Translated from the Bulletin of the Faculty of Fisheries, Hokkaido University, 15 (1): 25-33, 1964. Goro Nagase, translator; George C. Grant, editor

Kawashima, Rihei

Kyuûshin, Ken-ichiro

English

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W&M ScholarWorks Reports 1968 On the analysis of chum salmon scale pattern by use of auto-correlation coefficient Rihei Kawashima Ken-ichiro Kyuûshin Follow this and additional works at: https://scholarworks.wm.edu/reports  Part of the Aquaculture and Fisheries Commons, Marine Biology Commons, and the Zoology Commons Recommended Citation Kawashima, R., & Kyuûshin, K. (1968) On the analysis of chum salmon scale pattern by use of auto-correlation coefficient. Virginia Institute of Marine Science, College of William and Mary. https://scholarworks.wm.edu/reports/44 This Report is brought to you for free and open access by W&M ScholarWorks. It has been accepted for inclusion in Reports by an authorized administrator of W&M ScholarWorks. For more information, please contact scholarworks@wm.edu. From the Bulletin o£ the Faculty of Fisheries, Hokkaido University, 15(1):25-33, 1964. ON THE ANALYSIS OF CHUH SALHON SCALE PATTERN BY USE OF l\UTO-COIZR.ELATION COEFFICIENT by "h . K h" d K . h" A K A h" Rl el '"awas lma an '-en-lc lro yuus ln (Abstract in English) I. Intr0duction \J \ '{{,"S OJ\ 2.-0\ 19<:: ,JI,b, d.O The scale of chum salmon is cycloid. The characteristic of the scale pattern is mainly shown by the width of the ridge interval. The compactness of the formation of ridges is considered to be dependent on the rate of scale growth and the rate of expansion of the scale. In a broad sense the ridges represent a biological time measure, and the change of expansion of scales (the ridge interval) :i.n the course of time shows an irregular wave pattern. Therefore the auto correl.ation method is used to analyze the characteristics of the scale pattern. In recent years the auto correlation method, together with the development of the technique of data analysis, has played a very important role in the fields of engineering, medicine; and biology. It is used, for instance, in the statistical treatment of auto-controll.ed systems, the detection of signal.s hidden in the noises, and the detection of certain properties in the physiol.ogical and ecol.ogical irregular phenomena of l.iving organisms. The analytical method of auto correlation is treated in 11 Spectra analysis of constant probability process 11 by the Statistical Institute (see references). This study was conducted by the scal.e detection research team at the Department of Fisheries Science, University of Hokkaido and the Marine Institute of Hokkaido. (Acknowledgements are omitted). Preface to Trans1ation1 TransJ.ation of this paper was undertaken to aid a research project on the popvJ.ation dynamics of striped bass, Roccus saxatiJ.is (WaJ.baum). 2 AJ.though an effort has been made to keep the trans-J.ation as near the origina1 as possibJ.e, some degree of free-dom has peen used in rendering the manuscript more readibJ.e. Distortion of the authors 1 meaning may have resuJ.ted from this treatment, and for this we can onJ.y apologize to the authors and readers. This transJ.ation is intended as a service to researchers. Though effort has been made to make it comprehensible, accurate and useful, it is likely that improvements can be made. Should J.iterary improvements or verification appear desirable it is suggested that the researcher make his own translation. We will appreciate constructive suggestions for improvements in this and future translations. Appreciation is extended to Mrs. Alice Lee TilJ.age of the Virginia Institute of Marine Science for typing and assembling the manuscript. 1 Virginia Institute of Marine Science Translation Series No. 20 2 Translation and editing supported by funds from the Anadromous Fish Act (P.L 89-304) through the Bureau of Sport Fisheries and Wildlife. I I Kawashima and Hyu~shin, 1964 Page 2 II. Materials and Methods of Scale Measurements. The scale samples were collected from chum salmon caught iri July and August in 1959 and 1960 jn the Yukon and Skeena Rivers of Canadian-American waters and in the Bolshaya and .Amur Rivers of .Asian waters. .As the scale pattern is considered to be different according to age, samples of 4 ycar-olds were studied. Samples of five females and five males were collected from each above-mentioned river, but in the Bolshaya river group in 1960, only 4 females were used due to an undefinable scale pattern on the plastic impression. Scale impressions on plastic were used. The measure-ments of scales were performed at a magnification of 100 X, using an Olympus projector. The longest axis of the scale was chosen for measurement, and the distance betvJeen the edges of the successive ridges was chosen for the ridge interval (See Fig. 1). Scales vJere taken from above or below the lateral line between the adipose fin and the posterior end of the dorsal fin. One scale was studied for each fish. Calculations of the auto correlation coefficient and power spectra were performed by the automatic digital calcula-tion of the auto correlation coefficient at this department. III. Expression of the Ridge Interval of the Scale as the Function, and the Calculation of the Correlogram and Power Spectra. Let the ridge number counted from the center of the scale be.expressed as the biological time measure t and let the ridge interval be x(t). X(t), which changes as t changes, is called the time pattern system. Since we can choose the time pattern system in numerous ways, it can be expressed in the probability process S = x(t,w). On the condition that the time pattern system of ridges are random samples (events?) in the stationary probability process, and it is ergodic*, we may calculate the correlogram and estimate the power spectra. i:Translator's note: "This terminology is a little bit different in each book of probability (especially on the chapter of Markov chain). It could also mean trpersistenttr from the general ergodic theorems (for Markov processes) that under any circumstance the limits lim PnCt) = Pn exist and are independent of the initial I'\ ..,I- 0<> II conditions. Kawashima and Kyu0sl~inJ 1964 .Page 3 Let Xi be the reading value of the ridge of the ridge iJ and let M be the number of ridges. interval We first · calculate the sample mean x and the deviation from A the mean xi. - 1 X = l1 l1 L: i=l ~i = X:i_ -x x. l i = l) 2 J ••• J l1 i = lJ 2 J ... J l1 Then we calculate the ·covariance Cxx(k)J using the M deviations) and we get (1) ( 2) 1 m-k A CxxCk) =-~ 2: Qi xi+k k = oJ.lJ2J ... Jh (3) M i=l Considering the number of ridges in each scale to be between ~0 and 80) we assume spectra dispersion number h = 36. The auto correlation coefficient Rxx(k) can be obtained in the following equation: RxxCk) = CxxCk) I CxxCO) (4) The graph of ~x(k) in (4) is called a correlogram. The graph of Cxx(k) in (3) is also called a correlogram. Power spectra Px(f) can be obtained from Cxx(k) h-1 Px( 26rth) =~t [CxxC0)+2 Z CxxCk)cos -rr rk+C-llcxxCh)l k=l ~ th (5) where f = r J the interval of ridges A t=lJ r=O J lJ ... Jh. -::-2.._,.6.--,t"-h-Using average .x,oefficient in Px(f) in (S)J we calculate final , power spectra Px(f) A r-1 p ( r ) =.1tLQ:"23PxC-2~'"="",.t..,..h-) +0.54PxC r X 2.£lth A 2Ath ) 0 23-P cr+l L-7 + . X 2Ath (6) Kawashima and Kyudshin, 1964 Page 4 Since 6,t=l, h=36, i.t follows that pov;er spectra of the time pattern system of the ridges in (5) and (6) were calculated on the frequencies of ridges, i.e. 0) 1/72, 2/72, 3/72,---- 36/72. IV. Results and Discussion Fig. 3 shows the correlogram Cxx(k) of the biological time measure t for the data of the Yukon group in 1959. From the fiS:Jure, we can see that there is no significant difference between male and female. This is also true with other data. Therefore, the mean of combined male and female samples was calculated for each river group for each year, and from the result) the correlogram RxxCk) was calculated (Fig. 4). In each case Rxx(k) shows the wave motion pattern. As far as the result in 1959 is concerned, the Bolshaya and Amur river groups show the maximum value at t = 18, disregarding the value a~ t = 0, and shows minimum values respectively at t=9 am 26. On the other hand the maximum value for Yukon and Skeena groups is respectively at t = 22 and t = 25 and the mini-mum value is respectively at t = 10 and t = 34. Both.these rivers have t values greater than those for the Asian waters. 1he absolute values of maximum and minimum values of RxxCk) in the Yukon are greater than in the other three rivers. From the results of 1960, it is also characteristic of the Yukon group that the absolute maximum and minimum values are greater than those in the other three rivers. It appears that there are no significant differences in maximum and minimum values among the other three rivers. Rxx(k) = 0 at t = 0, and it decreases greatly as t gets larger but no significant difference in this decreasing tendency is shown among the river groups. The correlogram CxxCk) in Fig. 5 shows the actual amount of fluctuation and the maximum and minimum values are the same as those of RxxCk). However the pattern of the correlogram is a little different from that of RxxCk) and a more pronounced difference in maximum and minimum values between the Yukon and the other the other three river groups is shown in Cxx(k). The power spectra (Fig. 6) was determined from CxxCk) by theAFourier cosine transformation by the equations (5) and (6). Px has a remarkable peak at f = 1/20 for the Yukon, 1/24 for· the Skeena, 1/18 for the Balshaya, and 1/20 for the Amur groups in 1959. In 1960, each river shows the peak respectively at f = 1/20, 1/20, 1/18 and 1/18. Kawashima and Kyu6shin, 1964 Page 5 A Tne peak of Px in the Yukon group is much higher than in the other three rivers. No difference is shown between that of the Yukon group. 'l'he value of the Amur group is some-what smaller than that of the Skeena and Bolshaya groups. Comparing the va1ues in the r:L ver groups for each year, the va1ue for each river in 1960 is smaller ti1an 1959 and there seems to be a simi1ar yearly change in each river group. In the Yukon group in both years and the Amur group in 1959, we find the components of long periodicity with more than 72 ridges. We assume the correlogram determined from the measure~ ment of the interval of the ridges of the scale consists of different components. Separating these components and estimat-ing the original pattern, we can divide them into a random component and a periodic component. The random component has the property to decrease the stimulus of the pattern itself against the external stimulus, so it is considered to show the characteristics of the internal response of the chum salmon against the stimulus of the environment. We can assume from the various studies of the scales of chum salmon (see the references) that the samples in this study come from different phylogenetic and local groups. The characteristics shown in the random compenent show no differences in river groups and ages and it may be considered an internal specific characteristic of chum salmon. On the other hand there is a difference in river groups and ages in the periodic components. The periodic components judged from the correlogram are not single, and they are composed of severa1 different wave components. These are considered to reflect the conditions of the external environment of chum salmon, such as water tempera-ture, change of food, and the biological changes of growth and maturation. Judging from the fact that chum salmon mature and lay eggs once in a life time, and that growth and other biological properties are quite dependent on the environmenta1 conditions, the main cause of the periodic component is environmental in nature. This study cannot pin-point the conditions reflected on the scale pattern, but it can be seen from the results of correlogram and power spectra analysis that the changes of va~ious conditions in the Yukon groups are generally greater than those in other river groups. ~-----Kawashima and KyuD.shin, 1964 Page 6 The frequency and power ((u.mplitude) 2 ) of the periodic components is already shown in the power spectra results. There are about 18 to 24 ridges among the compact ridge zones or widely spaced ridge zones, and more ridges are present in Canadian-American river groups. The fluctuation of the ridge interval is greater in this order: Yukon, Skeena or Balshaya and Amur groups. According to the time pattern system (Fig. 2) the component of long per:i-odicity found in Yukon samples in both years and Amur groups in 1959 shows that the. ridge interval gets smaller as the scale diameter gets bigger, and it is a characteristic of the scale pattern. However it is unknown whether this characteristic reflects th~ external environmental condition or internal properties of the groups for each river and year. There have been many studies concerning the analysis of scale patterns of salmon and trout. The 1ength between the center of the scale and its resting zone, the number of ridges present between them, the number of ridges in a unit length in a certain area of the scale, or the length of the scale where certain numbers of ridges are formed are used as indicators to distinguish phylogenetic groups. This study made use of all measurements of ridge intervals on which various conditions might reflect, and tried to analyze the characteristics of the scale pattern. This is a different approach compared with previous studies. If we are able to measure the environmental condition of the fishes and also the biological. internal condition of the fish in the future, werll be able to clarify the factors producing the ffects on the changes of ridge intervals, using the mutual correlation coefficients and so on. V. Summary The scale pattern of chum salmon was analyzed with the auto correlation coefficient and its characteristics were , pointed out. The scale samples were taken from the Yukon and Skeena populations of Canadian American waters and the Bolshaya and Amur populations of Asian waters for 1959 and 1960. The Correlogram (Fig. 4) showed a wave motion pattern, and from this result, we estimated the original pattern and divided it into 2 components: the random component and the periodic component (Fig. 7). As far as the random component is concerned, no difference was found between the river and age .groups. The periodic component showed a difference between the Canadian-American and Asian populations. Kawashima and Kyu~shin, 1964 Page 7 In Canadian-American populations, a difference was found between the Yukon and Skeena groups. The difference in ages was also seen in Canadian-American popu1c:ttions. The numbers of ridges among compact ridge zones or widely-spaced ridge zones ranged from 18 to 24, and there was a difference in the fluctuation of the r:i_dge interval among each river and age group, as evidenced by the power spectra analysis (Fig. 6). The characteristics of scale pattern seen in correlo-gram and power spectra are considered to be of use in distinguish-ing the churn salmon groups phy1ogenetically. VI. References 1) Statistical Institute. 1963. Spectra analysis of irregular vibration. Tokyo, 156 pp. (In Japanese) 2) Tanaka, S., Shapard M. P. and Bilton. T. H. (1960). Scale characteristics of chum salmon in coa~tal areas and on the high seas of the North Pacific Ocean. I.N.P.F.c. Doc., Ser. 405, 27 p. 3) Sato, R. (1959). The use of probability paper for the graphical analysis of percentage compositions of chum salmon with different scale characteristics. Tohoku Jour. of Agr. Res., 10(1) 75-87. 4) Kobayashi, T. (1961). Studies on the age, growth and stock of Oncorhynchus Keta (Walbaum). Research Bull. of Hokkaido Salmon and Trout Hatcheries, (.16), 1-102. (In Japanese). Puge 8 A B ·. Fig. 1. A: Scale pattern of chum salmon B : Central portion of scale showing the standard of distance between ridges 1/JOO!r.m 10 5 0 10 I 40 Ukon River Sk~cnu River Amur Riv~r 60 I 80 Ridgn nwnbcr Fig. 2. Variations of the distance between ridges versus tho ridge number . ·-R., (k) 1.oL -0.5 R,. (k) !.o~ -0.5 -1.0 Pig. 3. Fe J11.:de ·-<>--:.rf.l!u ... ~.-Correlog-ram of the distance between ridges calculated from the data for the Ukon river in 1959 1959 1960 Skccna River ---c---Bolshaya Ri"vcr-0--Amur River ---o---Fig. 4. Correlogram of the distance between ridges, jz .. (k) R . I k 40 Puge 9 -!.0 -1.0 Ukon River ~­Sk<:enJ. Riv.:or ---.o--~­Rolshly.l Rivcr-o-Amur River --<>-.... Fig. 5. Correlogram of tho distance between ridges, ju(k) c Page 10 1959 20 1960 15 Fig. 6. Power spectra I.Q JO -o.s Fig. 7. Component of corrdogram Ukon Hivcr -o--Skeena Hivcr -- .. 0.--Bols!.aya Hivcr -0---A111ur Hivcr ---o---A represents the correlogram of the distance between ridge~;, Rxx(k); B represents random component; C represents p<3riodic component. Page ll r 

On the analysis of chum salmon scale pattern by use of auto-correlation coefficient

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On the analysis of chum salmon scale pattern by use of auto-correlation coefficient

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