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An ecological study and theoretical considerations of butter sole (Isopsetta isolepis) population in.. 1963

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AN ECOLOGICAL STUDY AMD THEORETICAL CONSIDERATIONS OF BUTTER SOLE (ISOPSETTA ISOLEPIS) POPULATION IN HECATE STRAIT r MADASSERI KRISHNAN KUTTY B.Sc, The University of Madras, I95U M. A., The University^ of Madras, 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Zoology We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 19^3 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 h i s representatives. I t i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Zoology, The University of B r i t i s h Columbia, Vancouver 8, Canada. September ; 1963- GRADUATE STUDIES F i e l d of Study: Zoology Biology of Fishes • Experimental Zoology Fisheries Biology and Management Marine F i e l d Course Quantitative Methods i n Zoology Seminar i n Fisheries Biology Theoretical Population Dynamics N. C.C. Lindsey W.S. Hoar P.A. Larkin P.A, Dehnel P.A. Larkin Staff P,A. Larkin J. Wilimovsky Other Studies: Economics of Natural Resources Fisheries Law Hydraulics Introduction to B i o l o g i c a l Oceanography Introduction to Synoptic Oceanography A.D. Scott G.F. Curtis E.S. Pretious B.McK. Bary G.L. Pickard The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of MADASSERI KRISHNAN KUTTY B.Sc, University of Madras, 1954 M.A., University of Madras, 1956 THURSDAY, SEPTEMBER 26, 1963, AT 3:00 P.M. IN ROOM 3332, BIOLOGICAL SCIENCES BUILDING COMMITTEE IN CHARGE Chairman: F.H. Soward J.R. Adams W.S. Hoar E.C. Black p.A. Larkin I.E. Efford N.J. Wilimovsky External Examiner: R. Van Cleve Dean-of the College of Fisheries The University of Washington AN ECOLOGICAL STUDY AND THEORETICAL CONSIDERATIONS OF BUTTER SOLE (ISOPSETTA ISOLEPIS) POPULATION IN HECATE STRAIT ABSTRACT The ecology of the Hecate S t r a i t population of butter sole (Isopsetta i s o l e p i s (Lockington)) i s studied to f a c i l i t a t e a better understanding of the fluctuations in abundance and to permit a more optimal u t i l i z a t i o n of the stock. The reaction of the population to varying degrees of exploitation and natural mortality rates i s analysed for steady and fluctuating recruitment using Ricker's model. The magnitude of error inherent i n the models used for the theoretical studies of exploited populations i s also examined by subjecting a hypothetical population i n a steady state to various mortality and growth rates. This i s done both for a continuous fishery and after appropriate modifications in Beverton's model for a seasonal fishery as well. Butter sole population spawning in Skidegate Inlet i s confined to the'Hecate Strait bank. The species show depth s t r a t i f i c a t i o n , the young ones being found i n shal- lower waters. Although the population exhibits seasonal - movements between shallow and deeper waters, a north- south migration i s limited mostly to the spawning popu- l a t i o n . Sexual differences in the time of onset of ma- t u r i t y and migratory pattern are also observed. No association between butter sole and related species of f l a t f i s h is noted. A study of the discreteness of the Hecate S t r a i t population suggests that this area i s in= habited by a single self-contained stock. Growth studies of butter sole indicate that there are annual, seasonal,' regional and sexual differences. The average growth of butter sole belonging to a strong year class seems to be influenced by i n t r a - s p e c i f i c competition, even though a tendency i n later years to compensate for the i n i t i a l difference in growth i s also exhibited. The survival rate of butter sole above six years i s r e l a t i v e l y low. A comparison of the relative abundance of young butter sole taken i n the 1952-1954 samples from along the Graham Island coast with the success and age compo- ' s i t i o n of the fishery which existed from 1958-1960 when these year classes became f u l l y exploitable, i n d i - cates that fluctuations i n the butter sole population are mainly due to variations i n early survival rate, Y i e l d isopleths and equilibrium y i e l d curves indicate that the maximum equilibrium y i e l d w i l l be obtcned when the age of exploitation i s 4.83 years or greater only when F i s higher than 1.8. The f i s h i n g mortality operates for only a short time each year while natural mortality is continuous, and a change i n the l a t t e r therefore i n - fluences the y i e l d and biomass more than a similar change i n the fi s h i n g mortality. A higher increase in the natural mortality with age res u l t s , under fluctuating recruitment, in greater deviations i n y i e l d and biomass. As the older age groups now contribute less to the population, the effects of fluctuations i n abundance of the entering year class on the stock become more pronounced. There i s l i t t l e difference i n the y i e l d per recruit (Yw/R) estimates from Beverton's or Ricker's model for a hypothetical population under various situations, provided Ricker's model makes use of an exponential average of the biomass during each time period. The s l i g h t difference observed i s due to the manner of depicting the growth pattern. Due to seasonal differences i n growth rate, Yw/R estimate from Beverton's model need not be more accurate than from Ricker's model. A heavier exploitation of the butter sole population i s warranted on the basis of the theoretical studies, provided the heavier exploitation does not decrease the number of f e r t i l i z e d eggs by over-exploiting the males that are more abundant on the spawning grounds. Due to sexual differences i n the population parameters and the migratory and recruitment patterns, the two sexes may be treated i n further studies, as a special case of two competing populations exploited simultaneously. Abstract The ecology of the Hecate S t r a i t population of butter sole (isopsetta i s o l e p i s (Lockington)) i s studied to f a c i l i t a t e a better understanding of the fluctuations i n abundance and to permit a more optimal u t i l i s a t i o n of the stock. The reaction of the population to varying degrees of exploitation and natural mortality rates i s analysed for steady and fluctuating recruitment using Ricker's model. The magnitude of error inherent i n the models used for the theoretical studies of exploited populations i s also examined by subjecting a hypothetical population i n a steady state to various mortality and growth rates. This i s done both for a continuous fishery and after appropriate modifications i n Beverton's model for a seasonal fishery as well. Butter sole population spawning i n Skidegate Inlet i s confined to the Hecate S t r a i t bank. The species show depth s t r a t i f i c a t i o n , the young ones being found i n shallower waters/ Although the population exhibits seasonal movements between shallow and deeper waters, a north-south migration i s l i m i t e d mostly to the spawning population. Sexual differences i n the time of onset of maturity and migratory pattern are also observed. Wo association between butter sole and related species of f l a t f i s h i s noted. A study of the discreteness of the Hecate S t r a i t population suggests that t h i s area i s inhabited by a single self-contained stock. Growth studies of butter sole indicate that there are annual, seasonal, regional and sexual differences. The average growth of butter sole belonging to a strong year class seems to be influenced by i n t r a - s p e c i f i c competition, even though a tendency i n l a t e r years to compensate for the i n i t i a l difference i n growth i s also exhibited. The survival rate of butter sole above s i x years i s r e l a t i v e l y low. A comparison of the r e l a t i v e abundance of young butter sole.taken i n the 1952-195^ samples from along the Graham Island coast with the success and age i i i composition of the fishery which existed from 1958-I96O when these year classes became f u l l y exploitable, indicates that fluctuations i n the butter sole population are mainly due to variations i n early survival rate. Y i e l d isopleths and equilibrium y i e l d curves indicate that the maximum equilibrium y i e l d w i l l be obtained when the age of exploitation i s ^ .83 years or greater only when F i s higher than 1 .8. The f i s h i n g mortality operates for only a short time each year while natural mortality i s continuous, and a change i n the l a t t e r therefore influences the y i e l d and biomass more than a similar change i n the f i s h i n g mortality. A higher increase i n the natural mortality with -age res u l t s , under fluctuating recruitment, i n greater deviations i n y i e l d and biomass. As the older age groups now contribute less to the population, the effects of fluctuations i n abundance of the entering year class on the stock become more pronounced. There i s l i t t l e difference i n the y i e l d per r e c r u i t (^/R) estimates from Beverton's or Ricker's model for a hypothetical population under various situations, provided Ricker's model makes use of an exponential average of the biomass during each time period. The s l i g h t difference observed i s due to the manner of depicting the growth pattern. Due to seasonal differences i n growth rate, Yw/R estimate from Beverton's model, need not be more accurate than from Ricker's model. A heavier exploitation of the butter sole population i s warranted on the basis of the theo r e t i c a l studies, provided the heavier exploitation does not decrease the number of f e r t i l i z e d eggs by over-exploiting the males that are more abundant on the spawning grounds. Due to sexual differences i n the population parameters and the migratory-and recruitment patterns, the two sexes may be treated i n further studies, as a special case of two competing populations exploited simultaneously. Acknowledgement The author wishes to express his deep gratitude to Dr. W.J. Wilimovsky, under whose direc t i o n the present work was conducted, and to Dr. P.A. Larkin for t h e i r unstinted help and c r i t i c i s m throughout the course of t h i s study and during the preparation of t h i s manuscript. The author i s also grateful to Dr. J.R. Adams, Dr. E.C Black and, W.S. Hoar for c r i t i c a l l y reading the manuscript and to Mr. J.R.H. Dempster for providing the f a c i l i t i e s of the Computing Centre and for his assistance i n s t a t i s t i c a l methods. Thanks are due to Mr. E.C. Wiklund who programmed Beverton's and Ricker's y i e l d equations and for his help i n modifying Beverton's y i e l d equation for a seasonal fishery, and to Mr. T. Pletcher for taking photographs of the "butter sole ovary,and o t o l i t h . Special thanks are due to Dr. K.S. Ketchen of the P a c i f i c B i o l o g i c a l Station, Wanaimo, who made available information on butter sole, for permitting the use of the research vessels f o r c o l l e c t i n g additional information on the species and for c r i t i c a l l y going through the manuscript. The assistance of the undermentioned Research Personnel of the Wanaimo B i o l o g i c a l Station, Messrs. T. Butler, J.A. Thomson, C.R. Forrester, W. Yates, R. Wilson, E. Lippa and the crew of the research vessels, A.P. Knight and Investigator Wo.l i n f i e l d work i s also g r a t e f u l l y acknowledged. Thanks are also due to Mr. D.L. Alverson of the U.S. Bureau of Commercial Fisheries for providing butter sole samples from the U.S. coast. The author has benefited from the informal discussions he had with Mr. J.C. Mason and Dr. T. Miura during t h e i r stay at t h i s University. F i n a l l y , the e f f o r t s of Mr. A. Hamilton for c a r e f u l l y going through the English i s also g r a t e f u l l y acknowledged. Table of Contents Page I Introduction 1 I I Materials and Methods 3 I I I Aspects of the l i f e history of butter sole 7 1. Introduction 7 2. Confines of the butter sole population spawning i n Skidegate Inlet 7 (a) Hecate S t r a i t habitat 7 (b) Pattern of d i s t r i b u t i o n of butter sole i n .... Hecate S t r a i t 11 (c) Behaviour and movements of butter sole 22 (d) Spawning migration 23 (e) Factors l i m i t i n g the d i s t r i b u t i o n of butter sole i n Hecate S t r a i t 27 ( f ) Relative importance of northern Hecate S t r a i t as a habitat for f l a t f i s h 28 (g) Inter-relationships among species of f l a t f i s h 29 (h) Conclusion 32 3- Discreteness of the Hecate S t r a i t population of butter sole 32 (a) Evidence from meristic study 36 (b) Conclusion 39 h. Aspects of the Population Characteristics of butter sole ... kO (a) Age and growth of butter sole kO ( i ) Body length - o t o l i t h radius relationship k2 ( i i ) V a l i d i t y of o t o l i t h reading hh v i i Page ( i i i ) Growth rate of butter sole - Comparison of the back calculated lengths and the lengths estimated by reading oboliths sampled from the spawning population - Yearly variations i n growth rate - Seasonal differences i n growth rate - Regional differences i n growth rate - Sexual differences i n growth rate - Length-Weight relationship of butter sole (b) Survival rate 63 (c) Conclusion 65 IV Fluctuations i n the abundance of butter sole population 67 1. Introduction 67 2. Examination of the butter sole Fishery ' 6] (a) Age of f u l l exploitation 67 ( i ) Mesh selection experiment 67 ( i i ) Length-girth relationship 72 (b) Variations i n butter sole landings 75 ( i ) Estimation of the catch per unit e f f o r t 79 - Relation of f i s h i n g power to tonnage - Standardisation of f i s h i n g e f f o r t and the catch per unit e f f o r t for the 30"59 ton classes ( i i ) Catch per unit e f f o r t as an index of abundance 86 (c) Conclusion 87 v i i i Page 3- Analysis of fluctuations i n the butter sole population 87 (a) Method adopted i n analysing changes i n abundance 88 (b) Results 89 (c) Conclusion „ 96 V. Theoretical y i e l d study of the butter sole population 98 1. Introduction 98 2. Procedure 98 3. Results 101 (a) Comparison of the y i e l d per r e c r u i t values obtained from.Beverton's and Ricker's model for a hypothetical population 101 (b) Changes i n the y i e l d and biomass of the butter sole population I l 8 (c) Effects of fluctuating recruitment on the biomass and y i e l d 126 (d) Conclusion 131 VI. Discussion 133 1. Ecology of the butter sole population 133 2. Further studies I38 3. Use of models i n studying the butter sole population li+2 VII. Summary 153 VIII. Literature c i t e d 159 L i s t of Figures Figure Page 1. Map of Hecate S t r a i t showing the general sampling l o c a l i t i e s numbered 1 to 6 h 2. Map of the north coast of B r i t i s h Columbia showing the three shallow banks off the main coast 9 3> Depth contours of the Hecate S t r a i t bank 10 k. Northern part of the Hecate S t r a i t bank showing the sampling positions i n 195^ • • 12 5. Northern part of the Hecate S t r a i t bank showing the approximate sampling positions i n 1961 13 6. Histogram showing the size frequency d i s t r i b u t i o n of butter sole i n the 1961 trawl hauls from northern Hecate S t r a i t 18 7- Histogram showing the age frequency d i s t r i b u t i o n of butter sole i n the 1961 trawl hauls from northern Hecate S t r a i t ; 19 8. Histogram showing the length frequency d i s t r i b u t i o n of butter sole i n samples from Butterworth ground (A) and Skidegate Inlet (b) collected during February 1962 by commercial trawlers 2k 9- Photograph of the ovaries of butter sole sampled from Skidegate Inlet and Butterworth ground during February 1962 25 10. Relative abundance of four species of f l a t f i s h i n the 1953 and- 195^ samples from the northern part of Hecate S t r a i t 31 11. Photograph of the butter sole o t o l i t h showing hyaline and opaque zones hi 12. Body length-otolith radius relationship of butter sole .... 43 13. Percent of butter sole o t o l i t h s i n the sample with opaque, hyaline or uncertain edges U7 lh. Dissection of the length frequency d i s t r i b u t i o n of female butter sole by the p r o b a b i l i t y paper method into modal length groups , 1 h8 X. Figure - Page 15. Wal-ford p l o t of the back calculated lengths of butter sole .... 52 16. Growth curve of butter sole 53 17.. Percent deviation of the back calculated lengths from the mean at different years for age groups III+ to VIII+ i n the July 1961 sample 57 18. Length-weight relationship of butter sole 62 19- Percentage of butter sole retained at each length by 5 . 2 " cod end mesh. (Alternate hauls) 71 20. Length-girth relationship of butter sole 7̂ - 21. Map showing the s t a t i s t i c a l areas of Hecate S t r a i t i n the neighbourhood of Skidegate Inlet 76 22. Butter sole landings and catch per unit e f f o r t for the period I9U5-I962 78 23. Relation of f i s h i n g power and gross tonnage of vessels equipped with 'double' gear engaged i n the butter sole fishery during the period I958-I962 8 l 2k. Relative abundance of the three species of f l a t f i s h i n the , samples from the Graham Island coast collected during 1952 and 1953 92 25- Comparison of the y i e l d isopleths for a hypothetical population obtained from Beverton's and Ricker's ( a r i t h . mean) models 10k 26. Comparison of the y i e l d isopleths for a hypothetical population obtained from Beverton's and Ricker's (arith.mean) models 105 27- Percent deviation") of Y^/R estimated by Ricker's method (arith.mean) from that of Beverton showing the trend for various f i s h i n g mortality rates and ages of exploitation 107 28. Percent deviation of Yyy'R estimated by Ricker's method ( a r i t h . mean) from that of Beverton showing the trend for various f i s h i n g mortality rates and ages of exploitation 108 29- Percent deviation of YyyR estimations by Ricker's method (exp. av.) from that of Beverton showing the trend for various f i s h i n g mortality rates and ages of exploitation x i Figure Page 30. Percent deviation of ̂ yj/R estimations by Ricker's methods 1 and 2 from that of Beverton for a seasonal fishery • 115 31. Butter sole: Isopleth diagram for biomass per re c r u i t for the post-recruit phase 119 32. Butter sole: Changes i n the biomass per rec r u i t for different f i s h i n g and natural mortality rates when T 1 i s k.83 years 121 33- Butter sole: Equilibrium y i e l d curves for various sets of natural mortality rates 122 3^. Butter sole: Equilibrium y i e l d curves for various sets of natural mortality rates 123 35- Butter sole: Y i e l d isopleth diagrams when different mortality rates are operating showing the y i e l d f o r different ages of exploitation and f i s h i n g mortality rates .. .. 125 36. Butter sole: Changes i n the biomass per rec r u i t at different ages when no f i s h i n g mortality i s operating 127 37- Butter sole: Percent deviation i n y i e l d and biomass (post-recruit phase) under fluctuating recruitment for d ifferent ages of exploitation and mortality rates 130 L i s t of Tables Table Page I. Percent size composition of butter sole i n the 195̂ + trawl hauls taken from northern Hecate S t r a i t using 1.5" mesh cod end . ih o I I . X analysis of the percent size composition of butter sole i n different haul groups given i n Table I 15 I I I . Percent size and age composition of butter sole i n the 1961 trawl hauls taken from northern Hecate S t r a i t 16 2 IV. X analysis of the percent size composition of butter sole from Hecate S t r a i t i n the 1961 sample given i n Table I I I 17 V. Percent length composition of butter sole i n the 1 9 6 l trawl hauls taken from Dixon Entrance 21 VI. Length frequency d i s t r i b u t i o n of male and female butter sole i n two half-hour small-meshed ( 1 . 5 " ) trawl hauls from Skidegate Inlet during February 1961.•• 26 VII. Age composition of butter sole i n samples taken from Skidegate Inlet during the 1953 sampling survey using 1.5" mesh cod-end 26 VIII. Analysis of dominance of butter sole i n the 1953 an-^- 195^ samples from the northern Hecate S t r a i t bank 30 IX. Analysis of r e l a t i v e abundance of butter sole, lemon sole, rock sole and sand sole i n the 1953 ancl 195̂ + samples from the northern Hecate S t r a i t bank 30 X. The association of young butter sole, lemon sole• and sand sole along the Graham Island coast as indicated by the rank correlation test 33 XI. The association of butter sole, lemon sole, rock sole and sand sole from the Hecate S t r a i t f l a t as indicated by the rank correlation test ............... 33 XII. Details of the meristic counts of butter sole i n the samples from Hecate S t r a i t and the U.S. coast 37 x i i i Table Page XIII. t-values and t h e i r p r o b a b i l i t y levels obtained from a comparison of dorsal and anal f i n ray counts i n the samples from Skidegate Inlet and the U.S. coast collected during February 1962 37 XIV. Analysis of variance on the dorsal f i n ray counts within the samples from Hecate S t r a i t 3^ XV. Analysis of variance on the anal f i n ray counts within the samples from Hecate S t r a i t 3^ XVI. Analysis of variance on the number of l a t e r a l l i n e pores within the samples from Hecate S t r a i t 38 XVII. Body length - o t o l i t h radius relationship - analysis of covariance among sexes to test the homogeneity of the regression c o e f f i c i e n t s k6 XVIII. Estimated percent of o t o l i t h s with opaque or hyaline zones at the edge i n the July 1961 and 1958-1960 winter samples k6 XIX. Comparison of mean back calculated lengths at different ages from o t o l i t h s and the estimated modal lengths obtained from length frequency d i s t r i b u t i o n of female butter sole i n the sample collected during July 1961 ^ XX. Mean lengths of butter sole at various ages estimated by reading o t o l i t h s sampled from the spawning population during January 1953 using a small meshed shrimp trawl 50 XXI. Mean lengths of female butter sole at various ages estimated by reading o t o l i t h s from commercial catches f o r the period I958 - i 9 6 0 50 XXII. Weighted back calculated lengths at the end of each year of l i f e of 316 males and hk6 females collected during July 1961 51 XXIII. The mean length-of butter sole at the end of each year's l i f e • 56 XXIV. Percent deviation of the .back calculated lengths from the mean for age groups III+ to VIII+ given i n Table XXII.. 56 XXV. The estimated age composition of butter sole i n the samples taken from northern Hecate S t r a i t during July 196I , 56 x i v Table Page XXVI. Percent growth increment up to July of butter sole of various age groups i n the 1961 sample 60 XXVII. Back calculated lengths at various ages calculated from o t o l i t h samples collected from different regions of Hecate S t r a i t during July 1961 60 XXVIII. Length-weight relationship - covariance analysis to test the homogeneity of the regression c o e f f i c i e n t s 60 XXIX. Instantaneous and annual t o t a l mortality rates of butter sole estimated from the age composition data 6k XXX. Length frequency d i s t r i b u t i o n of butter sole above 2k cm. caught i n two hauls with each cod-end and the estimation of the percentage retained by the 5-2" mesh i n an alternate haul experiment 70 XXXI. Landings of butter sole from Skidegate Inlet and the estimated catch per unit e f f o r t f o r vessels of the 30-59 ton range 77 XXXII. Estimation of the f i s h i n g power of 'single* gear taking 'double' gear as the standard 77 XXXIII. The estimated catch per day of 30-39, k0-k9 and 50-59 ton classes 814- XXXIV. Analysis of variance of the log catch per day of the 30-39 and U0-49 ton classes 85 XXXV. Analysis of variance of log catch per day of 1+0-̂ 9 and 50-59 "ton classes 85 XXXVI. Analysis of variance of log catch per day of 30-39 and 50-59 "ton classes 85 XXXVII. Analysis of dominance of butter sole i n the 1953 and. 195^ samples from the Graham Island coast 90 XXXVIII. Analysis of r e l a t i v e abundance of young butter sole, lemon sole and sand sole along the Graham Island coast during 1952 and 1953 91 XXXIX. The abundance of I+, 11+ and > 11+ age groups of butter sole taken i n the small meshed ( 1 . 5 ") trawl hauls along the Graham Island coast during 1952-195^ .' 9k XL. Age frequency d i s t r i b u t i o n s of female butter sole i n the commercial catches during 1958-1960 95 XLI. Yy/R estimations i n grams by the methods of Beverton and Ricker (arith.mean) for a hypothetical population i n a steady state subject to a continuous fishery - Data 1 102 XV Table XLII. Yy/R estimations i n grams by the methods of Beverton and Ricker (arith.mean) for a hypothetical population under steady state subject to a continuous fishery - Data 2 Page 103 XLIII. Percent deviation of Yy/R estimated by Ricker's method (arith.mean) from that of Beverton for the different values of K, M, F and T pt . Data from Tables XLI and XLII 106 XLIV. Yy/R estimations i n grams by the methods of Beverton and Ricker (exp.av.) for a hypothetical population under steady state subject to a continuous fishery 1 ^ XLV. Percent deviation of Y^/R estimated by Ricker's method (exp.av.) from that of Beverton for the different values of M, F and T , . Data from Table XLIV I l l XLVI. Yy^R estimations i n grams by the methods of Beverton and Ricker for a hypothetical population under steady state subject to a seasonal fishery 113 XLVII. Percent deviation of Yw/R values obtained by Ricker's methods 1 and. 2 from that of Beverton for a seasonal fishery as estimated from Table XLVI 11̂ + XLVIII. Butter sole: changes i n biomass (post-recruit phase) and y i e l d i n grams under fluctu a t i n g recruitment i n s i x successive years (N to N+5) compared to y i e l d and biomass under steady state conditions 129 Appendix Table I. Size composition of butter sole i n hauls of cod ends with different mesh -size taken during February 1961 from Skidegate Inlet 166 Appendix Table I I . Butter sole of age seven years and above i n the commercial sample from Skidegate Inlet taken / during 1951, 195U, 1955 and duvinp; trawl survey i n 1953, used to estimate the toLal. 'oi'L.33ity j/ates • 167 I. Introduction The Hecate S t r a i t population of butter sole (isopsetta i s o l e p i s (Lockington)) has been exploited on i t s spawning grounds during the winter months each year since 19^3- Catch s t a t i s t i c s have been maintained by the Nanaimo Station of the Fisheries Research Board of Canada since the inception of the fishery. During the spawning season a large part of the spawning population i s concentrated i n a very l i m i t e d area i n Skidegate Inlet (Figure l ) and hence i s e a s i l y accessible to the commercial gear. The productive Hecate S t r a i t area i s inhabited by other closely related groundfish such as halibut (Hippoglossus stenolepis Scmidt), lemon sole (Parophrys vetulus Gerard), rock sole (Lepidopsetta b j l i n e a t a (Ayres)) and sand sole (Psettichthys melanostictus Girard). Several other species including the P a c i f i c cod (Gadus mac roc ephalu s T i l e s i u s ) are also of commercial importance. The ecological relationship and fluctuations i n abundance of these species have been analysed by Ketchen (1956, 1 9 6 l ) and others. Butter sole landings have shown considerable annual fluctuations. This may be attributed p a r t l y to the yearly v a r i a t i o n i n f i s h i n g pressure and p a r t l y to changes i n the a v a i l a b i l i t y and abundance of the population. However as a result of the small size of the fishery -and i t s r e l a t i v e l y low commercial importance, the dynamics of the population of I . i s o l e p i s has not, u n t i l the present time, been studied i n any d e t a i l . Very l i t t l e information was available on the d i s t r i b u t i o n and movements of the population or i t s growth and survival rates. The discreteness of the butter sole stock and i t s r e l a t i v e -abundance and i n t e r - r e l a t i o n s with other f l a t f i s h were not understood either. Hence t h i s study of the ecology of I . i s o l e p i s and the possible responses of the population to various f i s h i n g and natural mortality rates under steady and fluctuating recruitment i s undertaken to provide a better understanding of the population i n r e l a t i o n to i t s environment. 2. Theoretical studies of f i s h population are done "by constructing mathematical models of the system. The indispensable role of models i n population problems i s emphasised by Beverton and Holt (1957). Their use i n understanding the dynamics of the stock i s also indicated by Moran ( 1 9 5 M who points out that even an inadequate model which does not represent the system completely often separates the important - and unimportant factors i n a p a r t i c u l a r s i t u a t i o n and thus aids i n a better understanding of the system. When studying f i s h populations the two basic kinds of a n a l y t i c a l models used to relate y i e l d and biomass to mortality rates, growth rates and gear characteristics are those of Beverton and Holt (1957) and Ricker (1958). Both-these models attempt to measure the main population variables and incorporate them into the models, but as'yet no studies on the magnitude of error involved due to the manner of representing the system by the two conceptual models are found i n the l i t e r a t u r e . In addition, since the butter sole fishery i s highly seasonal, Beverton's model cannot be applied without appropriate modifications. Hence before studying the butter sole population the two models were applied to a hypothetical population i n a steady state to test t h e i r a p p l i c a b i l i t y to a variety of situations. These situations included cases when the fishery was either continuous or seasonal. The age and rate of exploitation were varied as were the natural mortality rates and growth rates. The a p p l i c a b i l i t y of the two models was studied by comparing the y i e l d per r e c r u i t estimated by them. The choice of a mathematical model for studying the butter sole population i s based on t h i s analysis. I I . Materials and methods. Considerable amounts of data collected by the Fisheries Research Board of Canada, Nanaimo, were used during t h i s study. Part of the data were collected from trawl hauls taken from the Hecate S t r a i t area during February and July, 1961. Commercial samples taken during February, 1962 were also used. The areas sampled are shown i n Figure 1. Movements of butter sole. Studies on the depth d i s t r i b u t i o n and seasonal movements of butter sole were based on the size and age composition of butter sole i n the trawl hauls taken during.I95U and 1961 from several l o c a l i t i e s i n Hecate S t r a i t (Figures k and 5 ) . The nature of the spawning migration was determined from the size composition i n the catches from Skidegate Inlet collected during 1961 and 1962 and from Butterworth ground during 1962. The age composition of butter sole i n the samples c o l l e c t e d by the special sampling survey during January 1953 w a s useful i n studying differences i n : the spawning migration of the two sexes. Abundance of butter sole and related species of f l a t f i s h . Data collected on the catch composition of species of f l a t f i s h during the trawl survey of Hecate S t r a i t i n the summer months of 1952-195'+ ancL the o t o l i t h samples collected from the fishery during 1958-1960 were used i n studying abundance and association of butter sole and related species i n the area. Discreteness of the stock. Meristic counts were taken from 19U specimens collected from Hecate S t r a i t during July 1961 and February 1962 and 95 specimens from the U.S. coast sampled during February, 1962. Studies on growth. To study the growth of butter sole, over 1000 o t o l i t h s were collected from sampling areas 1, 2, 3> k and 6. Of these 762 o t o l i t h s from areas 1 to k were read for back calculations because the Figure 1. Map of Hecate S t r a i t showing the general sampling l o c a l i t i e s numbered 1 to 6. 5- remainder of the o t o l i t h s were:- from the wrong side of the head (right side); had i n d i s t i n c t demarcation of the opaque and hyaline zones to be measured accurately; or had to be rejected due to inadequate sampling of the catch f o r o t o l i t h s . To f a c i l i t a t e back calculation a t o t a l of 1113 measurements from samples collected during i 9 6 0 and 1961 summer hauls were used to establish o t o l i t h radius - body length relationship. To check the back calculated lengths from o t o l i t h s , modal lengths i n the length frequency d i s t r i b u t i o n and the time of formation of opaque and hyaline zones were also studied. Length measurements of ^k6 females i n the July 1961 samples were used to dissect the length frequency d i s t r i b u t i o n by the p r o b a b i l i t y paper method (Harding 19*+9> Cassie 1950, 195*0- T n e "time of formation of opaque and hyaline zones was determined from 2101 o t o l i t h s taken from July 1961 trawl hauls and from the commercial samples collected during 1958-1960. Weights of 32*+ ungutted specimens were taken during February 1 9 6 l a n d of 536 specimens during July 1961 to study the length-weight relationship. Survival rate. Estimates of survival rate were based on the data on age composition of butter sole i n the commercial sample collected during 1951* 19and. 1955 and- by the special sampling survey during January 1953- Studies on fluctuations of butter sole population. Catch and e f f o r t data on butter sole collected f o r the period 19^5-1962 were used to examine the trend i n the yearly "landings. A mesh selection experiment conducted during February 1961 used 1 .5" , 3.*+", 3-5" and 5-2" mesh cod-ends. The 1.5" and 5-2" mesh cod-ends were of cotton, the 3-*+" mesh cod-end was of manila thread and the 3-5" mesh cod-end of drumline. To v e r i f y the results from mesh selection experiment the length and g i r t h measurements of 319 f i s h were taken to obtain the length-girth relationship of butter sole. Data collected on young butter sole along Graham Island coast during 1952-195*+ 6. trawl survey and the age composition and landings for the years 1958-1960 were also u t i l i z e d to study the abundance. The trawl survey by the B i o l o g i c a l Station during 1952-195^ was conducted using small meshed ( 1 . 5 ") shrimp trawl. During July 1961 a small meshed shrimp trawl was used i n sampling areas 1, 2, and 3-' In sampling area k a trawl having a k" mesh with a small meshed cod-end cover was used. A t o t a l of 21 useful hauls were made from the sampling areas (Figure 5)- Of these,with the exception of two hauls i n area 1 and one i n area 2, the entire catch was taken for estimates of length composition. In area 1 sampling was necessary due to heavy catches. The o t o l i t h s were taken from a l l of the specimens i n 11 of the hauls. Of the remaining 10 hauls, o t o l i t h s from seven hauls were not used for reading since the catch was not adequately sampled. Otoliths from commercial catches were collected at random .by the sampler from a box of butter sole taken at random from a boat. I I I . Aspects.of the l i f e history of "butter sole. 1. Introduction Isopsetta i s o l e p i s i s a f l a t f i s h belonging to the family Pleuronectidae. The accepted common name (Bailey et a l i 9 6 0 ) for the species i s butter sole although Roedel (1953) gives the name sc a l y - f i n sole to the species. Butter sole i s known by other l o c a l names such as Bellingham sole and Skidegate sole. Since development of asymmetry during metamorphosis i s characteristic of a l l f l a t f i s h e s , the s k u l l and other structures exhibit remarkable asymmetry as a result of d i s t o r t i o n and displacement. A l l members of the family pleuronectidae are dextral so that the topographically dorsal side of the metamorphosed f i s h represents the o r i g i n a l right side of the symmetrical larva. According to Roedel (1953) i n butter sole the l a t e r a l l i n e curves upward over the pectoral f i n and has a dorsal branch. The maxillary extends beyond the anterior half of the lower eye. Scales are rough on the eyed side and number 90 or fewer •along the l a t e r a l l i n e . The species i s e a s i l y recognized i n fresh condition by the yellow and green blotches on the eyed side and bright lemon colour on the t i p s of the dorsal and anal f i n s . Clemens and Wilby (1961) state that butter sole i s known to occur from Southern C a l i f o r n i a to Southeastern Alaska. They were also recorded i n recent samples collected along Aleutian Islands (Wilimovsky - personal communication). Examination of the stomach contents indicate that butter sole feed on polychaetes, bivalves, prawns and crabs, cirripedes, young sand d o l l a r s , certain species of fishes and species of algae. 2- Confines of the butter sole population spawning i n Skidegate Inlet, (a) Hecate S t r a i t habitat. The following description of the Hecate S t r a i t habitat i s p a r t l y based on the account given by Ketchen (1956) and p a r t l y on the accounts by Barber (1957 and 1958). The continental shelf o f f the west coast of Canada i s narrow and i n many places shelves very rapidly seaward. 8. Off the main coast of B r i t i s h Columbia there are three shallow hanks (Figure 2 ) , each separated from the other by waters deeper than 50 fathoms. The Hecate S t r a i t bank which i s the largest of the three i s an extension of the Queen Charlotte Islands and the 50 fathom contour encloses an area of approximately U550 square miles. This bank i s w e l l isolated i n the north by the deep water of Dixon Entrance and i n the south and southeastern side by the Queen Charlotte Sound. Hecate S t r a i t bank i s connected to the shoal areas along the mainland only on i t s northeastern side by waters shallower than 50 fathoms. The depth contours of the Hecate S t r a i t bank are given i n Figure 3- T n e gradient between 20 and 50 fathom contour i s sharp on the north and northeastern sides but i s more gradual i n other regions. The upper region of the bank has considerable areas of smooth sand. In central and lower regions the bottom i s very rough and contains gravel, shale, hard sand and branacles. On the edge of the bank the composition of the bottom changes to soft sand and mud. Barber (1957) has shown that there i s a c y c l i c alternation of summer and winter deep water. The strong southeast winds during winter cause an accumulation of surface water along the coast of B r i t i s h Columbia displacing the cold deep water offshore. The deep winter water i s thus r e l a t i v e l y warmer and less saline than the deep summer water. Weak southeast winds during summer cause the accumulated surface waters to move offshore enabling the return of the deeper waters." Barber (1958) has also shown that associated with L l i s alternation of water masses there i s a seasonal v a r i a t i o n i n the oxygen content of deep water, reaching lowest values during summer (Figure 2 ) . 9- '34° 133" 132° 131* 130° 129" 128° 127° Figure 2. Map of the north coast of B r i t i s h Columbia shoving the three shallow banks off the main coast. The dotted region represents the area where the bottom water has oxygen less than 3 mg/-£- during the summer months of 195*+ and 1955 (adopted from Barber 1958 and Ketchen 1961, s l i g h t l y modified). Figure 3. Depth contours of the Hecate S t r a i t bank. 11. (b) Pattern of d i s t r i b u t i o n of butter sole i n Hecate S t r a i t . The range of the butter sole population inhabiting the Hecate S t r a i t area i s examined by studying the d i s t r i b u t i o n , movements, factors l i m i t i n g d i s t r i b u t i o n and i t s r e l a t i o n to other species i n the area. Unpublished reports on the Hecate S t r a i t trawling surveys conducted during 1953 and I95U recorded heavy catches of butter sole between F i f e Point and Butterworth ground. The area 3 off F i f e Point (Figure l ) supported a summer fishery during 19^5 and I9U6. Butter sole occur only i n small numbers on the central and lower regions and along the edge of the Hecate S t r a i t bank. No butter sole were represented i n the 5 half-hour trawls made along the edge during July 1961 at a depth of 15-22 fathoms. They were found again between 28 and 33 fathoms but were absent i n the single haul made at 62 fathoms. Ketchen (1956) ob served that young lemon sole inhabiting Hecate S t r a i t were distributed nearer the Graham -Island shore and older and larger specimens progressively away from the shore i n deeper waters. Length frequency d i s t r i b u t i o n of butter sole i n the 195^ hauls from Hecate S t r a i t 2 i s presented i n Table 1. The results of the X analysis of the data f o r hauls grouped approximately at 5 mile intervals from F i f e Point (Figure k) are presented i n Table I I . The length and age frequency d i s t r i b u t i o n s of butter sole collected during 1961 (Figure 5) are given i n Table I I I and 2 Figures 6 and f. A X analysis of the length frequency -distribution of the Butterworth and F i f e Point samples i s presented i n Table IV. The size d i s t r i b u t i o n of butter sole i n the 195*+ samples indicated that butter sole i n the 9-12 cm. length group were dominant i n samples along the Graham Island coast (Haul-group i ) and butter sole less than 20 cm.- length made up over 97$ of the entire catch. The length frequency d i s t r i b u t i o n of butter sole i n haul-groups II-V showed s i g n i f i c a n t difference and gave a 12. Figure k. Northern part of the Hecate S t r a i t bank showing the sampling positions i n 195U. Positions 11 and 15 are approximate. The dotted l i n e s are drawn approximately at 5 mile intervals from F i f e Point to indicate the 5 haul-groups. Figure 5. Northern part of the Hecate S t r a i t hank showing the approximate sampling positions i n I 9 6 I . Table I. Per cent size composition of butter sole i n the^l95^ trawl hauls taken from northern Hecate S t r a i t using 1.5" mesh cod- end. The sampling positions are given i n Figure k. Haul- 1 .(0 to 5 11 .(5 to 10 111.(10 to 15 IV.(15 to 20 V(20 miles group miles from miles from miles from miles from to edge of : F i f e Point) F i f e Point) F i f e Point) F i f e Point) the Bank) j | - Haul Nos. - Haul Nos . - Haul Nos. - Haul No. - Haul Nos. i 1 1 -"_L__ 6 - 10 11 - Ik 15 ,_l6_-__20 jLength Per- Sub- Per- Sub- Per- Sub- Per-. =Sub- Per- Sub- lin cms. i cent t o t a l cent t o t a l cent t o t a l cent t o t a l cent t o t a l 5 1.32 6 0 . 7 1.32 0.1+2 ! 8 2.63 2.1+0 1.09 i 9 9-21 1+.95 3-75 O.5I+ 0.1+3 ! 10 28.95 l+.8l 2.1k 0.5!+ 0.72 ! 11 19.7*+ 2.69 1.79 0 0.51 12 13-16 1-13 O.89 0 0.1+3 ! ! 3 3-95 0.99 0.71 0 0.51 ; ik 0 I . 9 8 1.1+3 1.09 1.95 i x 5 2.63 3-82 1.07 1.Q9 2.03 ! 16 1.32 2.69 2.1k O.5I+ O.58 i I T 6.58 3-39 1.79 3-26 2.17 1 1 8 2.63 6 . 0 8 O.5I+ 5-^3 3-OU 1 !9 3-95 97-39 1+.95 1+0.30 2.1k I 8 . 3 9 3-80 17.38 I+.56 16.93 20 0 3-68 2.86 2.17 3-11 21 1-32 1 2 .83 2.32 U-35 2-97 22 0 ; 3-96 1+.29 3-26 I+.78 23 0 3-68 2.32 2.17 5-11+ ! 2k 1.32 5.09 5.51+ 6.52 6 .58 25 3-96 U , 8 2 5.98 6.37 26 3-39 3.21 3-80 6 . 0 8 27 3-25 3-93 2.72 3-91 28 2.69 3-21 I . 6 3 3-69 29 2.6U 1.98 3 ^ 5 1 2.11+ 3U.6U 2.17 3^-77 3.76 1+6-39 30 2.12 2.68 3.26 3-01+ 31 I . 5 6 3-75 2.17 3-55 32 1.70 3-39 I+.89 k.3k 33 j 3-68 6.61 U-35 5-86 ' 3*+ i h.95 7-32 1 9.78 k.kl 35 1 3-82 6.1+3 8.70 5-21 36 3-68 5-71 U-35 I+.85 37 | 2.1+0 l+.ll I+.89 2.17 38 .' 0 .57 3-0U 3-26 I.7I+ 39 1 ! 0.1+2 1.07 1-63 0.87 ko I i 0 . 2 8 i 2 .32 0.5U 0.11+ ki 1 i 0 • 0.29 k2 . 1 0 i 0 . 0 7 1+3 1» t 25.18 i 0.5I+ I+6.97 3 1+7.82 36.5^ Total ! 100 1 100 100 1— 100 100 J L _ . 1 ...7.6_. — i _ . 7 ° 1 _ 56O _552 1382 Table I I . X analysis of the percent size composition of butter sole i n different haul groups given i n Table I. Haul group I I I I I IV V Total Length group (cms.) (5-10 miles from F i f e Point) (10-15 miles from F i f e Point) (15-20 miles from F i f e Point) (20 miles to edge of the Bank) x 2 0-19 20-29 29+ 1+0.30 3 ^ 5 1 25.18 18.39 Ik. 6k U6.97 17.38 3^-77 1+7.82 16.93 ^6.39 36.5^ 9 3 . 0 0 150.31 156.51 28.11 Total 99-99 100.00 99-97 99.86 399.82 N 707.O 56O.O 552.0 I382.O 16. Table I I I . Per cent size and age composition of butter sole i n ^ l 9 6 l trawl hauls taken from Northern Hecate S t r a i t . The approximate sampling posit ions are given i n Figure 5. General East coast of 8 miles off Butterwortl- East coast o f ! 8 miles off f Butterworth area Graham Island 1 F i fe Point ground 1 Graham Island 1 F i fe Point j ground Haul Wo. 1 to 6 18 to 19 20 to 21 1 1 to 6 i 18 to 19 ~[ 20 to 21 & depth 2 to 8 f 10 to 12 f 32 to 34 t ] 2 to 8 f ; 1 10 to 12 f 32 to 34 f Length Per- Sub- Per- Sub- Per- Sub- i Age 5 Percent 1 Percent Percent (cms.) cent t o t a l cent t o t a l cent tota l 9 1.24 0-57 1 1 I + 58.50 0.57 0 10 12.44 0 j 11 21.66 0 ( 11+ 38.59 14.28 6.56 12 13-69 1.14 13 7-V7 2.28 1.00 . III+ 2.49 i 23-43 14.14 14 6.22 5-71 0 ) 1 15 8.71 0-57 1.51 ; IV+ 0 ! 10.28 11.62 ] 16 4-98 3-U3 1.00 j i 17 5-39 1.14 2.01 1 v+ 0 1 21.71 15-15 18 7-47 ^-57 1.00 ! y j 19 3-32 92.09 4.57 23.98 0.05 6-57 ' V I + 0.41 i 24.00 29.80 20 ^-15 6.28 2-51 21 2.07 4.57 4.02 * VII+ 4.57 15-66 ! 22 0 6.28 5.02 ! I 23 0.83 4.00 3-01 JVIII+ 1.14 5-55 24 o :4 i 3-^3 6.03 25 5-lk 5-02 ; ix+ 1.51 26 5-lk 5-02 27 11.42 5-53 j 28 5-14 6.03 29 7-46 3-43 54.83 5-53 ^7-72 i 30 2.86 8.04 31 4.00 4.02 32 2.86 11.56 33 0.1+1 2.86 5-53 3k 5-71 3-01 35 1.14 5-53 36 1.71 4.52 37 0.05 38 2.01 39 1.00 kO Q.kl 21.14 45.27 Total 100 100 100 100 100 100 N 241 " l 7 5 ~ ~ 199 ~ 1 241 175 198 17- 2 Table IV. x analysis of'the percent 1size composition of butter sole from Hecate S t r a i t i n the 1961 sample given i n Table I I I . Length \ group -. (cms.) 8 miles off F i f e Point Butterworth ground Total X 2 0-19 20-29 29+ 23.98 5^.83 21.14 6-57 47.72 . 45.27 30.55 102.55 66.41 19.18 Total 99-95 99.56 199-51 N 175 199 z 2 0 0 I O O O CL 2 O 2 0 O Id I O M to O z u 2 0 0 CL IO b l Q. O EAST COAST OF GRAHAM ISLAND EIGHT MILES O F F FIFE POINT BUTTERWORTH GROUND J I I I I I I I I I I I I I I I I I I 1 I I I I I I I I * I 1 1 1 1 I 10 15 2 0 2 5 3 0 L E N G T H IN C E N T I M E T E R S 3 5 4 0 Figure 6. Histogram showing the size frequency d i s t r i b u t i o n of butter sole i n t h e j ^ o l trawl H hauls from northern Hecate S t r a i t . ?° 19- 6 0 J 1 I I I I 1+ 11+ 111+ IV + V+ VI+ VII+VHI+IX+ A G E GROUP Figure 7» Histogram showing the age frequency d i s t r i b u t i o n of butter sole i n t h ^ ^ G l trawl hauls from northern Hecate S t r a i t . 20. h i g h X v a l u e o f 28.11 . However a X t e s t d i d not i n d i c a t e any s i g n i f i c a n t d i f f e r e n c e i n the s i z e c a t e g o r i e s of b u t t e r s o l e i n h a u l - g r o u p s I I I t o V . W h i l e young b u t t e r s o l e l e s s than 20 cm. l e n g t h e x h i b i t d e f i n i t e depth s t r a t i f i c a t i o n and are dominant i n h a u l - g r o u p s I and I I which l i e m o s t l y w i t h i n the 10 fathom b e l t , no t r e n d i n s i z e d i s t r i b u t i o n i s seen i n the h a u l - groups I I I t o V . D u r i n g the summer b u t t e r s o l e o c c u p i e s the s h a l l o w Hecate S t r a i t bank, t h e i r main summer1 f e e d i n g ground. W i t h i n t h i s a r e a the g r a d i e n t between 10 and 20 fathoms i s v e r y g r a d u a l . T h i s may obscure the depth .preference o f b u t t e r s o l e above 20 cm. l e n g t h which were dominant i n h a u l groups I I I t o V a l l l y i n g w i t h i n the 10-20 fathom b e l t . The d i s t r i b u t i o n o f b u t t e r s o l e i n 1 9 6 l samples from areas 3 .and k ( F i g u r e l ) at depths o f 10-12 and 32-3^ fathoms r e s p e c t i v e l y i n d i c a t e d a depth s t r a t i f i c a t i o n o f b u t t e r 2 s o l e w i t h r e s p e c t t o s i z e and age. The X v a l u e was s i g n i f i c a n t . The age d i s t r i b u t i o n o f b u t t e r s o l e i n 1952-1953 samples (Table XXXIX) a l s o showed t h a t b u t t e r s o l e o f age 1+ were m a i n l y c o n f i n e d t o the east c o a s t o f Graham I s l a n d . B u t t e r s o l e are g e n e r a l l y scarce i n h a u l s , t a k e n from the s h a l l o w water a l o n g the D i x o n E n t r a n c e s i d e o f Graham I s l a n d . However, heavy catches were o b t a i n e d i n the 1961 summer h a u l s from t h i s a r e a . T o t a l c a t c h and l e n g t h frequency d i s t r i b u t i o n o f b u t t e r s o l e i n the h a u l s taken from t h i s a r e a are g i v e n i n Table V and the sampling p o s i t i o n s i n ' F i g u r e 5« The dense p o p u l a t i o n s sampled a t s h a l l o w depths may be l o c a l aggregat ions on good f e e d i n g grounds. The o t h e r samples taken a t d i f f e r e n t depths i n t h i s a r e a however d i d not i n d i c a t e a d e f i n i t e depth s t r a t i f i c a t i o n . The wide range i n the d e n s i t y o f b u t t e r s o l e i n the 1961 h a u l s (Tables I I I and V) suggest t h e i r p a t c h y d i s t r i b u t i o n w i t h i n the Hecate S t r a i t bank. 21. TULV Table V. Percent length composition of butter sole in the*196l trawl hauls taken from Dixon Entrance. Sampling positions are given in Figure 5- General area Haul number and depth Length(cms.) Dixon entrance side of Graham Island 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 3h 35 36 37 38 39 „Jtft-. . Total Sample Size Total catch 10 4f 11 6f 0.64 0 1.28 0 .64 1.28 2 .24 3-51 3-19 3-83 5-11 6.34 2.87 4.15 2.87 3-51 2.55 2.87 5.11 3-83 5.11 6.34 8.31 11.18 6.34 4.15 O.96 O.96 0.32 9-3.2 3-33 I 6.66 110.00 ! 13-33 20.00 j 6.66 113-33 i10.00 3-33 3-33 3-33 0 0 0 3-33 1 3-33 100 j 100 313 f 30 t 313 ; 30 12 8f 21.43 7-14 14.28 14.28 14.28 0 7-14 0 0 7-14 7-14 7.14 100 14 14 13,15 lOf 1-32 13.15 21.05 25.OO 23-68 1.32 6.58 2.63 2.63 1.32 0 0 0 1.32 4 I 100 ":' 76" • 76 14 20f 19.04 14.29 33-33 9-52 4.76 0 4.76 9.52 0 0 0 0 4.76 100 21 21 7 8f 0 .42 0 0 .84 0 .42 0 .84 I .67 3-35 4 .18 2. 3- 4. 5- 5- 51 76 60 86 44 5.86 7-11 7-11, 5-86 7-11! 6.70 10 .46 7-11 5.44 2-93 0.42 lOf O.63 2.50 0 O.63 O.63 1.88 2.50 4.38 2.50 5.00 6.88 6.88 10.00 7.50 14.38 IO.63 12.50 6.25 1.88 1.88 O.63 100 239 , j 600 i 100 160 1000 lbs. 16 lOf 17 j 15f i 1 7.70 7.70 j 0 ! 0 i 0 I 7 -70 ! 0 ; 7.70 1 0 i 0 < 0 I 7.70 I 7 -70 S 7 -70 j 7 -70 ; 0 ; 7 -70 j 14.38 ; 7 -70 I 7-70 j 2 4 6 2 0 10 10 10 12 10 10 2 2 4 6 2 2 0 0 0 2 0 0 2 0 2 13 13 100 J100 50 50 (c) Behaviour and movements of "butter sole. From an examination of trawl catches Alverson ( i 9 6 0 ) found that a l l commercially important f l a t f i s h i n the P a c i f i c northwest area tend to occupy r e l a t i v e l y shallow water i n summer and deeper water i n winter. Tagging experiments conducted by Ketchen (1956) showed that adult lemon sole populations i n Hecate S t r a i t exhibit a northward migration i n spring and early summer and a southward migration during early f a l l . On the basis of information provided by t r i p reports he showed that lemon sole migrate from deeper to shallower waters during late winter. Since heavy concentrations of butter sole occur during summer months i n the shallow Hecate S t r a i t f l a t s the tendency to occupy shallower waters i n summer seems to be shared as w e l l by butter sole. The presence of a spawning population at depths of 30-35 fathoms i n Skidegate Inlet and the occurrence of a large percent of immature females* along Butterworth ground (Figure l ) at depths less than 50 fathoms suggest that butter sole migrate to deeper waters during winter months. Barber (1957) has postulated that the seasonal movements of the f l a t f i s h of the area are i n general associated with the c y c l i c alternation of the water masses i n Hecate S t r a i t . I t has been suggested that t h i s may be a result of t h e i r preference f o r warmer waters. The seasonal movements of butter sole seem to coincide with t h i s general hypothesis. Nothing i s known of the movements of 0+ and 1+ groups of butter sole that occupy the area along Graham Island coast. Young pla i c e i n the North Sea are known to spend t h e i r f i r s t winter buried i n the sand (Wimpenny 1953)- Whether t h i s i s true of butter sole i s not known. Evidence from Manzer's (19^9) tagging experiments i n Skidegate I n l e t , even though not extensive, indicates that most of the butter sole move * In the February 1962 sample from the Butterworth ground only one of the U5 females examined showed any sign of maturing. 23- north after spawning i n Skidegate Inlet as 11 out of 12 tag recoveries were made north of Skidegate Inlet. The absence of mature females i n the sample taken during February 1962 from Butterworth ground (Figure 9) commercial trawl suggest that only mature specimens show any oriented movement towards the spawning s i t e . A comparison of the size frequency-and ovary condition of butter sole i n the samples from Butterworth ground and the spawning population i n Skidegate Inlet (Figures 8 and 9) also suggest that the non-spawners are non-migrants and that only the spawning population migrates south from northern Hecate S t r a i t to Skidegate Inlet. I t i s uncertain whether the maturing males i n the Butterworth sample would have migrated to Skidegate Inlet as the spawning season progressed. Wo tag recoveries were made from 550 f i s h tagged i n July 1953 at the northern region of the bank. This may have been due primarily to tagging mortality or to the poor fishery e x i s t i n g i n 195^- I t could also indicate the presence of other spawning site s i n the area. Certainly more convincing evidence on the movements of butter sole can best be obtained by -extensive tagging studies, (d) Spawning migration. Manzer (19^9) attempted to analyse the spawning migration by studying the changes i n sex r a t i o of the commercial sample during the season. He concluded that the males arrive at the spawning s i t e e a r l i e r and leave the area e a r l i e r than the females. This aspect can be studied only by analysing small meshed trawl hauls taken during the entire spawning season. The length composition of two half-hour trawl hauls (Table VI) taken with a shrimp trawl i n the beginning of the f i s h i n g season i n 1961 show a predominance of males i n the sample, the sex r a t i o being 5-51 « 1> The sampling survey conducted during January 1953 with small meshed trawl hauls i n Skidegate Inlet also showed that the sex r a t i o of the spawning population i s predominantly i n —1—1 I • I • ' • I I ' I ' I I I I I I I I I I I I I I I I I I l_l I I O 1 5 2 0 2 5 3 0 3 5 4 0 4 5 L E N G T H IN C E N T I M E T E R S Figure 8. Histogram showing the length frequency d i s t r i b u t i o n of butter sole i n samples from Butterworth ground (A) and Skidegate Inlet (B) collected "'during February 1962 by commercial trawlers. 25- Figure 9 . Photograph of the ovaries of butter sole sampled from Skidegate Inlet and Butterworth ground during February 1962,- A - mature ovary of butter sole (31cms. ) from Skidegate Inlet. C - immature ovary of butter sole (30cms.) from Butterworth ground. 26. Table VI. Length frequency d i s t r i b u t i o n of male and female butter sole i n two half-hou* SffiaLl meshed . (1 .5") trawl hauls from.Skidegate Inlet during February, I 9 6 I Length i n cms. Male Female 13 1 Ik 5 15 7 16 9 17 12 18 9 1 19 8 20 2 21 1 22 11 23 3 2k 3 25 10 26 15 27 12 28 11 29 10 1 30 Ik 31 35 2 32 29 5 33 26 3k 12 12 35 11 5 36 2 10 37 1 3 38 3 39 1 ko 259 1+y Table VII. Age composition of butter 'Sole i n samples taken from Skidegate Inlet during the 1953 sampling survey using 1.5" mesh cod-end. Age I I I I I IV • V ,VI VII VIII IX. X "XI Male 1U1 301 11+30 159k 1001+ 902 365 109 11+ 0 Female 21 11 50 118 305 369 198 61 7 1 27- favour of males, the sex r a t i o being 5-1^ : 1- The preponderance of males over the females among the spawning population i s only p a r t l y due to the early - a r r i v a l of males at the spawning s i t e . Males mature e a r l i e r than females and most of the f i s h migrating to Skidegate Inlet are mature. In the 1953 samples males of age f i v e occurred with the greatest frequency whereas the most frequent age of the females was seven years. From t h e i r d i s t r i b u t i o n i n the 1953 samples given i n Table VII i t i s evident that young males are much better represented than young females. As suggested f o r plaice by Wimpenny (1953) male butter sole may be ripe for a longer time and may remain longer at the spawning s i t e . These factors may-explain the predominance of males at the spawning s i t e . (e) Factors l i m i t i n g the d i s t r i b u t i o n of butter sole i n Hecate S t r a i t . In Hecate S t r a i t butter sole are never caught at depths greater than 50 fathoms. The depth contours of the Hecate S t r a i t area show c l e a r l y that the shallow Hecate S t r a i t f l a t i s we l l iso l a t e d by the deep water of Dixon Entrance i n the north and Queen Charlotte Sound i n the south. Because of the r e l a t i v e l y sharp depth gradient around Hecate S t r a i t bank, the depth barriers may be an important l i m i t i n g factor i n the d i s t r i b u t i o n of butter sole. They are known to occur at depths between 55 and 65 fathoms i n lower latitudes along the Washington and Oregon coast. This l a t i t u d i n a l difference i n depth d i s t r i b u t i o n and the movement to deeper warmer waters during winter also suggest, that temperature has an important role i n l i m i t i n g the d i s t r i b u t i o n of butter sole. Since butter sole occur within a narrow depth range i n a medium of high oxygen content, the presence of large areas of water of low oxygen content near the bottom during summer, as shown by barber (1958)^ may also act as a l i m i t i n g factor. 2 8 . Another important factor to be considered i s the extent to which butter sole are distributed during t h e i r pelagic phase. Since no work has been done on the early l i f e history of butter sole i t can only be deduced from what i s known of related species. Most f l a t f i s h e s spawn during winter months and i n most cases the eggs and larvae are passively d r i f t e d by the current u n t i l they adopt a benthic habit after metamorphosis. The northerly current of the surface water through Hecate S t r a i t as shown by the d r i f t b o ttle experiments of Thompson and Van Cleve (1936) may carry the eggs and larvae of butter sole from Skidegate Inlet northward. These larvae on metamorphosis may contribute to the young butter sole population, found mainly i n the inshore area along the Graham Island coast north of Skidegate Inlet. The larvae moving into the deep water of Dixon Entrance may perish and not contribute to the Skidegate spawners. My studies on the fluctuations of the butter sole population (Section IV) show that the young butter sole along Graham Island coast are eventually recruited to the spawning population i n Skidegate Inlet. (f) Relative importance of northern Hecate S t r a i t f l a t as a habitat for f l a t f i s h . The above consideration of the b i o l o g i c a l and environmental factors l i m i t i n g the d i s t r i b u t i o n of butter sole suggests that the Hecate S t r a i t bank i s the main area of d i s t r i b u t i o n of butter sole spawning i n Skidegate Inlet. Since other species of f l a t f i s h also occur i n the samples the r e l a t i v e importance of the Hecate S t r a i t bank for these species should also be examined. The most frequently occurring species i n the samples are butter sole, lemon sole, rock sole and sand sole. The r e l a t i v e abundance and association of these species i n the summer hauls taken during 1953-1954 were studied by the rank correlation methods of Kandall (1955)- Their use i n ecological studies i s also discussed by Fager (1957)- Since the duration of the hauls used to 29. take the 1953 samples varied they were f i r s t weighted to conform to a standard 15 minute trawl haul. The results of the analysis of dominance and r e l a t i v e abundance are given i n Tables VIII and IX. Table VIII shows that the order of dominance of f l a t f i s h e s i n the area i s butter sole>rock sole > lemon sole > sand sole. In 1953 t h i s was s t a t i s t i c a l l y s i g n i f i c a n t at the 0 .05 l e v e l and i n 1954 at the 0.01 l e v e l . From the rank values the dominance of butter sole over the others i n the area i s very conspicuous. This can further be seen from the results- of analysis of r e l a t i v e abundance taking two species at a time (Table IX). The r e l a t i v e abundance of the four species i n the 1953 and 195^ samples i s represented i n Figure 10, which i l l u s t r a t e s that butter sole i s more dominant i n the northern part of Hecate S t r a i t bank. The abundance of young f l a t f i s h e s along the Graham Island coast i s examined l a t e r (Tables XXXVII and XXXVIII) when the flu c t u a t i o n i n the butter sole population i s analysed. The results show that the r e l a t i v e abundance of young f l a t f i s h e s i n t h i s area varies from year to year. This may be due to two reasons. F i r s t l y the Graham Island coast may be the chief nursery ground for the young butter sole, lemon sole and sand sole, as no one species i s p a r t i c u l a r l y dominant i n the catches. Ketchen (1956) has shown that t h i s area i s the main nursery ground for lemon sole. Secondly variations i n the year class strength of these species are better expressed i n the samples because only young ones occupy t h i s area, (g) Inter-relationships among species of f l a t f i s h The analysis of r e l a t i v e abundance (Tables VIII and IX) has shown that the dominant species of f l a t f i s h over the northern Hecate S t r a i t bank i s butter sole. Since lemon sole, rock sole and sand sole are represented i n t h i s area by individuals of approximately the same size range as, butter sole, 30. Table VIII. Analysis of dominance of butter sole i n the 1953 and 1954 samples from the northern Hecate S t r a i t bank. W = co e f f i c i e n t of concordance. P = p r o b a b i l i t y of getting the observed W by chance. Butter sole Lemon sole Rock sole Sand sole No. of replicates £rank _1953_ Deviation' 19 33 ; 27 i 37 • 12 • 100 16 4 6h w 0.255 Table IX. Analysis of r e l a t i v e abundance of butter sole, lemon sole, rock sole and sand sole i n the 1953 and 195^ samples from the northern Hecate S t r a i t bank. 1953 1954 Respective t P N Respective t p N £ rank £ rank Butter sole x Lemon sole I 8 5 . 5 279.5 1-95 0.027 15 112.0 239.0 3.26 .0005 13 Butter sole x Rock sole 147.5 203.5 1.44 O.O76 13 247.0 281.0 0.64 0.26 16 Butter sole x Sand sole 81 .0 173.0 3-'05 0.001 11 118.0 233.0 2.95 0.002 13 Lemon sole x Rock sole I 8 7 . 5 163-5 0.615 0.27 13 160.5 139-5 0.61 0.27 12 Lemon sole x Sand sole 111.0 142.0 1.02 0.15 11 151.0 149.0 0.06 0 .48 12 Rock sole x Sand sole 85.O 168.0 2.725 0.003 11 145.5 205.5 1.54 0.06 13 1 1 31- 1953 BUTTER SOLE p < 0 0 5 „ LEMON SOLE U.S. U.S. ROCK SOLE p < O.OI SAND SOLE 1954 BUTTER SOLE P<OOI LEMON SOLE ROCK SOLE N . S . SAND SOLE Figure 10. Relative abundance of four species of f l a t f i s h i n the 1953 and 195^ samples from the northern Hecate S t r a i t . 32. the 1953 and 195^ samples taken from t h i s area were analysed to see whether the species exhibit any negative or positive association. This might indicate, for example, whether i n t e r s p e c i f i c competition has any s i g n i f i c a n t role i n c o n t r o l l i n g the abundance of these groundfishes. The results of rank correlation analysis are given i n Tables X and XI. Neither the results from the inshore area along Graham Island nor the main bank indicated any strong association between the species. The only s i g n i f i c a n t c o r r e l a t i o n values observed were between butter sole and sand sole and between butter sole and lemon sole. This was not consistent for a l l the years examined, (h) Conclusion The analysis of d i s t r i b u t i o n , abundance and movements of butter sole on the Hecate S t r a i t bank indicates that ( l ) There i s a general depth- s t r a t i f i c a t i o n according to size and age groups with the young ones being r e s t r i c t e d to inshore areas along the Graham Island coast (2) Within Hecate S t r a i t a summer migration to shallower waters and a winter migration to deeper waters occur. A north-south migration i s shown only by the spawning population. (3) The sex-ratio of the spawning population i s influenced by sexual differences i n the onset of maturity and spawning migration. (U) The population spawning i n Skidegate Inlet i s mainly confined to Hecate S t r a i t both during the l a r v a l and adult phases because of the physical conditions of the area and the existence of a depth ba r r i e r . The temperature and oxygen content may also function as l i m i t i n g factors. (5) There i s no active i n t e r - s p e c i f i c association of the f l a t f i s h i n the area during the post-pelagic phase. 3. Discreteness of the Hecate S t r a i t population of butter sole. The i d e n t i t y of s e l f contained stocks i s analysed by examining the Table X. The association of young butter sole, lemon sole and sand sole along the Graham Island coast as indicated by the rank correlation test. Year Butter sole - lemon sole Butter sole - sand sole Lemon sole - sand sole 1952 f = O.9888 P = 0 N = 10 T = 0.1363 P = 0 .66 N = 10 T = 0.0733 P = 0.-82 N = 11 1953 T =K).257 P = 0 .31 N = 11 T = 0.0221+ P = 1.0 N = 10 T = o.kghk P = O.O58 N = 10 195^ f = 0 .60 P = 0.23U N = 5 f = O.738 P = 0.067 N = 5 ' T = 0.527 p = 0.17 N = 5 Table XI. The association of butter sole, lemon sole, rock sole and sand sole from the Hecate S t r a i t f l a t . As indicated by the rank correlation test. Butter Butter Butter Lemon Lemon Rock Year sole- sole- sole- sole- sole- sole- lemon rock sand rock sand sand sole sole sole sole sole sole -r=0.kkkk T- -O .23U T=0.679 r =-0.1558 r =0.2076 I 5 = - 0 . 1 3 2 1 1953 P=0.025U p= = 0.30 p= 0 .005 p= 0.1+29 p= - o.h3 p= 0.6U • N = 15 N = 13 N = 11 N = 13 N = 11 N = 11 r= 0 . 3 2 2 5 r= -0.3025 X= 0.1161 r= 0.1212 r= = 0.0153 T=-o.2i+5 195^ T=0.lh p= =0.11 P=0.62 p= 0 . 6 l p = 1.0 p = 0 .27 N = 13 N = 16 N = 13 N = 12 N = 12 N = 13 34. p o s s i b i l i t y of effective interchange between populations during l a r v a l and adult phases of the l i f e history. This i s done by analysing the areas inhabited by butter sole for t h e i r a b i l i t y to maintain an independent stock; and by comparing the b i o l o g i c a l characters such as the size composition, gonad condition and morphological features of the samples collected from s different areas. The nearest known spawning population besides the Skidegate spawners i s along the Washington coast. The two populations being separated by approximately 600 miles make the p o s s i b i l i t y of intermingling by passive d r i f t during the early developmental stages remote. Ketchen (195&) states that lemon sole larvae could cover ,a distance of 150 - 370 miles assuming that the pelagic phase l a s t s from s i x to ten weeks. The factors l i m i t i n g the d i s t r i b u t i o n of butter sole w i l l also tend to maintain the discreteness of the two stocks so that there i s l i t t l e mixing of the adult populations by active migration. The question remains whether the Hecate S t r a i t population of butter sole i s a single self-contained stock. By means of tagging experiments Ketchen and Forrester (1955) showed the existence of l o c a l , s e l f - contained resident stocks of lemon sole i n the S t r a i t of Georgia d i s t i n c t from a migratory stock entering the s t r a i t from offshore during the summer. He also postulated that l o c a l populations of lemon sole i n the i n l e t s along the B.C. coast may be self-contained and d i s t i n c t from the lemon sole population found along the edge of the Hecate S t r a i t bank. Butter sole occur along the edge of the bank throughout the year even when the spawners congregate i n Skidegate Inlet during winter. I t i s not known whether there are other spawning site s i n Hecate S t r a i t that maintain more spawning populations, however, spawning was successful during the cold years, 19̂ +9 and 1950, when butter sole were absent from Skidegate Inlet. This i s evident from the success of the 1956 and 1957 f i s h e r i e s i n Skidegate Inlet (Table XXXl). 35- Since no additional spawning site s were indicated either by the 1953 survey or by the commercial trawlers engaged i n f i s h i n g i n the area, spawning on a large scale outside Skidegate Inlet may occur only during years when environmental conditions prevent t h e i r entry into Skidegate Inlet. Parish (1956) has pointed out that an area must possess certain features i f i t i s to maintain an independent self-contained stock. I t must be suitable for reproduction and growth and i t should possess a current system that does not carry the early pelagic stages beyond i t s boundaries. The current system i n Hecate S t r a i t appears favourable f o r the d i s t r i b u t i o n of the early developmental stages of butter sole from Skidegate Inlet to th e i r nursery ground along the Graham Island coast. Manzer's tagging study (1949) and the analysis of abundance of butter sole from the northern part of Hecate S t r a i t indicate that t h i s area i s the main summer feeding ground. The Hecate S t r a i t habitat i s thus adequate to maintain a self-contained population. The current pattern i n Hecate S t r a i t and the proximity of the deep Dixon Entrance make the Butterworth ground an unfavourable spawning area. There i s considerable i n d i r e c t evidence to support the theory that there i s a single self-contained stock of butter sole on the Hecate S t r a i t bank. F i r s t there was a dominance* of 6+ butter sole i n the 1961 summer hauls taken i n the northern part of Hecate S t r a i t (Table XXV"), t h i s was followed by a successful fishery for spawning adults i n Skidegate Inlet (Table XXXl). In comparison at spawning time there i s a very large percentage of immature females on the Butterworth ground. This evidence when coupled-with length frequencies of commercial samples taken from these areas (Figure 8) and the above analysis of the movements of butter sole also lend support to t h i s theory. 36. (a) Evidence from meristic study. Since no tagging studies were done to ascertain the existence of independent self-contained populations, meristic counts were taken on "butter sole from different areas to examine whether they show s i g n i f i c a n t differences. Four samples were collected from the Hecate S t r a i t area and one sample each from the Washington and Oregon coasts. Regarding size composition, the populations sampled from Hecate S t r a i t during summer and winter were not homogeneous. The summer samples were from the nursery ground and consisted of both adults and juveniles, while the winter sample from Skidegate Inlet represented the spawning population. The winter sample from Butterworth ground, judging from the condition of the gonads, includes mostly non-spawners of the season. The winter samples from the Washington and Oregon coasts again represent only the adult spawners. Sampling was not uniform since the gear used during summer was small meshed while the samples during the winter, with the exception of that from the Oregon coast, were taken from commercial catches. Three characters selected for counts were dorsal f i n rays, anal f i n rays and l a t e r a l l i n e pores from the base of the pectoral f i n to the t i p of the anal f i n because, below subspecific l e v e l s , s i g n i f i c a n t differences between isolated populations are more ea s i l y -detected among these, the most variable characters. The analysis i s r e s t r i c t e d to one sex only to avoid the complic- ation of any sexual differences. The results are given i n Tables XII to-XVI. In spite of the deficiencies i n sampling, a clear difference i n the dorsal and anal f i n ray counts was observed between the samples taken from Hecate S t r a i t and the samples from the Washington and Oregon coasts. Since the samples collected during the winter of 1962 from -Skidegate Inlet and the United States coast were of mature specimens, t h e i r differences i n f i n ray 37- Table XII. Details of the meristic counts of butter sole i n the samples from Hecate S t r a i t , and the U.S. coast. Hecate S t r a i t summer Hecate S t r a i t hank s Mean •H •P !* a • Range H o St. w o error u o & Sample fi size Mean Range a •H C St. =h o error O rH a Sample size a •H H CO H <D cS U U O (U Ph -P (Si Hi ;• Mean . Range , St. ferror \ Sample I size 86.35 80-92 0.1+19 ^9 66.1+7 61-72 !0-333 ^5 7 5 A 5 71-80 0.285 1+2 Butter- worth ground winter Skidgate Inlet 85.86 80-92 0.390 kk 66.19 62-71 10.267 i 1. 1 75-32 J O - 7 9 l '0 .297 l+l 86 .08 81-92 0.322 50 65.81+ 57-70 0.289 50 75-^0 71-80 j o . 2 5 1 50 Butter. worth ground Washv*-coast winter 8-10 miles SW to WSW off Quillayute Oregon coast winter Between Umatila and mouth of River Lapush Table XIII. t-values and t h e i r p r o b a b i l i t y levels obtained from a comparison of dorsal and anal f i n ray counts i n the samples from Skidegate Inlet and the U.S. coast collected during February, 1962. 1 Skidegate Inlet Dorsal f i n ray Anal f i n ray ' t P t P Washington coast ! I+.36 < 0 . 0 0 1 3.87 <0.001 1 | Oregon j coast 1+.86 < 0.001 3-16 < o . o o 5 38. Table XIV. Analysis of variance on the dorsal f i n ray counts within the samples from Hecate S t r a i t . Sourc e D.F. S.S M.S. F. Total 193 1214.6 1.724 Means 3 32.19 10.73 N.S. Residual 190 1182.41 6.22 — - _ Table XV. Analysis of variance on the anal f i n ray counts within the samples from Hecate S t r a i t . Source D.F. S.S. M.S. F Total 186 707.9 O.83 Means 3 9.48 3-161 N.S. Residual 183 698.42 3.816 Table-XVI. Analysis of variance on the number of l a t e r a l l i n e pores within the samples from Hecate S t r a i t . Source D.F. S.S. „ M.S. F Total 182 647.3 0.186 Means 3 2.011 O.67 N.S. Residual 179 645.29 3-6o 39- counts were examined separately (Table X I I l ) . The results showed highly s i g n i f i c a n t differences between the Skidegate Inlet population and those from the United States coast. No s i g n i f i c a n t differences were observed i n the meristic counts of butter sole from the Washington and Oregon coasts. I t i s not known whether they belong to the same population or represent two spawning populations. Tables XIV to XVI give the results of analysis of variance for samples taken within Hecate S t r a i t . No si g n i f i c a n t variance r a t i o was observed for any of the three characters examined. However, a t- t e s t indicates that the difference i n the mean values of dorsal f i n ray counts i n the samples from Butterworth ground during the summer and winter i s s i g n i f i c a n t at. the 5$ l e v e l with a t-value of 2.198 for 93 df. This difference i s interpreted here as an a r t i f a c t p a r t l y due to the fact that the Butterworth ground samples were taken from commercial catches during the winter and from small meshed trawl hauls during the summer and p a r t l y due to seasonal v a r i a t i o n i n the size composition of butter sole i n t h i s area. Lindsey (1962) discusses the bias introduced i n sampling as a result of the existence of a correlation between meristic count and size of f i s h from the same brood. In spite of sampling v a r i a b i l i t y and possible differences between slow and fast growers, the highly s i g n i f i c a n t differences i n meristic counts observed between the Hecate S t r a i t population and those along the United States coast seem to be the res u l t of genuine environmental differences of the areas inhabited by the respective populations, (b) Conclusion On the basis of meristic studies and other b i o l o g i c a l factors discussed above, the weight of evidence favours the view that there i s a single s e l f - contained stock i n Hecate S t r a i t which i s d i s t i n c t from those along the Washington and Oregon coasts. h. Aspects of the population characteristics of butter sole, (a) Age and grovth of butter sole. Because of i t s importance as a population variable the pattern and rate of growth of butter sole was studied i n considerable d e t a i l . In t h i s study the opaque and hyaline zones of o t o l i t h s were interpreted as being annular. A large amount of l i t e r a t u r e i s available on the use of hard parts of f i s h i n growth studies. Besides Graham (1929) and Van Oosten (1929) who reviewed the l i t e r a t u r e , H i c k l i n g (1933), Rollefsen (1935), Hile (19U1), Saetersdal (1953), Trout (1958) and others, have made valuable contributions. Otoliths of butter sole have f a i r l y w e l l defined opaque and hyaline zones which can, with the exception of older specimens, be read easily,(Figure l l ) . The o t o l i t h s sampled for age and growth studies were grouped at one cm. intervals of f i s h length and preserved i n a mixture of equal parts water and glycerine. A few thymol cr y s t a l s were added to the mixture to prevent the formation of moulds. Reading the o t o l i t h s * from specimens above 35 cm. i s more d i f f i c u l t than those from younger ones. For the back calculation of f i s h lengths the o t o l i t h radius can be measured from the nucleus to the end of the hyaline zones along a chosen axis. Radii along two axes ( F i sure l l ) of I9U o t o l i t h s from a length range of 15 to 38 cm. were measured. Variations i n the o t o l i t h radius measurements along the' two axes were found on the average * For reading, the o t o l i t h s were kept on the medial or s u l c a l side and the opaque and hyaline zones were examined against an illunimated black dish using 9 X magnification. Most of the readings were done i n a 2$ solution of papain, a proteolytic enzyme from the papaiya tree. Since butter sole spawn during February and March, the end of each winter season i s taken to mark the end of one year. In determining the age i t i s found that best results are obtained i f the reading i s f i r s t done on females starting from the youngest specimen. kl. POSTERIOR PROCESS Figure 11. Photograph of the butter sole o t o l i t h showing hyaline and opaque zones. U2. to be of the same magnitude. The axis from the nucleus to the rostrum was chosen to measure the zones since i t was along t h i s radius that the most zones could be distinguished at the outer edge of the older o t o l i t h s . The measurements were made using a one cm. eyepiece micrometer which had been graduated into 100 divisions. To f a c i l i t a t e back calculations the o t o l i t h radius-body length r e l a t i o n - ship was determined. Back ca l c u l a t i o n was based on the assumption that the of intercept or the time f i r s t formation of the o t o l i t h was constant and that any deviation of in d i v i d u a l points from the calculated regression l i n e was due to v a r i a b i l i t y i n the slope. To obtain a weighted mean back calculated length at different ages, back calculations obtained from different age groups were weighted according to the estimated numbers of these age groups i n the catches from sampling l o c a l i t i e s 1 and k shown i n Figure 1. Since regional differences i n the density of the population and i n growth rate were noticed t h i s procedure would increase the accuracy of the estimated length at various ages. ( i ) Body length-otolith radius relationship. Since the relationship between body length and o t o l i t h radius varies widely between different species an accurate estimate of t h i s relationship i s important to avoid errors i n back calculations. The estimated relationships for male and female butter sole are given i n Figure 12. The body length-otolith radius r e l a t i o n f o r the male was found to be Length (cms.) = 0.79M+R--*»0'..70 and for the j einale - Length (cms.) = 0 .09 + O.759I+R. The results of the analysis of covariance for these two regression l i n e s are presented i n Table XVII. Figure 12. Body length - o t o l i t h radius relationship of butter sole. kk. Within the length range examined, the body length-otolith radius relationship i s l i n e a r . Only the o t o l i t h s from the small meshed trawl hauls collected during 1961 were used for back calculation. I f material from e a r l i e r periods had been included i t may have increased the v a r i a b i l i t y , as suggested by Southward (1962) for halibut. Long periods of preservation may also increase the v a r i a b i l i t y . The s i g n i f i c a n t variance r a t i o for the regression c o e f f i c i e n t s suggests that the body length-otolith radius relationship for the two sexes i s different. Since the power of the covariance analysis i s very high with such a large number of degrees of freedom even a s l i g h t difference i n the two slopes may appear as s i g n i f i c a n t . Nevertheless back ca l c u l a t i o n of lengths from o t o l i t h s was done separately for the two sexes using the respective regression l i n e s , ( i i ) V a l i d i t y of o t o l i t h reading. The r e l i a b i l i t y of the age readings from scales and o t o l i t h s have been studied for many species of fishes. References include R i l e ( l9*f-l), Jensen and Clark (1958), Saetersdal (1953, 1958), Frost and Kippling (1959), Bratberg (1956) and others. Most of these authors found that the regular formation of zones i n the hard parts permitted r e l i a b l e estimates of the f i s h ' s age. In the case of an o t o l i t h the opaque zone i s generally l a i d down during the summer and the hyaline zone during the winter. However, Muller (1958) bas noted a reversal i n the timing of the zone formation i n certain populations of Lota l o t a (Linnaeus). In butter sole the r e l i a b i l i t y of o t o l i t h reading i s tested (a) by studying the timing of the zone formation (Figure 3) and (b) by comparing the estimated lengths at different ages with that determined by analysing the length frequency d i s t r i b u t i o n by the p r o b a b i l i t y paper method as described by Harding (l9*+9) and Cassie (l950> 195*0' The length measurements of 9*+6 females i n the July 1961 samples were 4 5 . used for t h i s purpose (Figure 14). The results are given i n Tables XVIII and XIX. In the summer a great proportion of the o t o l i t h s possess an opaque zone at the edge (Figure 13)- As the winter progresses t h i s proportion dwindles rapidly-and the number of o t o l i t h s with hyaline edges increases. The s l i g h t discrepancy i n the A p r i l sample may be due to inadequate sample size. This observation supports the view that the zones are l a i d annually, the opaque zone during summer and the hyaline zone during winter. The close ide n t i t y of the lengths at different ages estimated from o t o l i t h s with the various modal lengths obtained by dissecting the length frequency data for the females (Table XIX) lends further support to the r e l i a b i l i t y of the o t o l i t h s i n age determination. This study has, however, some li m i t a t i o n s . There i s a certain amount of personal bias introduced i n determining the nature of the zone at the edge of the older o t o l i t h s . Also the estimation, of modal lengths of the older age groups from the length frequency i s subjected to errors due to the greater overlap of age groups, the i n s u f f i c i e n t number of class intervals -between means and bias i n sampling. As an example i n the 1961 samples from the Hecate S t r a i t bank, older age groups dominated the r e l a t i v e l y heavy catches i n area 1. This may have affected the estimation of the modal lengths of the older age groups. Hence the s i m i l a r i t y of the estimated modal lengths obtained by the p r o b a b i l i t y paper method and by back calculation may'be p a r t l y due-to chance. However, such errors are minimal i n the estimates of modal lengths for the f i r s t three age groups. ( i i i ) Growth rate of butter sole. The lengths at various ages, estimated by reading o t o l i t h s sampled from the spawning population, are entered i n Tables XX and XXI. The back calculated Table XVII. Body length - o t o l i t h radius relationship:- analysis of covariance among sexes to test the homogeneity of the regression c o e f f i c i e n t s . Source oi Variation Residual s.s. df. M.S. F. Common Within sexes Reg.coef. 2Jlk.69 2681.07 33.62 1110 1109 1 2.1+176 33-6200 13.9060 Table XVIII. Estimated percent of o t o l i t h s with opaque or hyaline zones at the edge i n the July 1961 and I958-I96O winter samples. 1 i \ Number Opaque Hyaline uncertain examined edge edge 1961 July 3^8 87-35 6.61 6.O3 1958- '60 J anuary 138 60.87 36.96 2.17 February 982 1+1.55 kk.91 13.5^ March 576 25-52 6O.76 13-71 A p r i l 57 33-33 50.88 15-79 Table XIX. Comparison of mean back calculated lengths at different ages from o t o l i t h s and the estimated modal lengths obtained from the length frequency d i s t r i b u t i o n of female butter sole i n the sample collected during July 1961. Age group 1+ 11+ III+ IV+ V+.,' VI+ VII+ From o t o l i t h (unweighted) I I . 8 9 16.97 21.97 25-3^ 28.26 31-73 From o t o l i t h (weighted) 11-95 17.22 22. 5U 25.95 29.82 31.70 35-67 From length \ frequency ] (unweighted) 11-95 17.10 21.66 21+.70 28.00 31-66 3^-30 47- Figure 13. Percent of "butter sole o t o l i t h s i n the sample with opaque, hyaline or uncertain edges. 0.01 0.1 10 30 50 70 90 99 CUMULATIVE PERCENT LENGTH FREQUENCY 99.9 Figure lk. Dissected length frequency distributions of female butter sole by the p r o b a b i l i t y paper method into modal length groups. 00 i+9- lengths given i n Table XXII were determined from o t o l i t h s taken from both juveniles and adults. In obtaining mean lengths equal weights are assigned to each back calculated length from different age groups irrespective of the sample size. Because of the yearly variations i n growth rate a weighted mean based on the sample size of each age group cannot be estimated. Since the number of age groups from which the mean back calculated length at the end of each year of l i f e i s obtained progressively decreases, the estimated mean lengths are influenced more and more by errors i n back calculated lengths. In Table XXII the back calculated length vof 11+ females i s based on one o t o l i t h from a slow growing f i s h . This single specimen considerably reduces the estimated mean lengths of the ages greater than seven. The lack of adequate samples f o r the older age groups and yearly variations i n growth rate may thus influence the accuracy of the estimated lengths of older ages. Because of t h i s the lengths for higher ages were obtained by f i t t i n g a Wal-ford plo t to the mean lengths up to age s i x for females and age seven for males. The Wal-ford graph drawn for the butter sole data i s given i n Figure -15- The estimated growth together with the maximum length (LQQ) and K or the rate of deceleration i n growth increments obtained from the Wal-ford plot are entered i n Table XXIII. The growth curves for the two sexes are drawn i n Figure l 6 . Comparison of the back calculated lengths and the lengths estimated by reading o t o l i t h s sampled from the spawning population. The age estimated by reading o t o l i t h s from the spawning population i s subject to errors because the early year classes w i l l be represented i n the sample only by those maturing faster. As shown i n Table XIX the maximum growth increments occur between ages 1+ and 5- The mean lengths for older age groups do not seem to be representative. This may p a r t l y be due to decreasing 50, Taple_XX. Mean lengths of butter sole at various ages estimated by reading o t o l i t h s sampled from the spawning population during January 1953f using a small meshed shrimp trawl. MP. I i i i i ; V VII _ . y i i i IX- X XI Male - 13.90 18,3 21. k 27.1 30^9 32.9 33.8 33^5 34.8 - Female - 13 «96 17.2 21.9 36.2 3 ^ 3 35-3_ 36:2 36\8 39-4 35.0 Table_XXl• Mean lengths of female butter at various ages estimated by reading o t o l i t h s from commercial catches f o r the period 1958-19B0. Age V V i v i i v i i i IX X XI 32.90 34.43 "'"36780 " 3 7 7 6 8 37.81 39-5 - _ . Table XXII. Weighted back calculated lengths at the end of each year of life of 316 males and 446 females collected during July 1961. 51. Sex Age at capture Length (cms. ) at cap- ture No. of fish II III IV VI VII VIII IX XI 1+ 11+ III+ IV+ V+ VI+ VII+ VIII+ IX+ 11.07 16.94 21.86 26.06 28.39 30.01+ 32.16 33-06 35-00 1+ 11+ III+ IV+ v+ VI+ VII+ VIII+ IX+ XI+ .11-95 117.22 22.54 25.95 29.82 31.70 35-67 35-17 35-84 37.00 31 54 54 29 47 75 18 7 1 Mean Increment 44 103 79 38 53 78 31 13 6 _1 Mean 5-97 5.65 6.23 6.05 6.20 5.89 6.02 5- 76 6.62 "6764 "" "S". 6.81 6.22 6.49 6.48 6.56 6.44 6.88 6- 58 6.08 6.00 6.T5 " 13.02 13-38 13-55 12.89 12.16 12.56 11.63 13-95 i2.89~ 85" 5- increment 7. 13-01 13-96 13.24 13-02 12.55 14.68 13-24 13-56 14.12 "l3.'49 54 E 19-58 19.88 18.90 18.07 18.84 17-65 18.52 18778"" 24.26 23-76 22.95 23-71 22.70 j22^19 23.26" 26.79 26.51 28.81 26.83 28.92 31.10 26.30 28.85 31.19 _24.93_ 27.68 30 .̂42 2~6.27 "28.56""36.96 32.41 32.25 33.63 ' 4:4"8 " 3.01""" 2.29 " "2:"34" 32.33_33V6T I.T3 1.36' 20.12 19-66 19.12 18.74 21.29 18.89 19.08 20.02 19.61 .12 24.05 24.45 23- 73 26.63 24.12 24- 56 23-71 24 ."46 TT7B5 3"- 28.09 27-65 30.00 27-49 28.91 25^91 28.61 55" " 3~."< 30.40 33-01 30.76 32.05 29.25 34.80 32.38 33-77 30-73 34.16 34-85 32.20 34.92 _3l-31 34-79 31.09 32.92 33-74 3it.11 3 4 J 9 18 1.133 o".82 0.37 35^9 ~6"."68 n o - Figure 15. Wal-ford plot of the back calculated lengths of butter sole. ; ro 50 FEMALE @ MALE Fig. 16. Growth curve of butter sole. . '"-Solid points are the the o r e t i c a l lengths estimated from the Wal-ford plot. UJ 54. accuracy of aging older o t o l i t h s and p a r t l y to t h e i r inadequate representation i n the sample. The growth rates of females were estimated from the commercial sample collected during I958-I96O (Table XXI) and are influenced by market selection as w e l l as gear selection. Because of t h i s , the estimated lengths of 5 and 6 year olds i n p a r t i c u l a r , are considerably higher than would be representative of the general stock. Hart (19*4-8) has discussed the effect of gear and market selection on the accuracy of the growth rate estimates made by reading o t o l i t h s from the commercial butter sole catch. Since the sample for the back calculated lengths are from the nursery ground and the early age groups are adequately represented, the back calculated lengths (Table XXIl) provide a more r e l i a b l e estimate for the early ages. However, as mentioned e a r l i e r , even here the sample i s not adequate for the older age groups. Hence the th e o r e t i c a l growth rates entered i n Table XXIII are obtained from the Wal-ford p l o t . Yearly variations i n growth rate. Errors i n the back calculated lengths may arise f o r various reasons, •such as the use of an incorrect body length-otolith radius relationship, bias i n the sample due to selective f i s h i n g of faster growing f i s h and a higher mortality rate of the faster growing f i s h . They result i n the occurrence of Lee's phenomenon or a progressive decrease i n the calculated lengths from successively older o t o l i t h s . This aspect has been discussed recently by Parrish (1956) , Jones (1958) and Taylor (1958). The back calculated lengths i n Table XXII do not show any indication of Lee's phonomenon. Errors from selective f i s h i n g may not be s i g n i f i c a n t since f i s h i n g takes place primarily, on the small section of the population over seven years of age. Within the length range examined the l i n e a r relationship between body length and o t o l i t h radius seems to be r e l i a b l e . The back calculated lengths 55- thus provide not only reasonably accurate estimates of growth but also information on i t s variations. The yearly v a r i a t i o n i n growth from the means of 3 + to 8+ year olds i s given i n Table XXIV and Figure 17. Figure 17 shows appreciable differences i n growth rate which are p a r t l y explained by the r e l a t i v e brood strength, though factors such as changes i n the abundance of food, temperature and other environmental factors may also be involved. The 1953 year class represented by the 8+ f i s h i n the 1961 summer sample contributed heavily to the i 9 6 0 fishery as seven year old f i s h . The analysis of the r e l a t i v e abundance of the 1953 year class (Section IV) suggests that the 1953 spawning produced a moderately strong year class- S i m i l a r l y , judging from the abundance of ,6+ year olds i n the July 1961 sample (Table XXV), the 1955 spawning may also have been successful. Thus the slow growth rate of the 6+ and 8+ f i s h i n the July ' I96I sample (Figure 17) may p a r t l y be due to i n t r a s p e c i f i c competition. The growth rate of 7 + butter sole i s 'above average though t h i s i s not evident i n the males. Since the 1961 fishery was not successful i t i s presumed that 195^ was a poor brood year. The growth of k+ year olds i s also above average though t h i s trend i s seen only among males. This age group i s poorly represented i n the 1961 sample (Table XXV) suggesting that spawning i n 1957 w a s not successful. The association between the growth rate and the r e l a t i v e brood strength suggests the role of i n t r a - s p e c i f i c competition as one of the factors c o n t r o l l i n g yearly variations i n the growth rate of butter sole. I t i s also evident from Figure 17 that the per cent deviation of lengths from the mean gradually-decreases as the f i s h get older. Thus i f the growth rate i s slow i n i t i a l l y (6+ and 8+) i t i s compensated for i n l a t e r years by faster growth. The reverse also seems to be true. The 7 + females show a higher growth rate i n the beginning but the per cent deviation from the mean 56. Table XXIII. The mean length of butter sole at the end of each year's l i f e . The lengths at ages above 6 years for females and 7 years for males were obtained from the Wal-ford plot. Age I II III IV V VI VII VIII IX X XI XII K Male Female 6.04 6.45 12.89 13.49 I 8 . 7 8 19-61 23.26 24.46 26.27 28.01 28.56 31.09 30.90 33-38 32-31 35-18 33-37 36.59 34.17 37-69 3^.78 38.56 35-24 39-24 36.64 41.71 0.2814 0.2437 Sable XXIV. Percent deviation of the hack calculated lengths from the mean for age groups III+ to VIII+ given in Table XXII. Values up to fourth decimal place are retained in calculating percent deviation. Age in years I II III rv V VI VII VIII Male: Mean length(cms. ) 6.04 12.89 18.78 23-26 26.27 28.56 30.90 32.31 Sex Year Age Length Class at at cap- cap- ture (cms. ) ture 1958 II1+ 21.86 3-07 3-80 4.27 H 1957 IV+ 26.06 0.13 5.09 5-89 4.29 1956 V+ 28.39 2-55 - 0 . 0 2 O.65 2.14 I .96 1955 VI+ 30.04 -2.53 -5-65 -3-76 -1-3* O.89 0.84 1954 VII+ 32.16 -0.32 -2 .60 0.33 1.92 2.14 I .25 0.63 1953 /III+ 33-06 ^4.72 -9.82 -5-99 -2.40 0.09 _ l - 0 0 0.93 . 0 . 3 2 . . . Female Mean length(cms. ) 6.45 13-^9 19-61 24.46 28.01 31.09 33-38 35-18 1958 III+ 22. 54 0.53 3-52 2.58 <U 1957 IV+ 25-95 0.41 -1.79 0.21 -1.71 1956 V+ 29.82 I .69 -3 .50 -2-53 - 0 . 0 6 0.28 11 1955 VI+ 31-70 -0.21 -6.96 -4.47 -3-00 - I .30 -2.23 195^ VII+ 35-67 6.60 8.88 8-55 8.85 7.09 6.16 4.25 * 1953 /III+ 35-17 1-93 -1.86 -3-70 -1-39 - I .85 -1.09 -3-01 -2.91 Table XXV. Estimated age composition of butter sole in the samples taken from 1 northern Hecate Strait during July 1961. I II III IV V VI VII VIII _rx X -XI 15^ 249 390 312 469 860 346 13^ 66 0 1 57- 5 > UJ Q Z UJ u QC UJ 0. IO o -IO IO o -10 IO o - IO IO O -IO IO o - IO IO o -IO - MALE —1 1 1 _w.±__. - I 1 1 .1 iy>__. 1 rwC —T_ _| r«_ J£L+ I i . . - . . itlLfc. I 2 3 3 5 6 7 8 AGE IN YEARS FEMALE -IV.*.. *fc. VI* l vu.t_- . X l l l d t - - . A G E IN Y E A R S Figure 17. Percent deviation of the back calculated lengths from the mean at different years for age.groups 111+ to VIII+ i n the July 1961 samples. 58. gradually decreases i n l a t e r years. Such changes i n the growth pattern of a year class may he observed i f the species possess an asymptotic length which they tend to at t a i n . Since the Wal-ford plots (Figure 15) of butter sole data beyond two years of age are close to a straight l i n e the species may be said to possess an asymptotic length. Figure 17 also shows that most often the per cent deviation of the growth rate from the mean i s maximum during the second year. This may be expected since an i n f l e c t i o n to deceleration i n growth rate occurs around two years of age. These changes i n the growth pattern of a year class compared to the mean growth rate of the butter sole population may thus be described by means of i t s growth curve and the asymptotic length. Hence even though the growth rate may be influenced by environmental factors, i t seems reasonable to assume that butter sole possesses a chara c t e r i s t i c growth pattern. Unless there i s a long term change i n the growth of butter sole, these deviations i n the growth rate of a year class may be ignored i n theo r e t i c a l studies as they are compensated for i n l a t e r years. The year classes examined above, especially those with an i n i t i a l slow growth, a t t a i n t h e i r normal mean size at the end of four or f i v e years which i s before they are f u l l y recruited to the fishery. Seasonal differences i n growth rate. The samples taken between July 14 and 23, I961 were used to calculate the mean growth increment up to July for each of the age groups 1+ to VI+. These increments and the proportions of the mean annual increments that they represent are given i n Table XXVI. 1+ and 2+ butter sole have already completed a greater proportion of one year's increment by July. Pearcy (1962) also observed the same phenomenon i n an estuarine population of winter flounder Pseudopleuronectes americanu's (Walbaum). 3+ and older butter soles appear to be more uniform i n t h e i r growth. I f i t i s assumed that most of the year's 59- growth occurs after the beginning of A p r i l , then the 3+ and older age "groups complete approximately 50$ of the year's growth i n four months. This estimate, however, i s influenced by yearly variations i n the growth rate. Further confirmation i s required and can be obtained only by studying the seasonal growth over a period of several years. Seasonal growth could not be estimated for age groups above s i x years since inadequate representation of older age groups i n the sample has biased the estimated mean lengths of females above si x years and males above seven years. Regional differences i n growth rate. In his study on juvenile winter flounders of the Mystic River estuary i n eastern Connecticut, Pearcy (1962) observed regional differences i n the growth rates of the same population as a result of the larger f i s h moving farther into the shoals. Table XXVII gives the estimated growth of butter sole from di f f e r e n t sampling areas (Figure l ) within Hecate S t r a i t . Samples from area 2 have mostly 1+ and 2+ old butter sole and therefore are not considered here. S t r i k i n g differences i n the estimated growth rates are observed i n different areas. Minimum growth rates are found i n the sample off F i f e Point i n sampling area 3 (Figure l ) . The sample from area 1 exhibits maximum growth. When one considers the existence of a summer fishery o f f F i f e Point during 19^5 and 19^6 and the abundance of butter sole i n the sample collected during 1953 and- 195^> the presence of slow growing butter sole i n the 1961 sample suggest that the area o f f F i f e Point i s no longer preferred by the species. Short term fluctuations i n the habitat s u i t a b i l i t y within the shallow f l a t s can be brought about as a resu l t of constant wind and wave action. There i s also an abundance of sand dol l a r s i n the samples collected from t h i s area during recent years. Dendraster excentricus (Eschscholtz) and Echinarachnius parma (Lamark) are both found i n the area. The present 6o. Table XXVI. Percent growth increment up to July of butter sole of various age groups in the 1961 sample. Values up to fourth decimal place are retained in calculating percent deviation. H Age group 1+ 11+ III+ IV+ v+ VI+ Mean Increment 6.85 5-89 4.48 3-01 2.29 2.3b 1 Increment up to July 5-11 3-92 2.28 1.81 1.61 1.23 . $ Increment 74.54 66.52 50.92 59-97 70.06 52.75 Mean Increment 7.04 6.12 4.85 3-55 3-08 1 Increment up to July, 5.11+ 4.20 2.42 1.91 1.73 Ft $ Increment 73-14 68.62 49.82 53-80 56.28 Table XXVII. Back calculated lengths at various ages calculated from otolith samples collected from different regions of Hecate Strait during July 1961. Sex Area sampled (Figure l ) Noof ot- oliths I II III IV V VI VII VIII IX X XI Dixon Entrance (1) 116 6.22 13-16 18.99 23.41 26.36 28.56 30.90 32.30 33.63 Ma le  Off Fife Point (3) 80 5-34 11-35 16.96 22.13 25-75 28.68 30.69 33-75 Butterworth Ground (4) 65 5-84 11.90 17.70 22.14 25-69 28.92 31.14 Dixon Entrance (1) 155 6.53 13-64 19-77 24.64 28.44 31-20 33.OO 33-71 34.11 3^-79 35-89 •ma le Off Fife Point (3) 87 6.13 12.05 17.98 22.93 27-31 31-00 33-29 QJ Butterworth Ground (4) 110 5.52 12.83 18.59 23.09 26.76 30.27 32.74 35-27 Table XXVIII. Length-Weight Relationship. Covariance analysis to test the homogeneity of the regression coefficients. Source Residual S.S. D.F. M.S. F Common 1.88423 855 Error 1.85816 852 0.00218 Reg.Coef. for sexes O.OIO89 1 O.OIO89 5.00 Reg.Coef. for seasons 0.00121 1 0.00121 0-55 Sex-season Tnt.eracii nn_ 0.01397 1 0.01397 6.41 61. evidence, however, i s too scanty to assert that the Hecate S t r a i t bank forms a "mobile habitat" for butter sole within which short term alterations i n the habitat s u i t a b i l i t y of the sub-areas may be brought about by-waves and perhaps fluctuations i n the abundance of other bottom organisms. The data also suggest a segregation of fast and slow growers i n t h e i r summer feeding grounds. Sampling area 1 had a dense population of butter sole with a maximum growth rate while the areas 3 a n ( i h are sparsely populated and appear to have poorer growth rates. I t i s not known whether t h i s i s due to a possible tendency of the faster growing ones to move together. Sexual differences i n growth rate. The growth curves of males and females indicated i n Figure 12 show that females grow faster than males. I t i s also evident that the females reach the maximum or asymptotic length at a slower rate than the males and hence exhibit higher growth rates at older ages than the males. Length-Weight relationship of butter sole. The length-weight relationships of male and female butter sole by season are: > 2.023 Male (summer) : Weight (gms) = 0.009260L (cms) Male (winter) : Weight (gms)' = O.OO7236L (cms) 3-103 Female (summer) : Weight (gms) = O.OO73M+L (cms) 3-°9^ Female (winter) : Weight (gms) = O.027896L (cms) 2 ' ^ 6 The length-weight relationship for the two sexes i s shown i n Figure 18 and the results of the covariance analysis are given i n Table XXVIII. The low exponential value of 2-7^6 for the females collected during February, 1961 i s probably due to sampling error associated with the narrow length range of the f i s h i n the sample. Hennemuth (1959)' observed a similar s i t u a t i o n for skipjack tuna. This could not be avoided since the spawning population sampled 62. LENGTH IN CENTIMETERS LENGTH IN CENTIMETERS Figure l 8 . Length-weight relationship of butter sole. 63- contained only larger length groups. The rest of the .exponential values i n the length-weight" relationship for the sexes by season are greater than 3* The covariance analysis (Table 28) shows that the regression c o e f f i c i e n t s of the two sexes d i f f e r s i g n i f i c a n t l y . The high variance r a t i o for the i n t e r - action between season and sex shows that the difference within season i n females i s greater than i n males, (b) Survival rate. As Beverton and Holt (1956a) have indicated, the estimation of mortality rates from age composition and e f f o r t data depends on certain assumptions and hence i s subject to considerable error. Since butter sole' of seven or more years of age are f u l l y recruited and are adequately sampled by the commercial gear* the age composition data for these age groups were used to estimate the annual survival rate. These estimates may also be biased to a certain extent due to variations i n year class strength and d i f f i c u l t i e s i n 'aging' o t o l i t h s . The results for the two sexes are given i n Table XXIX. The mortality rates are found to be higher for the males i n a l l the years examined. This phenomenon, also observed by Hart (1948), may be due to higher natural mortality and/or f i s h i n g mortality. I f the males remain on the spawning ground longer than the females a higher f i s h i n g mortality f o r the males may "be expected. Since there was no f i s h i n g during I9H9 and 1950, and the f i s h i n g i n t e n s i t y during the period 1953-1955 was quite low (Table XXXl), the higher mortality estimate for males may be due to a higher natural mortality rate. Mortality rates also show an increase with * The commercial gear uses codend with a mesh size ranging from four to f i v e inches. From length-girth relationship (Section IV) t h e i r 50$ retention-'-'point would be less than the length of 7 year old f i s h . 64. Table XXIX. Instantaneous and annual t o t a l mortality rates of butter sole estimated from the age composition data. Z = Instantaneous t o t a l mortality rate; a = Annual t o t a l mortality rate. Age Interval Male 1951 iqrsa 1954 1955 z a z a z a z a VII- VIII V I I I - IX IX- X 1 . 1 2 9 1 . 8 3 0 1 . 7 3 5 0. '677 0 . 8 4 0 0 . 8 2 4 0 . 9 0 5 1 . 2 0 9 2 . 0 5 2 0 . 5 9 6 0 . 7 0 2 O .872 1 . 8 6 6 1 . 6 0 9 0 .845 0 . 8 0 0 1 . 5 2 3 1 . 7 4 9 2 . 0 7 9 O .782 0 . 8 2 6 O.875 VII- VIII V I I I - IX IX- X Female 0 . 6 9 3 1 . 1 2 8 1.959 0 . 5 0 0 0 . 6 7 6 0 . 8 5 9 0 . 6 2 3 1 . 177 2 . 1 6 5 o.k6h 0 . 6 9 2 0 . 8 8 5 0 . U 7 2 1 . 6 6 8 0 . 3 7 6 0 . 8 1 1 0 . 9 7 2 1 . 4 0 9 1 . 2 9 9 0 . 6 2 2 0 . 7 5 6 O .727 6 5 - age. Since butter sole above six years are equally vulnerable to the gear the increasing mortality rates are perhaps largely due to an increase i n the natural mortality rate with age. The separation of t o t a l mortality into i t s component parts requires a r e l i a b l e estimate of the f i s h i n g intensity-and usually involves the assumption that natural mortality i s constant with respect to age. The assumption of constant natural mortality i s not v a l i d f o r butter sole. An accurate estimate of the f i s h i n g i n t e n s i t y could not be made either (see Section IV), hence f i s h i n g and natural mortality rates were not separated. An estimate of the natural mortality rate for the early year classes could have been attempted from the age composition of the samples taken i n 1953 "by small meshed trawl hauls from the spawning population i f the per cent i n each year class that would have matured i n the succeeding spawning season could have been estimated. An examination of the sample collected i n July 1961 showed that t h i s could not be done as the gonads had not yet started maturing. The t o t a l mortality rates estimated i n Table XXIX are largely due to the natural mortality rates because, as previously mentioned, the f i s h i n g i n t e n s i t y was rather low for the years examined. Since the t o t a l mortality rates are high, butter sole seven years and above are presumably subjected to high natural mortality rates. This i s also suggested by the r e l a t i v e l y high value of K, the rate of deceleration i n growth increments. In t h e i r discussions, Beverton and Holt ( 1 9 5 9 ) and- Holt , ( 1 9 6 2 ) have pointed out that natural mortality and K are p o s i t i v e l y correlated, (c) Conelusion. 1. Zones i n the o t o l i t h of butter sole are found to be r e l i a b l e indicators of age. The back calculations of f i s h length based on the body length-otolith radius relationship are therefore used i n tracing the growth history of the species. 66. 2. The growth pattern of butter sole over two years of age i s adequately described by the Von Bertalanffy growth vcurve; even though seasonal differences i n the growth rate are superimposed on i t . 3- A year class with an i n i t i a l slower or faster growth shows a tendency i n l a t e r years to a t t a i n the mean values estimated for the population. h. Growth rates show differences with respect to year, season, region and sex. 5« The length-weight relationship based on ungutted specimens show seasonal and sexual differences. 6. The natural mortality rate beyond seven years of age i s r e l a t i v e l y high and i s found to increase with age. / IV Fluctuations i n the abundance of the butter sole population 1. Introduction Extreme fluctuations i n abundance are usually associated with pelagic fishes although they occur i n varying degrees i n a l l exploited populations. S e t t e ( l 9 6 l ) records a year class of western A t l a n t i c mackerel which was 1 5 , 0 0 0 times as large as the smallest year class recorded. Clarkeand Marr ( 1 9 5 5 ) mention a 7 2 0-fold difference between the smallest and largest recorded year classes of P a c i f i c sardine. Groundfishes also exhibit considerable v a r i a t i o n i n abundance (Hjort 1914, 1 9 2 6 , Ketchen 1 9 5 6 , S a v i l l e 1 9 5 9 , Beverton 1962 and others), but they are less extensive than those of pelagic fishes. Fluctuations i n the butter sole population were studied to examine the p o s s i b i l i t y of predicting t h e i r magnitude. This provides a means of studying t h e i r influence on the population biomass and y i e l d . 2 . Examination of the butter sole fishery (a) Age of f u l l e xploitation When studying the fluctuations of a f i s h population, a knowledge of the age at which the f i s h i s f u l l y exploited permits a comparison of the strength of a year class during i t s pre- and post- exploitation phases. I t also enables one to estimate the influence of the year class on the t o t a l y i e l d . In addition, such knowledge i s of use i n examining whether the e x i s t i n g age of exploitation i s the most desirable from the point of view of optimum fi s h i n g . Consequently, an analysis of the s e l e c t i v i t y of the trawl mesh was carried out f o r butter sole, ( i ) Mesh selection experiment The s e l e c t i v i t y of a gear i s the change i n the r a t i o of the abundance of di f f e r e n t size groups i n the catch to that of the population fished. Buchanan-Wollaston ( 1 9 2 7 ) showed that, depending on the size of the cod-end 68. mesh, a l l the f i s h below a certain length can escape through the mesh, while above a certain l e n g t h - a l l the f i s h encountered b y t h e gear are captured. Within the intermediate length or the "selection range" the e f f i c i e n c y of the gear increases with increase i n the length of the f i s h . The curve obtained by-plotting the per cent retained against the length i s the -"selection ogive" of the cod-end mesh.' Wollaston f i r s t pointed out that the selection ogive -approximates a-"normal ogive" and i t gives the proportion of f i s h entering the cod-end that are retained, i.e. the chance of a f i s h of that-size being captured. This was l a t e r confirmed by the mesh selection experiments of various workers such as Graham ( 1 9 5 ^ ) , Margetts ( l 9 5 5 ) > Gulland ( 1 9 5 5 ) and Davis (Graham 1 9 5 & ) . The method adopted for estimating the mesh selection of butter sole by commercial trawlers was to make two consecutive hauls of 30 minutes duration with 1 . 5 " ; 3 - 4 " , 3 - 5 " and 5 - 2 " cod-end meshes. In estimating the per cent retained by the commercial trawler, the catch of the 5 - 2 " cod-end was compared with that of the 1 -5" mesh. The length-frequency d i s t r i b u t i o n of the catch with 1 . 5 " mesh was adjusted by using.the catches of the 3 - 4 " and 3 . 5 " mesh to obtain an accurate estimate of the size composition .of the population. The procedure i s i l l u s t r a t e d i n Table XXX. Only the size groups beyond the f u l l retention point of the 3 - 5 " cod-end mesh as estimated from the length-girth relationship were considered for weighting. A comparison of the length-frequency d i s t r i b u t i o n of butter sole i n the catches of the 1 . 5 " and 3 . 5 " cod-end meshes (Table XXX). indicated that size groups 2k cms. and above could be used for weighting. The absence of f i s h below 2k cms. i n the catches of the 3 . 5 " cod-end mesh may have been caused by t h e i r absence i n the population fished. Because the 3-V* mesh fished a denser population, as shown by the catch (Table XXX), the estimation of the-adjusted size frequency 69- of the population was not done with respect to the mean catch of the three nets. Instead the size frequency of the catch w i t h ' 1 . 5 " cod-end mesh was corrected. Adjustment for the 3-5" mesh would y i e l d a very similar result since the t o t a l catch of 1.5" and 3-5" cod-ends were of the same magnitude. Cod-ends of the same material were not available f o r the above experiment. While the catches of the 3-4" and 3 . 5 " meshes were used for weighting, the possible effect of the different materials on the selective -properties of the cod-ends may not have influenced the calculations since the minimum size group considered l i e s beyond the f u l l retention point of the 3-5" cod-end. The results of the mesh selection experiment are given i n Table XXX. The estimated per cent of butter sole retained at each length up to 38 cm. by the 5-2" mesh i s shown i n Figure 19> The 50$ selection length was found to be 31.5 cm. The value sigma measuring the spread of the selection ogive, on the assumption that the selection ogive has the same properties as a normal ogive, was found to be 1.04 cm. The discrepancies observed beyond the f u l l retention point i n Figure 19 can be expected i n such alternate haul experiments due to the movement of shoals of f i s h about the ground or variations i n the populations fished (Graham 1956). Margetts (l955)> who used the same method, observed even greater discrepancies i n mesh selection experiments on sole. Hence the i n d i v i d u a l hauls should be° of s u f f i c i e n t duration to minimize these errors (Graham 1956). The population should also be of moderate density (Wollaston 1927). Otherwise the cod-end may become clogged, preventing the escape of small f i s h . Both these conditions were met i n the present study. However, hauls were taken over-a period of about 48 hours and thus resulted i n increased sampling v a r i a b i l i t y . This could be offset only "by taking more hauls with each cod-end. Certain trends'may-also be present i n the r a t i o s 7 0 . Table XXX. Length frequency d i s t r i b u t i o n of butter sole above 24 cm. caught i n two hauls with each cod-end and the estimation of the percentage retained by the 5 - 2 " mesh i n an alternate haul experiment. Length (cms.) Size composition of butter sole above 24 cms. in'hauls usingl- different cod-end meshes 1-5" 3 - 4 " 3 - 5 " Total Weighted percent Adjusted frequency with 1 . 5 " mesh. (Weighted & x 2 . 3 7 ) Catch of 5 . 2 " mesh cod end $ retained by 5 - 2 " mesh compared to that of 1 . 5 " mesh 24 3 12 4 19 1 . 7 6 1 0 0 25 10 57 l l 78 7 . 2 2 8 17 0 0 26 15 39 15 69 6 . 3 9 0 15 1 6 . 6 6 27 12 69 14 95 8 . 8 0 4 21 1 4 . 7 6 28 11 36 10 57 5 . 2 8 2 13 1 7 - 6 9 29 l l 34 9 54 5 - 0 0 4 12 1 8 . 2 5 30 14 38 19 71 6 . 5 8 0 16 2 1 2 . 5 0 31 37 42 21 100 9 . 2 6 8 22 11 5 0 . 0 32 34 76 4 0 150 1 3 - 9 0 1 33 17 5 1 . 5 1 33 30 6 0 32 122 1 1 . 3 0 6 27 29 107 .40 34 24 62 30 116 1 0 . 7 5 0 25 12 hd.o 35 16 23 21 6 0 5 . 5 6 1 13 9 6 9 . 2 3 36 12 26 9 47 4 . 3 5 6 10 5 5 0 . 0 37 4 14 6 24 2 . 2 2 4 5 3 6 0 . 0 38 3 5 2 10 0 . 9 2 6 2 2 1 0 0 . 0 39 1 3 2 6 0 . 5 5 6 1 0 0 40 0 0 1 1 0 . 0 9 3 0 1 - Total 237 596 246 v pl9 1 0 0 . 0 236 95 L E N G T H IN C E N T I M E T E R S Figure 19- Percentage of butter sole retained at each length by 5 . 2 " cod-end mesh. (Alternate hauls). The dotted l i n e indicates the 50$ release length. 72. retained by the cod-end. Beverton and Holt (1957) found that with increase i n mesh size the r a t i o s retained by the cod-end were greater than unity due to an increase i n f i s h i n g power with increase i n mesh size. They-also observed with the 72 .2 mm. and 113.0 mm. meshes that the observed ratios above the 100$ retention point not only attained values greater than unity but they gradually decreased l i n e a r l y with an increase i n the size of the f i s h . No such trends were observed i n butter sole. Although an increase i n mesh size may result i n an increase i n the f i s h i n g power t h i s i s not evident i n the data. This may be p a r t l y due to the small number of length groups beyond the f u l l retention point and p a r t l y to the i n s u f f i c i e n t number of hauls with the 5-2" cod-end. Hence, no adjustments for the f i s h i n g power were made when estimating the selection ogive of the 5-2" mesh. The length frequency d i s t r i b u t i o n s of the 3-4" and 3 -5" cod-end meshes also show no such trend. The r e l i a b i l i t y of the estimated 50$ selection point i s further v e r i f i e d by comparing the in t e r n a l perimeter of the cod-end and the g i r t h of the f i s h corresponding to the 50$, retention length as determined from the length-girth relationship, ( i i ) Length-girth relationship I f f i s h grow isometrically the length and g i r t h w i l l be proportionally related so that the average mesh size and the 50$ release length w i l l be proportional (Beverton and Holt 1956b). Thus, by using a length-girth relationship the 5°$ selection point of any cod-end mesh can be determined. This could be used to check the v a l i d i t y of the mesh selection experiment. Such studies have been done by Lucas et a l (195^), Margetts (195^) and Gulland (1955). Graham (195M has pointed out the usefulness of such studies because of random and systematic errors of mesh selection experiments. 73- Length and g i r t h measurements for 319 freshly caught butter sole were taken on the research vessel, A.P. Knight, during February, 1 9 6 1 . The g i r t h measurement was taken at .the widest part of f i s h with a measuring noose, tightened to such a degree as would permit the f i s h to be pulled from - i t when gentle pressure was applied. Margetts ( 1 9 5 4 ) has defined t h i s measurement as the constricted g i r t h . Figure 20 i l l u s t r a t e s the length-girth relationship of butter sole. The f i t t e d regression l i n e shows the relationship: g i r t h (cms) = 0-9486 length (cms) - 3-409 The i n t e r n a l circumference of the 5 - 2 3 " mesh i s 10.46". The estimated g i r t h of f i s h at the 50$ release length of the 5 . 2 3 " mesh i s 26 .47 cms. or 1 0 . 4 2 " . The analysis i s based on two hauls only so the close s i m i l a r i t y between the estimated g i r t h of the f i s h at 50$ length and the in t e r n a l circumference of the corresponding cod-end may be due to random and systematic errors. Nevertheless the s i m i l a r i t y of the two values indicates that the length-girth relationship of butter sole could be used to check •' the v a l i d i t y of the estimated 50$ release length from the selection ogive. The estimated 50$ release lengths for the 3-4" and 3-5" meshes are 21 .80 and 22.34 cms. respectively. These estimates, however, could not be v e r i f i e d by mesh selection experiments. The minimum size group represented i n the catch of the-3>5" cod-end mesh i s 24 cms. This may be due to the size composition of the population fished. A similar situation occurs with the 3.4" cod-end mesh when none of the length groups below the 50$ retention point, as estimated from the length-girth relationship, are represented (Appendix i ) . I f the 20 and 21 cm. groups are as scarce i n the-spawning population as indicated by the catch of the 1 . 5 " mesh (Appendix i ) then they probably represent the tail-ends of two adjacent modal groups. This may Figure 20. Length-girth relationship of butter sole. The dotted l i n e indicates 50$ release length for the 5-23" cod-end mesh. 75- p a r t l y explain the absence of length groups below 22 cms. i n the catch of the 3-4" mesh cod-end. (b) Variations i n butter sole landings The butter sole fishery depends on the spawning population that migrates to the eastern part of Skidegate Inlet and i s thus highly lo c a l i z e d . Fishing i s very seasonal and l a s t s only for about two months of the year. Since '1953 the peak f i s h i n g season has shifted to February-March. The magnitude of the fishery compared to that for other ground fishes of Hecate S t r a i t i s quite small. Butter sole i s used for human consumption and for mink feed, but there i s r e l a t i v e l y " l i t t l e demand for i t . For t h i s reason, and because of the favourable economic pos i t i o n of the fishermen,. the population i s exploited only i f i t i s s u f f i c i e n t l y abundant at the spawning s i t e to bring a reasonable p r o f i t to the fishermen. However, i t does afford a sheltered fishery when f i s h i n g i n Hecate S t r a i t i s undependable (Hart 1948). The estimated butter sole landings f o r 1945-1962 are given i n Table-XXXI. Except for 194-5 and. 1946, when there was also a summer fishery i n Hecate S t r a i t , the catches came e n t i r e l y from the spawning population i n Skidegate Inlet. Sporadic catches from s t a t i s t i c a l area 4 (Figure 2 l ) were not included i n these estimates. Since 1953 the butter sole landed were used p a r t l y as food f i s h and p a r t l y -as mink feed. In addition to gear selection, the f i s h destined for human consumption are further selected to meet the market requirements. The mink feed landings of butter sole include those not selected for the market plus the entire 'landings of boats operating for mink feed alone. Catch figures show considerable annual variations (Figure 2 2 ) . In addition to changes i n the density of the spawning population, the changes i n the f i s h i n g e f f o r t .also influence the yearly landings. The demand immediately 7 6 . Figure 21. Map showing the s t a t i s t i c a l areas of Hecate Strait in the neighbourhood of Skidegate Inlet. 77- Table XXXI. Landings of butter sole from Skidegate Inlet and the estimated catch per unit e f f o r t f o r vessels of 3°-59 ton range. The landings f o r 1945-1950 are corrected for the difference between log book t o t a l and Department record. Total catch- Catch per day Catch per day Food f i s h (Food and for boats for boats Year (pounds) mink) f i s h i n g for f i s h i n g both (pounds) food alone for food and (pounds) mink (pounds) and mink alone 1945 1 ,542 ,856.0 > 1 6 , 8 9 9 . 0 _ 1946 1 ,715 ,605.0 - 11 ,866.0 - 1947 271 ,533.0 - 3,523-0 - 1948 649 ,032.0 - 9 , 7 8 2 . 0 - 1949 1 8 , 8 9 0 . 0 _ 1 0 , 4 9 4 . 0 - 1950 1 ,545.0 - 1,717-0 - ; 1951 1 , 8 3 8 , 1 2 8 . 0 - 2 8 , 7 6 1 . 0 - ! 1952 3 , 7 0 8 , 2 3 2 . 0 - 1 0 , 9 0 2 . 0 - 1953 2 2 4 , 0 5 2 . 0 3 9 3 , 0 5 2 . 0 10,113.0 2 6 , 2 2 2 . 0 1954 181 ,430.0 2 0 1 , 9 3 0 . 0 11 ,560.0 1 5 , 8 0 4 . 0 1955 4 7 0 , 3 3 9 - 0 7 2 7 , 8 0 3 . 0 8 , 4 0 0 . 0 7 ,997-0 1 1956 7 1 6 , 2 4 4 . 0 1 , 4 1 9 , 0 8 5 . 0 5 ,764.0 12 ,859.0 ; 1957 1 ,291,579-0 1 , 4 3 6 , 9 3 6 . 0 10,166.0 I 0 , 8 i 4 . 0 ! 1958 4 9 9 , 6 4 2 . 0 9 6 0 , 1 7 0 . 0 1 2 , 6 8 0 . 0 2 2 , 9 6 6 . 0 ! 1959 2 1 2 , 9 0 2 . 0 U 4 9 , 4 9 4 . 0 1 0 , 4 9 5 . 0 14 ,532.0 j i 9 6 0 9 3 , 8 5 7 - 0 1 , 2 5 2 , 8 4 0 . 0 4 , 4 8 1 . 0 13,973-0 i 1961 15 ,846 .0 543,177-0 - 7,297-0 ! 1962 4 1 , 5 4 9 . 0 1 , 3 9 4 , 9 3 7 . 0 — 1 3 , 8 0 6 . 0 Table XXXII. Estimation of the f i s h i n g power of 'single' gear taking 'double' gear as the standard. Year Tonnage Catch i n pounds Fishing Number ofjweighted class - per day power of t r i p s geometric Single single made by mean Double gear the gear gear tonnage class 1946 40-49 5547-3 6758.5 0.8207 9 1951 40-49 27218.0 31175-0 O.873O 10 1952 20-29 8203.8 8524.7 O.9623 14 1952 30-39 8615.1 9676.38 O.89O3 28 0.8955 1952 40-49 9234.55 14925.19 O.6187 16 1952 50-59 14587.95 9104.23 1.6023 9 1957 30-39 8796.2 9272.8 0.9486 13 1957 30-39 8796.2 9723.94 0.9046 13 78. 3800 3600 3400 3200 g 3000 I 2800 °" 2600 1 1 J L J L J L 1945 1947 1949 1951 1953 1955 1957 1959 1961 YEAR cc 35 U. CO U- Q 3 0 ^ 1 2 5 ^ 3 f e 20 or to l 5 s r § I 0 X 2 o _ - 5 1- - Figure 22. Butter sole landings and catch per unit e f f o r t for the period I9U5-I962. • — Food f i s h landings,—r»—-Total landings (food and mink), — o — Catch per day of boats f i s h i n g for food alone,-— o——Catch per day of boats f i s h i n g f o r mink feed 'alone and both for mink feed and food. Data from Table XXXI. ) I 7 9 . a f t e r the second World War supported a summer fishery i n 1945 and 1 9 4 6 . The fishery was also p a r t i c u l a r l y heavy during 1952 . Separate food and mink feed categories i n the landings made since '1953 introduce further variations i n the catch figures. The number of boats engaged i n f i s h i n g for food, f o r mink feed, or for both, may vary i n different years. Hence the-use of catch figures as an index of abundance may be biased by year to year variations i n the f i s h i n g i n t e n s i t y and the demand for the food and mink feed items of the landings. The p o s s i b i l i t y of studying variations i n the density of the spawning population by estimating the catch per unit e f f o r t i s therefore examined. ( i ) Estimation of the catch per unit e f f o r t A r e l i a b l e estimate of the catch per -unit e f f o r t can serve as a valuable index of abundance when the effect of f i s h i n g and the fluctuations of a population are being studied. An accurate estimate of the f i s h i n g . i n t e n s i t y i s a prerequisite for the calculation of catch per unit e f f o r t . A constant improvement i n gear and a gradual increase i n tonnage of vessels are two conspicuous features i n the fishery. 'Single' gear where the trawl i s towed with one cable i s better adapted for small vessels. 'Double* gear i s towed with two cables. Ketchen ( l 9 5 l ) found that, at normal towing speed, the spread of the-American style trawling gear ('double' gear) i s about l.k times that of the 'single' gear. The assessment of the performance of trawlers by Ketchen and Thomson (No date) also indicates that the f i s h i n g power increases with tonnage. Gulland's ( 1 9 5 6 ) extensive analysis of the f i s h i n g power of English trawlers also confirms t h i s conclusion. , As the average size of the Canadian trawlers increased, more 'double' gear was used by the fishermen. To the butter sole fishery, these changes are only incidental since such changes are associated with the more important trawl f i s h e r i e s of the area. 80. However, such changes i n the f i s h i n g power have to he accounted f o r hy standardizing the f i s h i n g e f f o r t . Relation of f i s h i n g power to tonnage The catch data from 1958 to 1962 permit a r e l i a b l e estimate of the f i s h i n g power f o r vessels equipped with * double * gear and operating f o r mink feed alone and for both mink feed and food. The catch per hour for ind i v i d u a l t r i p s was calculated f o r a l l bdats. Taking the catch per hour of one boat as the standard, the re l a t i v e f i s h i n g power of a l l boats was calculated taking care to see that such comparisons of catch per unit e f f o r t were made of boats f i s h i n g , as fa r as possible,.at the same time as the standard vessel. In addition to such direct comparisons, a number of in d i r e c t estimates of the f i s h i n g power of vessels were -also made using the chain l i n k method described by Beverton and Holt (1957)- Thus the catch per hour of.one boat was linked to that of the standard vessel through a varying number of catch per hour estimates of other vessels. For example, i f 4 Cc n i s the catch per hour of a boat represented by the s u f f i x on . i t s right side, and the time of f i s h i n g by the s u f f i x on the l e f t , then i c x x jfm x l ^ d x kfb x off c c c c c i m j d l b k f o standard vessel would be one estimate of the f i s h i n g power of vessel X. The regression analysis of f i s h i n g power on tonnage was based on a t o t a l of 897 estimates. The data were at f i r s t transformed by taking the square root of the f i s h i n g power. The r e l a t i o n of f i s h i n g power to tonnage i s given i n Figure '23 along with the confidence b e l t of /^Y for any X. The estimated relationship i s / Fishing power = O.782O + O.OO85 Tonnage 81. Figure 23. Relation of fishing power and gross tonnage of vessels equipped with 'double* gear engaged in the butter sole fishery during the period I 9 5 8 - I 9 6 2 . 8 2 . A The sample standard deviation of Y calculated for drawing the confidence b e l t i s i — = / 0 . 0 0 0 9 9 3 6 + 0 .000001108(X-X) . The slope i s s i g n i f i c a n t with a t-value of 6 . 5 5 for 895 degrees of freedom. Figure 23 shows considerable scatter -even i n the transformed data. Some of the factors that could contribute to the v a r i a b i l i t y are the differences i n the ages of the vessels, the a b i l i t y of the skippers and i n the d i s t r i b u t i o n , density and migratory patterns of butter sole within the spawning ground. Since only two boats equipped with- 1 single' gear fished during the period I 9 5 8 - I 9 6 2 , the r e l a t i o n of f i s h i n g power to tonnage of vessels using 'single' gear was not studied for that period. In estimating the mean catch per unit e f f o r t adjustments f o r the increase i n f i s h i n g power with tonnage were not based on the above relationship. Accurate e f f o r t data i n terms of actual number of hours fished were available only from 1957- Hence the catch per unit e f f o r t had to be calculated taking each day as a unit . Furthermore, with the exception of one boat i n 1 9 5 5 , vessels above 6 0 tons did not appear regularly i n the fishery u n t i l 1 9 5 8 . Since vessels i n the 3 0 - 5 9 "ton range were w e l l represented, the standardization of f i s h i n g e f f o r t was done for vessels within t h i s range. Standardization of f i s h i n g e f f o r t and the catch per unit e f f o r t for the 3 0 - 5 9 "ton classes. In comparing the e f f i c i e n c y of 'single' and 'double' gear or of the tonnage classes, the data used were r e s t r i c t e d to the period when the different units compared were represented i n the e f f o r t data. The catch per day was taken as a unit,since the e f f o r t data-did not permit the choice • of a smaller unit. The e f f i c i e n c y of the 'single' gear was-adjusted by taking a weighted geometric mean of the r e l a t i v e f i s h i n g power (Table XXXIl), 8 3 - using the number of t r i p s made by -the respective tonnage class for the weighting. Taking 'double' gear as the standard, the estimated fishing.power of 'single' gear was found to be O .8955. After adjusting the f i s h i n g power of 'single' gear, differences i n the e f f i c i e n c y of tonnage classes were tested for the 3 0 - 5 9 ton range (Tables XXXII to-XXXVl). The e f f i c i e n c y of any two tonnage classes was tested by-analysis of variance treating each p a i r of data as a separate blcok (Table XXXIIl).- Since the landings contained only one category u n t i l 1 9 5 2 , the monthly estimations of the catch per day pertained only to food f i s h . Since 1953 the catch per day for the tonnage classes was calculated, wherever possible, both for food f i s h and f o r t o t a l landings. This procedure increased the number of blocks compared. The results are given i n Tables XXXIV to XXXVI. The analysis shows no s i g n i f i c a n t difference i n the e f f i c i e n c y of the tonnage classes within the 3 0 - 5 9 ton range. This i s to be expected when one considers the varying a b i l i t i e s of the skippers and the variations introduced by the migratory pattern. The small tonnage range and the short f i s h i n g season also contribute. Extreme l o c a l i z a t i o n of the fishery makes the species vulnerable to any gear. The number of boats i n each tonnage class available f o r the estimation of catch per day was not large. This was p a r t i c u l a r l y so since 1953 because after t h i s date boats could operate for either food f i s h or mink feed. In addition, some boats took f i s h for both purposes. This increases the sources of error i n the data. A separate analysis of the catch per day of boats operating for food f i s h alone and for boats operating f o r mink feed alone, or for both, may not increase the accuracy of the data because the d i v i s i o n of the 3 0 - 5 9 tonnage range into the three groups further reduces the number of boats i n each category. Such an analysis i s not worth attempting when the low variance Table XXXIII. Estimated catch per day of 3 O - 3 9 , 40-49 and 5O-59 ton glasses. Tonnage class 3 0 - 3 9 40-49 - 5 0 - 5 9 1945 J 18476.0 1 8 8 6 3 . 0 4 F 8040.0 1 3 8 5 2 . 9 0 - 1946 J 7040.03 5 7 9 1 - 2 0 6 2 5 0 . 0 F 8 9 3 3 - 5 5 8 3 3 3 - 3 0 6 2 5 0 . 0 1947 J 2 3 0 7 . 7 0 1 7 8 5 . 7 1 F 2 7 8 3 . 7 0 2 0 0 0 . 0 2 1 4 2 . 8 0 1948 J 9305-04 3 0 0 0 . 0 -F 6 3 1 9 . 1 3 II695.O • - 1951 J . 2 6 2 9 5 . 0 2 2 3 3 0 . 0 2 6 6 6 4 . 0 F 2 3 4 5 8 . 0 3 0 6 2 5 . 0 3 3 5 7 8 . 0 1952 J 8 3 5 3 - 8 0 1 4 0 0 6 . 7 0 1 0 0 3 5 . 4 0 F 1 0 3 3 7 . 2 0 1 2 0 9 2 . 3 0 1 1 7 9 7 . 6 0 1953 J - 1 6 6 6 . 6 0 9 0 0 0 . 0 1955 J 1 2 1 6 6 . 3 0 5 5 1 1 . 7 5 8 2 2 4 . 2 5 F 8 2 1 3 . 6 0 1 0 1 6 0 . 0 9 3 2 9 - 6 6 1956 J 4000 .60 4 1 8 8 . 7 0 3 1 9 1 . 2 0 F 4170.40 8 7 0 7 . 3 0 • 9 3 6 0 . 3 0 J - 8 2 6 6 . 0 7 . 6 9 2 9 . 2 6 i F 6 3 1 4 . 7 0 1 1 4 3 5 . 0 -M H 9 3 . 7 4 1 7 8 3 4 . 2 8 7 4 1 5 . 3 0 M 1 0 9 1 4 . 0 3 1 6 9 1 . 1 4 1 8 5 7 3 . 9 0 A 1 6 2 8 7 . 2 0 4 4 0 0 0 . 0 1 2 8 9 2 . 7 0 1957 J 9 1 9 7 . 8 0 2 4 4 8 . 7 0 -F 96OI .65 8 2 5 5 . 8 0 9 8 9 4 . 9 0 v ; F 1 0 3 6 5 . 3 0 9 8 3 6 . 8 0 1 3 2 3 5 . 1 3 M 9 3 6 6 . 5 0 1 1 7 4 6 . 0 3 3 4 2 7 . 1 0 1958 F 1 6 4 5 1 . 8 0 8 8 3 6 . 5 3 1 1 8 7 8 . 8 0 F - 1 2 1 2 3 . 4 0 3 0 8 6 1 . 6 0 M 3 3 2 5 - 0 1 7 2 6 7 . 5 0 1 7 1 4 2 . 5 0 M - 2 2 1 6 8 . 7 0 3 5 6 4 6 . 5 0 1959 F 2 6 0 6 3 . 0 6 8 2 6 . 8 8 -M 1 5 9 4 3 . 7 0 5 1 7 6 . 7 8 5 2 0 4 . 0 M - 1 0 9 9 8 . 8 0 1 6 0 8 6 . 6 0 I 9 6 0 F — 1 2 2 5 5 . 0 4 4 8 0 . 6 0 j F - 2 2 8 8 0 . 0 3 2 6 9 . 2 5 • I M - 1 8 6 0 7 . 1 0 1 3 6 8 9 . 0 8 5 . Table XXXIV. Analysis of variance of the log catch per day of 3O-39 and 40-1+9 ton classes. Source of Variation D.F. Sum of Sq. Mean Sq. Variance ra t i c Total 53 5.1699 0.0975 Months 26 3.O831 . I . I 8 5 8 O.O837 Tonnage classes 1 O.OO67 O.OO67 N.S. Error 26 2.0800 0.0800 Table XXXV. Analysis of variance of the log catch per day of 1+0-1+9 and 50-59 ton classes. Source of Variation D.F. Sum of Sq. Mean Sq. Variance ra t i c Total Months Tonnage classes Error 57 28 1 28 6.7081 5.4326 0.0043 1.2712 O .II76 0.1940 0.0043 0.0454 0.0947 N.S. Table XXXVI. Analysis of variance of the log catch per day of 3O-39 and 50-59 ton classes. Source of Variation D.F. Sum of Sq. Mean Sq. Variance r a t i o Total 39 3-9171 1.0043 Months 19 2.9191 0.1536 1.596 Tonnage classes 1 0.0773 O.O773 N.S. Error 19 0.9206 0.0484 86. r a t i o i s considered. Thus i n estimating the catch per unit e f f o r t for the 30-59 tonnage class adjustments were made only for vessels using 'single' gear. The estimated catch per unit e f f o r t of butter sole for the years 1945-1962 i s entered i n Table XXXI and Figure 22. ( i i ) Catch per unit e f f o r t as an index of abundance An examination of the catch per unit e f f o r t does not suggest that i t could be used as an index of abundance. In 1949 butter sole were almost absent i n Skidegate Inlet. After the heaviest recorded fishery i n 1952, the fishery i n 1953 w a s poor. I t was to be expected, from the numerical strength of the 1952 year class appearing as 1+ f i s h i n the 1953 sample (Table XXXIX), that the density of the 1959 spawning population would be below average. This was l a t e r substantiated by the t o t a l landings (Table XXXl) and age composition of the 1959 commercial catch (Table XL). The estimated catch per unit e f f o r t for these years i s comparatively high. Catch per day may not be as 1 sensitive a unit as catch per hour for expressing the index of abundance. Variations i n the catches as a resul t of the migratory behaviour affecting the di s t r i b u t i o n and density of the population could be minimized i f a large number of boats were available for the estimation of the mean catch per unit .effort. The short f i s h i n g season, the small size of the fishery, and the r e l a t i v e l y low demand for the species, allow only a small number of vessels to operate i n any one season. The estimates of the catch per unit e f f o r t were made from fewer boats since 1953, because after t h i s the t o t a l e f f o r t was divided between boats operating for food f i s h alone, f o r mink feed or for both. The secondary selection of food f i s h by fishermen may vary considerably from year to year depending ,on the demand. In poor years f i s h i n g may be r e s t r i c t e d to the period of highest density. Variation i n the density of the spawning population i s thus not adequately expressed by the catch per unit e f f o r t . 8 7 . However, catch per hour would be a more accurate index of abundance. Because of the r e l a t i v e l y low demand for the f i s h and the favourable economic position of the fishermen, the t o t a l landings cannot be expected to indicate more than the general trend i n the abundance. This could be p a r t i a l l y v e r i f i e d for the years 1958-1960 by comparing, the r e l a t i v e abundance of the 1951-1953 year classes i n the 1952-195^ samples and t h e i r contribution to the 1958-1960 fishery. This aspect i s dealt with below where the fluctuation of the butter sole population i s considered, (c) Conclusion 1. The 50$ selection length of the 5-2" mesh was found to be at 31-5 cms. with a sigma (6) value of 1.04 cms. Because of the random and systematic errors i n the mesh selection experiment the 50$ retention length-of 5-2" mesh was also v e r i f i e d by studying the length-girth relationship. (2) Butter sole landings show considerable year to year fluctuations. The estimated catch per day,was not found to be a sensitive index of the abundance of the spawning population i n Skidegate I n l e t . 3- Analysis of fluctuations i n the butter sole population The factors c o n t r o l l i n g the a v a i l a b i l i t y of the butter sole population i n Skidegate Inlet are not understood. Butter sole were almost t o t a l l y absent i n Skidegate Inlet during 19^9 and 1950. There are suggestions that the temperature of the bottom water influences the a v a i l a b i l i t y of butter sole. Barber (1957) has shown f o r Hecate S t r a i t that the southeast winds i n winter cause a displacement of the deep cold water by warmer, less saline surface water. He records that the southeast winds were very weak i n January 1950. The alterations i n the migratory course of the 1950 spawning population and the re s u l t i n g absence of a fishery i n Skidegate Inlet may thus be due to a lack of s u f f i c i e n t mixing. The low surface temperature during 19^9 and 88. 1950 may-also have prevented t h e i r entry across the shallow s i l l at the entrance of Skidegate Inlet. Simpson (1953) has also shown that the North Sea cod and p l a i c e avoid very cold water i n the winter and thus change thei r migratory route during unfavourable years. Flemming and Laevastu (1956) point out that fishes are more sensitive to temperature changes during .the spawning season. B u l l ' s (1952) experiments indicate that teleosts can respond to changes as small as 0.03°C i n temperature, 0 . 0 2$oin salinity-and 0 .05 p'.H;." (a) Method adopted i n analysing changes i n abundance Buckmann (1930) points out that the peculiar depth d i s t r i b u t i o n of bottom fishes makes precise sampling d i f f i c u l t for a study of the r e l a t i v e abundance of year classes i n the nursery ground. Hence a r e l i a b l e estimate of the catch per unit e f f o r t cannot e a s i l y be obtained. Besides, i t measures only the abundance of the whole population and not the ind i v i d u a l year classes. I f sampling i s not proportional the age composition of the sample w i l l not be representative of the population. I t i s possible that an average year class, which shows up very strongly -when compared with a series of poor year classes, may be mistaken for a strong year class. However, the l i m i t e d range of the Hecate S t r a i t population of butter sole f a c i l i t a t e s t h e i r sampling. Estimates of the catch per unit e f f o r t from the commercial sample i n conjunction with the age composition of the market sample can be used to study abundance, but t h i s does not permit-prediction of the success of the fishery. In t h i s study the abundance of young butter sole i n the small-meshed trawl hauls taken along the Graham Island coast during 1952-1954 was analysed. This was done by studying the order of dominance and r e l a t i v e abundance of butter sole and the related species, lemon sole, rock sole and sand sole, by means of the ranking technique. This analysis was interpreted after a consideration of the r e l a t i v e strengths of the 1+ and 2+ butter sole i n the 1952-1954 samples. 89. Since these f i s h were old enough to be f u l l y exploited by the 1958 to i 9 6 0 fishery, i t s success and the age composition of the commercial catch were also considered. Because the length frequency d i s t r i b u t i o n of the age groups i n the 1952-1954 sample show very l i t t l e overlap, they could be separated e a s i l y and accurately. Hence no refined techniques for dissecting the length frequency were used. Since the durations of the hauls, especially during 1952, were not steady, the catch from each haul was weighted to 20 minutes duration, (b) Results The results of the dominance and r e l a t i v e abundance analysis are given i n Tables XXXVII and XXXVIII.' For the year 1952, the order of dominance i n the sample was lemon sole > sand sole > butter sole, s i g n i f i c a n t at the 0.05 l e v e l . The order of dominance for 1953, s i g n i f i c a n t at the 0 .01 l e v e l , was sand sole > lemon sole > butter sole. The order of dominance for 1954 was lemon sole > butter sole > sand sole, but i t i s not s t a t i s t i c a l l y s i g n i f i c a n t . The results of the r e l a t i v e abundance analysis are presented i n Figure 2k (data from Table XXXVIIl). The figure shows the same order of abundance among the species as indicated by the analysis of dominance for the two years. In 1952 no one species was found to be p a r t i c u l a r l y more abundant than the other two, however, i n 1953 sand sole was s i g n i f i c a n t l y more abundant than butter sole. There was not enough samples i n 1954 to permit the analysis of r e l a t i v e abundance. In the above analysis, the abundance of young sand sole and lemon sole also influences the r e s u l t s , since the Graham Island coast i s the main nursery ground for these species. Ranking techniques can be used to study the r e l a t i v e abundance of young butter sole alone over a period of years. Because of the lack of s u f f i c i e n t data, a consideration of the age composition of Table XXXVII. Analysis of dominance of butter sole i n the 1953 and 1954 samples from the Graham Island coast. Low rank values indicate numerical superiority of the species i n the sample. The grouping procedure eliminates rock sole from the Graham Island coast since they are present i n less than half the number of samples. 1952 1953 1954 ^rank S w p ^rank S W p £rank s w p Butter sole 26 < 28 14.5 67.I 0.34 0.05 128.0 0.64 0 . 0 1 12.7 0.19 N.S. Lemon sole 14-5 20 9-5 Sand sole 21-5 12 12.5 No. of replicates 10 10 6 Mean 20.7 2 0 . 0 12 .2 91- Table XXXVIII. Analysis of r e l a t i v e abundance of young butter sole, lemon sole and sand sole along the Graham Island coast during 1952 and 1953. 1952 1953 Number Respective Number Respective of rep- l i c a t e s ^ rank t P of rep- l i c a t e s rank t P .- Butter sole x Lemon sole 10 124.0 86-0 1.44 'O.O75O 11 150 101 1-54 O.0618 Butter sole 10 123.0 87.O 1.36 O.O869 10 149 61 3-33 0.0004 x Sand sole Lemon sole x Sand sole 10 111.5 141-5 O.96 O.1676 10 123 87 I . 3 6 0.0869 92. 1 9 5 2 L E M O N S O L E / \ / \ / \ / \ / \ B U T T E R S O L E - * " S AND S O L E 1 9 5 3 S A N D S O L E B U T T E R S O L E - * - — L E M O N S O L E Figure 2k. Relative abundance of the three species of f l a t f i s h i n the samples from the Graham Island coast collected during 1952 and 1953. The species to which arrow i s indicated i s less abundant. Dotted l i n e s indicate that the difference i s not s t a t i s t i c a l l y s i g n i f i c a n t . 93- butter sole i n these samples helps i n the interpretation of the above analysis. Table XXXIX indicates c l e a r l y that butter sole of age 1+ and 2+ are poorly represented in,1953 compared to 1952- The scarcity of 1+ butter sole i n 1953 i s at least p a r t l y due to the poor 1952 year class which i n turn may be a result of the heavy fishery i n 1952- -Since seven year olds contribute heavily to the fishery, one would expect better f i s h e r i e s i n 1958 and I960 than i n 1959- This i s supported by the catch figures for these years even though unselected mink feed forms a considerable portion of the landings and hence the younger age classes would also contribute part of the catch. A comparison of the age composition of the commercial catches (Table XL) with the abundance of 1+ f i s h i n the 1952-1954 samples also supports the above contention. The adequacy of the food sample as compared with the unselected mink feed sample was examined by analysing the age composition of the food and mink feed samples for i 9 6 0 (Table-XL). This analysis showed that the selection by the fisherman over and above the gear selection does not influence the number of females of age seven or older. The moderate abundance of 1+ and 2+ butter sole i n the 1952 summer hauls i s ref l e c t e d i n the equal representation of seven and eight year olds i n the 1958 catches. In 1959 s i x , seven and eight year olds occurred at approximately the same frequency and together-they formed the major proportion of the r e l a t i v e l y poor fishery. Because of the weakness of the 1952 year class the s i x and eight year olds formed a proportionately larger share of the catch than i s the case i n normal years. The abundance of the 1953 year class and the scarcity of the 1952 year class i n the 1954 samples are s i m i l a r i l y reflected i n the high percentage of seven year olds and poor representation of eight year olds i n the i 9 6 0 landings. Thus the estimates of abundance of young butter sole belonging to-different year classes could be substantiated s i x Table XXXIX. The abundance of I+, 11+ and > 11+ age groups of butter sole taken i n the small meshed (1 .5") trawl hauls along the Graham Island coast during 1952-1954. The values i n brackets are the corrected estimates made by adjusting the hauls to a standard 20 minutes. (Duration i haul Unsteady - less than 20 minutes 20 minutes 20 minutes ! Sample j Number 1952 1+ 11+ >II+ 1+ 1953 11+ >II+ 1+ 1954 11+ >n+ ! 1 i I 3 Age gro- ups not : separated 25 Nos. 39 Nos. 26 Nos. - 10to25 cms.(50) mostly 1+ (52) mostly 11+ (52) 6 4 2 4 l 0 4 l 1 3 17(43) 1 n ! 3(8) 0 0 2 ( 5 ) 4 5 ! 6 i 7 :• 8 ! 9 : 10 11 7(18) 2(5) 10(20) 3(6) 14(16) 7(8) 1(2) 0 0 3(6) 2(4) 6(7) 4(5) 3(6) 0 0 1(2) 0 4(5) 2(2) 3(6) 3 0 0 2 1(1) 0 0 2 0 0 2 3 2(2) 0 __8(16J_. 0 1 6 12 90 1(1) 2 7(14) 0 14 24 ! 1 i 6 i 2 i ! J J f 1* 2 1 1 j Mean 6.29 (10.71) 2.57 ( 4 . 0 0 ) 1.43 (2.14) 1.73 (1 .73) 2.00 (2-73) 11.36 ( 1 2 . 0 0 ) 10.00 (14-33) \ 2 .00 | ( 2 . 8 3 ) i7oo ~ ( 1 . 5 0 ) *net badly torn 95- Table XL. Age frequency d i s t r i b u t i o n of female butter sole i n the commercial catches taken during 1958-1960. Age 5 6 7 8 9 10 11 Total 1958 Food sample Number Percent 8 1.43 80 14-34 170 30.47 187 33-51 92 16.49 2 O.36 558 100 1959 Food sample Number Percent 14 2.47 180 31.71* 166 29.27 154 ' '27-16 44 7.76 9 1-59 - 567 100 i 9 6 0 Food sample Number Percent 5 1.88 71 26.79 119 4 4 . 9 0 53 2 0 . 0 10 3-77 7 2.64 - 265 100 i 9 6 0 Mink- feed sample Number Percent l l 3.31 i l l 33 A 3 147 44.27 44 13-25 14 4.21 5 1-50 - 332 100 „,, 96. years l a t e r when these f i s h became exploitable. I t then appears that the fluctuations i n abundance are determined during the early l i f e history and once a benthic habit has been adopted the year class strength remains r e l a t i v e l y stable. This analysis also establishes that the area along the Graham Island coast i s the major nursery ground for young butter sole. Thus i f a r e l i a b l e estimate'of the year class strength can be made from t h i s area, then i t i s possible to predict the success of the fishery that depends on these year classes. The r e l a t i v e abundance analysis performed by the ranking technique cannot be used to measure the magnitude of abundance. I t can only detect s i g n i f i c a n t changes i n abundance. Since most of the young butter sole are distributed along the Graham Island coast, a density index can be determined by taking a s u f f i c i e n t number of samples from t h i s area each year. From t h i s a r e l a t i v e index of the abundance of the year classes can be estimated by using the chain-link method. These results could be used i n studying changes i n biomass and y i e l d . Since butter sole i s r e s t r i c t e d largely to the northern part of Hecate S t r a i t during summer, estimates of the abundance of young year classes along the Graham Island coast can be checked i n subsequent years by taking samples from northern Hecate S t r a i t . The abundance of 6+ f i s h i n the July, 1 9 6 l , samples from t h i s area (Table XXV) and the successful fishery i n 1962 (Table XXXl) also indicate the usefulness of butter sole samples from Hecate S t r a i t , (c) Conclusion ( l ) The above study based on an examination of (a) dominance and r e l a t i v e abundance of young butter sole i n the nursery ground i n r e l a t i o n to other species of f l a t f i s h e s (b) variations i n the numerical strength of butter sole of age 1+ i n the 1952-1954 samples (c) the success and age composition 97- of the commercial catches when these year classes become exploitable indicates that fluctuations i n the butter sole population are largely determined during the early period of t h e i r l i f e history. (2) Their abundance tends to remain r e l a t i v e l y stable once they adopt a benthic habit. (3) The estimation of the year class strength i n samples from the Graham Island coast i s a r e l i a b l e index of abundance for studying changes i n biomass and y i e l d . The v a l i d i t y of these estimates could also be checked i n subsequent years with samples from northern Hecate S t r a i t . V Theoretical y i e l d study of the butter sole population 1. Introduction Theoretical studies of animal populations are done by means of analogues and/or models. The most complete of the main types of conceptual models are those of Beverton and Holt (1957) and Ricker (1958). The l a t t e r model was chosen for studying the butter sole population as i t describes adequately the chara c t e r i s t i c s peculiar to t h i s population and can be used when the population parameters are not constant. The adequacy of Ricker's model compared to Beverton's was examined for a hypothetical population i n a steady state exposed to a continuous and seasonal fishery under different growth and mortality rates and with different ages of exploitation. Using Ricker's model the following aspects of the butter sole population were studied: (a) changes i n the mean biomass of the spawning population and y i e l d under steady state with changes i n f i s h i n g and natural mortality rates and age of exploitation. (b) v a r i a t i o n i n the mean biomass and y i e l d when the recruitment varies 1. e. when the assumption of steady state i s released. 2. Procedure Before using Ricker's model for studying the butter sole population, the y i e l d per re c r u i t estimates f o r a hypothetical population using both Ricker's and Beverton's models were compared to examine the magnitude of error. After assuming that Bertalanffy 1s growth equation describes the growth pattern of t h i s population, the growth rate was altered by changing the value of K, the rate of deceleration i n growth increments, while maintaining T Q and L w constant although more often a change i n K i s accompanied by changes i n T and L K . The population i s also assumed to 99- exhibit isometric growth. The two models were then applied to the data both for a continuous and seasonal fishery . In using Ricker's model to study changes i n y i e l d and biomass of the spawning population of butter sole the average weight of stock during time t may be estimated by taking the arithmetic mean or the exponential average. When studying the magnitude of error, the y i e l d per re c r u i t estimates from both cases were compared with the results obtained from Beverton's equation. The present th e o r e t i c a l study of the butter sole population makes use of the b i o l o g i c a l information given i n Sections I I I and IV above. A weighted growth curve i s estimated based on the sex r a t i o of males and females i n each age group i n the 1953 sampling survey (Table VII) . Since f i s h of seven years and above are beyond the selection range of the gear and recruitment i s complete, one weighting factor found by estimating the geometric mean of the sex r a t i o i s used beyond t h i s age. Each year was divided into the following i n t e r v a l s : A p r i l to July, August to January and February to March. This was done because i t was known that approximately 50$ of the year's growth occurred by the end of July and i t was assumed that l i t t l e growth would occur during the peak spawning season i n February and March. Butter sole exhibit seasonal differences i n growth and t h e i r a v a i l a b i l i t y to the fishery i s highly seasonal, being li m i t e d to the peak spawning season. Under these Computer programmes for Ricker's and Beverton's equations are available at the In s t i t u t e of Fisheries, University of B r i t i s h Columbia. *"*Back calculated lengths used i n theo r e t i c a l studies were obtained using the regression l i n e of o t o l i t h radius (Y) on length (x) even though i t should be based" on the regression .line of-.-^length. (Y)- on "otolith radius (x) since-the sum of squares of deviation has to be based on the dependent variable or the variable to be predicted. The estimated lengths i n Table XXIII are based on the correct regression l i n e . However, there i s very l i t t l e difference i n the two estimates especially for f i v e years and above. 100. conditions "knife edge" selection "by the gear cannot be assumed since f i s h i n g takes place on a population consisting of I . 8 3 , 2 . 8 3 , etc. year old f i s h . Hence to study the effect of a change i n mesh size or 50$ retention age (Tp 1 ) on y i e l d , the proportion of f i s h of different ages retained within the selection range of the gear i s f i r s t estimated assuming that the selection ogive resembles a normal ogive. The calculated sigma (£") value of 1.04 cms., which measures the spread of the selection ogive of the 5.2" mesh, i s used for t h i s purpose. The respective f i s h i n g mortality rate i s obtained using t h i s proportion. To-study the effect of varying recruitment on the y i e l d and biomass an index of abundance for the entering year class i s introduced i n Ricker's model. This index i s obtained from the yearly landings as they indicate the possible range of fluctuations i n the year class strength. There are certain l i m i t a t i o n s i n the present analysis which could be overcome only "by acquiring more detailed knowledge of the ecological l i f e h i story of the population. They are: (a) The data on the seasonal differences i n the growth rate are not extensive .and the d i v i s i o n of the year y into three time intervals to f i t the yearly differences i n the growth rate may be subject to error. (b) The length-weight relationship used i n the present study i s estimated from ungutted specimens and ignores the sexual and seasonal differences i n weight as a result of differences i n the gonad condition. (c) The exact recruitment pattern to the spawning ground i s not studied. Hence an ar b i t r a r y age of 4 .83 years i s chosen to represent the age of entry to the exploitable phase. This value i s chosen because i t i s assumed to be a close approximation of the actual age of recruitment and the net increase i n weight at t h i s age i s not too low for studying the effect of various mortality rates, (d) The mdrtality rates appear to increase with age. Since the t o t a l mortality could not be separated into i t s component 101. parts, the most l i k e l y theoretical values had to he chosen to represent the natural mortality rate (M). A preliminary p l o t of the t o t a l mortality rate against age beyond seven years suggests a l i n e a r increase i n the t o t a l mortality with age and since a l l f i s h above seven years are equally l i a b l e to be captured by the gear the natural mortality -would also appear to increase l i n e a r l y with age. Hence the two selected natural mortality rates were each made to increase, i n steps of 0 . 2 and O.h respectively, at the end of each year beginning at the age of six. (e) The index of year class strength was estimated from .the t o t a l landings as data available were not extensive enough to measure the actual brood strength over a period of years. (f) Even though i t i s l i k e l y that the spread of the selection curve may increase with increase i n mesh size, the proportion of different ages retained within the selection range of different mesh sizes i s estimated on the assumption that th i s i s constant for a l l meshes. This aspect can be studied only by extensive mesh selection experiments. 3. Resuits (a) Comparison of the y i e l d per re c r u i t values obtained from Beverton's and Ricker's models for a hypothetical population. The y i e l d per re c r u i t (Y^yR) estimates using Beverton's and Ricker's models for different mortality rates and age of exploitation (Tpt) using different growth rates having a K value of 0.05128 and O.I7327 respectively are given i n Tables XLI and XLII and i n the form of y i e l d isopleths i n Figures 25 and 26. The average weight of stock during time t as estimated by Ricker's model i s obtained by taking the arithmetic mean. The percent deviation of Y^/R estimates obtained by Ricker's method from those obtained by Beverton's are entered i n Table-XLIII and Figures 27 and 28 and show that the difference i n the two estimates increases with increase i n age of T a b l e X L I . ^ j y ^ e s t i m a t i o n s i n grams "by t h e methods o f B e v e r t o n and R i c k e r ( a r i t h . mean) f o r a h y p o t h e t i c a l p o p u l a t i o n u n d e r s t e a d y s t a t e s u b j e c t t o a c o n t i n u o u s f i s h e r y . D a t a ( l ) K = 0.05128, Wn,- 293O.3 ems. ; T Q = 0 ; 1 = 1 ; Tj, =21 y e a r s . T _ t = F i r s t age o f f u l l e x p l o i t a t i o n o r 50$ r e t e n t i o n age. N a t u r a l M o r t a l i t y (M) M = 0.2 M = 0.6 F i s h i n g M o r t a l i t y ( F ) F =0.2 F =0.6 F = 1.0 F = 1.4 F - 1.8 F =0.2 F =0.6 F = 1.0 F = 1.4 F = 1.8 Yy^R b y t h e r e s p e c t - i v e methods f o r v a r i o u s T p , v a l u e s B e v . R i c k . Bev. R i c k . Bev. R i c k . Bev. R i c k . Bev - R i c k - Bev. R i c k . B e v . R i c k . Bev. R i c k . Bev. R i c k . Bev. R i c k . T p , = 1 v = 6 T p , = 11 T p . = 16 I3 .89 13.88 25.78 25.78 23.95 24.06 13-43 13-52 5-33 5-30 25.28 25.67 30.40 31.36 21.54 22.39 2.85 2.80 23.76 25.06 31.24 33-86 23-43 25.69 1.90 1.84 22.87 25.58 31.50 36.55 24.10 28.38 1.43 I .38 22.32 26.90 31.62 39.79 2U.44 31.28 I .78 I.77 1.14 1.16 0.19 0.19 0.02 0.02 1.71 1.68 1.93 2.03 0.34 O.37 0.03 0.04 1.36 1.31 2.21 2.47 0.41 0.48 0.04 0.05 1.11 1.07 2.35 2.83 0.45 O.57 0.05 0.06 0-95 0.93 2.43 3-19 0.47 O.65 0.05 0.07 Table X L I I . Y„/R estimations m grams "by the methods of Beverton and Ricker ( a r i t h . mean) for a h y p o t h e t i c a l p o p u l a t i o n under steady state subject to a continuous f i s h e r y . D a t a(2) K = 0.17327; Vfe = 2930-3 gms. ; T Q = 0 ; Tp = 1 ; Tj; = 2 1 years. T_ t= F i r s t age of f u l l e x p l o i t a t i o n or 50 percent retention age. Natural M o r t a l i t y M - 0 2 (M) M = 0.6 F i s h i n g M o r t a l i t y ! _ „ 1 F = 0.6 F = 1.0 j F = 1.4 F = 1.8 F = 0.2 ! I F = 0.6 1 F = 1.0 1 F = 1.4 F = 1.8 — 1 Y-wyR "by the respect- j ive methods for i Bev. Rick, various Tpt values Bev. Rick. Bev. Rick. Bev. Rick. Bev. Rick. Bev. Rick. , "' - i Bev. Rick, j Bev. Rick. 1 Bev. Rick. 1 1 Bev. Rick. 1 •• Tp, = 1 ,172.16 171-71 Tp, = 6 I236.75 237-33 1 T p , = 1 1 139-90 141.13 Tpt = 16 , 54-51 55-13 101.44 100.26 293.47 301.01 201 . 4 6 210.08 91.55 96.02 6 5 . 2 1 63-63 299.37 321.41 217-92 240.12 102 . 4 6 113-86 47.88 46.25 299.78 343.43 225.40 266.99 107.22 128.33 38.33 37 - 0 4 299-21 370.98 229.65 295.88 109.92 143.29 1 1 33-81 33 - 4 2 13.24 13-58 1.23 1.28 0.08 0.08 3 9 - 1 3 38.18 134.20 33.04 j 29.81 2 8 . 8 1 2 4 . 3 1 26.10 '28.98 3 3 . 2 0 ; 31.50 39.05 2.39 2 . 6 4 | 2.95 3.49 j 3.27 4.21 0.15 0.17 0.19 0.23 i 0.21 0.28 26.56 26.10 33-05 44.75 3 - 4 8 4.91 0.23 O.32 10k. 0 0.2 0.6 1.0 1.4 1.8 FISHING MORTALITY RATE (F) Figure 25- Comparison of the y i e l d isopleths for a hypothetical populat- ion obtained from Beverton's and Ricker's (arith.mean) models. Yy/R estimates f o r M = 0 .6 are rounded at the 4 t h decimal place for drawing y i e l d isopleths. (A)', k = 0.05128, M = 0 . 2 ; (B):K = 0.05128, M = 0 . 6 . Data from Table XLI. Figure 26. Comparison of the y i e l d isopleths"for a hypothetical population obtained from Beverton's and Ricker's (arith.mean) models. Yw/R estimates for M = 0 .6 are rounded at the " 4 t h decimal place for drawing y i e l d isopleths. (A).'K = O .I7327, M = 0 . 2 . (B):K = 0.17327, M = 0 . 6 . Data from Table XLII. Table XLIII. Percent deviation of Yw/R estimated by Ricker's method ( a r i t h . mean) from that of Beverton f o r the different values of K, M, F and T p t. Data from Tables XLI and XLII. Y wyR values f o r M of 0 . 2 are rounded to the 2nd decimal place i n calculating the $ deviation, and for M of 0 . 6 the values are rounded to the 4 t h decimal place. K = 0.05128 ; = 2930 .3 gms. ; T Q = 0 • T =1 t X = 21 years. Natural Mortality (M) M = 0 . 2 M = 0 . 6 Fishing Mortality (F) F =0.2 F=0.6 F= 1.0 F=1.4 F=1.8 F=0.2 F=0.6 : ?= 1.0 F= 1 .4 F= 1 .8 V = 1 -O.O72 -O.563 -I .754 -3-158 -37497 -0.677 - 1 . 8 5 0 -3 .018 -3-495 -2.616 V = 6 0 1.543 5-471 II . 8 5 O 20.520 I . 5 4 6 5.472 11.8U1 20.470 31.254 0.459 3 .158 8.387 16.03 25 .840 3.104 8-373 16.011 25.834 37-605 V = 1 6 O.67O 3.946 9 .646 17-759 27.987 3 .202 8.524 16.171 26.018 37.740 K = 0.17327 ; = 2930 .3 gm- ; t Q = = 0 i ^ = 1 ; t ^ = 21 years V = 1 -0.261 -I . I 6 3 -2 .423 -3-404 -3-366 -1 .164 -2 .426 -3-392 -3-193 -1-777 V =6 0 .245 2.56s 7 .362 14 .561 23.986 2.569 7 .360 14 .561 23.988 35-403 V = 1 1 O.879 4.279 IO.187 18 .452 28 .840 4 .277 IO . I76 18 .448 28.837 41.095 Tp. = 16 1.137 4.883 11.126 19.688 30.358 U .89I 11.091 19.701 30 .342 42.870 0 0.2 0.6 1.0 1.4 1.8 0 2 6 10 14 16 FISHING MORTALITY RATE (F) 50% RETENTION AGE (Tp') 0 0.2 0.6 1.0 1.4 1.8 0 2 6 10 14 16 FISHING MORTALITY RATE (F) 50% RETENTION AGE (Tp") Figure 27- Percent deviation of Yy/R estimated toy Ricker's method (arith.mean) from that of Beverton showing the trend for various f i s h i n g mortality rates and ages of exploitation. (A) K = 0.05128, M = 0 . 2 ; (B) K = O.O5128, M = 0 . 6 . Data from Table X L I I I . H O 0 02 0.6 1.0 14 18 0 2 6 10 14 16 0 02 0.6 1.0 1.4 IB 0 2 6 10 14 16 FISHING MORTALITY RATE (F) 50% RETENTION AGE (Tp') FISHING MORTALITY RATE (F) 50% RETENTION AGE (Tp') Figure 28. Percent deviation of Y^/R estimated by Ricker's method (arith.mean) from that of Beverton showing the trend for various f i s h i n g mortality rates and ages of exploitation. (A) K = 0.17327, M = 0 . 2 ; (B) K = 0.17327, M = 0 . 6 . Data from Table XLIII. H O CO 109- exploitation. This difference also increases with increase i n growth rate, natural mortality rate and f i s h i n g mortality rate. Hence a maximum difference of 42.8$) i s observed i n the table fo r a combination of the highest values of Tp,, K and t o t a l mortality. The figures also indicate that for t h i s population a sharp increase i n the per cent deviation occurs at a T , of s i x years. TP Another comparison of the Y^/R values obtained by the two methods i s presented i n Table XLIV. In t h i s case the average weight of stock during time t , as determined by'Ricker's method, i s obtained by taking the exponential average. The per cent deviation of the two sets of values i s given i n Table XLV and Figure 29- By using the exponential average i n Ricker's model, the difference i n the Y^/R estimates by the two methods has decreased considerably. Figure 29 shows that the difference between the two estimates decreases with increase i n the age of exploitation. A s l i g h t increase i n the per cent deviation with increase i n mortality rates i s also noticed although i t s magnitude i s ne g l i g i b l e at higher T_, values. The maximum per cent deviation i n the above example i s observed when the value of Tp, i s one. A l l estimations i n the above tables were for a continuous fishery. The Y^yR values f o r a seasonal fishery-as estimated by the methods of Ricker, using both the arithmetic mean and exponential average as the average weight of,stock during time t , and that of Beverton, are given i n Table XLVI. Their per cent deviations from those of Beverton are presented i n Table XLVII and Figure 30. It',is evident from a comparison of Table XLVII with'Tables XLIII and XLIV or Figure 30 with Figures "27-29 that when the f i s h i n g season i s reduced, the per cent deviation i n the Y^yR values i s very s l i g h t even when Ricker's model makes use of an .arithmetic mean for an estimate of the average weight of stock. When an exponential average i s used the difference Table XLIV. estimations in grams by the methods of Beverton and Ricker (exp.av.) f o r a hypothetical population under steady state subject to a continuous fishery. Data (2). K =0.17327 ; W,,, = 2930-3 gms. ; T Q = 0 ; T p = 1 ; ^ = 2 1 years. T_» = F i r s t age of f u l l exploitation or 50$ retention age. Natural Mortality (M) M = 0.2 M = 0.6 Fishing Mortality (F) F = 0.2 F = 0.6 F = 1.0 F = 1.1) F = 1.8 F = 0.2 F = 0.6 F = 1.0 F = 1.1* F = 1.8 Yy-/R by the respective methods for various Tp, values Bev. Rick. Bev. Rick. Bev. Rick. Bev. Rick. Bev. Rick. Bev. Rick. Bev. Rick Bev. Rick. Bev. Rick. Bev. Rick. T p, = 1 T p, =6 Tp, = 11 T p, = 16 172.16 169.91 236.75 236.05 139.90 139.78 54.51 54.49 101.W 98.25 293-47 292.30 201.46 201.21) 91-55 91-52 65.21 61.95 299.37 298.03 217.92 217.66 102.1)6 102.1)2 1*7.88 1)1*. 71 299.78 298.37 225.1*0 225.13 107.22 IO7.18 38.33 35-29 299.21 297.79 229.65 229.38 109.92 109.88 33-81 32-75 13-24 13-19 1-23 1.23 0.08 0.08 39-13 37-17 21*. 31 21*. 20 2.39 2.39 0.15 0.15 31*.20 31.93 28.98 28.81* 2.95 2.95 0.19 0.19 29 8l 27.1*5 31.50 31-35 3.27 3.27 0.21 0.21 26.58 21*.21 33.05 32.90 3-48 3.1*8 0.23 0.23 Table XLV. Percent deviation of Y^/R estimated by Ricker's method from that of Beverton for the different values of M, F and Tpt given i n Table XLIV- YyyR estimates f o r M of 0 . 2 are rounded to the 2nd decimal place i n calculating deviation and for M of 0 . 6 the values are rounded to the 4 t h decimal place. K = 0.17327, = 2930. 3 gms. ; T Q = 0 m ' P 1 ; T A = 21 years Natural M o r t a l i t y (M) M = 0 . 2 M = 0 . 6 Fishing Mortality (F) 0.2 0 . 6 1.0 1.4 1.8 0 . 2 0.6 1.0 1.4 1.8 T P, = 1 T P, = 6 T P, ;= 11 T P, = 16 -I .3O7 -O.296 - 0 . 0 8 6 -0 .037 -3-145 -O.399 -0.109 -O.O33 -4 .999 -0.448 -0.119 -0 .039 -6.495 -0.U70 -0.120' -O.O37 -7.931 -0.475 -0.118 -0.036 -3-140 -0.402 -0.114 -0.040 -4 .995 -0.448 -0.117 - 0 . 0 6 6 -6.6215 - 0 . 4 6 9 -0 .122 0 -7 .928 ' -0 .476 -0.119 -0.047 -8.914 -0.475 -0.121 -0.044 0 02 06 10 14 18 0 2 6 10 14 16 0 02 0.6 10 14 18 0 2 6 10 I4) 16 FISHING MORTALITY RATE (F) 50% RETENTION AGE (Tp') FISHING MORTALITY RATE (F) 50% RETENTION AGE (Tp') Figure 29. Percent deviation of Yw/R estimated by Ricker's method (exp.av.) from that of Beverton showing the trend for various f i s h i n g mortality rates and ages of exploitation. (A) K = O . I 7 3 2 7 , M = 0 . 2 ; (B) K = O.I7327, M = 0.6. Data from Table XLV. 1-1 H ru Table XLVI. %/R estimations m grams by the methods of Beverton and Ricker f o r a hypothetical population under steady state subject to a seasonal fishery. T , = F i r s t age of f u l l exploitation or 50$ retention age K = 0.17327; W,, = 2930-3 j T Q = 0 ; = 2 1 years M = 0.2 Fishing Mortality (M) 0.2 0.6 1.0 1.4 Yw/R by the respective methods for various Tpi values. Rick.l Rick.2 (arith. (exp. mean) av.) Bev. R i c k . l (arith. mean) Rick.2 (exp. av. ) Bev. R i c k . l ( a r i t h . mean) Rick.2 (exp. av. ) Bev. R i c k . l ( a r i t h . mean) Rick.2 (exp. av. ) Bev. R i c k . l Rick.2 ( a r i t h . (exp. mean) av.) a o & a 01 CO <u . •H tQ O P 1 |114.56 114 56 6 '109.42 109 46 1 1 57-33 57 36 16 19.30 19 32 1 '157.56 157 56 6 173-35 173 50 1 1 ! 95.76 95 98 16 i 34.20 34 30 114.51 164.78 164.96 164.67 109 . 4 2 j214.74 215.19 214.72 57-33 126.10 126 . 4 6 126.10 19.31 47.63 47.78 47.63 150.71 151.15 257.19 258.57 162.70 163.79 6 6 . 4 8 66.96 150.57 j 257-16 i 162.70 I 66.49 j 127.86 276.50 184.02 79-28 128.59 2 7 9 - 3 1 186.25 80.30 127.69 276 . 4 6 184.02 79.28 107.24 IO8.25 107.06 286.11 290.85 286.06 197.51 201.31 197.51 88 . 1 4 89.92 8 8 . 1 5 01 01 M > bo ir\ 5 d tn H *P T P *P 157-19 1144.30 144 . 4 8 143.63 173.24 [ 2 6 7 . 9 8 269.93 267.76 95-75 ! 171-94 173-83 171-91 34.20 72.01 72.90 72.01 104.11 104.52 289.23 294.90 199.58 204.79 89.79 92.34 103.34 288.95 199-53 89.79 77.26 77.90 76.47 1 60.05 60.92 59.25 295 - 5 2 306.82 295.21 297.47 316.25 297-14 212-97 223.12 212.92 220.75 237.42 220.70 104.01 98.98 104.25 112.53 104.24 114. Table X L V I I . Percent deviation of values obtained by Ricker's methods 1 and 2 from that of Beverton for a seasonal fishery as estimated from Table X L V I . Values up to 4 t h decimal place are retainedALn calculating $> deviation. K = 0.17327; Wa, = 2930.3 gms, j T Q = 0 ; T A = 21 year's#SM:%<;0.2 Fishir Mortal 'itv'"" .Q&2-. 0 .6 1.0 1.4 1.8 V R i c k . l Rick.2 R i c k . l Rick.2 R i c k . l Rick.2 R i c k . l Rick.2 R i c k . l Rick.2 1 crj CU CO LT\ bo OJ •H O • A •• u to 3 a •H O <U 1 1 . 6 11 16 0.016 - 0 . 0 4 0 O.O33 - 0 . 0 0 7 0.063 0 .001 O.O78 0.005 0.108 - 0 . 0 6 6 0 .208 - 0 . 0 1 0 0.285 0.0007 O.316 0.005 0.294 -O.O95 O.535 - 0 . 0 1 3 O.669 0.0002 0.720 0.005 O.571 -0.129 1.016 -0 .015 1.217 - 0 . 0 0 0 3 1.288 0.005 0.941 -O.165 I . 6 5 7 -0 .017 I.927-O.OOO7 2.020 0.005 1 cd CO a 0 •H w a a •H O OJ l 6 11 16 0.001 - 0 . 2 3 4 0.090 - 0 . 0 6 l 0.230 -O..OI6 0.289 - 0 . 0 0 2 0.126 - 0 . 4 6 4 0.725 -0.'083 1 filOO - 0 . 0 2 0 1.238 -Q.002 •393 -0-737 1.962 - 0 . 0 9 7 2 . 6 l 4 - 0 . 0 2 2 2.839 - 0 - 0 0 3 0.825 -1 .032 3.825 - 0 . 1 0 8 4.768 -0.024 5.082 - 0 - 0 0 3 1-455 -1-337 6.312 0«112 7-549 0.025 7.950 0.003 115- Figure 30. Percent deviation of Y^/R estimated by Ricker's methods 1 and 2 from that of Beverton for a seasonal fishery. The l i n e s of negative de\rfetion are for values from Ricker's method using exponential average. (A) Duration of f i s h i n g season = 0.25 year. (B) Duration of fi s h i n g season = 0 - 5 year. Data from Table XLVII. 116. i n the Y^R estimations by the methods of Beverton and Ricker for a seasonal fishery becomes extremely small. The hypothetical population .under consideration i s assumed to be i n ,a steady state with constant growth, recruitment and mortality rates. Since a t h e o r e t i c a l set of data are used for studying the magnitude of error, the difference i n the y i e l d per r e c r u i t estimations from different models as a result of discrepancies i n the data i s minimal. Hence any such difference would arise only from the manner of representing the data by the model. For purposes of comparison, Y^/R estimations from Beverton's equation are taken as the standard since the mathematical treatment of the data i s more elegant. The'Y^R estimations made by Ricker's method for various mortality rates, growth rates and age of exploitation vary considerably from those of Beverton when the average-weight of the stock i s obtained by taking the arithmetic mean. By using an exponential average the per cent deviation i s made ne g l i g i b l y small. Ricker (1958) suggests that an arithmetic mean may be a better average than the exponential. However, when the model assumes exponential growth and mortality rates within each time i n t e r v a l , an accurate estimate of the average weight.of stock f o r the time t i s given only by an exponential average. Under these conditions the use of an arithmetic mean results i n an over estimation of the y i e l d and thus introduces an error i n the calculation. The magnitude of the error i n the Y^/R values would depend on the difference i n the estimates of mean biomass at the beginning of each exploitable age, the values of the growth and mortality rates and the duration of the time t . The steepness of the exponential curve describing the change i n the biomass during time t depends on the value assumed by growth and mortality rates. With low growth or mortality rates, the exponential curve approaches a straight l i n e so that there i s l i t t l e difference i n the two 117- estimates of the mean biomass and hence the estimates of y i e l d w i l l also be similar. Thus the per cent deviation i n the Y^/R values i n Table XLIII shows a continuous increase with increase i n Tp, values, mortality rates and-K values when an arithmetic mean i s used. The error i s less when the f i s h i n g season i s reduced (Table'XLVIl). The arithmetic mean can be used only " i f the biomass i s a l i n e a r function of time. A comparison of the Y^yR estimates by Ricker's model, using an arithmetic mean, and those obtained by Beverton's method i s found to be either an over or an under-estimate. I f the weight of stock i s on the average decreasing, then use of an arithmetic mean overestimates the y i e l d . On the other hand i f the stock i s increasing then i t may, dependinng on the curve describing the change i n biomass, under-estimate the y i e l d . Hence at the optimum Tpt, when the changes i n biomass due to growth and mortality balance each other, the Y^yR estimate from Ricker's model using an arithmetic mean would be an over-estimate compared to Beverton's even for the smallest f i s h i n g mortality rate. The assumption of exponential growth and mortality rates f o r each time i n t e r v a l should mean that the biomass i s an exponential function of time. Hence the per cent deviation of the YyyR values estimated by "Ricker's model using an exponential average from .those of Beverton i s very much les s , although the Y .R i s now found to be always W/ less than that obtained by "Beverton's model. However, the s l i g h t difference observed i n the two estimates i s mainly-due to the manner of representing the growth pattern i n the two models. The chief drawback i n Beverton's equation i s the complexity assumed by the model when the parameters are not constant. In the present study, i n order to calculate one Y^yR value fo r a seasonal fishery, changes involved i n modifying Beverton's equation for a seasonal fishery maintaining a l l other parameters constant alone makes the equation over twenty times more time 118. consuming. When the exploitable phase l a s t s twenty years with one short f i s h i n g season, the y i e l d f o r each season i s calculated i n exactly the same manner as i t i s fo r a continuous fishery. In addition, the number of recr u i t s at the beginning of each season has to be calculated separately. I f growth i s also seasonal and f i s h do not grow isometrically, the appropriate modifications involve complex numerical integration. Ricker's equation, on the other hand, accomodates changes i n growth and mortality rates with no modifications i n the o r i g i n a l method. When one considers (a) the complexity assumed by Beverton's model under these circumstances (b) the simple calculations required i n Ricker's method and f l e x i b i l i t y with which i t accomodates changes i n growth and mortality rates (c) the v a r i a b i l i t y inherent i n the b i o l o g i c a l data and (d) almost i d e n t i c a l results from the two equations, Rickers model may be preferred for studying the changes i n y i e l d and biomass when growth and mortality rates are not constant or when the f i s h do not grow isometrically. / (b) Changes i n the y i e l d and biomass of the butter sole population The reaction of the butter sole population to varying degrees of exploitation at dif f e r e n t ages and mortality rates i s examined for f i s h above 4.83 years of age, although the recruitment to the spawning ground i s not complete at t h i s age as seen from Table VII. The mesh size of 50$ retention must have a perimeter much'less than the g i r t h of f i s h U.83 years i n order to account for the recruitment pattern. Since t h i s pattern i s not known prec i s e l y , changes i n the biomass and y i e l d are examined assuming that f i s h above U.83 years of age represent a post-recruit phase of the population. The i n d i v i d u a l or simultaneous effect of a change i n the f i s h i n g mortality rates and the age of exploitation ( i . e . the 50$ retention age) on the biomass i s presented i n the form of an isopleth diagram i n Figure 31« With increase ( U 9 - Figure 31- Butter sole: Isopleth diagram for biomass per re c r u i t for the post-recruit phase. (A) M = 0 . 1 , A M = 0 . 2 . (B) M = 0 . 2 , A M = 0 . 2 . (c) M = o . i , A M = o.U. (D) M-= 0 . 2 ,AM = o.k. 120. i n the age of exploitation, the mean biomass of the spawning population increases. Increase i n the natural and f i s h i n g mortality rates reduces the biomass of the post-recruit phase. However, the r e l a t i v e effect of a change i n the two mortality rates on the biomass are very different (Figure 32) . When the i n i t i a l natural mortality rate i s 0.1 (Figure 32A), a change i n the fi s h i n g mortality rate from 0.2 to 0.6 reduces the mean biomass per r e c r u i t from 880.77 gms to 778.55 gms. A change i n the natural mortality rate from 0.1 to 0.2 (Figure 32B) reduces i t from 880.77 to 732-39 gms. The effect of a change i n the f i s h i n g mortality rate i s not f e l t i n the biomass as much as a change i n the natural mortality rate. This i s because f i s h i n g i s highly seasonal and operates at a time when the growth rate i s at i t s minimum, whereas natural mortality operates throughout the year. A r e l a t i v e l y high f i s h i n g mortality rate i s required to s i g n i f i c a n t l y lower the mean biomass. Since the v u l n e r a b i l i t y or c a t c h a b i l i t y of the f i s h to the gear i s f a i r l y high, a high f i s h i n g mortality-rate can be generated during the spawning season and thus bring about -an appreciable dent i n the population. The effects on the y i e l d of changing the age of exploitation for four sets of natural mortality rates are given i n Figure 33- I f the age of exploitation i s very low, a low f i s h i n g mortality-would r e s u l t i n higher y i e l d since more young f i s h with faster growth rates are l e f t to re a l i z e t h e i r growth p o t e n t i a l i t i e s . With increase i n the age of exploitation, the fi s h i n g mortality rate that would give the maximum y i e l d also increases. F i n a l l y , at the age when the increase due to growth and the decrease i n numbers from natural mortality balance each other, an i n f i n i t e l y high f i s h i n g mortality rate i s required to obtain the pot e n t i a l y i e l d as designated by Holt (1958). The weight of a year's brood i s maximum at t h i s age. The equilibrium y i e l d curves presented i n Figure 33 have t h e i r modes at ages less 121. IOOO = 3 0 0 - 2 0 0 0 2 O 6 I O 14 18 FISHING MORTALITY RATE (F) Figure 32. Butter sole: Changes i n the biomass per rec r u i t for different f i s h i n g and natural mortality rates when T , i s 4 . 8 3 years. (A) M = 0 . 1 , A M = 0 . 2 . (B) M = 0.2,hlP= 0 . 2 . (c) M = 0 . 1 , A M = 0.4. (D) M = 0 . 2 , A M = o.k. 122. Figure 33- Butter sole: Equilibrium y i e l d curves for various sets of natural mortality rates, (A) M = 0 . 1 , A M = 0 . 2 . (B) M = o . 2 , A M = 0 . 2 . (c) M = o . i , A M = o.k. (D) M = 0 . 2 , AM = o.k. 123- T p i=4.83 T p i=5.83 Tpi=6.83 T p i =783 T D 1 = 8.83 - B - ."^,= 4.83 / > .T p l = 5.83 / / _^ Tpia6.83 / / ^ ^ T p i = 7 . 8 3 ^______Tpi = 8.83 l i 140 u» 120 < a. o z IOO g BO UJ a. a. Q -1 Ul > 4 0 2 0 - c - /TPI3 4.83 / / T p i=5.83 ^ - T p l - 6 . 8 3 T p.=7.83 . T p , = 8.83 1 J - D — T p i s 4 . 8 3 - / Tp. = 5.83 _.T pi=6.83 - / / ^__________Tpi=7.83 - — r - Tp.-ft A3 ' 1 O 0.2 0.6 I.O 1.4 1.8 FISHING M O R T A L I T Y RATE(F) O 0.2 0.6 I.O 1.4 1.8 FISHING M O R T A L I T Y R A T E ( F ) Figure 34. Butter sole: Equilibrium y i e l d curves for various sets of natural mortality rates. (A) M = 0.1,AM = 0.2. (B) M = 0.2, A M = 0.2. (C) M = 0.1,AM = 0.4. (D) M = 0.2,AM = 0.4. 12k. than U.83 years for a l l the f i s h i n g mortality rates examined. Since the -age of f i r s t exploitation i s f a r i l y high the equilibrium y i e l d curves plotted i n Figure 3^ do not a t t a i n the maximum at the f i s h i n g mortality rates examined. Above the optimum age of exploitation the population biomass i s decreasing since the biomass l o s t because of natural mortality i s no longer f u l l y compensated for by growth. Hence beyond t h i s age an increase i n the f i s h i n g mortality rate always increases the y i e l d however, the same y i e l d can be reali z e d at a lower f i s h i n g mortality rate i f the age of exploitation i s below the optimum age. The curve which maximizes the sustained y i e l d for a given f i s h i n g mortality rate by adjusting the age of exploitation i s defined as the eumetric y i e l d curve by Beverton and Holt (1956b). They define the eumetric f i s h i n g curve as the "curve defining the relationship between the f i s h i n g mortality and the Tp, needed to produce a eumetric y i e l d curve". The eumetric f i s h i n g curve can be drawn by joining the modes of the contours of y i e l d per re c r u i t drawn i n a y i e l d isopleth diagram. The highest y i e l d per re c r u i t values for a given f i s h i n g mortality l i e along t h i s l i n e flanked on either side by lesser y i e l d per re c r u i t values. The y i e l d isopleth diagrams for butter sole presented i n Figure 35 permit an analysis of the effect of a simultaneous change i n the f i s h i n g mortality and the age of exploitation. The eumetric f i s h i n g curve cannot be drawn even when the i n i t i a l natural mortality rate i s as low as 0 . 1 , since the modes of the contours of y i e l d per rec r u i t l i e below the age of 4 .83 years. This i s also seen from the equilibrium y i e l d curves i n Figures 33 and- 3^ which have th e i r modes at ages less than U.83 years for a l l the f i s h i n g mortality rates examined. Hence the maximum y i e l d fo r a f i s h i n g mortality rate less than 1.8 i s obtained only below t h i s age. For t h i s reason the f i s h i n g mortality rate 125- Figure 35* Butter sole: Y i e l d isopleth diagrams when different mortality rates are operating showing the y i e l d for different ages of exploitation and f i s h i n g mortality rates. (A) M = 0 . 1 , AM = o . 2 . (B) M = 0 . 2 , A M = 0 . 2 . (c) M = 0 . 1 , AM = o.k. (D) M = 0 . 2 , A M = O.k. 126. that would result i n the maximum sustained y i e l d when the age of exploitation i s U.83 i s well above 1.8. I t should, however, be noted that as the f i s h i n g season l a s t s only two months or O.17 year the effective f i s h i n g mortality i s only 1.8 x 0.17 or O.306. However, because the population i s highly vulnerable to the gear a higher f i s h i n g mortality may be generated. The isopleth diagrams drawn by Beverton and Holt (1957) North Sea populations of,plaice and haddock i n a steady state assume that (a) recruitment i s independent of the size of the spawning stock (b) the growth pattern conforms to Bertalanffy's equation and (c) that f i s h i n g and natural mortalities are continuous and constant for a l l ages. There are s i g n i f i c a n t seasonal differences i n the growth of butter sole even i f the growth pattern i s described by Bertalanffy's equation. Natural mortality also varies with age. Since the butter sole fishery i s highly seasonal, changes i n the biomass and y i e l d per re c r u i t with changes i n the mortality rates and age of exploitation are estimated i n r e l a t i o n to the spawning population on which the fishery exists. With respect to the spawning population, the greatest biomass per rec r u i t i s attained at 5•83 years for a l l the natural mortality rates studied (Figure 36) even i f the greatest weight of a year's brood may not be attained at t h i s age (Figure 36A). Since the a v a i l a b i l i t y of butter sole to the fishery i s highest during the spawning season, the p o s s i b i l i t y of increasing the y e i l d by moving the f i s h i n g season to a period when the weight of stock i s greatest i s not considered. In addition, t h i s increase i n the biomass of a year class above 5-83 years i s observed only for the lowest natural mortality rate chosen and even then i t i s very s l i g h t (Figure 36A). (c) Effects of fluctu a t i n g recruitment on the biomass and y i e l d In the above analysis of the reaction of the butter sole population to varying mortality rates and ages of exploitation i t i s assumed that the 127- 260 h 4.83 5B3 6JB3 7.83 8.83 9.83 10.83 11.83 A G E IN Y E A R S Figure 36. Butter sole: Changes i n the biomass per rec r u i t at different ages when no f i s h i n g mortality i s operating. (A) M = 0 . 1 , A M = 0 . 2 . (B) M = 0 . 2 , A M = 0 . 2 . (c) M = O.I,AM = o.k. (D) M = 0 . 2 , A M = O.k. 128. population parameters are constant from year to year. Although the factors c o n t r o l l i n g .fluctuations i n the hutter sole population are not known, evidence i s presented i n Section IV which suggests that they are largely determined during the early stages of the l i f e history and that an index of year class strength can he obtained by sampling young butter sole along the Graham Island coast. The results of an analysis of the changes i n biomass and y i e l d using an index of abundance based on the yearly landings are presented i n Table XLVIII and Figure 37' Since the entering year class i s subjected to fluctuations, the age composition also varies from year to year and no relationship between the size of the biomass of the post-recruit phase and y i e l d can be arrived at unless the fluctuations occur i n a de f i n i t e pattern. In Figure 37A the mean biomass for the post-recruit phase during year N + 1 i s very close to that of a steady state population, but i t resulted i n a y i e l d considerably higher than that for the steady state. During the next year both the biomass and y i e l d remain close to the base l i n e . As long as the f i s h i n g mortality rate i s steady, the effect of different mortality rates on the y i e l d and biomass i s very similar. However, t h i s i s not the case when the natural mortality rate increases at different rates. A comparison of the Figures 37A and 37C o r 37B and 37D shows that fluctuations i n the biomass and y i e l d are much greater when the mortality rate increases i n steps of 0.4 instead of 0 .2 f o r the f i s h over s i x years of age. This i s expected since the older year classes now contribute less to the size -of the stock and to the y i e l d so that fluctuations of the entering year classes are not as we l l dampened as before. In general the seven year old f i s h are best represented i n the fishery, followed by s i x and eight year olds. Changes i n the biomass and y i e l d can be traced i f an accurate estimate of the year class strength can be obtained. The effect of a change i n the -age of exploitation (TQI) from 5-83 years to 6-33 years i s higher when the natural mortality rate Table XBTIII. Butter sole. The changes in biomass (post-recruit phase) and yield in grams under fluctuating recruitment in six successive years (N to N+5) compared to yield and biomass under steady state conditions. The age of recruitment is 4.83 years. The two sets of natural mortality rates increase in steps of 0.2 and 0.4 respectively at the end of each year beginning from 6 years of age. Fishing mortality operates during the Natural mort.rate(M) M = 0.1, A M = 0.2 from 6 years M = 0.1, AM = 0.4 from 6 years 50# retent'n age(Tpt) 5.83 years 6.33 years 5.83 years 6.33 years Fishing mort.rate(F) F=0.2 F=0.6 F=0.2 F=0.6 F=0.2 F=0.6 F=0.2 F=0.6 Age group Index of abundance Biomass Yield Biomass Yield Biomass Yield Biomass Yield Biomass Yield Biomass Yield Biomass Yield Biomass Yield O.83 I . 8 3 2.83 3-83 4.83 5.83 6.83 7.83 8.83 9.83 10.83 11.83 1.40 O.57 1-25 0.45 O.96 1.44 1.42 0-73 0.20 O.39 3.70 1.84 892.66 18.66 8 O I . 8 7 19.08 896.08 18.59 903.57 20.57 995-37 23.78 21.92 829.15 5O.5O 737-79 50-94 826.68 49.58 836.13 5>+-8l 936.01 64.71 60.06 901.51 14.32 8IO.5O 16.75 905.83 14.79 914.56 18.84 IOO5.25 20.21 16.89 832.68 38.85 76O.89 43.48 852.89 39.54 866.26 51-33 963.21 55-96 46.67 686.88 12.82 591-90 12.21 664.27 11.58 696.62 12.83 825.13 16.87 16.25 651-90 35-83 563.61 33-21 6 2 9 . I O 32.14 658.03 35.03 793-87 46.90 45.85 684.79 8.40 597-06 9-67 670.20 7.72 704.24 11.09 832.26 13.36 11.29 666.89 23.65 577-96 27.34 645.46 21.37 679.38 30.90 813.87 37-77 32.26 OJ S ro 0 0 0\ CVJ Si * CO <M O cE) TTN & * VO CO CO ro rH V£) ON rH * CO * OJ i r \ O vo NO vo CO -=f * a & CO * O ro t- rH & * ITS t - rH t- C -vo ro * H ON O O t- rH * r- * ITS rH ~1 ^° CO CO CO VO CM * The respective biomass and yield per recruit values under steady state. z O > < O z m UJ u. o o a. ui a. IO IO i/\ If \ If \ ~ If \ / \ c + ^ \ • / 30 20 Z o > a uj —1 _ Q UJ O z ui o an UJ a lOh 2 0 h 30 IOh // X N N+l N+2 N+3 N+4 N+5 YEAR • - s,\ / \ B + X/ ' A // // 1/ // \ • + / / 1 1 A / N \ \/ \ \ 1 1 1 1 • D + / hit N+l N+2 N+3 N+4 N+5 YEAR FIGURE 37. BUTTER SOLE*. PERCENT DEVIATION IN YIELD AND BIOMASS (POST-RECRUIT PHASE) UNDER FLUCTUATING RECRUITMENT FOR DIFFERENT AGES OF EXPLOITATION AND MORTALITY RATES. (AY.TpU5.83 YEARS, M.O. I ,AM=0.2 , F=0.2 5 F«0.6 . (B)!Tp« = 6.33YEARS,M=O.I, AM=0.2, F=0.2, . — F=0.b.(C):Tp.= 5.83YEARS ; M = O.I,AM=0.4, F=0.2, F=0.6 . (D) :T p - .6 .33YEARS,M B O.I ,AM = 0 4 , F = 0 . 2 , F=0.6. 131- increases i n steps of 0.1+ (Figure 37D). (d) Conclusion 1. The version of Ricker's model that makes use of an exponential average as the weight of stock during time t i s more accurate than the one using the arithmetic mean. Compared to Beverton's model, Ricker's equation i s equally • accurate for studying changes i n the y i e l d and hiomass of an exploited population, especially when the v a r i a b i l i t y inherent i n the b i o l o g i c a l data i s considered. I t i s more f l e x i b l e and e a s i l y accomodates seasonal changes i n growth and mortality without increasing the complexity of the model. 2. Using Ricker's model changes i n the butter sole population and y i e l d are studied f o r varying mortality rates and age of exploitation. Results are presented i n the form of isopleths and equilibrium y i e l d curves. The present study i s confined to the spawning season since the fishery depends on the spawning population and the a v a i l a b i l i t y of butter sole i s not as high at other times. 3- Since f i s h i n g i s highly seasonal, a change i n the natural mortality rate exerts a greater influence on the biomass than a similar change i n the f i s h i n g mortality rate. An increase i n the age of exploitation increases the mean biomass while an increase i n the mortality rates decreases i t . 4. As the age of recruitment i s f a i r l y high the f i s h i n g mortality rate that results i n maximum y i e l d i s higher than 1 .8. Hence the y i e l d per re c r u i t contours i n the y i e l d isopleth diagram do not have t h e i r modes at the f i s h i n g i n t e n s i t i e s examined. Therefore the i n i t i a l slope of the eumetric f i s h i n g curve i s absent ,in the isopleth diagram drawn for the spawning population above 4.83 years. 5. When the strength of the entering year class varies from year to year, the relationship between the size of the biomass and y i e l d i s less precise. 132. Under steady state conditions with a given age of exploitation and given mortality rates, the biomass and y i e l d are always constant. When the natural mortality rate increases i n steps of 0.4 instead of 0 . 2 beyond s i x years of age the older year classes contribute less to the size of the stock. Consequently, deviations i n biomass and y i e l d become more pronounced since the fluctuations of the entering year classes are less dampened by the older age groups of the population. VI. Discussion 1. Ecology of the butter sole population Fluctuations i n abundance of f i s h populations are due to variations i n the b i o t i c and abiotic factors of the environment. While certain populations are comparatively steady, others, especially the pelagic species such as sardine and mackerel, show extreme fluctuations. Populations often exhibit changes i n the reproductive output, growth_and mortality rates as a result of such fluctuations. Wynne-Edwards (1962) discusses the self-regulatory mechanisms of populations. He also points out that the homeostatic adaptations of populations are recognized i n developing the modern theory of exploitation of f i s h populations. This i s evident both i n Russel's ( l 9 3 l ) exposition of the idea of r a t i o n a l f i s h i n g and i n subsequent works by "Graham (1935), Schaefer ( 1 9 5 M , Beverton and Holt (1957) and others. Despite the various views that exist to explain fluctuations i n abundance, t h i s problem can be understood only by studying the ecological l i f e history of the species as outlined by G i l l (1910) and recently by Koster (1955)- The butter sole that spawn i n Skidegate Inlet are inhabitants of the Hecate S t r a i t f l a t . Trawling surveys indicate that they are more abundant on the northern part of the bank. There seems to be a l a t i t u d i n a l difference i n the depth d i s t r i b u t i o n of the species. Generally, f i s h of the Hecate S t r a i t population are not found at depths greater than 50 fathoms, although on the Washington and Oregon coast they are found at depths between 55 and 65 fathoms. Examination of the factors l i m i t i n g t h e i r d i s t r i b u t i o n suggests that the population spawning i n Skidegate Inlet does not extend i t s range beyond the Hecate S t r a i t bank either 'during the l a r v a l or adult phases. Analysis of the length composition of butter sole (Tables I-V) i n the 195^ 134. and 1961 samples Indicates a depth s t r a t i f i c a t i o n according to size and age groups. The young ones are r e s t r i c t e d to the inshore area along the Graham Island coast while the larger and older ones occur progressively farther away from t h i s area. Two factors which tend to obscure t h i s depth d i s t r i b u t i o n pointed out i n Section I I I are: (a) The shallow Hecate S t r a i t bank forms the main summer feeding ground for butter sole. They are found i n shallower waters during summer and deeper waters during winter and (b) the change from the 10 to 20 fathom • contour i s very gradual compared to the 2 gradient between the 20 and 50 fathom contours. Hence the x value f o r 1954 samples l y i n g i n t h i s b e l t (haul-groups I I I to V) i s not s i g n i f i c a n t which suggests no depth s t r a t i f i c a t i o n of butter sole within t h i s area. However, the length composition i n samples collected from areas 1 and 2, especially area 1, consist mainly of young butter sole. A north-south migration i s exhibited only by the spawning population. This i s shown by the length composition data of butter sole collected from the spawning ground i n Skidegate Inlet and from Butterworth ground (Figure 8 ) . Sexual differences i n the onset of maturity and spawning migration are evident i n the size composition and sex r a t i o of the spawning population (Tables VI and V I l ) . S i m i l a r i t y i n the r e l a t i v e .abundance of young butter sole along the Graham Island coast during 1952-1954 and i n the success and age composition of the fishery i n Skidegate Inlet when these year classes reach an exploitable age (Section IV) suggests that the Graham Island coast i s the chief nursery ground for the young butter sole that w i l l l a t e r spawn i n Skidegate Inlet. A study of the i n t e r s p e c i f i c association of butter sole and related species of f l a t f i s h inhabiting the same general area indicates no strong p o s i t i v e or negative association between these species. Hence no definite conclusion can be made with respect to the degree of i n t e r - s p e c i f i c association 135- that might exist between these species. No sizable coastal populations which could mix with the Skidegate spawners i n t h e i r summer feeding ground are known to -exist. The analysis of homogeneity of the Hecate S t r a i t population of butter sole (Section I I I ) also does not suggest the p o s s i b i l i t y of more than one self-contained stock i n the area. This aids considerably i n the interpretation of growth data of butter sole collected from the Hecate 'Strait bank. The growth of butter sole above -two years of age i s described by Von Bertalanffy's growth curve although seasonal differences i n the growth rates are superimposed on i t . Males grow slower than females. Growth rates estimated f o r different year classes indicate annual differences which are p a r t l y explained by i n t r a - s p e c i f i c competition. I f the i n i t i a l growth i s above or below average, a tendency to compensate for t h i s difference i n l a t e r years i s also observed. Regional difference i n the growth rates of butter sole (Table XXVIl) and the r e l a t i v e abundance i n these areas (Tables I I I and V) suggest variations i n habitat s u i t a b i l i t y and segregation of the fast and slow growers. Examination of the survival rate indicates a r e l a t i v e l y high natural mortality rate that increases with age. I t i s also found to be higher for the males. Because the population migrates to Skidegate Inlet f o r spawning during the winter months t h e i r a v a i l a b i l i t y to the commercial gear increases sharply during t h i s period, supporting a highly "localized and seasonal winter fishery. Butter sole of seven years and above contribute the greater portion of the landings. Hence only a small section of the population i s exploited. This i s due to two things: (a) they are recruited to the spawning ground r e l a t i v e l y late (Tables VI and VII) and (b) the demand for butter sole as food f i s h compared to related species of f l a t f i s h i s low, 136. r e s u l t i n g i n considerable secondary selection by the fishermen. Only recently more and more unselected catches have been landed as mink feed and hence the younger f i s h , p a r t i c u l a r l y the males of less than seven years of age, have been better represented. Landings show considerable fluctuation as a result of changes i n demand and-fluctuations in, the size of the spawning stock. An examination of the r e l a t i v e abundance of young butter sole along the Graham Island coast and the success and age composition of the fishery i n Skidegate Inlet s i x years l a t e r indicate that fluctuations i n abundance are largely determined during the early period of the l i f e history. Hence estimations of year class strength from samples taken on the Graham Island coast are a r e l i a b l e index of abundance that can be checked i n subsequent years with Hecate 'Strait samples. Since the information collected on the ecological l i f e history of the population i s l i m i t e d , only certain general conclusions are drawn from the t h e o r e t i c a l study of the changes i n biomass and y i e l d with changes i n the mortality rates and abundance. Fishing mortality i s highly seasonal, hence i t s effect on the biomass i s less noticeable than a change i n the natural mortality rate. However, as the v u l n e r a b i l i t y of butter sole to the gear during the spawning season i s high, a heavy f i s h i n g mortality could be generated. The equilibrium y i e l d curves and the YyyR contours of the y i e l d isopleth diagrams were without a mode for a l l the ages of exploitation and mortality rates examined. Figures 33 _ 35 also indicate that when the age of exploitation (Tpt) i s k.83 years, the maximum equilibrium y i e l d f o r a l l natural mortality rates examined can be obtained only with a f i s h i n g mortality rate higher than 1 .8. The relationship between the size of the biomass and y i e l d becomes less precise under fluctuating recruitment. A higher rate of increase of the 137- natural mortality^rate for ages above s i x years causes greater fluctuations i n y i e l d and biomass since fluctuations i n recruitment are now less dampened by the older year classes. On the other hand, since the f i s h i n g mortality rate i s constant for a l l ages, a change i n the f i s h i n g mortality rate i s not accompanied by-a similar deviation i n the size of biomass and y i e l d . Biomass per r e c r u i t at different .ages constantly decreases beyond 5-83 years for a l l but one set of natural mortality rates (Figure 36)- The highest f i s h i n g pressure that i s economically feasible may therefore be exerted on t h i s section of the population provided the population maintains a steady state. The heavy fishery i n 1952 might have affected the poor 1952 year class. However, there i s no direct evidence of the effect of f i s h i n g on the strength of the year class. Since the fishery i s very localized,heavy trawling removes a considerable number of spawners. I t may also decrease the s u i t a b i l i t y of the spawning ground or destroy s i g n i f i c a n t numbers of eggs. However, there are no signs of the population being overfished at present. The maximum u t i l i z a t i o n of the existing mesh regulation, i.e. use of k" mesh cod-end followed by -a heavy fishery, would result i n greater exploitation of males than females because- of the sex composition of the spawning population a r i s i n g from sexual differences i n the recruitment and migratory patterns. This may eventually-alter the sex-ratio of the population. However, since males are i n m i l t for a longer time and appear to remain longer on the spawning ground, the effect of greater exploitation may not be serious u n t i l the sex-ratio i s altered d r a s t i c a l l y . The male-female-ratio of the spawning population i s about 5*1 and- the possible e f f e c t , i f any, of greater exploitation of males can be determined only by harvesting the stock. Beverton and Holt (1957) state that male plaice .are i n m i l t for a longer time than females so that there may be an excess of ripe males on the spawning 138. ground even though males are less abundant. They c i t e Simpson's remark that i n plaice the proportion of u n f e r t i l i z e d egg i s very small. 2. Further Studies Butter sole exhibit sexual differences i n growth, mortality rates, recruitment and migratory patterns. The two sexes may, therefore, be treated as a special case of two competing populations exploited simultaneously. Hence a more detailed study requires information on the above characteristics of the population so that the effects of varying degrees of exploitation on the two sexes can be studied separately. A knowledge of the recruitment pattern i s needed for assessing the biomass of the spawning population, i n estimating the stock-recruitment relationship and i n a r r i v i n g at the best exploitation l e v e l . A rough estimate of the recruitment can be obtained by estimating the per cent males and females i n each age class that would mature i n the next spawning season from samples taken from Hecate S t r a i t p r i o r to the spawning migration. An alternative procedure would be to obtain natural mortality rates of the population i n the pre-recruit phase from age composition data collected by extensive sampling of the nursery ground. I f fluctuations i n recruitment are not great, then the per cent of the incompletely recruited age classes can be obtained by expressing t h e i r numbers on the spawning ground as a per cent of the f i r s t f u l l y recruited age group after adjusting for natural mortality. I f recruitment varies considerably then t h e i r numbers have to be adjusted f i r s t by the reciprocal of the index of abundance for each age class. A mean estimate of the per cent recruitment based on many year's data would give a f a i r l y accurate estimate of the -recruitment pattern. A t h i r d possible method i s by comparing d i r e c t l y the estimated numbers of each age class i n the nursery and spawning grounds. A comparison of these different estimates would 139- confirm the accuracy of the estimated recruitment pattern. Since the fishery depends on the spawning population, subjected to both immigration and emigration, a knowledge of the migratory pattern i s required to avoid bias i n the estimates of the biomass and f i s h i n g mortality of the spawning population. Very l i t t l e i s known of the migratory pattern. Immigration and emigration may both be a continuous process or, depending on the nature of spawning, emigration may begin l a t e r after the spawning season i s w e l l advanced. An attempt to either tag the population p r i o r to t h e i r spawning migration to obtain data on immigration or to tag the spawning population to study the eimigration pattern would be an extensive program. This may not be feasible since the fishery i s small and i t s demand r e l a t i v e l y low compared to other species. Ketchen (1953) obtained r e l i a b l e information on the migration of lemon sole using a modified Delury method by p l o t t i n g catch per unit e f f o r t against cumulative catch and recaptured lemon sole. In applying the method to butter sole the migratory pattern of the two sexes have to be studied separately. The average male-female r a t i o beyond the post-recruit phase as determined from extensive sampling during 1953 i s 2 :1 . Because t h i s r a t i o i s not influenced by the recruitment pattern, t h i s difference i s p a r t l y due to v a r i a t i o n i n the migration of the two sexes. Various methods of estimating f i s h i n g and natural mortality rates are reviewed by Beverton and Holt (1956a, 1957) and Ricker (1958)- Beverton and Holt (1956a) have indicated that separation of t o t a l mortality rate into f i s h i n g and natural m o r t a l i t i e s often involves the assumption that natural mortality rate i s constant for a l l ages. However, methods involving catch sampling require considerable yearly changes i n the f i s h i n g i n t e n s i t y which would resu l t i n s i g n i f i c a n t v a r i a t i o n i n the estimates of t o t a l mortality rates. The natural mortality rate of butter sole i s f a i r l y high and the 140. f i s h i n g mortality operates for only a short period. The demand for the species i s also not high. Hence yearly changes i n f i s h i n g intensity may not he s u f f i c i e n t l y reflected i n the t o t a l mortality to allow t h e i r estimation with accuracy. An accurate estimate of the f i s h i n g i n t e n s i t y i n terms of the actual number of hours fished i s also required, especially since the fishery i s small. However, the f i s h i n g mortality rate can be estimated by tagging. Manzer's (1949) data on the size d i s t r i b u t i o n of tagged and recaptured butter sole suggest that the tagged f i s h disperse randomly and hence t h e i r behaviour may be similar to the untagged f i s h . During the f i s h i n g season large numbers of f i s h can be tagged i n a short time. Since the f i s h i n g season i s very short, bias from tag loss and tagging mortality w i l l be*small. The fishery i s r e s t r i c t e d to Skidegate Inlet and the number of boats operating at a time are few, so that the f a i l u r e to report recovered tags' should be at a minimum. Estimation of the mortality of the butter sole population from the r a t i o of the number recaptured during time t to the number of tagged f i s h at large at the beginning of time t would be a r e l i a b l e estimate of the f i s h i n g mortality f o r the period. Natural' mortality during such short intervals may be small and not cause serious errors i n the estimate. However, t h i s estimate may be biased due to immigration and emigration. Hence the Delury method, as used by Ketchen (1953) for studying the migratory pattern can also be used. This method would account f o r immigration, emigration and natural mortality. One requirement i n the Delury type analysis, however, i s that the catch per unit e f f o r t should decline, due to f i s h i n g as the season advances. Once the f i s h i n g mortality i s estimated, natural mortality may be obtained by subtracting the f i s h i n g mortality from the t o t a l mortality rate. An estimate of the natural mortality may also be obtained from tagging provided tag loss and tagging Im- mortality are not serious. There were no recoveries from the 55O f i s h tagged during July "1953 from Hecate S t r a i t f l a t . I t i s not known whether t h i s i s due to tagging mortality or to the poor fishery during 1954. As i s the case i n the estimation of f i s h i n g mortality, tagging offers the best method of estimating the biomass of the spawning population. Various methods such as those of Petersen, Schnabel, Delury or Ketchen's modified version of Delury may be used. The f i r s t three estimates involve the assumption that the population i s closed, i.e. there i s no immigration, emigration or natural mortality. From the estimate of the biomass and age composition of the spawning population an estimate of the number of f u l l y recruited age groups can be made. Since i t i s found (Section IV) that the abundance of young butter sole along the Graham Island coast may indicate the success of spawning i n Skidegate I n l e t , an estimate of t h e i r number by adequate sampling w i l l also be useful i n studying the stock-recruitment relationship and i n predicting the success of the fishery. Even though the number of eggs l a i d during the spawning season can be estimated from the number of spawning females and mean fecundity, information on the early survival rate cannot be obtained e a s i l y . A study of the effect of d i f f e r e n t i a l exploitation of the two sexes due to sexual differences i n the population cha r a c t e r i s t i c s i s useful i n understanding the dynamics of the stock. Since i t i s an exploited population the f i s h i n g mortality i s an important factor i n c o n t r o l l i n g population abundance through changes i n the reproductive p o t e n t i a l , growth and mortality rates. However, fluctuations i n population abundance can be understood only by studying the effect of the environment as a whole on population parameters during the various stages i n the l i f e history. Watt (1956), Wicket (1958) and Wynne-Edwards (1962) have reviewed the effect of some of the environmental 142. factors on population parameters. The growth rate of butter sole i s described by Bertalanffy's growth equation despite seasonal variations i n growth rate. In his equation, K or the rate of deceleration i n growth increments i s proportional to the catabolic rate. Beverton and Holt (1957) suggest that an increase i n temperature affects anabolism and catabolism equally, r e s u l t i n g i n a higher K value. The asymptotic weight i s influenced by the a v a i l a b i l i t y of suitable food. The growth rates of butter sole belonging to a strong brood year are generally slower i n the early years due to i n t r a s p e c i f i c competition although compensation occurs i n l a t e r years. In addition to the direct effect of a change i n growth on the biomass, variations i n the growth rate may influence the reproductive p o t e n t i a l and natural mortality rate. Some of the major contributing factors to the natural mortality are deaths due to predation and competition and the scarcity of suitable food. Unfavourable climatic and physico-chemical factors of the environment, especially during certain c r i t i c a l stages i n the l i f e history are also important contributing factors. The natural mortality rate i s subject to v a r i a t i o n depending on the i n t e n s i t y of these and other mortality factors. A number of studies on the fluctuations i n f i s h populations by Hjort (1914, 1926), Sette (1943, 1961), Murphy (1961) and Beverton (1962) have shown that the greatest fluctuations i n population abundance are due to changes i n survival rates during the early stages of the l i f e history. Analysis of the fluctuations i n butter sole also indicates that fluctuations i n the year class strength are due to variations i n the early survival rates. (3) Use of models i n studying the butter sole population Once the population parameters are estimated the understanding of the population dynamics i s f a c i l i t a t e d by constructing mathematical models of the 143- population for various situations. The different types of models used i n f i s h population studies can be c l a s s i f i e d into emperical, deductive or l o g i c a l , and inductive or a n a l y t i c a l . Emperical models, unlike deductive and inductive models, do not assign any b i o l o g i c a l meaning to t h e i r constants. Deductive and inductive models are conceptual models i n that, as Pringle (i960) points out, the properties of the system as a whole are assumed to be derived from the properties of certain known parts. Watt (1956) c l a s s i f i e d the e x i s t i n g models into four groups depending on the extent of information required i n each case. The emperical analysis as done by Royce and Schuck (1954) requires data on the e f f o r t and catch by age for a series of years. Their methods have some predictive value provided an estimate of the e f f o r t for the year concerned can be obtained i n advance. As Watt indicated, since the method does not make use of b i o l o g i c a l informations t h i s model i s not useful f o r studying optimum exploitation. The models developed by Graham (1935); Schaefer (1954) and others, are largely deductive and are based on the l o g i s t i c theory of population growth for a li m i t e d environment. As pointed out by Beverton and Holt (1957) these models assume that population growth i n weight follows a symmetrical sigmoid curve which implies that rate of increase i s dependent only on the weight of stock present at any one time and hence independent of the age and size composition of the population. Models by Beverton and Holt (1957) and Ricker (1945, 1958) are a n a l y t i c a l since the main population parameters are measured and incorporated into the model. The basic difference between these two models, aside from the manner of representing growth pattern, i s that, while Ricker divides the entire fishable l i f e span into a series of discrete periods, Beverton and Holt consider the age d i s t r i b u t i o n as continuous and integrate the rate of- change of y i e l d i n weight between the l i m i t s of the fishable l i f e span. Watt (l956,J959) Ikk. proposed a model that would also consider the effect of fluctuating envi ronmenta l f a c t o r s . Following,-An 'drewavtha and B i r c h ( l 9 5 4 ) he divides the environment into four main components such as weather, food, other animals and a place to l i v e . The relationship of the net effect from each of these factors on the population parameters such as recruitment, growth and mortality has to be obtained by regression analysis from data collected for a number of years. The biomass of a year class at time t i s then obtained as the product of the estimated number and mean weight and the productivity (P ) i s the difference between the biomass at the-beginning and end of time t. However, his model cannot be applied u n t i l a thorough knowledge of the population i n r e l a t i o n to i t s environment i s obtained. Hence, of the e x i s t i n g models, those of Beverton and Holt and Ricker are the most widely used to study f i s h populations. Moran (195*0 has pointed out that they also represent the two types of model studies of populations which involve multiple age classes by treating the age d i s t r i b u t i o n either as continuous or as discrete units. Ricker divided the fishable l i f e span into a series of discrete periods whose duration could be adjusted to suit the cha r a c t e r i s t i c s of the population. Assuming exponential growth and mortality rates within each time i n t e r v a l , the equation for y i e l d i n weight developed by him i s YW ~ ^ F..W, w h e r e t=T Y t = successive time periods, Ty = age of f i r s t e xploitation, T̂  = maximum exploitable age, Fh- = instantaneous f i s h i n g mortality rate during time t , W+ = average weight of stock during time t . l U 5 . Since the model assumes that the weight of stock during time t changes exponentially, the exact average weight of stock for t h i s period i s obtained by integrating the rate of change i n stock between the time l i m i t s and dividing i t by the time i n t e r v a l . Hence f 1 t , - * 0 or i n i t s integrated form ^ . ( i t - z t ) A second, less accurate, method of determining the average weight of stock during time t i s to take the arithmetic mean of the standing crop at the beginning and end of time t , i . e . , In Beverton's model where the growth pattern i s considered to follow Bertalanffy's equation, the rate of change of y i e l d i n weight i s integrated between the l i m i t s of the fishable l i f e span (T^ - T p i ) for a continuous age d i s t r i b u t i o n , i . e . , Y W = F / N t w t dt "Tp" where F = instantaneous f i s h i n g mortality rate, Nj- = number at time t , Wt = weight at time t . 146. The equation f o r y i e l d i n weight (Yw) developed hy him for a continuous _(F + M +v»*X TA- TP',) fishery i s : v/ * -*iK(rP«-Ta) Yw = f tfw. 1 ±a_£ . where T Q = theo r e t i c a l age at which f i s h i s of zero length had i t been growing according to Bertalanffy's growth equation throughout i t s l i f e , Tpt = f i r s t age of f u l l e xploitation*, T̂  = maximum exploitable age, K = the rate of deceleration i n growth increments i n Bertalanffy*s growth equation, n = the exponential value i n the equation describing the length-weight relationship, F = instantaneous f i s h i n g mortality rate, M = instantaneous natural mortality rate, R' = number of rec r u i t s (r) of the age at which f i s h become f u l l y exploitable, and = the average maximum attainable weight as determined by Bertalanffy's growth equation. Since Ricker's equation divides the fishable l i f e span into a series of time periods, population parameters such as growth and mortality rates can vary for each time i n t e r v a l . As he assumes exponential growth and mortality rates during time t , changes i n these parameters with respect to season or age can be e a s i l y introduced into the model. V i t a l s t a t i s t i c s of different age groups at different times and conditions, may be estimated from the relationships expressing the effects of density dependent and independent factors on population parameters. These relationships need not d i r e c t l y -*The authors have shown that t h i s age corresponds approximately to the age of 50$ retention by the gear provided the age of recruitment i s below the selection range of the gear. enter the y i e l d equation and hence the s i m p l i c i t y of the o r i g i n a l equation can be retained. In Section V, an index of abundance for the entering year class i s used to study the effect of varying recruitment on the y i e l d and biomass of butter sole. Hence, i n t h i s case, the y i e l d from a year class i s given by the equation I. - the index of abundance for the respective year class i n the population = the average weight of a normal year class at time t . Although the factors responsbile for v a r i a t i o n i n recruitment were not understood, i t was found (Section IV) that an index of the abundance of year classes could be estimated f o r butter sole. I f recruitment i s the only factor subject to va r i a t i o n then, for any year, y i e l d and biomass can be calculated by multiplying the average weight and y i e l d of each age group comprising the population i n a steady state by the appropriate index of year class strength. I f f i s h i n g i n t e n s i t y varies annually, or i f growth and natural mortality are not steady within each age group, then the biomass and y i e l d from each year- class i n the population i s calculated separately. Relationships expressing variations i n population parameters enter d i r e c t l y i n Beverton's model. To avoid undue complexities, Beverton and Holt consider the effects of variations i n population parameters such as recruitment, growth and mortality with respect to age, time and density taking one parameter at a time. The modifications involved i n applying Beverton's model to a seasonal fishery may-be i l l u s t r a t e d as follows. In Beverton's simple y i e l d equation for a continuous fishery, the change i n the t~-TA where and 148. number of r e c r u i t s with respect to F and M during the exploitable phase i s given by T p c T p , Ta I f the mortality rates are not constant within the exploitable phase, the change i n the number of re c r u i t s with respect to F and M may be shown graphically as 11+9- Since F and M are not constant, the number of recrui t s at the beginning of each f i s h i n g season has to be estimated before obtaining the y i e l d per re c r u i t for each period. The y i e l d for the f i r s t period i s given by Yw, = F.V^R', I -fzi ins© F, + M, + >» K To obtain the y i e l d f o r the second period the number of ' r e c r u i t s at the beginning of the second f i s h i n g season i s calculated as follows. The number of re c r u i t s at the end of the f i r s t f i s h i n g season i s R 2. = The number of re c r u i t s at the beginning of the second f i s h i n g season i s Inserting Rg' i n the y i e l d equation, the y i e l d from the year class for the second f i s h i n g season i s given by Yw* . . f t w ^ . - ^ ^ i , - * u < 1 > ' * * ' U ^ e * k ( T p , * " T J L ^ W l ' + Ŵ2̂  '̂ -s t o t a l contribution from the year class for the. exploitable phase. Hence the y i e l d per r e c r u i t i s obtained by dividing the t o t a l y i e l d by the number of re c r u i t s at the beginning of the f i r s t season, i.e . Yw _ (y*, + Yw%) R R(, I f the rate of deceleration i n growth increments i s different f o r the two f i s h i n g seasons, then the appropriate K values are used i n the equation to obtain the y i e l d during the two periods. The general form of the equation when K, M and/or F varies within the exploitable phase may be written as 150. •5 _ru «T 7 , k ( T ^ - T 0 ) I - e - (F f +M* + "»»h)(VrT?) where for j > 2 , I. = 1.0 where j = 1 and j ranges from 1 ,2,3* , m since the post-recruit phase i s divided into m equal or unequal intervals of any duration each expressed as a f r a c t i o n of one year. In the modified Beverton's equation given above, there i s an abrupt change i n the mortality rate at the end of each time i n t e r v a l . However, by setting the time i n t e r v a l s u f f i c i e n t l y short, the model can be used, without losing accuracy, to obtain y i e l d irrespective of the manner i n which the mortality factors vary with age or season. Therefore the equations describing these relationships do not enter the model as such. The growth pattern within the exploitable phase may possess one or more stanzas due to physiological or environmental changes, each described by Bertalanffy's growth equation. Beverton and Holt (1957) have indicated that a change i n temperature changes the metabolic rate which i n turn may a l t e r the rate of deceleration i n growth increments (K) keeping T Q and constant. I f the a v a i l a b i l i t y of food varies, the asymptotic weight also w i l l be influenced. For such cases the equation 9-H of Beverton and Holt gives the y i e l d for a continuous fishery. I f there i s a change i n TQ and associated with a change i n K "then the equation for y i e l d given above for a seasonal fishery becomes 151. To sura up, the modifications i n Beverton's model involve an estimation of the number of rec r u i t s at the beginning of each f i s h i n g season. The mortality "factors are considered to be constant within each time period and the rate of change of y i e l d i n weight i s integrated between the l i m i t s of each season. The growth pattern i s assumed to be described by Bertalanffy's growth equation. The i n d i v i d u a l f i s h i s also assumed to grow isometrically and hence the exponential value i n the equation describing the length-weight relationship i s taken to be three. The y i e l d per re c r u i t estimates obtained from Beverton's and Ricker's models (Section V) were almost i d e n t i c a l under a l l conditions of growth and mortality rates provided the mean standing crop during time t used i n Ricker's equation was the exponential average. Use of the arithmetic mean of biomass implies that the biomass i s a l i n e a r function of time. As the model assumes exponential growth and mortality rates within each time i n t e r v a l , the arithmetic mean i s a less accurate estimate than the exponential average, the magnitude of error depending on the steepness of the exponential curve describing the change i n the biomass during time t. S i m i l a r l y i t i s also found that, i f the weight of stock i s on the average decreasing, then the use of an arithmetic mean overestimates the y i e l d or, i f the stock i s increasing, then i t may, depending on the curve describing the change i n biomass, under- estimate the y i e l d . Hence, above the optimum Tp f, since the stock i s decreasing, the Yyy'R estimates from Ricker's model using an arithmetic mean 152. would always be an over-estimate compared to Beverton. Even though the mathematical treatment i n Beverton's model i s more elegant, the results obtained using h i s model need not be more accurate. In Beverton's model the growth pattern of the f i s h i s described by Bertalanffy's growth equation. However, seasonal differences i n growth are often superimposed on i t . These authors have pointed out that i f f i s h i n g i s not continuous then the seasonal differences i n growth have also to be taken into account. Considering the f l e x i b i l i t y of Ricker's model i n accomodating changes i n growth, recruitment and mortality rates, t h i s model, using the exponential average for the mean weight of stock during time t , i s preferred f o r studying the butter sole population. VII. Summary Aspects of the l i f e h istory of butter sole 1. The butter sole population spawning i n Skidegate Inlet does not extend i t s range beyond the Hecate S t r a i t bank because of the physical conditions of the area and the presence of a depth b a r r i e r . The possible role of temperature and low oxygen content of deep waters as l i m i t i n g factors affecting d i s t r i b u t i o n i s indicated. 2. The species seem to exhibit a l a t i t u d i n a l difference i n depth d i s t r i b u t i o n . While no butter sole from the Hecate S t r a i t population were found at depths greater than 50 fathoms, along the United States coast they were caught at depths between 55 and 65 fathoms. 3. The size composition of butter sole i n the samples from Hecate S t r a i t suggested a depth s t r a t i f i c a t i o n . Young butter sole were r e s t r i c t e d to the inshore area along the Graham Island coast while the larger and older ones were caught farther offshore. h. In summer the population migrates to the shallow Hecate S t r a i t bank while i n winter i t occupies deeper waters. 5. The spawning members of the population exhibit a north-south migration from the Hecate S t r a i t bank to Skidegate Inlet during winter months. 6- Sexual difference i n the onset of maturity and migratory pattern influence the sex r a t i o of the spawning population. 7. Rank correla t i o n analysis did not suggest any i n t e r - s p e c i f i c association between butter sole and related species of f l a t f i s h during the post-pelagic phase. 8. Movements, factors l i m i t i n g d i s t r i b u t i o n and a comparison of the meristic counts of butter sole taken from different areas favour the theory that the Hecate S t r a i t population of butter sole i s a single self-contained stock. 154. 9- The body length-otolith radius relationship was found to be l i n e a r . The relationship for the two sexes was described by the equation, Male: Length(cms. ) = 0-7944R - O.7O Female: length(cms. ) = 0 .09 + O.7592+R 10. The o t o l i t h zones were l a i d down annually and were found to be r e l i a b l e indicators of age. 11. Growth of butter sole beyond two years of age was described adequately by Ber t a l a n f f y 1 s growth curve. The asymptotic length ( L ^ ) and the rate of deceleration i n growth increments (K) for the two sexes from the Wal-ford plo t were: Male: = 36.64 cms. K = 0 . 2 8 l 4 Female: L a = 41.71 cms. K = O.2U37 12. Annual differences i n growth rate are p a r t l y due to i n t r a - s p e c i f i c competition. The population shows a tendency to compensate in l a t e r years for any i n i t i a l differences from the average growth pattern. 13. Butter sole of age 1+ and 2+ seem to complete*a greater portion of the year's growth by the end of July while roughly 50 P e r cent of the year's growth i s completed at t h i s time by f i s h of age 3 + and above. More extensive study on the seasonal differences i n growth i s necessary. 14. Regional differences i n the growth and density of the Hecate S t r a i t population suggest va r i a t i o n i n habitat s u i t a b i l i t y and a tendency of fast and slow growers to segregate. 15. Males were found to grow slower than females. 16. Length-weight relationships for the two sexes based on ungutted specimens were: Male (summer) : weight (gms.) = 0 . 0 0 9 2 6 0 L(cms. ) 3 ' 0 2 3 Male (winter) : weight (gms.) = 0 . 0 0 7 2 3 6 L(cms.) 3" 1 0 3 155- Female(summer; t weight(gms.) = 0.007344L(cms.; Female (winter) : weight(gms. ) = 0.027896L(cms. ) 2 - ^ 17- The natural mortality rate beyond seven years of age was r e l a t i v e l y high and increased with age. I t was also higher for the males. Fluctuations i n abundance of the butter sole population 18. The 50$ retention length of the 5-2" cod-end mesh as estimated from the 'mesh selection experiment was 31-5 cms. with a sigma ( o") value, measuring the spread of the selection curve, of 1.04 cms. The r e l i a b i l i t y of t h i s estimate was v e r i f i e d by comparing the int e r n a l perimeter of the cod-end and the g i r t h of the f i s h corresponding to the 50$> release length based on length-girth relationship. The two estimates were nearly i d e n t i c a l . 19. The calculated length-girth relationship of butter sole was girth(cms.) = 0.9846L(cms.) - 3-409 20. The small and highly l o c a l i z e d fishery during the winter months depends on the spawning population migrating to Skidegate Inlet. Butter sole i s landed both as-mink feed and as food f i s h . Because of the r e l a t i v e l y low demand, food f i s h landings are subjected to secondary selection by fishermen, to meet the market demands. 21. Catch figures show considerable annual variations due to changes i n the demand for mink feed and food f i s h as w e l l as the a v a i l a b i l i t y and abundance of butter sole. 22. Catch per unit e f f o r t was estimated after standardizing the e f f o r t to determine whether i t would provide a suitable index of abundance. 23. The estimated relationship of f i s h i n g power to tonnage for vessels equipped with'double*gear was J Fishing power = O.782O + O.OO85 Tonnage 156. The considerable scatter i n the estimates of f i s h i n g power was p a r t l y due to differences i n age of vessels and a b i l i t y of skippers and p a r t l y due to the d i s t r i b u t i o n , density and migratory patterns of the butter sole. 24. Due to lack of adequate data the above relationship was not used i n estimating the catch per unit e f f o r t . Since the majority of vessels belonged to the 30-59 tonnage class the catch per unit e f f o r t was obtained from the catch and e f f o r t data of vessels within t h i s range. The e f f i c i e n c y of vessels using single gear compared to those equipped with double gear was estimated by taking catch per day as one unit. The f i s h i n g power of single gear compared to double gear was found to be 0.8955- Analysis of variance of the f i s h i n g power of vessels i n the 30-39; 40-1+9 and 50-59 tonnage classes shows no s i g n i f i c a n t difference. Therefore i n standardizing f i s h i n g e f f o r t the only adjustments made were for vessels equipped with single gear. 25- The estimated catch per unit e f f o r t was not found to be a sensitive index of abundance. This may be due to several reasons, including the small number of boats i n the fishery and the d i v i s i o n of the e f f o r t into food and mink feed categories. In poor years, f i s h i n g may be r e s t r i c t e d to the period of highest density. In addition, catch per day may not be as sensitive a unit as catch per hour, but the l a t t e r could not be calculated f o r lack of data. 26. Study of the r e l a t i v e abundance of young butter sole, lemon sole and sand sole along the Graham Island coast i n the samples collected during 1952- 1954, indicated that butter sole was less abundant i n 1953 than i n 1952 and 1954. Their abundance was p a r t l y reflected i n the age composition and success of the fishery when the young butter sole i n the 1952-1954 samples became f u l l y exploitable, suggesting that fluctuations i n abundance were large due to variations i n early survival rate. The usefullness of the year class strength of young butter sole i n samples from the Graham Island coast as an index of 157- abundance was also suggested. Theoretical y i e l d studies of the butter sole population 27. The magnitude of error involved i n using Beverton's or Ricker's model was f i r s t examined. Ricker's model assumes exponential growth and mortality rates. Hence the use of an arithmetic mean for the average weight of stock during time t i n his equation introduces an error and results i n an over-estimation of the The magnitude of error i s dependent on the steepness of the curve describing the change i n biomass during time t. Consequently the per cent deviation i n the Y^yR estimates increases with increase i n age of exploitation, mortality rates and rate of deceleration i n growth increments. 28. When the arithmetic mean i s used the Y^R values from Ricker, compared to those of Beverton,are either over or under-estimates, depending on whether the stock i s decreasing or increasing. Above the age of optimum exploitation the stock i s decreasing, and the Y ,R values, obtained from Ricker's model W/ are always over-estimates. 29. The Ŷ /R estimate from Ricker, using an exponential average, i s very s l i g h t l y less than that of Beverton. However, t h i s difference i n the two estimates i s greatest at the youngest age of exploitation and decreased with increase i n age of exploitation. This difference i s largely due to the manner of depicting the growth pattern by the two models. 30. The modified Beverton's equation for a seasonal fishery can accommodate changes i n the natural and f i s h i n g mortality and i n K, the rate of deceler- ation i n growth increments. 31. In nature, since seasonal differences i n growth are superimposed on Bertalanffy's growth curve, the Y^yR estimates from Beverton's model need not be more accurate than those of Ricker. 32. Ricker's model can e a s i l y be applied to populations when the parameters 158. vary with age, season or when the f i s h do not grow isometrically. 33- The information collected on the population characteristics of butter sole was not extensive. Hence only general conclusions were drawn from the theoretical study of the butter sole population. Since the f i s h i n g mortality was highly seasonal i t s effect on the population biomass and y i e l d was less than that of the natural mortality rate. 34. Y i e l d isopleth diagrams and equilibrium y i e l d curves were devoid of a mode and indicated that the maximum equilibrium y i e l d when the age of exploit- ation was '4 .83 years would be obtained only when the f i s h i n g mortality rate was higher than 1 .8. 35- Under fluctu a t i n g recruitment the relationship between biomass and y i e l d i s less precise. In the present study the natural mortality was increased i n steps beyond s i x years of age. This i s i n contrast to the f i s h i n g mortality rate which was constant f o r a l l ages above the f u l l retention point of the gear. The fluctuations i n y i e l d and biomass were considerably greater when the natural mortality rate was increased i n steps of O.k rather than 0 . 2 . This i s because fluctuations i n the entering year class were less affected by the older year classes i n the fishery. In comparison, an increase i n the fi s h i n g mortality rate did not result i n any appreciable change i n the fluctuations of the y i e l d and biomass. 36. There are sexual differences i n the population parameters, and the r e c r u i t - ment and migratory patterns. Hence i t i s suggested that the two sexes be treated separately i n any further study of the population. V I I I Literature c i t e d Alverson, D.L. i 9 6 0 . A study of annual and seasonal bathymetric catch patterns f o r commercially important ground fishes of the P a c i f i c northwest coast of North America. Pac. Mar. Fish. Comm. B u l l , 4 , 66j>. Andrewartha, H.G., and L.C. Birch. 1954. The d i s t r i b u t i o n and abundance of animals. Univ. Chicago Press, Chicago. •7&2p. Bailey, R.M., E.A. Lachner, C.C. Lindsey, C.R. Robins, P.M. Roedel, W.B. Scott and L.P. Woods, i 9 6 0 . A l i s t of common and s c i e n t i f i c names of fishes from the United States and Canada. , Am. Fish. Soc. Publ. 2, 102p. Barber, F.G. 1957' The effect of p r e v a i l i n g winds on the inshore water masses of the Hecate S t r a i t region, B.C. J. Fish. Res. Bd. Canada. 1 4 ( 6 ) : 945-952. Barber, F.G. 1958- On the dissolved oxygen content of the waters of the Hecate S t r a i t region, B.C. Fish. Res. Bd. Canada. Progr. Rept. Pac. Coast Sta. 110:3-5- Beverton, R.J.H. 1962. Long term dynamics of certain North Sea f i s h populations, p.242-259- In E.D. Le Cren and H.W. Holdgate, (ed.), The ;exploitation of natural animal populations. Br. Ecol. Soc. Symp. No.2, Blackwell, Oxford. Beverton, R.J.H. and S.J. Holt. 1956a. A review of the methods of estimating mortality rates i n f i s h populations with special reference to sources of bias i n catch sampling. Rapp. Conseil Expl. Mer. 140:67-83- Beverton, R.J.H., and S.J. Holt. 1956b. Theory of f i s h i n g , p.372-441. In Ml Graham, (ed. ), Sea f i s h e r i e s . Their investigation i n the United Kingdom. Edward Arnold, London. Beverton, R.J.H., and S.J. Holt. 1957- On the dynamics of exploited f i s h populations. U.K. Min. Agric. and Fish. Fish Invest. Ser.II, 19>533P' Beverton, R.J.H. and S.J. Holt. 1959* A review of the l i f e spans and mortality rates of f i s h i n nature and t h e i r r e l a t i o n to growth and other physiological c h a r a c t e r i s t i c s , p.l42 - l 8 0 . In G.E.W. Wolstenhome and M. O'Conner, (ed.), The lifespan of animals. Ciba foundation colloquia on aging. 5- C h u r c h i l l , London. Bratberg, E. 1956. On the interpretation of opaque and hyaline zones i n the o t o l i t h s of immature red f i s h (Sebastes marinus L.) J. Conseil Expl. Mer. 22(l) : 6 6 - 7 4 . Buchanan-Wollaston, H.J. 1927' On the selective action of a trawl net. J. Conseil Expl. Mer. 2(3) :343"355- l 6o . Buckmann, A. 1930. Die Erforschung der Fluktuation ser Scheinungen bei der Scholle (Pleuronectes platessa L.) Rapp. Conseil Expl. Mer. 6 8 : 5 7 - 8 1 . B u l l , H.O. 1952. An evaluation of our knowledge of f i s h behaviour i n r e l a t i o n to Hydrography. Rapp. Conseil Expl. Mer. 13 :8-23 . Cassie, R.M. 1950. The analysis of Polymodal frequency d i s t r i b u t i o n s by the p r o b a b i l i t y paper method. N.Z. Sci. Rev. 8 :89-91 . Cassie, R.M. 1954. Some uses of the p r o b a b i l i t y paper i n the analysis of size frequency di s t r i b u t i o n s . Aust. J. Mar. Freshw. Res. 5(3):513~523. Clarke, F.N. and J.C. Marr. 1955- Population dynamics of the P a c i f i c sardine; C a l i f . Coop. Ocean. Fish. Invest. Progr. Rep., 1st July 1953 "to 31st March 1955. Part I I . p. 11-1+8. Clemens, W.A. and G.Y. Wilby. 1961. Fishes of the P a c i f i c Coast of Canada. Fish. Res. Bd.'Canada. B u l l . 6 8 , 443p. Fager, E.W. 1957- Determination and analysis of recurrent groups. Ecology 38(i+):586-595- Flemming, R.H. and T. Laevastu. 1956. The influence of hydrographic conditions on the behaviour of f i s h . F.A.O. Fish. B u l l . 9:181-196. Frost, W.E. and C. K i p l i n g . 1959- The determination of the age and growth of pike (Esox lucius L. ) from scales and opercular bones. J. Conseil Expl. Mer. 24(2) :314-341. G i l l , T. 1910. A plea for observation of the habits of fishes and against undue generalization. U.S. Bur. Fish. B u l l . 28:1059-1069. Graham, M. 1929- Studies of age determination i n f i s h , Part I I - a survey of the l i t e r a t u r e . U.K. Min. Agric. and Fish. Fish. Invest. Ser. I I , 11 (3) , 50p. Graham, M. 1935* Modern theory of exploiting a fishery and application to North Sea trawling. J. Conseil Expl. Mer. 10(3):264-274. Graham, M. 1954- T r i a l s of mesh selection i n trawls and seines. J. Conseil Expl. Mer. 20(l ) : 6 2 - 7 1 . Graham, M. 1956. The p l a i c e , p.332-371. In M. Graham, (ed.), Sea Fisheries. Their investigation i n the United Kingdom. Edward Arnold, London. Gulland, J.A. 1955- On the selection of hake and whiting by the mesh of trawls. J . Conseil Expl. Mer. 2l(2) : 2 9 6 - 3 0 9 - Gulland, J.A. 1956. On the f i s h i n g e f f o r t i n English demersal f i s h e r i e s . U.K. Min. Agric. and Fish. Fish. Invest. Ser. I I . 20(.5), 41p. l 6 l . Harding, J.P. 19^9• The use of p r o b a b i l i t y paper for the graphical analysis of polymodal frequency d i s t r i b u t i o n s . J.Mar. B i o l . Assoc. U.K. 2 8 ( l ) : l U l - 1 5 3 . Hart, J.L. 1948. Age and growth rate i n the butter sole. Trans. Roy. Soc. Canada. Ser. I l l , 1+2:65-72. Hennemuth, R.C. 1959- Additional information on the length-weight relationship of skipjack tuna from the eastern-tropical P a c i f i c Ocean. Inter-Amer. Trop. Tuna Comm. B u l l . 4 :23-37 . Hickling, C.F. 1933- The natural h i s t o r y of hake. Part IV - Age determination and the growth rate. U.K. Min. Agric. and Fish. Fish. Invest. Ser. I I , 1 3 ( 2 ) , 81+p. H i l e , R. 1 9 4 l . Age and growth of the rock bass, Ambloplites rupestris (Rafinesque) i n Nebish Lake, Wisconsin. Trans. Wise. Acad. S c i . , Arts and Letters, 33:189-337. Hjort, J. 1914. Fluctuations i n the great f i s h e r i e s of northern Europe. Rapp. Conseil Expl. Mer. 20:228p. Hjort, J. 1926. Fluctuations i n the year classes of important food fishes. J. Conseil Expl. Mer. l ( l ) : 5 - 3 8 . Holt, S.J. 1958. The evaluation of f i s h e r i e s resources by the dynamic analysis of stocks, and notes on the time factors involved, p.77-95- Intern. Comm. N.W. A t l . Fish. Some problems for the b i o l o g i c a l fishery survey and techniques for t h e i r solution. Spec. Publ. No.l. Holt, S.J. 1962. The application of comparative population studies to fi s h e r i e s biology - an exploration, p.51-71- I n E.D. Le Cren and M.W. Holdgate, (ed.). The exploitation of natural animal populations. ; Br. Ecol. Soc. Symp. No.2. Blackwell, Oxford. Jensen, A.C. and J.R. Clark. 1958. Time of formation of scale annuli, p - 1 9 3 - 197- Intern- . Comm. N.W. A t l . Fish. Special problems for b i o l o g i c a l fishery survey and techniques for t h e i r solution. Spec. Publ. No.l. Jones, R. 1958- Lee's phenomenon of "apparent change i n growth rate" with p a r t i c u l a r reference to haddock and p l a i c e , p.229-242. Intern. Comm. N.W. A t l . Fish. Some problems for b i o l o g i c a l fishery survey and techniques for t h e i r solution. Spec. Publ. No.l. Kendall, M.G. 1955- Rank correla t i o n methods, 2nd edition. Charles G r i f f i p , London. 196p. Ketchen, K.S. 1951. Preliminary experiments to determine the working gape of trawling gear. Fish. Res. Bd. Canada., Progr. Rept. of Pac. Coast. Sta. 8 8 : 6 2 - 6 5 . 162. Ketchen, K.S. 1953- The use of catch-effort and tagging data i n estimating a f l a t f i s h population. J. Fish. Res. Bd. Canada. 10(8):l+59-l+85. Ketchen, K.S. 1956. Factors influencing the survival of the lemon sole (Parophrys vetulus) i n Hecate S t r a i t , B r i t i s h Columbia. J. Fish. Res. Bd. Canada. 13(5):6kf-69k. Ketchen, K.S. 1961. Observations on the ecology of the P a c i f i c cod (Gadus macrocephalus) i n Canadian waters. J., Fish. Res. Bd. Canada. 18(4): 513-558. Ketchen, K.S. and C.R. Forrester. 1955- Migrations of the lemon sole (Parophrys vetulus) i n the S t r a i t of Georgia. Fish. Res. Bd. Canada. Progr. Rep. Pac. Coast Sta. 104:11-15. Ketchen, K.S. and J.A. Thomson. (No date). On the standardization of s t a t i s t i c s of f i s h i n g e f f o r t f o r P a c i f i c Coast. Fish. Res. Bd. Canada, Pac. B i o l . Sta. Nanaimo. (Manuscr. Rep.) l6p. Koster, W.J. 1955- Outline for an ecological l i f e history study of a f i s h . Ecology 36(l):141-153- Lindsey, C.C 1962. Experimental study of meristic v a r i a t i o n i n a population of three spined sticklebacks, Gasterosteus aculeatus. Canad. J. Zool. 40:271-312. .Lucas, C.E., A. Rit c h i e , B.B. Parrish and J.A. Pope. 1954. Mesh selection experiment i n the round f i s h seine. J. Conseil Expl. Mer. 20(l) :35~50. ' Manzer, J. I . 1949- The a v a i l a b i l i t y , exploitation, abundance and movement of the butter sole (Isopsetta i s o l e p i s Lockington) i n Skidegate I n l e t , Queen Charlotte Islands, during 1946. M.S. Thesis. Dept. of Zool., Univ. of B.C., 41p. Margetts, A.R. 1954. The length-girth relationships i n haddock and whiting and t h e i r applications to mesh selection. J. Conseil Expl. Mer. 20(l ) : 5 6 - 6 l . Margetts, A.R. 1955- Selection of soles by the mesh of trawls. J. Conseil Expl. Mer. 20(3):276-289- Moran, P.A.P. 1954- Logic of mathematical theory i n animal populations. J. W i l d l . Mgt. l 8 ( l ) : 6 0 - 6 6 . Muller, W. 1958. Das Wachstum der Quappe (Lota l o t a L.) im Oderhaff und i n deutshcen Gewassern. Verh. Intern. Ver. Limnol 13t743~747- Murphy, G.I. 1961. Oceanography and va r i a t i o n i n the P a c i f i c sardine populations. C a l i f . Coop. Ocean. Fish. Invest. Rept. 8:55-64. 163- Parrish, B.B. 1956. The cod, haddock and hake, p .251-331. In M. Graham, (ed.)* Sea Fisheries. Their investigation i n the United Kingdom. Edward Arnold, London. Pearcy, W.G. 1962. Ecology of an estuarine population of winter flounder, Pseudopleuronectes americanus (Walbaum). Parts I-IV. B u l l . Bingh. Ocean. C o l l . l 8 ( A r t . 1 ) , 78p. Pringle, J.W.S. i 9 6 0 . Models of muscle, p.41-68. In J.W.L. Beament, (ed.), Models and analogues i n biology. Symp. Soc. Exp. B i o l . 14. Cambr. Univ. Press, London. Ricker, W.E. 1945- A method of estimating minimum size l i m i t s for obtaining maximum y i e l d . Copeia. 2 :84-98. Ricker, W.E. 1958. Handbook of computations for the b i o l o g i c a l s t a t i s t i c s of f i s h populations. Fish. Res. Bd. Canada. B u l l . 119, 300p. Roedel, P.M. 1953- Common ocean fishes of the C a l i f o r n i a coast. C a l i f . Fish and Game, Fish. B u l l . 91 , l 8 l p . Rollefsen, G. 1935- The spawning zone i n cod o t o l i t h s and prognosis of stocks. Rep. Norw. Fish. Invest. 4 ( l l ) , lOp. Royce, W.F. and H.A. Schuck. 195*+• Studies of Georges Bank haddock. Part I I : Prediction of catch. U.S. Fish and Wi l d l . Serv. Fish. B u l l . 5 6 ( 9 0 ) , 6p. Russel, F.S. 1931. Some theoretical considerations on the 'overfishin problem. J . Conseil Expl. Mer. 6 ( l ) : 3 - 2 0 . Saetersdal, G. 1953- The haddock i n Norwegian waters I I . Methods i n age and growth investigations. Rept. Norweg. Fish. Invest. 1 0 ( 9 ) , 46p. Saetersdal, G. 1958. Use of o t o l i t h s and scales i n the Arctic haddock p.201-206. Intern. Comm. N.W. A t l . Fish. Some problems for the b i o l o g i c a l fishery survey and techniques for t h e i r solution. Spec. Publ. No.l. S a v i l l e , A. 1959- Plankton stages of haddock i n Scottish waters. Scottish Home Dept. Mar. Res. 3* 23p- Schaeffer, M.B. 195^. Some aspects of the dynamics of populations important to the management of the commercial marine fishes. Inter-Amer. Trop. Tuna Comm. B u l l . 1, 56p- 164. Sette, O.E. 1943- B i o l , of the A t l a n t i c mackerel (Scomber scombrus) of Worth America, Part I; Early l i f e history, including growth, d r i f t and mortality of the egg and l a r v a l populations. U.S. Fish and Wil d l . Sere. Fish. B u l l . 50(38):149-237- Sette, O.E. 1961. Problems i n f i s h population fluctuations. C a l i f . Coop. Ocean. Fish. Invest. Rept. 8:21-24. Simpson, A.C 1953- Some observations on the mortality of f i s h and the d i s t r i b u t i o n of plankton i n the southern North Sea during the cold winter 1946-47. J. Conseil Expl. Mer. 19(2) :150-177- Simpson, A.C. 1956. The pelagic phase, p.207-250. In M. Graham, (ed.), Sea Fisheries. Their investigation i n United Kingdom. Edward Arnold, London. Southward, G.M. I962. A method of calculating body lengths from o t o l i t h measurements for P a c i f i c halibut and i t s application to Portlock-Albatross grounds data between 1935 and 1957- J- Fish. Res. Bd. Canada. 19(2):339~362. Taylor, C C 1958- A note on Lee's phenomenon i n Georges Bank haddock, p.243-251. Inter. Comm. for the N.W. A t l . Fish. Some problems for b i o l o g i c a l fishery survey and techniques for t h e i r solution, Spec. Publ. No.l. Thompson, W.F., and R. Van cleve. 1936. L i f e history of the P a c i f i c halibut ( 2 ) . D i s t r i b u t i o n and early l i f e history. Dept. Intern. Fish. ( P a c i f i c Halibut) Comm. 9, l 8 4 p . Trout, G.C. 1958. Otoliths i n age determination, p.243-251. Intern. Comm. N.W. A t l . Fish. Some problems for the b i o l o g i c a l fishery survey and techniques for t h e i r solution, Spec Publ. No.l. Van Oosten, J. 1929. L i f e history of the lake herring (Leucichthys artedi Le Sueur) of Lake Huron as revealed by i t s scales, with a criticme of the scale method. U.S. Bur. Fish. B u l l . 44(1053) : 265-428. Watt, K.E.F. 1956. The choice and solution of mathematical models for predicting and maximizing the y i e l d of a fishery. J. Fish. Res. Bd. Canada. 13(5):6l3-645. Watt, K.E.F. 1959. Studies on population productivity I I . Factors governing productivity i n a population of small mouth bass. Ecol. monographs 29(4):367~392- 165. Wickett, W.P. 1958' Review of certain environmental factors affecting the production of pink and chum salmon. J. Fish. Res. Bd. Canada. 15(5):1103-1126. Wimpenny, R.S. 1953- The p l a i c e . Edward Arnold, London. l45p- Wooster, W.S. 1961. Fisheries Oceanography. C a l i f . Coop. Ocean. Fish. Invest. Rept. 8:73-74. Wynne-Edwards, V.C. 1962. Animal dispersion i n r e l a t i o n to s o c i a l behaviour. Oliver Boyd, London. 653P- 166. Appendix I. Size composition of butter sole i n hauls of cod-ends with different mesh size taken during February 1961 from Skidegate Inlet. Length Cod end mesh size group (cms. ) 1.5" 3-V 3-5" 5 . 2 " 13 1 14 5 15 7 16 9 17 12 18 10 19 8 20 2 21 1 22 11 9 23 3 11 24 3 12 4 25 1.0 57 11 26 15 39 15 1 27 12 69 14 1 ' 28 11 36 10 1 29 11 34 9 1 30 14 38 19 2 31 37 42 21 11 32 34 76 40 17 33 30 60 32 29 3h 24 62 30 12 35 16 23 21 9 " 36 12 26 9 5 37 4 14 6 3 38 3 5 2 2 39 1 3 2 0 40 0 0 1 1 Total 306 616 246 95 167. Appendix I I . Butter sole of age seven years and above i n the commercial sample from Skidegate Inlet taken during 1951* 1954, 1955 and during the trawl survey i n 1953* used to estimate the t o t a l mortality rates. Male Age 1951 1953 1954 1955 7 328 902 97 211 8 106 365 15 '46 9 17 109 3~ 8 10 3 14 0 l Female 7 482 369 85 238 8 24l 198 53 90 9 78 61 10 22 10 11 7 0 6

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