( c t + A? (C2) For a specific size subclass of a l i f e history group, the annual instantaneous relative growth rate (g) i s : g = In w. t+1 w. (C3) and: g = In q(ct + l * )z or: g = ? ln(oi +. i f ) - yln 1, (C4) Thus g i s a function of y , z , a , and l t . Since y,z, and tt are constants at any size during a particular physiological phase,within a particular l i f e history group g changes only with change i n l t , i . e . the relationship i s an "average size-50 specific instantaneous relative growth rate" as proposed by Larkin, Terpenning and Parker ( 1957 ) . Average size at the ultimate annulus, mean a and the fi d u c i a l interval of a. for each l i f e history type of chinook are presented i n Table VIII. Table IX presents size-specific empirical average values of g, and the 0 .95 f i d u c i a l inter-vals. Figure 15 graphically presents the empirical average annual instantaneous relative growth rate of each l i f e , history type as a function of size. Also included i n Figure 15 i s the zone of instantaneous natural mortality. Clearly, the total mass of each l i f e history group gains weight u n t i l the ultimate year, the only exception being the largest members of the slow-growing 0 /5 group. The 0 / 2 , 0 / 5 , and 0/4 groups mature and leave the marine en-vironment before the instantaneous growth rate decreases to equality with the instantaneous mortality rate. If\ maximum yi e l d , i n pounds of f i s h , from the sotck i s de-sired, fishing should be restricted to the maturing i n d i -viduals i n their ultimate year. If fishing i s allowed on the immature stock a dilemma arises i n choosing a size l i m i t . It i s impractical, i f not impossible, to separate the l i f e history groups while immature. Yet a size limit which would allow cropping, say the 0 /2 group, would be wasteful of the potential growth 51 Table VIII. Average size at ultimate annulus, mean ct > -1 (z = 1.3) and f i d u c i a l intervals for chinook l i f e history groups. Data from Tables VI and VII. Li f e No. Average size Mean Fiducial interval history of at ultimate ct oL-i t ^ CS-group f i s h annulus Lower Upper 0/2 27 20.8 0/3 150 27.7 0/4 60 . 33.3 0/5 8 37.6 34.10 32.06 36.14 29.82 28.98 30.66 27.49 26.11 28.87 25.89 20.34 31.44 ^Thile the variance of a was calculated using the number of observations ( i . e . number of f i s h times number of obser-vations per f i s h less one), standard error was calculated using above variance and number of f i s h . Table IX. Average annual size specific instantaneous growth rates and 0.95 f i d u c i a l intervals for each l i f e history type. Li f e history type 0/2 0/3 0/4 0/5 , j& Mean gat £ Mean ^ L Mean ^ L Mean y t g S g g 5 3.88 4.00 4.11 3.68 3-74 3.79 3.49 3.59 3.68 3.04 3.47 3.84 10 15 20 25 30 35 40 2.32 1.61 1.21 0.96 0.79 0.66 0.57 2.41 1.69 1.28 1.01 0.83 0.70 0.60 2.50 1.76 1.34 1.06 0.87 0.74 0.63 2.17 1.50 1.12 0.89 0.72 0.61 0.52 2.21 1.53 1.15 0.91 0.74 0.62 0.53 2.26 1.56 1.17 0.93 0.76 0.64 0.55 2.03 1.38 1.03 0.81 0.66 0.55 0.47 2.10 1.44 1.07 0.85 0.69 0.58 0.50 2.17 1.49 1.12 0.88 0.72 0.61 0.52 1.70 1.14 0.84 0.65 0.53 0.44 0.38 2.02 1.37 1.03 0.81 0.65 0.55 0.47 2.29 1.59 1.20 0.95 0.78 0.65 0.56 U denote lower and upper f i d u c i a l intervals 53 4.0 30 2.0 ^0/2 ^ ^ ^ ^ 4 E OF N A.TURAL MORTAL ITY P" 075 0 5 10 15 20 25 30 35 40 fork length in inches Figure 1 5 . Length-specific average annual instantaneous growth (weight) rates of l i f e history groups of chinook salmon compared with zone of instantaneous natural mortality rate. 5 4 obtainable from the older l i f e history types. The bio-logical answer appears to be the r e s t r i c t i o n of fishing to areas which do not contain appreciable quantities of immature f i s h . At present, management agencies of the P a c i f i c Coast have size limit restrictions which i n effect, prevent the landing of f i s h less than 25.0 inches fork length. It i s seen from Figure 15 that f i s h maturing at e a r l i e r ages than 2+ and some portion of the 0/3 group are excluded entirely from the catch. This loss might be offset by the gain i n weight of the older l i f e history types, depending upon their relative strength within the year class. This, of course, is dependent upon the v a l i d i t y of the assumption of no release mortality. The following section deals with the evaluation of this mortality. D. MUSCULAR FATIGUE AND MORTALITY IN TROLL CAUGHT PACIFIC SALMON 7 INTRODUCTION That f i s h die i n captivity following strenuous muscu-lar exertion has been demonstrated by several authors. Among these are von Buddenbrock (1938) working with cod ( Gadus T-'Parker, R.R., E.JG.Black, and P.A.Larkin, 1959. Fatigue and mortality i n t r o l l caught Pac i f i c salmon (Oneorhynchus). In press. J. Fish. Res. Bd. Canada. 55 morrb.ua) and dab (Platessa limanda); Secondat and Diaz (1942) with tench (Tinea tinea); Milne and Ball (1956) with coho salmon (Oncorhynchus kisutch) and later (1958) with both coho and chinook (0. tshawytscha); Black (1957c) with sockeye (0. nerka); Bates and Vinsonhaler (1957) with smolt chinook, striped bass (Roccus saxatalis), and shad (Alosa sapidissima);, Fry (1958) with coho and chinook; and Parker and Black (1959) with chinook. In every case severe muscular a c t i v i t y was followed by significant mortality. Other authors have subjected these and other species to severe fatigue and have not observed significant ensuing mortality. Included here are Black (1957a,b) working with rainbow trout (Salmo gairdnerii) and lake trout (Salvelinus  namaycush). Paulik, DeLacy and Stacy (1957) working with coho, and Paulik and DeLacy (1958) with sockeye repeatedly subjected their animals to exhaustion without resulting s i g -nificant mortality. Jensen (1958) hooked and released s a l t -water-pond-reared chinook without significant mortality. Black (1958b) has reviewed the subject of hyperactivity and death. The specific causes of mortality have not been determined. Why fatigue should i n one case lead to mortality, and i n another case, not, remains a mystery. It has been suggested by colleagues that mortality i n l i v e boxes of fatigued f i s h reported by Parker and Black 56 (1959) was caused by factors other than fatigue, v i z . un-recognized injury, psychosis from enclosure i n a small space or from handling, breaking the mucous coat, etc. Q Perhaps a summation (Brett, 1958) of these stresses i s responsible. The v a l i d i t y of extrapolating mortality obser-vations i n holding experiments to apply to f i s h caught and released after tagging, or released because of a size li m i t r e s t r i c t i o n , i s thus open to question. However, in v e s t i -gators have repeatedly shown tag recoveries of less than 30 percent for troll-caught salmon (Milne, 1957) released i n the face of a fishery known to be much more intensive. Por example, Parker and Kirkness (1956) tagged selected chinook salmon, apparently unharmed and predomi-nantly of Columbia River origin. Por f i s h i n their ultimate year recoveries were only 21 percent, yet from data of Silliman (1948, 1950) i t can be estimated that a t o t a l fishing mortality of Columbia River chinook averaged 86 per „ cent per annum over the 11 years 1935 to 1945. & t o t a l non-fishing mortality (or tag loss which was known to be minimal) of over 70 percent i s necessary to account for this d i f f e r -ence. Parker and Kirkness (1956) estimated average annual natural mortality to be approximately 34 percent. Thus, a The word stress i s used i n this paper meaning any trauma and does not imply change i n anterior pituitary-interrenal activity, although this may be involved. 57 mortality i n excess of 45 percent remains unaccounted for by this rough approximation. Sedondat and Diaz (1942) reported that blood lactate concentrations of tench increased following forced a c t i v i t y but usually subsided by the end of six hours. They also ob-served that some f i s h died and blood lactate levels of these had f a i l e d to decrease. Black (1955, 1957a,b,c) demonstrated a similar response for several species of salmonids; i n generi al,.blood lactate levels continued to increase during post-exercise rest periods, and peak values were attained during the second or third hour of post-exercise rest. Blood lactate levels then decreased at a decelerating rate. Eesting levels were not attained before 12 hours. This sequence i s termed "typical response". Black (1957c) suspected a correlation between death and concentration of blood lactate, but lacked sufficient data for a conclusive demonstration. Parker and Black (1959), working with troll-caught chinook, demonstrated a positive association between blood lactate levels and death. While high blood lactate levels have not been shown to be a primary cause of death, they are a significant correlate of death following hyperactivity. It i s the purpose of this experiment to extend these observations to include coho salmon, to further explore the significance of death as related to hyperactivity, and to 58 examine the problem i n both salt and freshwater environments. METHODS AND MATERIALS Ocean Study Pish were obtained aboard a commercial t r o l l e r oper-ating i n the Gulf of Alaska i n 1958. During July fishing was i n the v i c i n i t y of the coast at Cross Sound (Lat. 58°N) and i n August i n the v i c i n i t y of Middleton Island (Lat. 60°N, Long. 147°W). Either four or six lines were used (depending upon the distance off shore) and from eight to twelve lures per l i n e . Lures were changed often and no general statement can be made of make and type. Hook size ranged from No. 6 to No. 8. Time, place and manner of fishing were at the dis-cretion of the Captain. Captured f i s h were l i f t e d aboard by the lure and placed i n a preliminary bath of sea water where the hook was carefully removed. Fish showing damage to v i t a l parts or heavy bleeding were excluded from further consideration ex-cept to obtain blood samples from specimens without post-exercise rest. A l l non - c r i t i c a l l y damaged f i s h were tagged at the origin of the dorsal f i n , using standard Petersen type tags with 5/8 inch red baffles and pure nickel pins. Fish to be retained i n captivity were transferred to a li v e box measuring 28 1/4 by 44 1/4 inches (72 X 112 cm) 59 inside horizontally and 25 1/2 inches (60 cm) between top and bottom. Access to the inside was through a 12 by 12 inch (30 cm square) chimney, eight inches (20 cm) high and f i t t e d with a removable cover. Water was introduced under pressure at the bottom and expelled through holes d r i l l e d i n the top panel. The water level was approximately four inches (10 cm) i n the chimney, which prevented sloshing or surge ihi the main box. Two identical boxes were used, and each was supplied with fresh sea water at a rate of approximately ten U.S. gallons (39 l i t r e s ) per minute. The top was f i t t e d with a 12 by 12 inch plexiglass panel through which f i s h could be observed. A maximum of four f i s h or less than 4-0 pounds (18 kg) of f i s h was held i n a live box at any one time. Fish which died i n the l i v e box were removed with a small gaff and a blood sample taken. Cessation of respira-tory movement was used as a c r i t e r i o n of death. Fish were under more or less constant observation and blood samples were obtained before rigor mortis. Survivors were l i b e r -ated without taking a blood sample. To do thi s , the water supply to the liv e box was cut off and contents drawn down , to approximately 50 U.S. gallons (190 l i t r e s ) . A sedative (Tricane methane sulfonate, MS222 Sandoz) was introduced into the water, and as soon as f i s h became disorientated they were removed by means of a polyethylene bucket and liberated. This method of release was unsatisfactory because (a) f i s h 60 were unable to orient themselves f o r some minutes u n t i l the e f f e c t s of the sedative wore of f and (b) f i s h i n l i v e boxes one-third f u l l were subject to severe sloshing, depending upon the state of the sea (seldom smooth). With the equipment at hand, however, the a l t e r n a t i v e of subjecting them to chase and s t r u g g l i n g i n a dip net appeared to be even l e s s s a t i s f a c t o r y . 'One m i l l i l i t r e or l e s s of blood was drawn r o u t i n e l y from the caudal v e i n . In some instances samples were also drawn from the heart. Blood was drawn int o a 2-ml Luer syringe coated with mineral o i l and r i n s e d with heparin s o l u t i o n . The sample was immediately expelled i n t o a poly-ethylene b o t t l e containing 9 ml of 10% t r i c h l o r a c e t i c a c i d . This mixture was then f i l t e r e d and the f i l t r a t e stored i n a second polyethylene b o t t l e u n t i l chemical a n a l y s i s . These samples were taken to the laboratory at the U n i v e r s i t y of B r i t i s h Columbia and analysed f o r l a c t i c a c i d by the method of Barker and Summers on (Hawk, Oser and Summerson, 194-9). Values of blood l a c t a t e are reported as milligrammes l a c t i c a c i d per 100 m i l l i l i t r e s of whole blood (mg%) and expressed to three i n t e g e r s . The true value, as determined from analysis of several t r i p l i c a t e d determinations, i s considered to be within a range of plus or minus 10 mg%. Live box sea water was drawn from a depth of approxi-61 mately 1.5 metres and was between 1 3 ° and 1 5 ° C. Fishing ranged over depths from 20 to 100 metres. Salmon were taken at a l l depths, but coho more frequently above a depth of 30 metres and i n water ranging from 1 0 ° upward, while chinook were more frequently below 30 metres and at 7-10°C. Reliable temperature data could not be taken for individual f i s h and the significance of temperature changes cannot be evaluated. Fish used were feeding coho and chinook. Coho were in their ultimate year but not showing sexual dimorphism typical of the species at maturity. Gonad examination showed signs of approaching maturity and tagging showed f a i r l y rapid subsequent movement into inside waters. Chinook used were probably either i n their ultimate or penultimate year of l i f e . Fish were disturbed as l i t t l e as possible during the rest period; Design of the l i v e boxes eliminated sloshing due to vessel motion, but vibration from the propulsion engine was present. When f i r s t placed i n the l i v e box, f i s h would generally swim about but quickly assumed and maintained a position. Some f i s h f a i l e d to maintain equilibrium and remained upside down either at the surface or bottom. This condition usually appeared after 15-30 minutes although a few individuals turned over when f i r s t placed i n the liv e 62 box. Some f i s h righted themselves after varying amounts of rest, others f a i l e d entirely to do so. These observations are similar to those made by Brett et al . ( 1 9 5 8 ) on fatigued juvenile sockeye and coho i n freshwater, and by Parker and Black (1959) on sub-adult chinook i n sea water. An attempt was made to determine the amount of time each f i s h spent on the t r o l l gear, but was largely unsuc-cessful, either because of failure to observe the strike or i n a b i l i t y to discriminate between several f i s h caught on the same l i n e . Prom the rel i a b l e data available, coho were on the gear for an approximate average of five minutes, and the time varied from less than two to more than 25 minutes. Coho were of a f a i r l y uniform size, averaging eight pounds (3.6 kg) and varying from six to ten pounds (2.7 to 4.5 kg). Chinook used varied between eight and 20 pounds ( 3 . 6 to 9.1 kg). Freshwater Study In September the l i v e boxes and equipment were taken to the Canyon Island Research Station 17 miles above salt water on Taku River, Alaska. Upstream migrating adult coho were captured by a fish-wheel (Anon., 1953) and used as test animals. These f i s h were of the same size range as those used i n the ocean study, were non-feeding, i n an advanced stage of sexual dimorphism, and were i n freshwater. The 63 l i v e boxes were set up on the pontoons of the fish-wheel and river water pumped at approximately the same rate as i n the previous experiment at sea. A pole was fixed to overhang the stream and standard t r o l l gear with a 20-pound (9«1 kg) weight attached. This device was used to simulate the action of t r o l l gear towed through the water. Stream velocity was approximately equivalent to t r o l l i n g speed. Fish were dip-netted from holding tanks, a hook was inserted from inside the mouth through the membranes and tissue posterior to the maxillary, and the f i s h was then released into the riv e r attached to the t r o l l gear. After intervals from less than one and up to 30 minutes on the t r o l l gear f i s h were landed by the lure and placed i n a preliminary water, bath containing sedative. Here the hook was removed, the f i s h tagged, and then placed i n a l i v e box. A maximum of six f i s h or 60 pounds (27 kg) was placed i n each box. Groups were anaes-thetized and removed from the l i v e boxes after post-exercise rest periods over a range of zero to 52 hours, and a blood sample was taken by caudal vein puncture. Sampled f i s h were further observed u n t i l recovery from the anaesthetic and then released into the r i v e r . A control group was dip-netted from the tanks directly into the sedative bath and sampled. Other aspects of the experiment were identical with the ocean study. 64 SUB-MATURE COHO IN SEA WATER Comparison, of Lactate of Blood of Heart and Caudal Vein Blood was drawn from both, the caudal vein and the heart of 11 coho to f a c i l i t a t e comparison between the present experiment and those of Black (1957c) and Parker and Black (1959). Three determinations were made on each sample and values of heart and caudal vein blood lactate compared. Table X gives the results of the determinations. Caudal vein blood lactate levels were sig n i f i c a n t l y lower than heart blood lactate levels i n the seven f i s h sampled immediately after catching (P = 9.01; d.f. 1, 6; 0.01>P>0.025). In the four f i s h sampled after one to five hours of rest caudal levels were s l i g h t l y higher than heart levels but differences were not significant (F =,2.13; d.f. 1, 3; 0.10>P>0.25). Thus the degree of blood lactate response may appear greater in the coho than reported for sockeye and chinook, but the anomaly may be due to the anatomical sampling location. Blood Lactate Levels Eleven coho were k i l l e d immediatley when landed to establish a post-exercise base l e v e l . One f i s h died i n the live box i n less than one-half hour and i s included i n the f i r s t group. Pish were held i n li v e boxes up to 14- hours. During this time 4-8 additional f i s h died, 4-7 of which were sampled for blood. These are grouped into half-hour time 65 .Table X. Repeated determinations of. blood lactate levels from tne caudal vein and heart of each of eleven, coho caught by t r o l l i n salt water. Values i n parentheses are dummy values for ease i n computation. Sampled immediately Sampled one to f ive hours after hooking after hooking Specimen Heart Caudal Specimen Heart Caudal 1 mg% 15.7 1517 (15.7) mg% 12.3 13.7 (13.0) 8 mg% 155. 162. 150. mg% 171. 165. 168. 2 62.4 63.0 (62.7) 60.8 62.5 (61.6) 9 180. 170. 166. 172. 172. 172. 3 120. 121. 121. 86.0 94.5 99.0 10 112. 1Q7. 109. 118. 113. 113. 4 75.6 90.5 80.0 49.6 60.9 65.5 11 234. 250. 248. 238. 248. 245. 5 43.O 48.7 42.5 31.7 30.6 30.2 6 38.8 43.0 39.8 31.2 32.3 (31.7) 7 63.0 64.4 63.7 57/4 59.9. 59.5 Mean 61.44 49.71; 17b. 3 174.6 6 6 periods i n c l u d i n g the time on the gear. Where t h i s s t a t i s t i c i s unknown (eight cases), average time spent on the gear i s used (4.74 minute, n = 50). Table XI gives average values and ranges f o r time and blood l a c t a t e values. These data are presented g r a p h i c a l l y i n Figure 16. A t y p i c a l delayed blood la c t a t e response i s depicted. Blood l e v e l s of l a c t a t e i n -creased at l e a s t f o u r - f o l d from pre-exercised l e v e l s . In t h i s study l a c t a t e l e v e l s d i d not subside; however, these samples are from f i s h which died. Lactate i n the blood of a single normal-appearing specimen d e l i b e r a t e l y k i l l e d i n the f i f t h hour was 115 mg%. While not by i t s e l f s u f f i c i e n t evidence, t h i s r e l a t i v e l y low value of blood l a c t a t e i n a survivor i s substantiated by previous work with chinook (Parker and Black, 1 9 5 9 ) . M o r t a l i t y During the course of the experiment 49 f i s h died. As 26 f i s h were released during the time periods when deaths oc-curred, the simple r a t i o , 49/115, i s not a v a l i d estimate of m o r t a l i t y . Further, the problem of s e t t i n g confidence l i m i t s i s complicated by a decreasing sample s i z e . Because the so-l u t i o n to t h i s s t a t i s t i c a l problem has general a p p l i c a b i l i t y to a v a r i e t y of s i m i l a r problems i t i s presented i n d e t a i l as an Appendix. The r e s u l t s , together with the o r i g i n a l obser-vations, are summarily presented i n Table XII. Two points are of s p e c i a l i n t e r e s t . F i r s t , the highest rate of m o r t a l i t y 67 Table XI. Blood lactate levels of troll-caught coho salmon which died during post-exercise period. Number Time period from hooking Lactic acid (n) Average Range Average Range • - -'~ hours mg% 12 a 0.10 0.03 0.43 53.3 13.0 93.2 4 0.78 0.57 0 .92 156. 123^ . 236. 12 1.20 1.03 1.42 187. 1 3 3 . 273. 9 ~1.65 1.50 1.83 211. 147. 282.. 9 2.25 2.03 2.50 209. 158. 280. .4. 2.75 2.58 2 .92 195. 154. 240. 1 3.25 • • • • • • • • 298, • • • • • • • • 2 4.28 4.27 4.32 292 . 280. 304. 1 4.92 .... • * • » 224. • • • • , • • • • 2 5 .27 5 .17 ., 5.42 220. 180. 260. 2 5.53 • • • • • • • • 265. 212. 318. . \ 1 8.88 • • • • • • • • ~ i' 219 . • • • • • • • • Eleven f i s h included i n the f i r s t time period were k i l l e d and sampled when landed. The remainder are f i s h which died i n the li v e boxes.;1 Table XII. Mortality of coho salmon during post-exercise rest period. Time 1 Number of Number which Number Instantaneous Cumulative total f i s h at died during released mortality mortality start of time period during time rate Point Confidence time period period estimate interval (n) (7) ( i ) Q hours 0 - 1 115 5 0 0.044 0.044 0.006 0.080 1 - 2: 110v 21 0 0.212 0.226 0.146 0.299 2 - 3 89 14 2 0.171 0.348 0.255 0.429 3 - 4 73 1 , 0 0.038 0.357 0.263 0.438 4 - 5 72 3 6 0.043 0.384 0.288 0.474 5 - 6 63 4 7 0.066 0.423 0.330 0.507 6 - 7 52 0 5 0 do-,. do do 7 - 8 47 0 6 0 do do do 8 - 9v 41 1 0 0.025 0.437 0.336 0.522 9 - 14 40 0 40 0 0.437 0.336 0.522 Total 49 66 0 1 2 3 4 5 6 9 10 II 28 + Time in hours from hooking. Figure 16. Coho blood lactate (expressed as mg% l a c t i c acid) response in time from hooking. Open ci r c l e s represent mean value for f i s h which died in salt water experiment. Dashed line drawn free-hand to indicate probable average. Solid c i r c l e s represent mean value for f i s h in. freshwater. Vertical lines through means indicate range of values. 70 took place i n the second and t h i r d hours after hooking. Second, mortality was substantially complete (97%) by the end of six hours. Recapture of fagged Fish If observed mortalities on t r o l l caught salmon held i n l i v e tanks aboard the vessel are representative of mortality experienced by lots of f i s h released immediately after capture, then survivors of lots held past the mortality period should show a higher percentage recaptured than those released im-mediately. This hypothesis was explored by releasing 60 f i s h immediately after capture and 40 f i s h held nine hours or longer (Table XII). Recoveries were entirely from subsequent commercial fishing and while probably not completely reported at time of analysis (October, 1958) no substantial change can be expected. Twelve of the f i r s t group and seven of the second have been recaptured. Comparison of the two ratios 60 to 12 and 40 to 7 re-quires certain precautions. The observed probability of re-capture, P, for the 60 f i s h released immediately after capture was 12/60 = 0.2000. This probability i s a product of the probability of surviving the hooking and tagging procedure and the "true" probability of recapture. The former can be estimated from the observed l i v e box survival probability, p_, = 0.5653 (Appendix, Table B), i . e . of the 60 f i s h l i b e r -71 ated i t i s estimated that 0.5633 X 60 = 33.8 survived. The "true" probability of recapture p M i s 12/33.8 = 0 .3551. The A "true" probability of recapture for the second group p ^ i s simply 7/4-0 = 0.1750. The ratio of 12 to 33.8 might be com-pared with the ratio of 7 to 40 by means of a chi-square test. However, this would involve only the assumption of sampling error and would ignore the variance associated with the estimate of survivors from the hooking and tagging pro-cedure. To avoid this error the survival rates can be com-pared using a " t " test: t = A A pb2 - *>bl p b l pb2 The value S-^  i s given by combining the variance associated Pbl with p a and the sampling variance of P-^. By the reasoning given i n the Appendix this combined variance i s given directly by the variance of the ratio 12 to 60 as estimated by the b i -nomial theorem, pq/n. The value of i s given directly by pb2 the bionomial theorem. The details of the particular test were therefore: t - 0.3351 - 0.1750 . 2 > 2 8 . d - f _ 2 f 0 # 2 < p < o a (0.00267 + 0.00361) 1 / 2 72 The hypothesis that an improved tag recovery would result from releasing only survivors held i n l i v e boxes need not be rejected, but neither i s i t validated. Although these data are homogeneous, many of the f i s h which recovered i n the li v e boxes were disoriented for vary-ing lengths of time and one might expect that f i s h which were released immediately would not only suffer the same mortality as those which were held but an additional mortality associ-ated with disorientation, i . e . loss to predators. As stated i n a previous section, there was reason to consider the re-leasing procedure unsatisfactory. Further studies are needed on proper techniques for testing the hypothesis. ADULT COHO IN FRESHWATER This phase of the experiment was designed to test the significance of time spent on the gear i n relation to levels attained by blood lactate and i t s associated mortality, and to compare these results for f i s h i n freshwater which have under-gone physiological changes of approaching maturity with those of f i s h feeding i n the ocean. In this experiment i t was possible to have re l a t i v e l y unexercised control f i s h which were not obtainable i n the ocean study. Results are summa-rized i n Table XIII. Blood lactate increased frpm the control level two-73 Table X I I I . Blood lactate levels of coho salmon during post-exercise period i n freshwater (exercise time, varying from less than one minute to 30 minutes, i s included In the "post-exercise" period). Number of Time period Lactic acid specimens Average Range Average Range hours mg% 25 Control (unexercised) 20.20 8.2 37.5 27 0.427 .05 .95 38.07 15.2 54.3 30 1.488 1.11 2.00 40.07 7.7 74.5 23 2.455 2.05 2.82 24.62 9.1 58.8 18 3.213 3.02 3.72 28.78 7.7 64.6 15 4.285 4.01 4.93 13.89 3.3 42.8 12 5.357 5.08 5.83 , 19.50 3.4 43.9 15 6.343 6.01 6.96 17.05 4.0 43.6 13 10.434 9.98 10.99 21.86 9.3 29.7 12 28 hours and more 12.46 7.2 19.6 74-fo l d i n the f i r s t two hours, then subsequently f e l l to a, level below that of the controls i n the f i f t h hour. This typical response i s depicted i n Figure 16 where i t may be compared with the lactate response of coho i n the ocean study. It i s obvious that lactate concentrations at no time approached those of f i s h dying i n the l i v e boxes at sea. Equally apparent i s the decrease i n range of lactate values as f i s h were held for longer periods. Multiple regression analysis was used to test the effect of time spent on the hook on the lactate response. Controls and f i s h held longer than five hours were excluded from the data; mean levels of blood lactate approximate a linear regression on time for the segment 0.05 to 5.0 hours of t otal time. The regression, i n ordinary units, i s : I = 4-3.855 - 6.297XX + 2.396X2 where Y estimates the blood lactate l e v e l , X-y i s the total time from start of exercise to sampling, X 2 i s the total time spent on hook. The standard regression of Y on X-^  independent of X 2 proved significant (t of hyi.2 = 5.676; d.f. 110; P < 0.01); however, the lactate response was not significantly influenced by the amount of time spent on the hook (t of by 2 ]_ = 0.269; P>0.5). This observation i s interpreted to mean that the i n i t i a l struggle from hooking plus f i n a l struggle of unhooking 75 e l i c i t e d maximum response of blood lactate that f i s h were capable of producing. Blood lactate levels from 0.05 to 0.5 hours were tested against the control group by analysis of variance and found significantly higher (F = 14.87; d.f. 1, 39; P < 0.01). Similar treatment shows blood lactate was significantly lower in f i s h held 28 hours or more than i n the control group (F = 7.38; d.f. 1, 36; P < 0.01). Thus the control group reflected blood lactate present from either work done i n swimming against the river current or i n i n i t i a l excitement i n the fish-wheel holding tanks. While exposed to treatment similar to the salt water group, f i s h i n these experiments did not respond with the same degree of violence on the gear. They appeared to be content to swim the same speed as the current and made few rushes against the gear. When landed they struggled less violently than their salt water counterparts. This was reflected i n the blood lactate levels which i n no case i n -creased above 77.5 mg%. Further, not one f i s h died during the experiment. The type of blood lactate response was the same for both groups, but the degree of response was much less for the freshwater group. c 76 OCEAN CHINOOK Secondat and Diaz (1942) followed the ri s e and f a l l of blood lactate of tench by taking three consecutive samples of blood from each f i s h ; the f i r s t immediately after exercise, the second at two hours, and the th i r d at six hours. Cardiac puncture was used. Subsequent workers have taken blood samples only from stunned, k i l l e d , or dying f i s h (Black, 1955, 1957a,b,c; Nakatani, 1957; Parker and Black, 1959), and from these data i t has been deduced that blood lactate level of survivors has at f i r s t risen and then declined. While there i s l i t t l e doubt of the type of response, actual evidence that blood lactate has been at concentrations equal to those of f i s h which died i s lacking. To examine this question 25 chinook salmon were landed and for 16 of them series of blood samples were taken by caudal vein puncture during the post-exercise period. Individuals were tested from two .to nine times, depending upon their survival. Repeated handling un-doubtedly contributed to fatigue and excessive mortality, hence this l o t cannot be compared with other studies. The results are summarized i n Table XIV. Thirteen of the f i s h died, reflecting excessive handling. Two were con-sidered very l i v e l y after three hours and were sampled and k i l l e d . Only one specimen survived repeated sampling and provided both a measure of high blood lactate three hours Table XIV.., Blood lactate (mg%) of 16 troll-caught ocean chinook which were sampled, more than once. Time period (hours) Blood lactate concentration, mg%, for individual f i s h . Fish which died Fish k i l l e d No.l 2: 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0- 0.5 51 101 72 32 46 29 51 49 85 181 49 45 91 74 59- 36 0.5- 1.0 86 95 104 - - - 84 144 - 138 - 92 112 174 106 - -1.0- !-5 105 138 142 - - 130 - 87 199 204 a 215 141 -1.5- 2.0 153 144 177 - - - 186 - 219 a 164 -2.0- 3.0 159 169 177 196 177 I l l - 178 224 262 - - _ -3.0- 4.0 173 206 245 - 217 at 187 261 268 4.0- 5.0 — — 251 2?2 173 201 174 -5.0- 6.0 231 224 1 6.0- 10.0 -10.0- 15.0 103 • * ^ i n a l blood sample not available. 78 after exercise and low blood lactate almost 14- hours after hooking. The serial samples confirm that death was associ-ated with the attainment of high blood lactate concentration but indicate a wide range of v a r i a b i l i t y i n individuals. In 10 of the 13 cases, death occurred when blood lactate ex-ceeded 200 mg% and i n two cases when i t reached 174- mg%. In contrast, the two specimens that were l i v e l y after three hours of rest showed blood lactate of over 260 mg% and blood lactate concentration of the survivor was at the same time 187 mg%. These observations demonstrate the v a r i a b i l i t y among f i s h i n the association between death and high blood lactate concentration following hyperactivity. SUMMARY OF RESULTS 1. Troll-caught coho showed a typical delayed blood lactate response after hooking. 2. Blood lactate levels of coho feeding i n the ocean i n -creased at least four-fold from pre-exercised levels i n two hours. 3. For coho which died i n the l i v e box no significant de-cline i n blood lactate level was evident. 4-. Mortality was estimated to l i e i n the range 0.336 to 0.522 at the 95 percent level of confidence. The empirical estimate i s 0.4-37. 5. The mortality rate of coho reached a maximum i n the second hour and then declined. 79 6. Mortality was substantially complete (97%) by the end of six,hours. 7. The recapture of tagged f i s h was not shown to be enhanced by holding i n l i v e boxes past the period of mortality. 8. A typical delayed blood lactate response to exercise was obtained for non-feeding adult coho i n freshwater. 9. Degree of lactate response i n freshwater was much less than i n (2) above. 10. No deaths occurred among f i s h tested i n freshwater. 11. It was noted (but not measured) that f i s h did not struggle as violently i n freshwater as i n salt water. 12. For ocean-caught chinook salmon which died, blood lactate was shown to have increased u n t i l death; while for a single survivor blood lactate reached a peak of 187 mg% at approximately the third hour and subsequently sub-sided to 103 mg% i n the 14th hour. DISCUSSION The fact that blood lactate levels of coho increased following exertion on t r o l l gear needs l i t t l e discussion. Black (1957a) has described adequately the typical delayed response and this has been subsequently confirmed for several salmonids by Black (1957b,c) and Parker and Black (1959). Blood lactate levels of other Pacific, salmon which died following hyperactivity were higher than blood lactate levels 80 obtained from comparable l i v i n g fish.. The present study has confirmed this relationship for an additional species, the coho. The fact that apparently uninjured f i s h died i s not surprising. It i s well known that severe muscular exertion may result i n death of several species of animals. As early as 1938 Huntsman suggested that mortality in f i s h might re-sult from severe muscular exertion. Subsequently several authors have reported instances of this occurring as out-lined i n the introduction to this section and reviewed by Black (1958b). That significant numbers of troll-caught salmon have died i n post-exercise captivity has been reported several times. These observations are compared i n Table XV. In each case significant mortality of f i s h captured by t r o l l i n g occurred while being held aboard the fishing vessel in l i v e tanks. These experiments must be compared with caution. That of Milne and Ball(1956) includes only f i s h judged to be un-injured and f i t for tagging, as were f i s h used by Fry (Fry and Hughes, 1951), by Parker and Black (1959), and i n the present experiment. It i s hot known i f such grading occurred i n Milne and Ball's (1958) second experiment. Fry's experi-ments were carried past the term of maximum mortality rate, as were Parker and Black's and the present one. Milne and Table XV, Comparison of delayed mortality observations on troll-caught salmon. Number Reported Total 0,95 binomial Investigators Species i n mortality time confidence sample estimate observed interval %: f hours %-Milne and Ball (1954) Coho 55 20 1 - 6 10 - 30 Milne and Ball (1958) Coho 289 18 1+ 13 - 22 ii II tt II Chinook 9IL 20 1+ 12 - 28 Fry (1958) Coho 88 38 16 - 24 28 - 47 it II Chinook 96 44 16 - 24 34 - 54 Parker and Black (1959) Chinook 66 71 8. 40 - 86 Present experiment Coho 115 ' 44 8 34 - 52 82 Ball liberated some f i s h prior to or during this period, either into a liv e pond or into the sea. A l l the experi-ments agree i n the use of submature feeding f i s h i n salt water. A l l investigators report that mortality i s delayed and substantially complete within six hours. Mortality rate i s closely correlated with blood lactate l e v e l . In Parker and Black's experiments with chinook and i n the present experiment with coho the rate of mortality ( i ) i s re l a t i v e l y low i n the f i r s t hour, i n -creases to a maximum i n the second or third hour and becomes negligible by the end of six hours (Table XII). This i s the same type of delayed response described for blood lactate. Further, with a single exception i n each of the above ex-periments, no f i s h died i n which blood lactate levels were less than 125 mg% (see Figure 16; also Parker and Black, 1959, Appendix). This also true of Black's (1957c) sockeye experiment. Blood lactate levels above 125 mg% may, then, be considered as a danger zone for three species of Pacific salmon. This i s not to say that when blood lactate levels rise above this point death w i l l follow; rather, dearth may follow. Several experimenters have subjected salmonids to hyperactivity but observed no ensuing mortality. Paulik DeLacy and Stacy (1957) repeatedly subjected coho, and 83 Paulik and DeLacy (1958) sockeye, to severe fatigue. Many of their test animals became so severely fatigued that e q u i l i b r i -um was los t , yet no significant mortality followed. In these experiments maturing adult f i s h were used i n freshwater. Black (1957a,b) subjected rainbow trout and lake trout to hyperactivity without ensuing mortality. He noted a blood lactate response well above 125 mg% i n these experiments. Jensen (1958) caught and released two and three-year-old chinook salmon reared i n salt water ponds. These f i s h were not fed six days prior to the experiment. Fish actively fought the lure for one to two minutes and were then easily netted and released. A small mortality of 2.0 percent oc-curred during the f i r s t week following treatment. In the freshwater experiment, adult coho were treated in a manner essentially the same as f i s h on the t r o l l gear. Lactate response was significant and typical. Quantitatively i t was much less than for the feeding, submature coho i n the sea. Further, from subjective observations, f i s h ceased to struggle after less expenditure of effort than their salt water counterparts. Most significant: no deaths occurred. These observations appear to exclude psychosis from close confinement, hook injury, abrasion of the mucous coat, etc. as primary factors of death. Death appears to be a con-dition brought about by severe fatigue of f i s h i n a par-ti c u l a r physiological state. 84 A greater recovery of tags was not realized by Fry and Hughes (1951) when only survivors held past the c r i t i c a l mortality period were released. These authors report a 1.63 percent recovery of tags from 123 chinook held overnight i n liv e tanks after catching. A control group of 179 chinook gave 18 percent tag recovery. It i s perhaps significant that tagging occurred at release, i . e . the survivors i n the tanks were subjected to additional stresses of capture, tagging, and releasing after the recovery period, while the controls were tagged and released after capture, at a time when further handling could have had l i t t l e effect i n producing fatigue. Milne and Ball (1958) obtained 27 percent recovery of 118 coho, tagged at capture, and held not less than one hour. In their earlier experiment (1956) 32 percent of 28 tagged coho were subsequently recovered after being held i n a floating l i v e pond for more than 30 days. While no control lots were liberated, these recovery rates are much higher than previously reported experiments on t r o l l tagging (Milne, 1957). In the present experiment f i s h were tagged when captured and survivors released and compared with a control group. Recoveries have suggested less chance of survival for experimental f i s h than controls, and,, as i n the case of Fry and Hughes (1951), the treatment during liberation i s 85 suspect. Survival from original fatigue i s not the only-consideration i n these cases. . A disoriented f i s h i s easy prey to predators known to he present i n the surface waters, i . e . mackerel shark (Isurus nasus) and northern sea lions (Eumetopias jubata). Further research i s indicated along these l i n e s . At present i t i s not possible to state methods by which mortality can be avoided; i t can, however, be measured. It i s suggested that fatigue i s an indiscriminate stress acting i n either a lethal manner or i n an impairing manner\(Brett, 1958) u n t i l f u l l return to normal i s achieved. The mechanisms responsible for the d i f f e r i n g suscepti-b i l i t y of salmon to effects of exercise i n fresh and salt water may find explanation i n the following arguments; Most f i s h are chronically i n oxygen distress because of low s o l u b i l i t y of oxygen i n water ( < 10 mg/1 for sea water i n most cases, Sverdrup et a l . , 1942, and < 15 mg/1 for freshwater i n most cases, Welch, 1935). The active rate of oxygen uptake i s restricted to a few multiples of the standard rate, i . e . approximately four-fold (F.E.J.Fry, 1957). As i n air-breathing animals, energy for a c t i v i t y i n excess of the active rate (F.E.J.Fry, 1957) must be derived anaerobically, mainly by glycolysis. Job (1954) reported oxygen consumption at near the active rate for digestion of food alone, which indicates that further a c t i v i t y i n a 86 glutted stage of feeding must be done anaerobically. The production of l a c t i c acid and i t s diffusion into the blood must be considered as a regular physiological process fo r v even moderate acti v i t y , and act i v i t y must be followed by rest. Loss of circulatory blood volume may result from severe muscular acti v i t y (Bainbridge, 1931). Black (1955) found a significant increase i n blood hemoglobin following severe exercise i n largemouth bass (Micropterus salmoides), and postulated an osmotic shift of water from the blood to the tissues i n response to a greatly increased number of osmotically active particles present from hydrolysis of the large glycogen molecule. It i s , of course, possible that increased blood hemoglobin results from introduction of stored erythrocytes into the circulating blood. If there i s a significant increase i n osmotically active particles-within the muscle c e l l s , i t i s possible that, i n some situations, so much water may be drawn from the effective circulating blood that circulatory shock may ensue. Further, upon diffusion of hydrogen ions and (or) lactate ions into the blood, the blood f l u i d may become severly hypertonic to the erythrocytes which may explain the observations of von Buddenbrock (1938) that the red blood c e l l s appeared to be collapsed and misshapen when blood lactate levels were high. This condition could further aggravate the situation by reducing oxygen transport a b i l i t y of the circulating blood. Fish incsea water obtain water from either oxidation of food or by drinking sea water 87 and excreting the salts, a process which involves c e l l u l a r work (see V.S.Black, 1957). Thus an osmotic imbalance caused by excessive production of lactate ions could lead to a distressed condition of suffocation. Sub-adult Pacific salmon, susceptible to t r o l l i n g , are i n a feeding stage. Large quantities of food are consumed, fat i s being stored and protein synthesized. Carbohydrate, available as l i v e r glycogen, blood glucose, and muscle glyco-gen, i s readily available for quick energy (unpublished ob-servations of E.G.Black). As maturity i s approached these f i s h cease feeding and enter freshwater. Energy for as-cending streams and for the spawning act i s available only through use of stored fat and catabolism of non-essential protein (Green, 1926; Hoar, 1957; Black, 1958a). This material i s not available for rapid consumption and thus the rate of supply can r e s t r i c t the action of the f i s h i n i t s re-sponse to stimuli. If feeding f i s h are starved for periods prior to exercise, the above mentioned sources of fat and protein must be drawn upon for energy. Thus, coho salmon did not struggle as violently i n freshwater, not because of any basic difference i n stimulus-response reaction, but because of limited stores or readily available evergy. Jensen's ex-periment i s consistent with this hypothesis. His f i s h were not fed for six days prior to the test. In addition they may-have been considerably adapted to handling. From these argu-88 ments, the lack of mortality following hyperactivity of f i s h i n freshwater may be explained as well as giving a mechanism for death following hyperactivity of feeding salmon i n sea wata?. It would appear that cessation of feeding by Pacific salmon, coincident with approaching maturity and entrance into freshwater, may have contributed significantly to the a b i l i t y of the f i s h to migrate extensive distances upstream. If large amounts of muscle glycogen were available there would be no check on the rate of energy expenditure and at rapids or other obstructions salmon might become disoriented from sustained severe a c t i v i t y . The slower mobilization of stored fats and non-essential proteins may act as an effective "peer", pre-venting disorientation following fatigue, a condition which might lead to passive displacement downstream, thus net loss and needless expenditure of energy. Lack of feeding i s thus viewed as a protective mechanism of survival value for Pacific salmon. CONCLUSIONS 1. Chinook and coho salmon caught by t r o l l i n g undergo hyper-a c t i v i t y . 2. This often leads to a distressed condition which i s de-layed and the severity of which cannot be predicted for any individual at the time of capture. 3. The distressed condition may advance beyond the a b i l i t y to respond to stimuli or to recover orientation, and 89 terminate i n death. 4. Death resulting from capture hy t r o l l has been observed to be of significant magnitude. For coho, mortality l i e s between 34 percent and 52 percent; for chinook, between 40 and 86 percent. 5. Mortality rate and blood lactate levels are closely cor-related i n relation to post-exercise time. 6. For f i s h which died, blood lactate rose u n t i l death. Survival occurred either when blood lactate did not reach c r i t i c a l levels (above 125 mg%) or reached a c r i t i c a l l evel and then subsided. 7. No remedy; i s suggested for delayed mortality from fatigue of t r o l l caught salmon. It i s important that i t be assessed i n tagging programs. 8. Holding salmon for tagging past the period of mortality did not improve tag recovery. It i s suggested that the manner of releasing i s responsible for additional indis-criminant stress acting i n both a lethal and impairing manner. 9 . This observation suggests that the largest number of returns can be gained by tagging a l l f i s h available and releasing immediately. Subsequent mortality can be assessed by holding lots on board. 10. Adult coho salmon did not appear susceptible to fatigue to a lethal degree i n freshwater. This has been postu-9G lated as due to cessation of feeding and to have adaptive significance for survival. E. THE VALIDITY OF SIZE RESTRICTIONS FOR A STOCK OF CHINOOK It has been shown that significant mortality as-cribable to hyperactivity results from catching and re-leasing chinook salmon. Additional mortality from direct injury has been recorded (Parker and Kirkness, 1956 and sub-sequent observations) amounting to approximately 20 percent. Milne and Ball (1956) report t o t a l mortality from coho salmon hooked i n the g i l l s , and 50 percent from f i s h hooked i n the eye (through the roof of the mouth). They further report 12 of 67 or 18 percent of the f i s h caught were either drowned or so severely hooked that they were nearly dead and unfit for tagging. These observations may be combined with delayed mor-t a l i t y observations into a single instantaneous rate. The instantaneous rate from physical injury i s estimated by: 0.2 = l - e " * . The delayed mortality rate from hooking and releasing l i e s between the lim i t s : 0.40 = l - e " 0 * 5 1 2 and 0.86 = 1- e " 1 , 9 6 6 while the empiri-—1 236 call y observed estimate i s : 0.71 = l - e ~ . The total instantaneous rate of mortality ascribable to catching and releasing l i e s within the limits 0.735 and 2.189. When i n -91 stantaneous natural mortality i s added (0.36~0.51 '"•) the most optimistic expectation of mortality for the f i r s t year after release i s an instantaneous rate i n excess of 1.0 and the rate may he as high as 2.5. This zone of tot a l instantaneous mor-t a l i t y i n relation to size specific growth rate curves from Figure 15 i s graphically presented i n Figure 17. Ignoring any production lost from the 0/2 group of f i s h , a size limit of not more than 22.5 inches and probably much less (approxi-mately 15.0 inches for a mean value) could be j u s t i f i e d as a r e s t r i c t i o n to increase the y i e l d i n pounds from the stock. Other advantages may perhaps accrue from a size re-st r i c t i o n such as increased spawning escapement, production of a larger size (hence a more valuable product ) and the avoidance of undersized stocks by the fishermen. The re-lationship between escapement and return for chinook i s not known at present and possible advantages from increased spawning cannot therefore be evaluated. It i s certain, how-ever, that the size li m i t (25.0 inches) applied to mature segments of the stock results i n increased escapement of the male fraction only (Anon, et a l . 1951). The increase i n value with increase i n size has not been analyzed, but i s simply l i s t e d as a possible benefit. The avoidance of ac-The 1958 price structure was such that chinook over 10.0 pounds (approximately 28.0 inches fork length) brought 1 1/2 times the price per pound paid for f i s h under that size. Figure 17. Length-specific average annual instantaneous growth (weight) rates of l i f e history groups of chinook salmon compared with zone of "size limit mortality". 93 cumulations of undersized f i s h by the fishermen has not been generally investigated. The degree to which a size limit w i l l influence such avoidance would depend upon the numbers of legal f i s h contained i n the stock. This fraction would be dynamic and hardly susceptible to a generalized statement. There remains the p o s s i b i l i t y that natural mortality rate may increase as the mature segment of the stock becomes increasingly concentrated along migration routes, i n channels, and i n estuaries. Again, no data appear to be published on this question, he.nee no evaluation of this effect on the c r i t i c a l size problem can be made. If an increase i n natural mortality rate were true, a c r i t i c a l size might be reached at an immature stage, thus indicating the need of a fishery on the immature stock. These remain problems for future research. With the information now available, the following general conclusions may be put foreward as means of increasing the y i e l d i n pounds from the stock of chinook, anticipating no net increase i n fishing intensity: (1) Fishing should be restricted to the maturing stock. This may be accomplished by re s t r i c t i n g the area and time of fishing. (2) Under conditions of (1) above, size limits should be abolished and the use of non-selective gear encouraged. ( 3 ) If fishing i s to be permitted on the immature stocks, an increase i n y i e l d cannot be expected from a size 9 4 limit r e s t r i c t i o n . A type of gear might he found which i s selective for larger f i s h ; however, this would sa c r i -f i c e the y i e l d possible from the shorter l i f e history types. F. GENERAL SUMMARY The peculiar l i f e history of chinook salmon neces-sitates consideration of a c r i t i c a l size for each l i f e histo-ry type i f maximum y i e l d i n pounds i s held as a desirable objective of management. The essential elements of c r i t i -cal size are growth and natural mortality rates. A concept of growth i s proposed i n which growth rate i s taken to be a product of both physiological and environmental opportunity and analogous to other physiological rates which may be de-scribed as proportional to the weight raised to some power. The mathematical result of this concept depicts instantaneous relative growth rate i n weight as a declining function of increasing length. Natural mortality rate was assumed to be constant and the general magnitude was computed from tagging and recovery data. The combination of these two rates clearly establishes that, for each l i f e history sub-group of any par-ticular year class, growth i n pounds of stock continues u n t i l the ultimate year (maturity). Biologically, fishing should be prohibited on the immature accumulations and non-selective fishing for a l l size groups of the mature elements should be encouraged. 95 The present practice of fishing on immature stocks, hut limiting the retention of f i s h to those over 25.0 inches, might have j u s t i f i c a t i o n i f no mortality resulted from catching and releasing f i s h below the legal l i m i t . Obser-vations have shown that approximately 20 percent of small f i s h taken by t r o l l are so injured as to produce complete mortality. Further observations, on apparently uninjured fish, have demonstrated a delayed mortality of between 40 percent and 86 percent and correlated with the degree of fatigue as measured by bipod lactate. This delayed fatigue mortality was studied further with coho salmon and i t was found to be serious only i n sub-adult feeding f i s h . Mature f i s h , after cessation of feeding and entrance into freshwater, were not susceptible to fatigue to the same degree and no deaths en-sued from the experimental treatment. This i s not to say that other unevaluated effects did not result from the treatment; these were beyond the scope of the present study. Three general recommendations are proposed: 1. Fishing be restricted to the mature segments of the stock. 2. The capture of a l l size elements should be encouraged, i . e . fishing made non-selective to size. 3. If fishing i s allowed on immature accumulations, size limits w i l l decrease the y i e l d i n pounds and should, there-fore, be abandoned!. Further need for research i s indicated i n each phase 96 of the problem studied. The major fi e l d s which appear p r o f i t -able are as follows: 1. The relationship between growth rate and metabolic rate i n respect to size. It may be possible to establish certain parameters of the growth equation by independent determination of size specific 0 2 uptake under standard conditions. 2 . Further study of the fatigue mortality problem with a view to establishing remedial action. This would do much to aid the study of population structure by taggin and re-leasing members of the population. 3 . The study of population structures with a view to es-tablishing the relative abundance of l i f e history types of each year class i n the immature population. From this knowledge a model could be constructed to give details i n gains or losses accruing from management rest r i c t i o n s . 4. Implied i n (3) above, further experiments to determine the magnitude and s t a b i l i t y of natural mortality should be implimented. 97 REFERENCES ADOLPH, E.F. 1?A9. Quantitative relations i n the physiologi-cal constitutions of mammals. Science, 109* 579-585. AL RTJSSAINI, A.H. 1949. On the functional morphology of the alimentary tract of some f i s h i n relation to differences i n their feeding habits. Anatomy and histology. Quart. £• Microscop. Sci., 90: 109-139. ALM, Gunner. 1949. Influence of heredity and environment on various forms of trout. Inst. Freshwater Res., Drottningholm, Report No. 29: 29-34. ALLEN, K. Radway. 1953. A method for computing the optimum size-limit for a fishery. Nature, No. 4370," p.210., ALLEN, K. Radway. 1954. Factors affecting the efficiency of r e s t r i c t i v e regulations. I. Size l i m i t s . New Zealand J. S c i . and Tech. Sect. B. 35(6): 498-529. ANON. 1951. Annual report of the Alaska Department of Fisheries. Rept.,No. 3. Biological Investigations, pp. 20-42. ANON. 1953. Annual report of the Alaska,Department of Fisheries. Report No. 5* Taku River Investigation, pp. 22-41. ANON. 1958. Report of the International North Pac i f i c Fisheries Commission for the year 1957. f H . The research program, pp.-23-86. BATES, Daniel W. and Russell VINSONHALER. 1957. Use of louvers for guiding f i s h . Trans. Am. Fish. Soc., 86: 38-57. ~7" = r- ~ ~" '• BAINBRIDGE, F.A. 1931. The physiology of muscular exercise. Third. Edition,, rewritten by A.V.BOCK and D.B.DILL. Longmans, Green and Co. Ltd., London. 272pp. von BERTALANFFY, Ludwig. 1938. A quantitative theory of organic growth, (inquires on growth laws, II) Human  Biology, 10(2): 181-213.- ~ von BERTALANFFY, Ludwig. 1949. Problems of organic growth, Nature, 163: 156-58. 98 von BERTALANFFY, Ludwig. 1950. An outline of General System Theory. B r i t t . J. Philo. S G j . , 1 (2) : 134-165. von BERTALANFFY, Ludwig. 1951. General System Theory: A new -1 ' approach to unity of science. I. Problems of general system theory^. Human Biol., 23* 302-312. ' von BERTALANFFY, Ludwig. 1957. Quantitative laws i n metabo-lism and growth. Quart. Rev. B i o l . , 32(3): 217-231. von BERTALANFFY,, Ludwig,and R.R.ESTWICK. 1953. Tissue respiration of musculature i n relation to body size. Am. J. Physiol., 173(1): 50-60.^ r von BERTALANFFY,. Ludwig and R.R.ESTWICK. 1954. Tissue respiration i n experimental and congenital^pituitary deficiency. Ibid., 177(1): 16-18. von BERTALANFFY, Ludwig and W.J.PIROZYNSKI. 1953. Tissue respiration, growth and basal metabolism. B i o l . B u l l . 105(2): 240-256. '' ~* BEVERTON, R.J.H. and S.J.HOLT. 1957. On the dynamics of exploited f i s h populations. Min. Agr. Fish, and Food, G.B., Fisheries Investigations. Ser. II. 29: 1 -5^. BLACK, Edgar,C. 1955. Blood levels of hemoglobin and l a c t i c a c i d i n some freshwater fishes following exercise. J. Fish. Res; Bd. Canada. 12(6): 917-929. BLACK, Edgar C. 1957a. Alterations i n the blood level of l a c t i c acid, i n certain Salmonid fishes following muscular ac t i v i t y . I~.' Kamloops trout, Salmo gairdneri. Ibid.,. 14(2): 117-134. BLACK, Edgar C. 1957b. Alterations i n the blood level of, lac t i c " a c i d In certain Salmdnid fIshes following'muscular ac t i v i t y . II. Lake trout,, Salvelinus namayeush. Ibid., 14(4): 645-649. ! BLACK, Edgar C. 1957c. Alterations i n the blood level of * l a c t i c acid i n certain Salmonid fishes following muscular act i v i t y . III. Sockeye salmon, Oncorhynchus nerka. Ibid,., 14(6): 807-814. v. BLACK, Edgar C. 1958a. Energy stores and metabolism i n relation to muscular activity of fishes." In The Investi-gation of Fish-rPower Problems (Ed. by P.A.LARKTN"), pp. 51 -57. University of B r i t i s h Columbia, Canada. 99 BLACK, Edgar C. 1958b. Hyperactivity as a lethal factor i n -fish. J. Pish. Res. Bd. Canada, 15(4): 573-586. BLACK, Virgi n i a Safford. 1957. Excretion and osmoregulation. - In The Physiology of Pishes.(Ed. by Margaret E. BROWN). Academic Press, N.Y., pp.,163-205. BRETT, J.R. , 1958. Implications and assessments of environ-mental stress. In The Investigation of Fish-Power  Problems (Ed. by P.I3ARKIN), pp. 69z8"3. University of Bri t i s h Columbia, Canada. BRETT, J.R., M.HOLMES and D.F.ALDERDICE. v 1958. The effect of temperature ijon ^  the cruising speedx of young sockeye and coho salmon. J.Fish. Res. Bd. Canada, 15(4'),: 587-605. BRODY, Samuel. 1927. Growth and development with special reference to domestic animals. III. Growth rates, their evaluation and significance. Missouri Agr. Exp.. St a. Res. Bull. , No. 97, 70 pp. BRODY, Samuel. 1937. Relativity of physiologic time and physiologic weight. Growth, 1(3)' 60-67. BRODY, Samuel. 1945. Bioenergetics and growth with special reference to the efficiency complex i n domestic animals. Reinhold, N.Y. 1023 pp. BROWN, Margaret E. 1946.s The growth of brown trout (Salmo  trutta). I. Factors influencing the growth of trout f r y . J. Exp. Mot., 22: 118-129. von BUDDENBROCK, W. 1938. Beobachtungen ueber das Sterben-gefangener Seefische und ueber den Milchsaueregehalt des Fischblutes. . Rapp. et Proc.-Verb., Cons. Inter. Explor. Mgr., 101(IV/2J: 3-7 ' ~~ ~~ CALHOUN, A.J., D.H.FRY, Jr. and E.P.HUGHES. 1951., Plastic deterioration and metal corrosion i n Petersen disk f i s h tags. California Fish and Game, 37(3): 301-314. COHN, E.A. and H.A.MURRAY. 1927. Physiological ontogeny. I. The present status of the problem. Quart. Rev. Bi o l . , 2:, 4469-493. CROXTON, Frederick E. and Dudley J.COWDEN. 1946. Applied general s t a t i s t i c s . (13th printing). Prentice Hall, N.Y. 944 pp. 100 DEMING, W.E. 1°A3. S t a t i s t i c a l adjustment of data. John Wiley and Son. 261 pp. ELSON, P.F. 1957. The importance of size i n the change from parr to smolt i n Atlantic salmon. Canadian Fish  Cult., No. 21: 1-6. FRASER, C. McLean. 1917. On the scales of the spring salmon. Cont. to Canadian Bi o l . 1915-16:( 21-28. FRY, D.H. 1958. O f f i c i a l correspondence, Cal. Dept. Fish and Game,,: Oct. 14, 1958. : FRY, D.H. and Eldon P.HUGHES.' 1951. The California salmon t r o l l fishery. Pac. Mar. Fish. Comm. Bull., 2: 7-4-2. FRY, F.E.J. 1957. The aquatic repiration of f i s h . In The. Physiology of Fishes. (Ed. by Margaret E.BROWN), Academic Press, N.Y., Vol. I,1 Chapter I: 1-63. GERKING, Shelby D. 1957. Evidence of aging i n natural popu-lations. Gerontologia, 1: 287-305. GRAY, J. 1929. The kinetics of growth* J. Exp. B i o l . , 6(3): 248-274-. ~ GREEN, Chas. W. 1926. The physiology of the spawning migration. Physiol. Rev., 6(2): 201-241. HAWK, Phi l i p B., L.OSSER and William H.SUMMERSON. 1949. Practical physiological chemistry, 12th Ed. The Blakiston Company, Philadelphia, 1323 pp. ~ HIATT^ Robert W. 1947., Food chains and the feeding cycle i n Hawaiian f i s h ponds. Part I. The food and feeding habits of mullet, (Mugil cephalus), milk f i s h (Chanos chanos) and the tenpounder (Elops msichnata) . Trans. : Am. Fish. Soc., 74: 250-61. ' - < ' ~~~ " HOAR, W.S.„ 1939. The thyroid gland of the Atlantic salmon. J. Morph., 65(2): 267-290. HOAR, W.S. 1957. Endocrine, organs. In The Physiology of " Fishes. (Ed. Margaret E.BROWN), Academic Press, N.Y., Vol. I, Chapt. VI: 245-285. HOAR, William S. 1957. The gonads and reproduction. In The ' Physiology of Fishes. Ibid., Vol., I, Chapter VII: 287^21. 101 HOAR, W.S. and G.M.BELL. 1950. The thyroid gland in.relation to the seaward migration of Pac i f i c salmon. Canadian J. Res. D., 28: -126-136. , : 1 HUNTSMAN, A.G. 1938. Overexertion as a cause of death of captured f i s h . Science, 87(2269): 577-578. JENSEN, Hans M. 1958. Preliminary report on hooking mortality study conducted at Bowman's Bay.from March^ 10-April 9, 1958. Wash. Dept. Fisheries, Seattle. Mimeo. 3 pp. JOB, S.V. 1954. Oxygen consumption of the speckled trout ' r — ' (Salvelinus f o n t i n a l i s ) . Ph.D. Thesis, University of Toronto Library. M.S.. (Not consulted, summary given by FRY, F.E.J. 1957). '' " JOB-, S.V. .1955. The oxygen consumption of Salve linus f p n t i -n a l i s . Univ. Toronto Studies, B i o l . Ser., No. 61., Pub. Ontario Fish. Res. Lab., 75:, 1-59. KALLEBERG, Harry. 1958. Observations i n a stream tank of t e r r i t o r i a l i t y and. competition i n juvenile salmon and trout (Salmo salar L. and S. trutta L.). Inst. Freshw. Res., Drottingholm. ' Report No. 59* 55-98. KAUFFMAN, Donald E. 1951. ; Research report on the Washington Stalte offshore t r o l l fishery. Pac. Mar. Fish. Comm. Bull . 2, pp. 77-91. ' KLUST, Gerhard. 1959,. Uher Entwicklung, Bau und Funktion ,des Darmes beim Karpfen (Cyprinus carpio L.). Int. Rev, d. gesam. Hydrobiol. u. Hydrograph. 39: .4-98-536. ~ t. " • ^ " ZLUST, Gerhard. 1940. Uber Entwicklung, Bau,und Funktion des Darmes beim Karpfen (Cyprinus carpio). Ibid., 40: 88-173. LARKIN, P.A., J.G.TERPENNING and R.R.PARKER. ,1957. Size as a determinant of growth rate i n rainbow trout Salmo gaird- neri . Trans. Am. Pish. Soc., 86: 84-96. LEE, Rosa M. 1920. A review of the methods of age and growth determination i n fishes by means of scales. Min. Agr. and Fish., London. Ser. II, 4(2): (microfilm). MAHER, F.P. and P.A.LARKIN. 1955.. L i f e history of the steel-head trout of the Chilliwack River, Br i t i s h Columbia. Trans. Am. Fish. Soc., 84: 27-38. 102 MARTIN, W.R. 194-9,. The mechanics of environmental control of body form i n fishes. Univ. Toronto Stud., Biol. Ser. No. 58. Pub. Ontario Pish. Res, Lab,., 70: 1-72~I MILNE, D.J. 1957. Recent Br i t i s h Columbia spring and coho salmon tagging experiments, and a comparison with those conducted from 1925 to 1930. Pish..Res. Bd. Canada Bull . No. 113, 56 pp. ^ , MILNE, D.J. and E.A.R.BALL. 1956. The mortality of small salmon when caught by t r o l l i n g and tagged or released untagged. Pish. Res. Bd. Canada. Pacific Progress Rept. No. 106: 10*=T5. — — ~ ~ " ~ MILNE, D.J. and E.A.R.BALL. 1958. The tagging of spring and coho salmon i n the Strait of Georgia i n 1956. Ibid. No. I l l : 14-18. MINOT, Charles Sedgewick. 1891. Senescence and Rejuvenation. J. Physiol. 12: 96-153. MILSEN,. Hans. 1941. Der Phasenwechsel des Rhelnlachses (Salmo  salar L.) unter besonderer Bertlcksichtigung des Ernahrungs-apparates: Rev., Suisse de Zool. Geneve. 48: supp. p.181. MOTTLEY, C. McC* 1942, The use of the scales of the rainbow trout (Salmo gairdneri) to make direct comparisons of growth.^ Trans. Am. Pish. Soc. 71, pp. 74-79. NAKATANI, Roy E. 1957. Changes i n the inorganic phosphate and lactate levels i n blood plasma and muscle tissue of adult "steelhead" trout after strenuous exercise. Univ. of  Washington; School of Fisheries, Tech. Rept;, No. 30, 14pp. NEAVE, Fer r i s . 1951. Observations on troll-caught salmon of the west coast of Vancouver Island, 1949. Pac. Mar / Fish. Comm. Bul l . 2: 94-101. NEWMAN, Murray A. 19/56. Social behavior and interspecific competition i n two trout species. Physiol. Zool. 29(1): 64-81. ---r-r~ ,.. , _ PARKER, Robert R. and Walter KIRKNESS. 1956. King salmon and the ocean t r o l l fishery of Southeastern Alaska. Alaska Dept; Fish. Res. Rept., No. 1, 64 pp. PARKER, Robert R. and Edgar C.BLACK. 1959. Muscular fatigue and mortality i n t r o l l caught chinook salmon (Oneorhynchus tshawytscha). J, Fish. Res. Bd. Canada, 16(1)1 95-106. 103 PARRY, Gwyneth.. 1958. Size and osmoregulation i n salmonid fishes. Nature, 181(461?): 1218-1219. PAULIK, Gerald J. and Allan C.DeLACY. 1958. Changes i n the swimming a b i l i t y of Columbia River sockeye salmon during upstream migration. Univ. of Washington College of  Fisheries, Tech. Rept., No. 4"6*, 67 pp. PAULIK, Gerald J., Allan C. DeLACY and Edwin F. STACY. 1957. The effect of rest on the swimming performance' of fatigued adult si l v e r salmon. Univ. of Washington School of  Fisheries, Tech. Rept. No. 31, 24 pp. PIROZYNSKI, W.J. and Ludwig von BERTALANFFY. 1951. Is the v rate of basal metabolism determined by tissue respiration? Proc. Canadian Physiol. Soc. 15th, Ann. Meet, pp. 37-38. ' PRICE, John W. 1931. Growth and g i l l development i n the small-mouthed black bass,' Micropterus dolomieu, Lacepede. Ohio State Univ., Franz Theodore Stone Laboratory, Cont. Np. 4; 4"6" pp. ^ . 1 PROSSER, C. Ladd (Editor). 1952. Comparative animal physiolo-gy. W.B.Saunders, Philadelphia, 888 pp. M II PUTTER, August. . 1920. Studien uber physiologische Ahnlichkeit. VI. WachtumsMhnlichkeiten. Pflugers Arch, f .d. ges. Physiol., 180: 298-340. RICH, W i l l i s H. 1925. Growth and degree of maturity of chinook salmon i n the ocean. U.S. Bur. Fish., Doc. No. 974," pp. 15-90. N RICKER, William E. „ 1948. Methods of estimating v i t a l sta-t i s t i c s of, f i s h populations. Indiana .University Publi-cations, Science Series No. 15, 101 pp. RICKER, W.E. 1945. A method of estimating minimum size limits for obtaining maximum yi e l d . Copeia. 1945(2): 84-^ 94. JL RICKER, W.E. 1958., Handbook of computations for biological s t a t i s t i c s of f i s h populations. Bul l. Fish. Res.'Bd. Canada No. 119, 300pp. ROBERTSON, 0..H. 1957. Survival of precociously mature king salmon male parr (Oncorhynchus tshawytscha juv.) after spawning. Cal. Fish, and Game, 43(2^: IT9-130. 104 SECONDAT, Marcel and Diego DIAZ. 1942. . Recherches sur l a lactacidemie ches le poisson d'eau douce. . Oom.pt. Rend. Acad. S c i . 215: 71-73. ' • • J STLLIMAN, Ralph P. 1948. Estimation of the t r o l l catch of, Columbia River chinook salmon, Oncorhynchus tshawytscha. U.S. Pish and Wildlife, Special S c i . Report, No. 50. 15pp. SILLIMAN, Ralph P. 1950. Fluctuations i n abundance of Columbia River chinook salmon. U.S. Fish and Wildlife  Service, Fishery B u l l . 51: 565-383. SMITH, S.B. 1955. The relation between scale diameter and body length of Kamloops trout, Salmo gairdneri kamloops. J. Fish. Res. Bd. Canada, 12: 74^753^ ! SNEDECOR, George W. 1950. S t a t i s t i c a l Methods. 4th Edition. Iowa State College Press. 485 pp. STRINGER, G.E. and: W.S.HOAR. 1955. Aggressive behavior of underyearling Kamloops trout. Canadian J. Zool., 33: 148-160. SVERDRUP, H.V., Martin W.JOHNSON and Richard H.FLEMING. 1942. The oceams, their physics, chemistry, and general biology. Prentice Hall, New Jersey. 1087 PP« SZARSKI, H., E.DELEWSKA, S.LEJA, S.OLECHNOWICZAWA, Z.PREDYGIER, and L.SLANKOWA. 1956. Uk^ad trawienny lexzxza (Abramis  brama L.).\ (The digestive system of the bream). In Polish with English summary. Studia Soc. Sc i . Torunesis, Sect. E ; 3(7): 113-146. WALFORD, Lionel A. 1946. A new graphic method of describing •"v" the growth of animals. B i o l . Bull., 90(2): 141-147. WELCH, Paul S. 1955. • Limnology. McGraw-Hill, New York, 1 - 471 pp. ' ' -WEYMOUTH, F.W., J.FIELD II,.and M.KLEIBER. 1942." Relationship between body size and'metabolism. Proc. Soc. Exp. Bi o l . Med., 49: 367-370. WILIMOVSKY, Norman J. and Warren O.FREIHOFER. 1957. .Guide1 to the literature on systematic biology of Pa c i f i c salmon. U.S. Fish and Wildlife Ser., Spec. Sc i . Rept., Fisheries, foT 2WT 2^ 6" pp. 105 ZEUTHEN, Erik. 1953. Oxygen uptake as related to body size i n organisms. Quart. Rev, Bi o l . , 28(1): 1-12. ZEUTHEN, Erik. 1955. Comparative physiology (respiration). Ann. Rev. Physiol., 17: 459-482. 106 APPENDIX A METHOD OF COMPUTING THE VARIANCE OP COMBINED PROBABILITY ESTIMATES Mortality of f i s h i s studied and a series of consecu-tive observations 'is., obtained. Each estimate of mortality may or may not be based on samples of identical individuals, i.e. each sample may be drawn independently from the popu-lation. It i s desired to estimate the probability Q that a f i s h w i l l die prior to or during a time period t and to set up confidence intervals for these probabilities. This pro-cedure would not, of course, be needed i f a constant instan-taneous mortality obtained throughout the time period. The assumption of random selection must be va l i d . The following notation i s used. A t p t estimates the probability p^ that a f i s h l i v i n g at time t survives u n t i l t+1. A q^ . estimates q^ ., the probability that a f i s h l i v i n g at time period t dies before time period t+1; q^ = 1-P+,* x^ . = number of f i s h alive at time t that survive u n t i l time t+1. y_l_ = number of f i s h alive at time t that die before time t+1. n^ . = number of f i s h alive and i n the experiment, at time t . = x, + t ~ * t T » p t " x t / n f 107 P t estimates the probability that a f i s h lives u n t i l time t+1. A estimates the probability that a f i s h dies prior to time t+1. Note: i t may also die prior to time t, t - 1 , etc. The qualification has been given that n^ may or may not equal x t - l * Now P t - p o P l . . . P t. 1P t or Pt=k = I 3£-0 P t / - ( 1 ) and / ^ o ^ i * • • ^ - t - l ^ t D e c a u s e a doi 1 1* probability of death cannot occur, but V w t : ( 2 ) and can be estimated from this relationship or by use of the log form -(coin p A + coin p-, + . . + coin p. n + coin p. ) = l-e: 0 1 t-1 t n7, Q 1 ~ ( i l + i 2 + ' • + H-2 + V l + V or Q. = l-e where i ^ = coin p^ = instantaneous mortality rate (Ricker, A In any case Q^. i s always estimated from P^ or i t s components. Variance of p^ i s estimated by: A A s £ = ~n—(Snedecor, 1950). p t t 108 The variance of P^ cannot he sums or products of variances of P^ -'s for resulting variances would rapidly diverge and lose meaning. The variance of In p^ (or coin p^) s f 2 p t may be approximated by S l T ) * —o— (Deming, 194-3, p.4-5). ' p t p t These variances are additive and thus: Confidence intervals of 0^. can now be set by the relationship: , (*.05 S l n p > < / A " ( t.05 S l n pt> 1-Ptei v = $t 1 _ p t e - . . . . (4). The resulting confidence limits are advantageous as they tend to the unequal limits of the Poisson distribution as values of P ——> GL or 1. A schedule of calculations i s presented i n Table A. Mortality observations were grouped i n time periods of one hour and calculations are carried out i n Table B. Table A. Schedule for calculation of standard deviation of log ..survival probability. XL y __ n A P A P s 2 -S l n p S l n P. G x 0 % n 0 V n 0 A p 0 y 0/x 0n 0 A )l / 2 p:o 1 X l y i n l X l / I 1 l * A P0P 1 y i / x i n i < * + s 2 * )V2 2 x 2 y-> • n 2 • x 2/n 2 • * A P l p 2 • y 2 / x 2 n 2 • v s^p 2 ) 1 / 2 • • • • • t " 1 X t - 1 * t - I n t - l x t - l / n t - l P t - 2 p t - l y t - l / x t - l n t - l i ( S m P. „ + S l n * > t 1/2: t-2 p t - l x t y t n t x t / n t A A p t - l 5 t V x t n t t - 1 + S 2 * )V2 1 2 1 p t H O Table B. Schedule of calculation of mortality, ocean coho • t X J n A P A P B? A In p S A °ln P A Q 3 i 0 110 5 115 0.9565 0.9565 .000395 .01987 0.006 0.044 0.080 0.044 1 89 21.. 110 0.8091 0.7739 .002145 .05040 0.146 0.226 0.299 0.212 2 75 14 89 0.8427 0.6522. .002097 .06810 0.255 0.348 0.429 0.171 3 72 1 73 0.9863 0.6433 .000190 .06948 0.263 0.357 0.438 0.038 4 69 3 72 0.9583 0.6165 .000604 .07370 0.288 0.384 0.474 0.043 5 59 4 63. 0.9365 0.5774 .001076 .08067 0.330 0~.423 0.507 0.066 6 52 0 52 1.0000 do do do do do 0 7 47 0 47 do do do do do do 0 8 40 1 41 0.9756 0.5633 .000610 .08436 0.336 0.437 0.522 0.025 ^ee text and Table A. for notation. LIST OF PUBLICATIONS LARKIN, P.A., J.G.TERPENNING and R.R.PARKER. 1957. Size as a determinant of growth rate i n rainbow trout, Salmo  gairdneri. Trans. Am. Fish. Soc., 86: 84-96. PARKER, Robert R. 1955. Two proposed methods of estimating animal populations. Proc. 7th Alaska Science Conference. PARKER, Robert R. and Walter KIRKNESS. 1951. Biological investigations. Alaska Dept. Fish., Ann. Rept. No. 2, 1950: 25-42. ~ PARKER, Robert R. and Walter KIRKNESS. 1954. Estimates of population of spawning king salmon i n the Taku River, Alaska, for the year 1951. Proc. 3rd Alaska S c i . Confer., pp. 179-191. PARKER, Robert R. and Walter KIRKNESS. 1956. King salmon and the ocean t r o l l fishery of Southeastern Alaska. Alaska Dept. Fish., Res. Rept. No. 1, 64 pp. PARKER, Robert R. and Robert E. VINCENT. 1956. Progress report on research studies at the Kit o i Bay Research Station. Alaska Dept. Fish., Ann. Rept. No. 7, 1955. pp. 25-67. — PARKER, Robert R. and Edgar C. BLACK. 1959. Muscular fatigue and mortality i n troll-caught chinook salmon (Oncorhynchus tshawytscha). J. Fish. Res. Bd. Canada. 16(1): 95-106T ~ PARKER, Robert R., Edgar C.BLACK and Peter A.LARKIN. 1959. Fatigue and mortality of Pacific salmon (Oncorhynchus). J. Fish. Res. Bd. Canada. In press. PARKER, Robert R. and P.A.LARKIN. 1959. A concept of growth of fishes. Submitted to J. Fish. Res. Bd. Canada. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0106514/manifest

Comment

Related Items