CALCULATIONS OF FISH LENGTHS FROM SCALES. RATES OF KAMLOOPS TROUT IN PAUL LAKE, BRITISH COLUMBIA. Stuart"Boiarid Smith

Transcription

1 CALCULATIONS OF FISH LENGTHS FROM SCALES. 2. GROWTH RATES OF KAMLOOPS TROUT IN PAUL LAKE, BRITISH COLUMBIA by Stuart"Boiarid Smith A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the Department of Zoology We accept this thesis as conforming to the standard regulred from candidates for the degree of MASTER OF ARTS: Members of the Department of Zoology THE UNIVERSITY OF BRITISH COLUMBIA September, 1952

2 ABSTRACT The logarithmic scale/body relationships of Kamloops trout(jias been Idiscussed vdth particular reference to its prior ' ~ use in the calculation of fish lengths previous;to capture. Growth of scales relative to body growth exhibits strong positive heterogony in the fork length range 3«5 cm. to 4«5 cm., above which the scale/body ratio is isometric. Calculation of fish.lengths, using only the diameter of the first growth ring (placode) of the scale and total scale diameter, shows close statistical agreement with actual measured lengths for the same specimens. In the population studied, the intense sport fishery is highly selective vdth respgct^ to rate of growth for all age-classes. In all comparisons, longer-lived fish were slower-growing and samples drawn from anglers* catches may not, in this case, be considered as representative of the population as a whole. In some years statistical differences exist in the mean lengths of spawning and non-spawning trout of the same age. It is suggested that attainment of sexual maturity and rate of growth may be closely associated. A change in lake ecology may be detected by growth comparisons of trout from various year-classes. Lowered growth rates of Paul lake trout are attributed to the effects of the recent introduction of the redside lake shiner, Richardsonius balteatus Richardson. Effects of the increase. in numbers of shiners also are manifested in the increased variability in growth rates of Paul lake trout.

3 TABLE OF CONTENTS INTRODUCTION 1 ACKNOWLEDGMENTS ' 5 MATERIALS AND METHODS 6 1. CALCULATIONS OF FISH LENGTHS FROM SCALES 7 Scale length - body length Page relationship in adult trout 7 Scale length - body length relationship in young Kamloops trout. 10 Length of young trout and the time of scale formation 14 Calculations of fish lengths previous to capture 15 Calculation of length of fish from a single scale specimen GROWTH RATES OF KAMLOOPS TROUT IN PAUL.LAKE 31 Growth rates and selectivity of the fishery 31 Growth rates of Paul lake trout and a major change in lake ecology 36 Growth rates of spawning and non- spawning two- and three-year-old trout, 41 v DISCUSSION 49 SUMMARY 57 LITERATURE CITED 60

4 INTRODUCTION Fluctuations in abundance and variations in growth rates of fishes are notable phenomena which(undoubtedly) are in large part associated with changes in ecological conditions. Evaluation of the possible factors concerned with, the changes in size and numbers of individuals of various species of fish is difficult. Changes in environmental conditions often are not observable, and must be deduced from (the interpretation of) data which may be only indirectly associated with the study under consideration. Growth rates of fishes may be used as an index of relative population density (Foerster, 1944)> or may reflect changes in feeding habits during changes in relative of food (Langford and Martin, 1940). availability A s t r i k i n g example of a change in growth rate resulting from a change in habitat may be (seen) in the vastly accelerated growth (as seen on the scales) of salmon orj -y trout which have spent a portion of their lives in salt V water. Variation!) in growth rates of fishes, therefore, may be considered as rather sensitive indices") of changes in \^ environmental conditions. Comparisons of growth rates of Kamloops trout, Salmo gairdnerii kamloops Jordan, from Paul lake, British Columbia, have been conducted with the object of adding to the knowledge of the ecology of this species.

5 Studies of the growth rates of fishes are enhanced by a knowledge of the previous life histories of individual fish. Unless extensive marking experiments are carried out, and large numbers of recaptures made, data pertaining to various age classes in different years must, of necessity, be extrapolated from captured fish in order to provide means of comparisons. For instance, three-year-old fish captured in any one year often are presumed to have had the same growth characteristics in their first year as had fish of the same year-class taken as yearlings two years previous. Certain difficulties may arise by reason of the above assumption, and only when "previous growth histories of individual fish are known can adequate statistical comparisons be made. The use of the "scale method" to calculate fish sizes at yearly intervals (previous to capture has enjoyed widespread use for many years. (^omno^ly/^t^s\ assumed that the scale length-body length relationship may be expressed by the equation y - ax, where "y" is the scale length (or diameter), "x"'is the length of the fish, and "a" and "b" are constants. Transformation to the logarithmic form results in the equation ^as follows^ log y 2 log a + b log x, and when plotted graphically, generally shows close agreement to linearity. (Fry, 1943). Since scales of teleosts are not formed until some time after hatching, various "correction factors" have been introduced by most workers to eliminate the apparent error in

6 3 "back-calculation" which results from ignoring the positive "X" intercept (where scale size is presumed to be zero) of the plot of scale length (y) on body length (x). Van Oosten (1941) corrected the calculated lengths of Lake Erie white bass by the following formula: L = L n L n where L - corrected length at the end of year n n L - standard length at capture 1 - avenge direct-proportion calculated length at end of year n 24 r point of intercept on the "length" axis. Brown (1943) used essentially the same method of correcting calculated lengths of Montana grayling, Thymallus signifer montanus. Fry (1943), in a description of a "proportionality machine" which may be used to calculate fish lengths previous to capture, made use of the following formula: log y log b + a log (X-x) where "y" is the scale diameter of the fish at capture, "b" and "a" are constants, "X" is the length of fish at capture and "x" is the length of fish when scale size is presumed to be zero. In each of the methods outlined above, the assumption is made that scale length (diameter) is proportional to"length of fish at capture" minus "length attained at the time of scale formation". In each case'length attained at

7 the time of scale formation" is obtained by extrapolation of the plot of scale length on body length to the "length" axis» The methods of calculating fish lengths from scale lengths, together with the assumptions upon which the methods are based, will be discussed at greater length in the following pages.

8 5 ACKNOWLEDGEMENTS Thanks are due Dr. P.A. Larkin, of the Department of Zoology, University of British Columbia, and Chief Fisheries Biologist, B.C. Game Department, for the problem and directing the work throughout. suggesting Fellow worker David P. Scott rendered invaluable assistance and advice regarding statistical treatment of the data* Thanks are due also to Dr. Wm. Cameron, Institute of Oceanography, University of British Columbia for criticism and advice concerning graphical presentation of data. The work was carried out as a portion of the fisheries research program of the biological division of the British Columbia Game Department at the University of British Columbia.

9 6 MATERIALS AND METHODS Scale measurements of 1322 Kamloops trout from Paul lake, British Columbia provided the data on which was based the study of the scale length - body length relationship of over-yearling trout. Measurements of the scales of young hatchery-reared Kamloops trout from Pinantan lake, British Columbia provided the basis for the study of the scale length - body length relationship of under-yearling trout. The young fish were raised at Smith's Falls Trout Hatchery at Gultus lake, B.C. Paul lake fish were sampled by various workers for the period Scales of over-yearling fish were impressed on cellulose acetate slides (a minimum of three scales was mounted for each specimen) and their images were projected onto X 5 n standard filing cards at a magnification of 38X. A Bausch and Lomb, 6-volt, 25-watt, Triple-Purpose Micro Projector was used in projecting the scale images. A line was drawn on each filing card, and total and annular scale diamters were measured as nearly as possible at right angles to the anterior radius of each scale, on an axis which passed through the center of the scale. Diameters of the projected images were measured t the nearest millimeter with a small, celluloid ruler. In cases where the annular diameters were not clearly defined, the scales were discarded.

10 7 Measurements of scale diameters were made for each fish from the scale impression which showed the annular diameters most clearly. Only those scales from non-spawning specimens were used in the study, and a l l scales with reabsorbed borders were discarded. Active reabsorption of the scale periphery would, obviously, result in an appreciable error if the scale were used to calculate fish lengths. No but attempt was made to select scales of a particular size, scales with obvious deformities such as twin nuclei of lateral line scales, and those with replaced centres were discarded. 1. CALCULATION OF FISH LENGTHS FROM SCALES Scale length - body length relationship in adult trout. Calculations of fish lengths from scales can be made only if the scale length - body length relationship is known, A logarithmic plot of magnified scale diameter (3&C in mm.) against fork length of fish (cm.) revealed that the scale length - body length relationship was isometric over the entire range of fork lengths in the sample (14 cm cm.) (See Figure 1.). Scale diameters were grouped according to each centimeter of fork length of fish from which the scale samples were taken, and the regression of mean logarithmic scale diameter on the logarithm of fork length was calculated. The'slope of the regression line of best fit (b - 0.9^ ) did not differ significantly from 1.00 ' (i.e. isometry). The correlation coefficient (r )

11 8 " 5 calculated from the dame data does not differ significantly from a perfect correlation. Table I. Scale diameters.and fork lengths of Kamloops trout, Salmo gairdnerii kamloops Jordan^ of Paul lake, British Columbia. (Scale diameters grouped according to each centimeter of fork length.) No. specimens Grouped fork length Group magnified scale diameter (mm. X 38) S S.5 9S G The mean logarithmic scale diameter for each group, rather than the logarithm of each grouped arithmetic mean scale diameter was used in the calculation (Table I) because of the possibility of correlation between mean and variance in the groups. Snedecor (1940) states that the calculation of regression using grouped data is only valid when the variance in each group is equal.

12 (9) Figure 1, Scale diameter - body length relationship of Kamloops trout. Note point of inflection in relative growth curve at 9»S mm, magnified scale diameter and 4,5 cm. fork length, (See text for explanation of plot*)

13 10 Scale length - body length relationship in young Kamloops trout. Neave (1936) has.shown that the scales of Salmo are laid down in pockets, or placodes in the skin. He states that the scale is composed of two layers, an outer, bony layer, and an inner, calcified layer. The growth "rings" (circuli) arise on the inner layer as a result of unequal thickenings around the periphery of the scale. It i s further suggested by Neave (1940) that the unequal thickenings are caused by precipitation of calcium salts on the inner layer of the scale when the scale is enlarging peripherally at a relatively slow rate. Conversely, if the peripheral border of the scale is unconfined, the scale increases in diameter at the expense of thickness. According to Neave, this would, apparently, account for the relative thinness, or "hollowing out" of the calcified layer between the growth rings. Scales from 37 small Kamloops trout which ranged in length from 3*70 era. to 7.56 cm. were measured under an ocular micrometer at 100 magnifications and the measurements were then converted to 3B magnifications for means of comparison with measurements of the scales taken from adult Kamloops trout. The mean logarithmic diameter of 10 scales from each specimen was plotted (y axis) against the logarithm of fork length (x axis). The resultant curve indicated a sharp inflection toward decreased growth of the scales relative to fork length at a magnified diameter (mm. x 3S) of approximately 10.0 mm. and a fork length of approximately 4.5 cm. ( See Fifmre 1. )

14 11 The sample of trout was then subdivided into two portions: (1) Those fish with a fork length in excess of 4.5 cm. and (2) those fish with a fork length less than 4.5 cm. Relative scale-body growth regression slopes were calculated for each sub-sample, and the point of inflection (intersection of the two regression lines) was calculated from the simultaneous equation derived from the regression equations of the two relative growth slopes. Point of inflection was calculated to be 9.8 mm. magnified scale diameter and 4.46 cm. fork length. From the regression slopes it was found that from 3.55 cm. fork length to 4.46 cm. fork length scales grow at a logarithmic rate of 3.99 ± relative to increase in fork length of the fish. Correlation coefficient (r) from the same data was found to be The logarithmic regression slope of the relative scale-body growth after a length of 4.46 cm. was attained was found to be , and the correlation coefficient calculated from these data was found to be 'also. It may be seen that the relative growth slope of does not differ significantly from the slope which was calculated for the scales of adult specimens (where b = i 0.064) nor does it differ significantly from After a fork length of 4.5 cm. is reached, therefore, relative scalebody growth may be considered isometric. Seale'measurements from which the above calculations were made are summarized in Table II.

15 12 It must be borne in mind that the relative growth slopes and the point of inflection are calculated from sample regressions, and may be considered only as the most probable estimates of the population regressions. In addition, the original division of the sample on the basis of fork length is arbitrary. However, since the regression slope of relative scale-body growth after the calculated point of inflection does not differ significantly from the regression slope calculated for adult fish, the estimate of the point of inflection may be considered reliable. Similarly, it may be" argued that the fitting of two straight lines to the data is arbitrary, and that three or more straight lines or a curve might better describe the scalebody length relationship. The practical advantages and theoretical significance of fitting two straight lines to growth data of this type is adequately discussed and recommended by Martin (1949). In order to reach a fuller understanding of the mechanics of scale growth in young Kamloops trout, a further consideration of the development of scales is necessary. When scales are first laid down in young trout, the pockets from which they arise are not contiguous. The scales, therefore, do not overlap during early development. As the fish increases in size, scales must grow at a rate relatively much greater than the growth of the order that eventually the scales shall overlap, fish, in as they do in adult specimens.

16 13 Table II. Magnified scale diameters (mean of 10 scales for each specimen) and fork length of young Kamloops trout Fork length less than 4.5 cm. Fork length in excess of 4.5 cm. Scale diameter (mm. x 38) Fork length (cm.) Scale diameter (mm. x 38) Fork length (cm.) 5, , , , by.x = 3.99 ±.865 by.x = r r r = Apparently when a length of approximately 4.5 cm. is reached, an adequate integument has been provided,, and from this point onward growth of scales and body is proportional.

17 14 Length of young Kamloops trout and the time of scale formation. Thirty-eight young Kamloops trout, ranging in length from 2.6*7 cm. to 4.29 cm. were examined to determine the ati/l*^ length of fish which)scales were first formed. The skin of each specimen was scraped carefully with a fine scalpel in the mid antero-postero region, between the lateral line and the dorsal fin. The mucous substance which adhered to the scalpel blade was examined under a microscope at 100 magnifications to determine if scales were present. Fork length measurements of the fish were obtained to the nearest 0.1 mm. by means of a vernier caliper, to the jaws of which had been glued fine needles. (^Reference tc^ Table III(will) indicate the approximate length at which young Kamloops trout form scales, (it may be observed tha^/vo scales were present on any fish with a fork length less than 3«3# cm., nor were scales absent from any fish with a fork length in excess of 3*71 cm. If 3.3# cm. is assumed to be the smallest fork length at which scales may be formed, and 3.71 cm. to be the greatest fork length at which scales may not have formed, then the mid-point of this range would indicate the fork length at which scales are most probably formed. This length was found to be 3.54 cm., and closely corresponds to the sample r mean of 3.55 cm. /It may also be observed from)table Ill^hat only three specimens with a fork length less than the sample mean of 3»55 cm. bore scales, and only three fish with a fork length in excess of 3.55 cm. had no scales.

18 15 Table III. Fork length of young Kamloops trout Salmo gairdnerii kamloops Jordan, and occurrence of scales. Fork length Fork length ft ft ft 3.38 ft 3.83 ft 3, ft ft 3.46 ft 3.90 ft ft ft ft ft 3.51 ft 4.26 ft ft ft Fish which bear scales. Calculations of fish lengths previous to capture. If the relationship of scale length and body length is isometric, i.e., if a fish is to have relatively the same coverage of scales at all lengths, the slope of a line measuring this relationship will be 1.00 on a logarithmic plot. Since the plot of the logarithm of scale length (diameter) versus the logarithm of fork length did not differ significantly from 1.00, and showed virtually no deviation from the regression line of best fit (for grouped data) over most of the range in length of the specimens examined, it was assumed that individual scales could be used to

19 16 calculate the lengths of fish at various periods previous to capture. A straight-edge was fixed near the lower border of a sheet of logarithmic graph paper, and a plastic 45 square laid over the graph paper. the square a fine line was Parallel to the hypotenuse of scratched on the surface of the square which would be in contact with the paper. With the base of the square in close contact with the straight-edge, the square could be ^li\^eas±ljjin a direction at right angles to the "Y" axis of the graph paper. (See Figure 2.) In order to calculate fish length from scale diameter the 45 square was moved so the fine hairline on i t s undersurface coincided with the point which indicated magnified scale diameter and fork length at the time the fish was captured. To obtain the length of fish at the time of formation of previous annular growth checks on the scale image, the hairline was followed down until it intersected the line giving the value on the "Y" axis which corresponded to the magnified diameter of the scale at the desired annular growth check. Fork length was then read off directly on the,r X" axis. Calculated fork lengths below 20 cm. were estimated on the graph paper to the nearest 0.1 cm., and above 20 cm. fork lengths were estimated to the nearest 0.5 cm. It is believed that fork lengths may be estimated as closely in this manner as field measurements are commonly taken.

20 een shown that below a fork length of 4.5 cm. the scales of Kamloops trout grow relatively more rapidly than they do after a fork length of 4.5 cm. has been exceeded, fish lengths may not be calculated below 4.5 cm. unless a slope of 3.99 is used. In most of the specimens examined, a length considerably in excess of 4.5 cm. was reached before the completion of the first annular growth check. Calculation of length of fish from a single scale specimen. If the assumptions are correct upon which the method of calculating fish lengths from scales is based, then it should be possible to calculate the length of a fish from its scale, using no measurements other than the total diameter of the scale and the diameter of the placode (first growth ring of the scale). In the following section, a method of obtaining fish lengths from scales alone is developed. The scale/body ratio of Kamloops trout is characterized by rapid growth of the scale relative to body growth during early development, a sharp inflection in the relative growth curve at fork length approximately 4.5 cm. and scale diameter approximately 10 mm. (x38), after which scale/body growth is isometric (Figure 1, and pages $-15). Figure 3 illustrates the way in which total scale diameter, placode diameter and logarithmic relative growth curve of scales may be used to calculate the fork length of fish.

21 STRAIGHT-EDGE J~ Figure 2. Galculatioh of length of fish previous to capture. Dotted lines indicate the scale diameter at each annular growth check from age 1 to age 4 and the respective fork length for each annular scale diameter.

22 19 The observed range of placode diameter for the sample in question is marked out at 0.5 mm. intervals along the dotted line M S M which corresponds to 3.5 cm. fork length, the observed length of fish at time of scale formation. With logarithmic slope 3.99 (from Figure 1) lines are drawn from the base line n S" to intersect the dotted line "I" which corresponds to 4.5 cm. fork length, and which is the observed length at which the point of inflection in the relative growth curve for scales occurs. From the points of intersection on the dotted line "I" the lines are projected on a slope of 1.00, which represents the isometric scale/body relationship above fork length 4.5 cm. In order to calculate the length of fish from the scale, placode diameter and total scale diameter are measured, and using the placode diameter as a datum point, the appropriate line is followed on the plot until it intersects the line which corresponds to total scale diameter on the "Y" axis. Fork length is then read off below on the "X" axis. An hypothetical example is illustrated in Figure 3, using a total magnified scale diameter of 80 mm. and magnified placode diameter of 4.5 mm. Fork length calculated from these two values is 30.0 cm. Comparison of the means from Table IV indicates that there is no significant difference between them (P>.999). Similarly, calculation of "z" reveals that no statistical difference exists in the variances of measured

23 Figure 3. Use of the scale/body ratio of Kamloops trout to calculate fork length from scale measurements alone.

24 21 Table IV. Measured fork length and fork length calculated from placode diameter and total scale diameter of the scales of 31 Kamloops trout from Paul lake, British Columbia. Placode Total scale diameter diameter Calculated Measured fork length fork length 4*0 mm. 83 mm cm cm Means * = i i 3.79

25 22 and calculated fork lengths (P>.99). (Fisher, 1930). Although differences as large as 6.5 cm. between calculated and measured fork length may be observed from Table IV, agreement is close for most of the specimens in the sample, and there is virtually no difference between means or variances. On the basis of the one sample examined, it would appear that adequate statistical comparisons of lengths of Kamloops trout can be made from lengths calculated from scales alone. It should be borne in mind that slight variations in size of fish when scales were formed, and slight differences in size of fish at the point of inflection of the scale/body relative growth curve will affect to a large degree the accuracy of estimation of lengths from scale measurements. For instance, in the example illustrated in Figure 3, a placode diameter of 4.5 mm. and a total scale diameter of 80 mm. resulted in a fork length of 30.0 cm. If the fish did not form its scales until it was 3.6 cm. in length, the estimated length from the scale would become 33.5 cm. A possible use for the method of calculating fish lengths from scales may be found in the study of early life growth characteristics of spawning anadromous salmonoids, the scales of which commonly become heavily eroded near the border, thus rendering the scale border useless as a reference point for calculations. Use of the placode, rather than the scale border as a datum point for calculations may obviate the difficulty.

26 23 The importance of considering the point of inflection in the relative growth curve of scales which are to be used in the "back-calculation" of fish lengths should not be minimized. A further consideration of the methods used in calculations of fish lengths from scales may serve to illustrate the above suggestion. All "scale methods" for calculating the lengths of fish previous to capture make use of the ratio describing the growth of scales relative to body growth. The simplest relationship of scale/body growth may be expressed as follows: L - S equation (1) I n s n where L - length at capture l n s length at some time (n) previous to capture S = scale diameter at capture s n» scale diameter at some time (n) previous to capture t h en L = _JL l equation (2) s n n Van Oosten (1941), as previously mentioned, introduced a correction factor to eliminate the error in "backcalculation" of fish lengths which resulted from the decrease in the length/scale ratio with an increase in length of Lake Erie white bass. For purposes of use of the "correction factor", Van Oosten assumed the scale/body-length ratio to be as follows:

27 24 S s a L - 24 n equation (3) where 24 r point of intercept (in mm.) on the "length" axis of the plot of body length on scale diameter, and - length at some time previous to capture when scale diameter was s n. Substituting equation (3) in equation (2) the resulting equation becomes L - L , equation (4) Ln- 24 ± n then L n L ~ 2l * l n equation (5) o r L n = L " 2 4 l n + 24 equation (6) XJ The equation in i t s final form is the same as that used by Van Oosten, except, that 1^ in his equation is the average direct-proportion calculated length of fish of age "n", The value 24 in the equation is assumed to be the length of fish (in mm.) at the time of scale formation, or when scale size is presumed to be zero. Certain features of the method used by Van Oosten give rise to serious doubts as to the efficacy of i t s application or the validity of i t s underlying assumptions. Close examination of the plot of scale-body length relationship suggests that the relationship is curvilinear, and plotting on a log-log basis results in a straight line.

28 25 Van Oosten apparently recognized this fact in his observance of the decrease in the length/scale ratio, yet he fitted a straight line arithmetically to the data and extrapolated the plot to obtain the value of 24 mm. on the length axis. The error resulting from the use of a linear plot to describe data which have a curvilinear relationship may be small in this case. However, use of the intercept on the length axis of the plot of body length on scale diameter does not appear to be justified when calculations of fish lengths from scales are to be made. It has been shown (page 7) that the body length - scale diameter relationship is isometric after a sharp inflection during early growth. There would appear, to be little biological justification for the use of a method which does not express the relationship of the growth of a body part (scale) to the growth of the whole animal (fork length). The method as used by Van O o s ten assumes that the growth of the scale is proportional only to that increment of growth which occurs after scales are first laid down. It may be argued that scale diameter - body length relationships may be different for different species of fish. If this is so, direct-proportion calculated lengths still may be used if the relationship is linear on a logarithmic plot within the range of scale diameter and fork length over which it is desired to make the calculations. It is suggested that the relationship probably is linear, in most cases, if the data are plotted in logarithmic form.

29 26 A further error results from extrapolation of the plot of body length on scale length when the point of inflection in, and different slopes of the relative growth curves of scales during early development is not taken into account. For instance, scales are formed by Kamloops trout at a fork length of 3.55 cm. and the average magnified diameter of the first growth ring (placode size) at that fork length is 4.5 mm. (X 38). Extrapolation of the plot of scale diameter on fork length to the length axis for Kamloops trout results in a value of scale diameter - 0 and fork length cm. The approach of Fry (1943) to the problem of calculation of fish lengths from scales more nearly obviates the difficulties encountered in giving adequate mathematical expression to the relationship of relative scale-body growth. Fry used a logarithmic rather than an arithmetic plot of scale diameter on length of fish to obtain a linear fit to the data. Fish lengths previous to capture were then calculated by direct proportion. However, Fry assumed a logarithmic proportionality relationship and as Van Oosten did, "corrected" for the positive x intercept. The relative growth equation as proposed by Huxley (1932) is written as y e ax f o r i n its logarithmic form as log y - log a + b log x. Fry assumed length of scales to be logarithmically proportionate to the length attained by fish since the formation of scales, and expressed this relationship by an equation written as : log y r log a + b log (X-x), where y r scale diameter,

30 27 X = length of fish at capture, x - length of fish at time of scale formation, and "a" and "b" are constants. Fish lengths are calculated by direct proportion using the above formula. The "length of fish at time of scale formation" is first subtracted from length of fish at capture, data converted to logarithms, length previous to capture calculated from the scale, and then "length of fish at time of scale formation" is added to the calculated arithmetic length to give true length at time previous to capture. "Length of fish at time of scale formation" is found by extrapolation of the plot of scale diameter on length in a similar manner as in the method used by Van Oosten. Since the "length of fish at the time of scale formation" is a constant value, its use in the calculation of fish lengths will introduce a serious error in the method. For instance, if the length of fish at time of scale formation is assumed to be 3*5 cm., the subtraction of this value from a fish length of 20 cm. will have relatively less effect on the back-calculation of "length previous to capture" than would the subtraction of the same amount from a fish length of 10 cm. In order to obtain true (fork or standard) length, 3.5 c m # m u s t b e a d d e d to the calculated length for each specimen. Addition of a constant value to calculated lengths of younger (smaller) fish will have relatively much greater effect than the addition of the same value to calculated lengths of older (larger) fish e

31 28 In summary, the more important theoretical and practical aspects of the use of fish scales in the calculation of lengths previous to capture may be outlined as follows: (1) The logarithmic growth curve of scales of Kamloops trout with respect to body length has a characteristic slope (3.99) and point of inflection (approximately 4.5 cm. fork length and scale diameter 10.0 mm. x 38) during early development, after which-the scale/body relationship is isometric. (2) It is suggested that the same or a similar scale/body relationship may hold for other species of fish. (3) The slope of a line measuring the logarithmic scale/ body relationship (for any one species) over a wide range of scale diameters and fish lengths is the most probable measure of the relationship of the dimension of individual scales to body length for any one fish of that species. In addition, it is suggested that if the slope does not differ significantly from 1.00, then a slope of 1.00 may be used to calculate fish lengths previous to capture without fear of serious error. However, if the slope of the line measuring the logarithmic scale/body relationship differs significantly from 1.00, then the slope as calculated from the sample regression should be used. (4) Calculation of lengths of fish previous to capture, using a single scale from each specimen and a slope as suggested above, needs no "correction" for "length attained since scale formation".

32 29 (5) Extrapolation of the plot of scale diameter on length to obtain "length at which scale size is zero" is. not considered to be justified in the light of present evidence. Such extrapolation does not take into account the slope of the relative growth curve and point of inflection during early development. (6) The size at which fish first form their scales need be considered in the back-calculation of lengths previous to capture only if it is desired to know the growth history previous to the inflection point of the scale/ body relative growth curve. (7) The method as developed in the 'foregoing pages is considered to have practical application, in that it requires no formula for the "correction" of calculated lengths of individual fish, and thus adds facility to the handling of large masses of data. In addition, when age determinations have been made and scale measurements recorded, any untrained person may calculate fish lengths previous to capture with considerable ease and rapidity. Much variation was encountered in the diameters of scales taken from fish of the same length. Three possible sources of variability may be considered: (1) The recorded range in lateral line scale count for Kamloops trout is (Carl and Clemens, 1948). Fish sampled from the extremes of this range probably would bear scales of widely differing dimensions.

33 30 (2) Individual variation in scale samples would result from the removal of scales from different parts of the body. Although scales commonly are removed from the area above the lateral line and immediately posterior to the dorsal fin, the samples upon which the present study is based were gathered by several workers, and it may be assumed that differences in technique when taking scales have introduced some variability into the samples. (3) Following the assumption that all scales grow at the same rate relative to body growth, any scale which arises from a relatively large placode will remain relatively large throughout the life of a fish. Examination of the scales from 31 adult Kamloops trout The thirty-one specimens examined had a mean placode size of 4.8 mm. (x 38"), and a range of 3.5 mm. to 6.0 mm. Placode size at time of laying down of the first growth ring considered (ossification of the scale) may, therefore, be as a major source of variability. The fact that scales from individual fish vary in size to a considerable extent introduces no error into calculations of fish lengths from scales. If all scales grow at the same rate relative to growth of the fish from which they are taken, use of scales of various diameters is, in effect, use of a scale projector of varying indicated that the range in placode size was considerable. magnifications.

34 31 Consideration of Figure 1 over the fork length range from 4.5 cm. to 45 cm. will indicate that regardless of, the vertical displacement of the scale/body plot, the proportion of scale diameter to fork length will not be changed. If either relatively large or relatively small scales are selected from which it is desired to calculate fish lengths previous to capture, scales of all sizes may be used with equal facility and confidence. The use of scales regardless of size may find greater application in studies based on scale samples submitted by anglers. In any event, no particular care need be taken when a scale sample is being removed from a fish, and greater confidence may be placed in the information obtained from samples gathered by technically untrained workers. 2. GROWTH RATES OF KAMLOOPS TROUT IN PAUL LAKE Growth rates, and selectivity of the fishery. Previous studies (Larkin et al. 1950) have indicated that active selection of faster growing yearling fish in Paul lake is effected by the intense angling pressure. Selection by the fishery of faster growing individuals may effectively obscure all but the extreme ranges of growth rates. In the following section, selection by the fishery of the faster growing fish in all age classes from one- to three-year-olds is considered. Mean lengths at first annular growth checks for the four year-classes were calculated from the scales

35 32 of fish captured as one-, two-and three-year olds. Since sampling did not commence until 1945, "back-calculations" of the lengths of the 1943 year-class could be made only from the scales of three-year-olds captured in 1946, and for the 1944 year-class from two-year-olds captured in 1946 and three-year-olds captured in 1947* Calculations of lengths at age I for the 1949 year-class were made from scales of yearlings captured in 1950 and two-year-olds captured in 1951, and for the 1950 year-class from the scales of yearlings captured in (See Table X.) In order to obviate the difficulty of comparison of lengths of fish captured at various periods during the summer fishing season, all lengths were calculated to the first growth ring laid down after completion of the previous winter growth check on the scales. For purposes of comparison it was assumed that all annular growth checks on the scales were completed by May first of each year. In the following discussion, length at age I, II or III shall indicate the calculated length attained by fish at the time of completion of the first, second or third annular growth check on the scales. Fish described as yearlings, two-year-olds or three-year-olds are I, II or III, plus the interval between the previous growth check and the time of capture. For the year-classes of 1945 and 1946, where the yearlings were first available in the anglers'catch in 1946 and 1947 respectively, comparisons of the mean lengths at age I of fish of the same year-class captured as two-year-olds revealed that no statistical differences existed between

36 33 them (P ). In both instances however, the longer lived fish were smaller, on the average, at the end of their first growing season. Similar comparisons for the 1947, 1948 and 1949 year-classes revealed that fish captured as yearlings were significantly larger at age I than were fish of the same year-class at age I, but which were captured as two-year-olds. Comparisons of mean lengths at age I of fish which were captured as two-year-olds with mean lengths at age I of fish of the same year-class which were captured as three-yearolds indicated that those fish which lived the longest were, on the average, smaller at age I. Although no statistical differences existed between the mean lengths at age I for fish of the same year-class in the above comparisons, analysis of variance of the two groups (captured as two-year-olds and captured as three-year-olds) for all year-classes combined resulted in a highly significant "F" ratio. (See Table V.) Table V. Mean lengths at age I of fish captured as two-yearolds compared with mean lengths at age I of fish of the same year-classes captured as three-year-olds. (All year-classes combined.) Analysis of variance: Source d.f. S. Sq. Mean Sq. Total 494 2, Groups Individuals 493 2, F r r (F m )

37 34 Comparisons of the mean lengths at age II of fish from the same year-classes, captured as two- and three-yearolds respectively, revealed no statistical differences between the two groups for the 1944 and 1945 year-classes. However, fish of the 1946, 1947 and 1948 year-classes which were captured as two-year-olds had a significantly higher mean length at the end of their second year than did fish of the same year-class which were captured as Even where it was not found possible to show three-year-olds. statistical differences in the mean lengths, in every comparison the longer-lived fish were the smaller at age II. Lack of significance in the differences of mean lengths at age II of fish of the 1944 and 1945 year-classes, as compared to significant differences in the mean lengths at age II of fish of 1946 and later year-classes will be discussed in a following section. Reference to Table VI illustrates the high degree of selectivity of the fishery with respect to growth rate of two-year-olds captured in Although a slightly larger mean length for fish captured in November is to be observed, as compared to fish captured in May, there is no significant difference in the two means of lengths of fish at capture (P ). The fish captured in November have a mean length only 1.6 cm. greater than those taken in May. Many features in the rates of growth of trout in Paul lake may be obscured by the fact that the probability of capture of a l l age groups increases directly with an i n crease in size. Comparisons of lengths of fish at time of

38 35 capture may become heavily biased where an intense fishery is removing the faster growing individuals at a higher rate than those which are slower growing. By virtue of the fishing regulations, selection of the faster growing fish is confined to those fish which exceed inches (20.3 cm.) during the fishing season. In addition, it has been suggested (Larkin et al. 1950) that "fish under 8 inches are not commonly attracted to lures" because few fish less than 8 inches are hooked by anglers. Table VI. Mean length of two-year-old immature Kamloops trout of Paul lake, British Columbia, captured in May and in November, Captured in May Captured in Nov. Length at 20.1 i age II (cm.) 6 s Length at capture (cm.) 25.2 t : '- 6 s r 3.71 Mean instantaneous growth rate ft K r K & Calculated for those fish captured in May as from May 1 to May 21, and from May 1 to November 9 for those fish which were captured in November. "K" was calculated from the formula K - (Log g L 2 = Log e L^)/n, where "n" is expressed in weeks. Calculation of instantaneous growth rates from the data in Table VI further illustrates the increasing probability of capture with an increase in size. It may be seen that the "K" value for the two-year-old fish captured in May is almost

39 36 five times as great as for those fish captured in Novembers Although-it may be argued that a decrease in growth rate is to be expected toward the latter part of the growing season, the individuals of both groups may be assumed to have been equally exposed to angling lures in the earlier part of the fishing season, but only the faster growing fish were caught. In addition, the fish which were captured in November almost certainly did not attain the legal size of 8 inches until a substantial portion of the summer season had elapsed. From the previous comparisons of lengths attained at age I and age II of fish captured as one-, two- and threeyear-olds, and from the above comparisons of fish taken by anglers at two different periods of the same year, it may be seen that the fishery is highly selective with respect to growth rate for all ages of fish in every year sampled. Growth rate of Paul lake trout and a ma.ior change in lake ecology. Examination of the differences in rates of growth of trout of all age-classes from 1944 to 1951 indicate the effects of a rapidly increasing shiner population. Reference to the date of introduction of the shiners into Paul lake is important in view of the differences in growth rates which were found to exist after C.C. Lindsey (in Larkin et al. 1950) states: " it may be concluded that the 1947 year-class of shiners taken from Paul lake was hatched in that lake. Therefore, the latest date of initial introduction is the spring of 1947, and as the 1947 year-class was abundant, it appears more probable that the introduction was one or more years previous, possibly during the break in the Paul creek weir in 1945."

40 37 As previously mentioned, there are no statistical differences in the mean lengths at age I of yearling trout of the 1945 and 1946 year-classes, and the mean lengths at age I of the two-year-olds of the respective year-classes. However, similar comparisons of the mean lengths at age I of yearlings of the 1947", 1948 and 1949 year-classes captured in 1948, 1949 and 1950 respectively, with mean lengths at age I of two-year-olds of the corresponding year-classes captured in 1949, 1950 and 1951, indicate a highly significant larger mean size at age I for those fish caught as yearlings. In addition, the mean lengths at age I of yearlings in the anglers 1 catch for the years are all higher than the largest mean lengths for any other year previous to and including (Table X.) Similar comparisons of the.mean lengths at age II of two-year-olds and three-year-olds of the same year-classes revealed the same relationship.. There were no differences in the means for the 1944 and 1945 significant year-classes, but for the 1946, 1947 and 1948 year-classes, fish caught as two-year-olds were significantly larger at the end of their second year than were fish of the corresponding year-classes which lived to be three-year-olds. Following the suggestion advanced by Larkin et al, (1950), that increased competition is associated with increased variability in growth rate, it would appear that the rapid increase in the shiner population, even in the first two years following the introduction of that species, in 1945, exerted a greater influence on the growth rate of the trout than did any previous fluctuation in abundance of the trout populations.

41 38 In other words, before shiners were introduced into. Paul lake, and even with the fishery operating in such a manner as to select faster growing individuals, the mean lengths at age I of yearlings from the very large 1946 year-class did not differ significantly from the mean lengths at age I of fish of the same year-class which were caught as two-year-olds. However, after the introduction of the shiners, and the subsequent rapid increase in numbers of that species, growth rates of the trout decreased and variability in growth rates of both of the one- and two-year-old trout increased to such an extent that the selectivity of the fishery became much more apparent, and significantly smaller mean lengths at age I and II were detectable for the longer-lived fish. Since the introduction of the redside shiner, it is probable that Paul lake has undergone, and is continuing to undergo a marked ecological transformation. Reference to Table X indicates that the growth rates of two- and three-year-old trout still is decreasing. Until 1949, examination of stomachs revealed no occurrence of shiners in the diet of Paul lake trout (Larkin et al. 1950). However, recent (July, 1952) examinations of trout stomachs from Paul lake have revealed that 8.83 percent of the stomachs contained shiners.(i. Barratt, personal communication). It is probable that the trout-shiner relationship has not yet reached an equilibrium, and that the effects of the shiners on the growth rates of the trout are as yet in a state of flux. Pinantan lake, which lies above Paul lake in the same chain, has contained trout and shiners for many years.

42 39 Although no quantitative data are available, local reports indicate that trout fishing apparently declined in Pinantan lake following first introduction of the redside shiner into that water body. In later years, the occurrence of larger trout has increased, and the stomachs of most trout taken by anglers in Pinantan lake contain shiners. In Paul lake it is possible that the role of the shiners with respect to the ecology of the trout will change, and that the shiners will assume the position of a forage, as well as a competitive species. The effects of the shiners on the growth rates of all age-classes of Kamloops trout in Paul lake with respect to the preponderance of the various age-classes in the anglers' catch are particularly evident in the catch records for 1950 and Although the percentage catch of yearlings has varied considerably from year to year, previous to 1950 it had never been less than 10.6 percent of the total. Reference to Table VII. indicates that the percentage of yearlings in the anglers' catch now has dropped to practically negligible proportions. Year-, lings comprised only 6.0 percent of the total catch in 1950, and 3.3 percent in 1951, despite the stocking of 300,000 fry in 1949 and 100,000 in In 1950 the two-year-olds and older fish contributed 93.9 percent to the total of all fish caught by anglers, and in 1951, 97.4 percent. Of these percentages, only 6.0 percent was contributed by four-year-olds in 1950, and only 1.6 percent in The percentage occurrence of the various ageclasses in the anglers' catch reflects two aspects of the present situation: (1) The strongly reduced growth rate of yearling fish. (2) The depletion of the older (larger) fish.