{"http:\/\/dx.doi.org\/10.14288\/1.0106514":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Science, Faculty of","type":"literal","lang":"en"},{"value":"Zoology, Department of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Parker, Robert Ray","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2012-02-20T20:46:59Z","type":"literal","lang":"en"},{"value":"1959","type":"literal","lang":"en"}],"http:\/\/vivoweb.org\/ontology\/core#relatedDegree":[{"value":"Doctor of Philosophy - PhD","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeGrantor":[{"value":"University of British Columbia","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"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 interacting components that determine growth, both of which are related to size attained. Growth opportunity occurs in stanzas which are entered at \"threshold\" sizes.\r\nThe function, dw\/dt = kw(x) is developed into a growth equation for linear dimentions, 1(z\/t+1) = \u0251 + (1z\/t) and three methods of fitting this equation to growth data are demonstrated.\r\nApplication is explored and discussed using steel-head 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 1(t+1), 1(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 subgroups of a year class must either be treated separately or weighted according to relative abundance in determining critical size. The former alternative is followed in lieu of necessary weighting data.\r\nNatural mortality of a chinook population is 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 estimated to lie in the range 0.3 to 0.4.\r\nThe 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, providing mortality due to hooking and releasing is negligible.\r\nCapture 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 indiscriminant stress was caused at release. Adult coho in freshwater did not appear capable of lethal hyperactivity. This led to the hypothesis that cessation of feeding during spawning migration has adaptive significance for survival of Pacific salmon.\r\nThe combination of natural mortality, mortality from hooking injury 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.\r\nIt 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 immature stock, size limits should be abolished.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/40821?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":"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 \u2022 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\u00a3, 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\u00bbc6nfidenc'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_\u00a3. 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 \u2022 . . . . . . . . 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 \u2022 , 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 \u2022 ! \u00ab 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 \u2022 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\u00b0*^ on l\u00a3* 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\u00b0*^ on 1\u00b0* 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\u00b0* 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\u00b0*^ on 1\u00b0* 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\u00a3*^ on l \u00a3 # ^ 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 \u00a3 # 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 \"\u2022' . . . 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 \u00a3 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\u00b0 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 \u00b0 \/ 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 \u2022 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\u00a3, 1^, etc. w i l l l i e a distance above a 45\u00b0 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\u00b0 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\u00b0 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 \u00ab 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 \u00a3 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 (\/ \u00b0 \/ o \/ \u00b0 0 yf i O \/ o co o %\u00b0 7 2 0 A 4.0 6.0 2.0 3.0 Figure 4-. Plot of , 1 ^ on l t and 1 \u00b0 ^ 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 \u00b0 o o \/ \u00b0 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 \u00b0 ' ^ 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 \u00b0 0 o 3 o o 0 o j j O o r P \/? ft \u00b0 o o o o \u00b0 0 \u00b0 o o o o o o o Q \u00b0 \u00b0 8 o o e c\u00b0 \u00b0o\u00b0 c?o\u00b0t> * 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 \u00b0 * 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 \u00b0 > o o o .
<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 \u00b0 o o 0 o o \u00b0 Vo \u00b0 o \/ \u00b0 \u00b0 \u00b0 8 \/ 0 \u00b0 \u00b06 c r 2\/2 35 1*1 30 25 20 \u00b0 V s o \/ 0 \/ o o o \u00b0\/ O \u2022o 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 \u00b08
\u00b0 o o =p \/ %\u00b0\u00b0 o ft \u00b0 %\u00b0 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