Title. Author(s)YAMADA, Juro; AOKI, Hideaki. Issue Date Doc URL. Type. File Information. Goldfish Scales

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1 Title The Rate f Overlapping f Fish Scales as an ndex Gldfish Scales Authr(s)YAMADA, Jur; AOK, Hideaki 北海道大學水産學部研究彙報 = BULLETN OF THE FACULTY OF FSHERES Citatin18(3): ssue Date Dc URL Type bulletin File nfrmatin 18(3)_P pdf nstructins fr use Hkkaid University Cllectin f Schlarly and Aca

2 The Rate f Overlapping f Fish Scales as an' ndex f Their Relative Grwth Rate. A Preliminary Examinatin n Gldfish Scales Jur YAMADA* and Hideaki AOK* nvestigatin int the relatin f the length f the fish t the size f its scales plays an imprtant part in ppulatin studies f fishes. Since such the relatinship seems t shw a straight line regressin, it has generally been accepted that the scale increases in size prprtinally with the increase in length f the fish. Strictly speaking, hwever, it shuld fllw an expnential equatin, S=aLb (S: scale length; L: bdy length; a,b: cnstant), when the grwth f scales is cnsidered frm an allmetric viewpint. n fact, it has frequently been suggested that in many fishes the "scale size-bdy length" relatinship shws a curvilinear character when traced thrughut their lives (reviews by Kub and Yshihara, 1957, and by Niklsky, 1963). Furthermre, ne might expect that the relative grwth rate f scales wuld vary accrding t seasns even within a year. The scale sizes pltted against a certain length f fish usually cver s wide a range that it is fairly difficult t discuss minute changes f the relative grwth rate by scale size-bdy length analysis. The grwth f a fish is naturally accmpanied by an extensin in area f its bdy surface. Since the number f scales remains unchanged after they have fully develped, the grwth rate f the scales in relatin t the bdy grwth shuld be reflected in their verlapping rates. The verlapping rate f a scale t the surrunding nes may be expressed by the rati f the size f the expsed part t the size f the entire scale, because the expsed part literally means the area f the scale that is nt cvered by the neighburing scales. A change, if any, in the verlapping rates f scales is therefre assumed t be mre useful than the "scale size-bdy length" relatinship as an index f the relative grwth rate f scales. n an attempt t ascertain this assumptin, an examinatin was carried ut n the scales f gldfish. t is a pleasure t recrd here ur gratitude t Prfessr Hidejir Niiyama fr his kindness in reading this manuscript... Material and Methd Three grups f the Wakin, the mst cmmn variety f gldfish (Oarassius auratus), were intrduced frm a fish farm and reared in an utdr pnd f ur labratry. The fish grups were respectively called "S", "M", and "L" {small, * Faculty f Fi8herie8, Hkkaid UniverBity -188-

3 1967] J. YAMADA and H. AOK: Rate f verlapping f fish scales Table 1. Grup Number, bdy length, and bdy weight f the gldfish used as material August Number By Length BdJ: Weight ' Number By Length BdJ: Weight f fish em g f fish em g mean (range) mean (range) mean (range) mean (range) s 42 M 35 L ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) T L Fig. 1. Diagram f a gldfish scale shwing the places measured. The hatched represents the expsed part f the scale. EE': Width f the expsed part, cnnecting bth lateral ends f the expsed part TT': Width f the entire scale, parallel t EE' and passing F (scale fcus) LL': Length f the entire scale, alng the lngitudinal axis passing M (midpint f EE') and F M'L' : Length f the expsed part, a part f LL' crrespnding nly t the expsed part medium, and large) accrding t size (Table 1). All fish f these three grups were in the secnd year f grwth but they differed distinctly in size, prbably because f differences f the length f the grwth perid in the preceding year due t different hatching dates. The first examinatin tk place in the middle f n 85 gldfish and the secnd at the end f August n the same fish except fr 26 which had died r were missing (Table 1). Five scales in sequence were remved frm a definite prtin n the left side f each fish in the first examinatin and the equivalent scales were remved frm the right side in the secnd examinatin. The length and width f each scale and the length and width f the expsed part were measured under a shadwgraph. The places measured are indicated in Fig. 1. n rder t -189-

4 Bull. Fac. Fish., Hkkaid Univ. [XV,3 measure the area f bth the entire scale and f nly the expsed part, an utline f an enlarged scale was traced n a piece f paper and it was weighed after cutting ut the figure. A few regenerated scales, judged as such frm their superficial patterns, were excluded frm the measurements. The measurements f the nrmal scales were then averaged fr each individual fish. Results During the examinatin perid, the fish in each grup shwed gd grwth bth in length and in weight (Tables 1, 2, and 3). The grwth rate f the S-grup appeared t be the highest and that f the L-grup was the lwest in inverse rder f size. The "scale length-bdy length" relatinships btained respectively in and in August are shwn in Fig. 2. t may apparently be cncluded that the scales grew at the same rate as the fish bdies frm t August, because n clear difference can be bserved between the tw regressins. A different cnclusin Table 2. Changes in the bdy length cmpsitin f the three fish grups frm t August Bdy Length in mm M L Table 3. Changes in the bdy weight cmpsitin f the three fish grups frm t August Bdy Weight in gram i 3 1 3s s s S s s 1 1 1s n

5 1967] J. YAl1ADA and H. AOX: Rate f verlapping f ftsh scales 88 'M' 8... "'-'.....,:... - 'i Q/. _ \l."\sj' ') \4 BOlY LD.GTll N O! Fig. 2. Cmparisn f the relatinships between the bdy length and the mean scale length f the same gldfish measured in ( ) and in August ( ) can be drawn, hwever, when the length f the scale is pltted against the length f the expsed part f the scale, rather than against the length f the bdy (Fig. 3). The length f the expsed part (1) relative t the length f the entire scale (L) was lwer in August than in. This is als evident frm Table 4 in which the frequency f the rati 1[L within each grup is shwn fr bth and August. A similar but mre bvius result was btained frm the relatin between the area f the entire scale (S) and the area f the expsed part (s) (Fig. 4), and by cmputing the rati sis (Table 5). The fact that the majrity f the dts fr August lie belw thse fr (Figs. 3 and 4) and that bth the ratis 1[L and ss clearly decrease between and August (Tables 4 and 5) prves that the verlapping rate f the scale increased during this perid. n ther wrds, the grwth rate f the scale exceeded that f the bdy in the perid between and August. t shuld be nted that this was nt pssible t shw by the cmparisn f the length f the scale t the length f the bdy (Fig. 2). n a similar cmparisn f the width f the scale t the width f the expsed part, the difference is als nticeable between and August thugh it is smewhat indistinct (Fig. 5, Table 6)

6 - f e ; M ;!,. B *'.g>. Q. :. 8 "..,: ':.; r) ::li''''', # CD ".-. OJ a, J" <.:.1 6'? i <::::t. 1 ENTln: SCAlF. Al4:A AllJlTtAR'.". tn TS Et.7RE SCALE LENGT\ 1;.1 J. Fig. 4. Cmparisn f the relatinships between the area f the entire _le and f the expsed part in ( ) and in August ( ) Fig. 3. Cmparisn f the relatinships between the length f the entire scale and the length f the expsed part in ( ) and in August ( )..,...

7 1967] J. YAMADA and H. AOK: Rate f verlapping f fish scales Table 4. S ll Changes in the frequencies f the rati "expsed part length: entire scale length" (/L) frm t August in each grup sl sl M L Table 5. Changes in the frequencies f the rati "expsed part area: entire scale area" (s/s) frm t August in each grup S M L sis 1 O.lsi S[ Table 6. Changes in the frequencies f the rati "expsed part width: entire scale width" (wfw) frm t August in each grup S w/w O. 7s1 O.SO 1.S21.S4 1.S61.ssl M L 11'1'1'1'1'1 Cmparing grups at the same mnth, r August, bth the ratis ll and ss seem t shw a little decrease frm the S- t the L-grup. But if the cmparisn is made in cnnectin with the bdy grwth frm t August (cmpare T.Wes 4 add 5 with 'fanes 2 and at. the- fllwing fts &re t be nted. 1) The fish f the S-grup in AliguMi ft.re still smal1er than th.se f the M-grup in. Nevertheless bth the ratil'l fl and ss are smaller in the frmer than in

8 Bull. Fat;. Fish., Hkkaid UnJv. [XV,3 1 Fig. 5. Cmparisn f the relatinships between the width f the entire scale and f the expsed part in ( ) and in August ( ) 1.15 "" 'b 8 6' '1::>.3' j e, ,... J 1\ fant-55 Fig. 6. The relatin between the fatness and the rati "expsed part area: entire scale area" (s/s) in ( ) and in August ( ) -194-

9 1967] J. YAMADA and H. AOK: Rate f verlapping f fish scales the latter. 2) The same relatin exists between the fish f the M-grup in August and thse f the L-grup in. Thus it is bvius that a certain rate f verlapping f the scales is nt crrelated t a definite length r weight f the fish. Since the relative area f the bdy surface is naturally cnsidered t be crrelated t the fatness f the fish, it is pssible t suppse that there exists sme relatin between the verlapping rate f scales and the fatness f fish. The relatin between the fatness and the rati ss is shwn in Fig. 6. N appreciable crrelatin was fund between the tw either in r in August. Discussin t was reprted by Kbayashi (1961) that the "scale size-bdy length" relatinship f salmn fry in seaward migratin differed remarkably frm that f the fry being reared in freshwater. This suggests that the scale grwth rate relative t the bdy grwth may vary accrding t envirnmental factrs. Cnsiderable difference in the relative size f the expsed part wuld have been bserved amng the three gldfish grups if it were pssible t cmpare the ratis ll r ss when their bdies were the same size. The reasn fr such difference is presumed t be different perids f grwth in the preceding year due t different hatching dates. Envirnmental cnditins may als have had an effect n the ratis. J Kub and Yamahira (1955) attempted t find differences in the "scale sizebdy length" relatinship amng Pacific salmn ppulatins. t has been shwn in this study that the grwth rate f the gldfish scales exceeded that f their bdies during the fur mnths frm t August. This cnclusin was btained by examining changes in the rati f the size f the expsed part t the size f the entire scale and nt by examining changes in the rati f the scale length t the bdy length. t seems t suggest that the methd emplyed in this study wuld apply t ppulatin analyses f fishes better than the cmparisn f the "scale size-bdy length" relatinships. The prblem awaits further research. Cncerning the relatin between the fatness f fish and the grwth f the scales, Sait (1955) reprted that the scales f crucian carp kept in a starved cnditin increased their verlapping rate visually alng the drs-ventral bdy axis. A crrelatin between the fatness f fish and the rate f verlapping f the scales was nt nticed in this study. Thugh the fish appeared t be smewhat fatter in August than in, it is unlikely that the lwer ratis f ll and sis in August are crrelated with this increase in fatness. Pssibly the situatin in nrmally grwing fish wuld be different frm that f starving nes. Summary Changes in the relative grwth rate f fish scales was assumed t be reflected -195-

10 Bull. Fac. Fish., Hkkaid Univ. [XV,3 in the rate f the verlapping f the scales. This can be expressed by the rati fl (length f the expsed part f scaleflength f the entire scale) r sis (area f the expsed partfarea f the entire scale). The scales f gldfish which were reared fr fur mnths frm t August were measured. The rate f the verlapping f the scales appeared t increase during that perid because bth the ratis fl and sfs were shwn t be smaller in August than in. This suggests that the grwth rate f the scales exceeded that f the bdy. An examinatin f the "scale lengthbdy length" relatinships failed t suggest the abve fact. Changes in the rate f verlapping f scales expressed by the relative size f their expsed parts are presumed t be a pssible index f their relative grwth rate. References Kbayashi, T. (1961). Bilgy f chum salmn, Onrrhynch1l8 keta (Walbaum), by th grwth frmula f scale. Sci. Rep. Hkkaid Salmn Hat. 16, Kub,. and Yshihara, T. (1957). Suisan Shigen-gaku. 345p. Tky; Kyritsu-Shuppan. Kub, T. and Yamahira, K. (1955). Seibutsu Chsa Hkku N.3, Suisan-ch (Rep. Bii. nvest. N.3, Fiah. Agency) Niklsky, G.V. (1963). The eclgy f fishes. (Translated int English by L. Birkett). 352p. Lndn; Acad. Pr. Sait, S. (1955). On the mechanism f the appearance f the scale structure.. On the regeneratin f the scales f the crucmn carp. Oarassius caras8ius (L.), when they are reared with the different fd. Bull. Fac. Fi8h., Hkkaid Univ. 5 (4),

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

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