The length-weight relationships in S. albella and S. gibbosa were estimated. In

5'. albella, the regression coefficients of the 20-39 mm group, the larger indeterminates of the

40-95 mm group and the sexes were found to be significantly different from one another and

from 3. In S.gibboia, the regression coefficients of the 20-39 mm group and the larger fish

(indeterminates of the 40-95 mm group and the sexes) were significantly different from

one another and from 3. In both species, the regression coefficients of the fishes of the

20-39 mm group were significantly higher than those of the fishes of the larger size-groups

Sekharan, K V

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L E N G T H - W E I G H T RELATIONSHIP I N SARDINELLA ALBELLA (VAL.) A N D S. GIBBOSA (BLEEK. )* K. V. SEKHARANI Central Marine Fisheries Research Institute, Mandapam Camp ABSTRACT The length-weight relationships in S. albella and S. gibbosa were estimated. In 5'. albella, the regression coefficients of the 20-39 mm group, the larger indeterminates of the 40-95 mm group and the sexes were found to be significantly different from one another and from 3. In S.gibboia, the regression coefficients of the 20-39 mm group and the larger fish (indeterminates of the 40-95 mm group and the sexes) were significantly different from one another and from 3. In both species, the regression coefficients of the fishes of the 20-39 mm group were significantly higher than those of the fishes of the larger size-groups. INTRODUCTION The study of the length-weight relationship in fishes is of primary impor-tance, among other things, in setting up yield equations (Beverton and Holt, 1957; Ricker, 1958), in estimating the number of fish landed, and in comparing popu-lations in space and time. The general expectation is that the weight of fishes would vary as the cube of length (Brody, 1945; Lagler, 1952; Rounsefell and Ever-hart, 1953; Brown, 1957). But the actual relationship may depart significantly from this (Le Cren, 1951), as fishes normally do not retain the same shape or body outline throughout their life span and the specific gravity of the tissues may not remain constant. Nevertheless, most workers have been content only to describe the estimated relationship, without proceeding further to test whether the depar-tures from cubic relationship that they had noted are statistically significant or not. This aspect has been taken into consideration in the present account of the length-weight relationship of Sardinella albella (Val.) and S. gibbosa (Bleek.) of the Mandapam area; this study is also part of an investigation into the biology and fishery of these sardines, results of certain aspects of which have already been published (Sekharan, 1955, 1959). * Was part of a thesis which formed the basis for the award of the Ph. D. degree of the Madras University to the author. 1. Present address: Department of Fisheries, University of Calicut, Calicut. LENGTH-WEIGHT RELATIONSHIP IN SARDINES 167 Of the nine species of Sardinella occurring in the seas around India (Misra, 1952), the length-weight relationship of only S. longiceps Val. is known (Dhulkhed, 1963). Ganapati and Rao (1957) have given the values of the condition coefficient of 5. gibbosa off \v'altair. MATERIAL AND METHODS All material was collected by the author from Thedai-PuUamadam and other fishing centres of the Mandapam area. Only fresh material was used. Specimens from gill-nets were not included in this study. The standard length of each fish was noted, correct to one mm; and before weighing in a physical balance, the moisture on each fish was removed. Weight was determined correct to 0.01 gin fish of up to about 80 mm in length and 0.1 g in larger fish. As mentioned by previous workers, length-weight relationship of each fish can be expressed by the formula, W = a L" where, W=weight, L= standard length, and a and n are constants. Logarithmic transformation of the formula gives a straight line relation-ship of the form. Log W=Log a+n Log L where, LogW is the dependent variable (y), log L the independent variable (x), n the regression coefficient or slope (b); and Log a the y — intercept. Log a and the regression coefficient (b) were estimated by the usual method of least squares. LEMGTH-WEIGHT RELATIONSHIP IN S. ALBELLA Estimated regressions—k\XogsX\vix 229 fish of the length range 20-124 mm were examined. A preliminary plot showed that the same equation would not fit the data for the entire length range and that breaks occurred around the 35-39 and 85-89 mm groups. Separate estimates were therefore made for different groups, as mentioned below: 1. Very small fish (20-39mm): Log W = 6.1075+3.6391 Log L 2. Larger indetermiiates (40-89 ram): Log W = 6"6782+3.2803 Log L 3. Females (72-124 mm): Log W = 678950-^ 3.1757 Log L 4. Males (77-123 mm): Log W = 5.1458+3.0518 Log L 168 K. V. SEKHARAN The significance of the differences between the regression coefficients (b) was tested, as usual, by the method of analysis of covariance. The relevant data are given below: N S(x-x)2 2(y-y)^ 5;(x-x) (y-y) b2(x-£) (y-~y) 2(y-;)^ 20-39 mm 67 0.3544 4.8656 1.2897 4.6933 0.1723 40-89 mm 98 0.9944 10.8135 3.2619 10.7000 0.1135 Female 63 0.2686 2.7455 0.8530 2.7089 0.0366 Male 68 0.2276 2.1868 0.6946 2.1198 0.0670 N=number of observations; 2(y-y)^== sum of squares of deviation from regression. The test of heterogeneity of the regressions is given below: Source of variation Degrees of Sum of freedom squares Mean F square Deviation from total average regression 291 0.4487 Deviation from individual regressions within samples 288 0.3894 0.001352 Difference 3 ' 0.0593 0. 01977 r4.62 F l % =3.86 The differences between the regression coefficients were significant at 1 % level. The test of heterogeneity was again performed for the last three groups (indeterminates of the 40-89 mm group, male and female) as shown below: Source of variation Degrees of freedom Sum of squares Mean square Deviation from average total regression 225 Deviation from individual regressions within sample 223 Difference 2 0.2275 0.2171 0.0104 0.0009735 0.0052 5.34 =4.70 The differences between the three were again found to be significant at 1% level. LE?JGTH-WEIGHT RELATIONSHIP IN SARDINES 169 But it was found that the diflference between female and male regression coefficients was not significant at 1% level (F=2.32; d.f. = l; 127; Fl%=6.84). Hence a pooled estimate was made for males and females. The formula was Log W=5.0110+3.1195 Log L. For the pooled male and female estimate the sum ot squares etc. were as follows: S(x-x)2 =0.4962, S(y-y)^=4.9336; 2(x-x) (y-y)=1.5479; b2(x-x)(y-y) = 4.8287; 2(y-y)2=0.1049. The differences between the regression coefficients of the sexes (male and female pooled) and iiideterminates of the 40-89 and 20-39 mm group were again tested; the F values are given below: F ^ly Degrees of freedom Between the sexes and 40-H9 mm group 8.66 Between the sexes and 20-:i9 mm group 39.86 Between the 40-89 and 20-39 mm groups 18.61 6.75 1; 225 6.76 1; 194 6.80 1; 161 It will be seen tb-^ t the diff"erences between the regression coefficients of the three groups were significant at 1 % level. The three regression lines (tor the 20-39 mm group, 40-89 mm group and sexes) are shown in Fig. 1. Among the I.550 0.9S0 t ^ \ > N ^ H ^ 0.350 o •-• UJ » O T.750 0 -J T.iso _ ! ' ' ' ! ' 2 0 - 35 m m --~ + ^ .?"" y \X , , 1 , , ' ' i ' 1 1 1 1 1 .^> \ 1 y \x A 1 1 ,1, 1 I 1 1 . F I G . / 4 0 - 8 9 m m + 1 y x- y <i> y jv' y • • y 1 1 1 1 .^* j ! - ^ SEXES . ^ ^ 1 7 2 - I 2 4 m m ) JHI^ y^ '^ — . _ • INDETERMINATES , 1 , , , 1 , 1.615 I.7SS 1.895 LOG LENGTH (X) FIG. 1. Length-weight relationship in 5. albella. 2.035 170 K. V. SEKHARAN three groups, the smallest fish (20-39 mm group) had the highest regression coeffi-cient (3.64), which shows that they increase in weight at a comparatively higher rate than the larger fish. Applying the t-test, it was seen that the regression coefficients of the three groups mentioned above were significantly different from 3 at 1 % level. The results are given below: Length-groups (mm) b-3 Degrees of freedom 20-39 40-89 Sexes 0.6391 0.2803 0.1195 7.39 8.13 2.96 65 96 129 2.66 2.63 2.62 LENGTH-WEIGHT RELATIONSHIP IN S. GIBBOSA Estimated regressions—Altogether 195 fish were examined. A preliminary plot showed that the relationship was different in the 20-39 mm group, compared to the larger fish. Hence, as in S. albella, length-weight relationship was estimated tor very small fish (20-39 mm), larger indeterminates (40-95 mm), females (90-137 mm) and males (90-134 mm). These are given below: L For very small fish (20-39 mm): LogW-7.6061+3.9547 Log L 2. Larger indeterminates (40-95 mm): Log W==6.8593+3.1428 Log L 3. Females (90-137 mm): 4. Males (90-134 mm): Log W=5.0660f3.0434Log L Log W= 6.9909+3.0780 Log L As before, the difference between the regression coefficients was tested by the method of analysis of covariance. The relevant data are given below: N 2(x-x)2 2(y-;)2 Z(x-x') (y-y) bE(x-x) (y-y) 2(y-yV 20-39 mm 33 0.2408 3.9173 0.9523 3.7661 0.1512 40-95 mm 112 1.3203 13.1878 4.1494 13.0407 0.1471 Female 25 0.0875 0.8168 0.2663 0.8105 0.0063 Male 25 0.0782 0.7541 0.2407 0.7409 0.0132 N= number of observations; 2 (y-y)^ = sum of squares of deviation from regression. LtNGTH-WEIGHT RELATIONSHIP IN SARDINES 171 The test of heterogeneity of the regressions was performed as shown below: Source of variation Degrees of freedom Sum of squares Mean square Deviation from average tc tal regression Deviation from individual regressions within samples Difference 190 187 3 0.4589 0.3178 0.1411 0.001699 0. 04703 Fr/ 27.68 = 3.89 It was found that the difference between the regression coefficients was significant at 1% level. The dififerencei. V etween the regression coefficients of the last three groups (larger indeterminates, female and male) were again tested as shown below: Source of variation Deviation from average total regression Deviation from individual regression within samples Difference Degrees of freedom 158 156 2 Sum of square 0.1679 0.1666 0.0013 Mean square 0.001068 0. 00065 F 0.61 Here the meai square for diiferences between regression coefficients was less than that for individual regression within samples. It could therefore be taken that the differences between regression coefficients of the last three groups were most probably not significant. A pooled regression estimate was therefore made for the 40-137 mm group (i.e., the indeterminatss of the 40-95 mm group and the sexed fish). The estimated regression was Log W=6.8573+3.1444 Log L The sum of sciuares etc. were: S(x-x)-=3.0400; S(y-y)^=30.2246; S(x-x) (y-y)=9.5589; b 2(x-x) (y-y)=30.0570; S(y-y)2 =0.1676. The difference between the regression coefficients for 20-39 mm and 40-137 mm groups was again found to be significant at 1% level. (F=86.06, d.f. = l; 191, F, 0/^6.75). The two regreiision lines are shown in Fig. 2. The test and the figure show that in relation to length, fish of the 20-39 mm group increase in weight at a higher rate than fish of the larger size groups. The most interesting point here is that 172 K, V. SEKHARAN for the 20-39 mm group, the regression coefficient almost equalled the value of 4, a very high figure compared to the estimate for even the corresponding length-stratum of S. albella. I J ' t> I .5IO I6SO r.790 19 30^ LOG LENGTH CX) FIG. 2, Length-weight relationship in S. gibbosa. Applying the t-test, it was seen that the regression coefficients of both the groups mentioned above differed significantly at 1% level from 3. The results are given below: Length groups (mm) b-3 Degrees of freedom 1 o/ 20-39 40-137 0.9547 0.1444 6.71 7.78 31 160 2.75 2.58 REMARKS The results show that in both the sardines, the regression coefficients of the 20-39 mm groups are higher than those of the larger size-groups. A partial explanation for this could be the change in the body outline of these fishes as they increase in length. It has been seen (Sekharan, unpublished) that in both sptcies, body-depth in relation to length increases more rapidly in the 20-34 mm LEl-JGTH-WEIGHT RELATIONSHIP IN SARDINES 173 groups than in the larger size-groups and that the differences in the regression coe-fficients of the body depth-length relationship of the two length-strata are statistically significant. The t-tests sho\/ed that the regression coefficients of the length-weight re-lationship in both the species differed significantly from 3. An interesting point here is the absolute value of the regression coefficient (b) of the length-weight re-lationship in the small fishes (20-39 mm). In both species it is more than 3.6; in S. gibbosa it approaches the high value of 4. It may be mentioned that Le Cren (1951) recorded a value of 3.59 for the regression coefficient of the length-weight relationship in the larvae of Perca fluviatilis. In the larger irdividuals of both sardines, however, the regression coeffi-cients are close to the expected value of 3. The main difference between the two species is in regard to tie regression coefficients of the fishes above 40 mm in length. In 5. albella, unlike in S. gibbosa, the regression coefficient for the sexes is signi-ficantly different from that for the larger indeterminates. The regression coeffi-cient, especially for larger indeterminates, is higher in S. albella than in S. gibbosa. ACKNOWLEDGEMENTS The author is greatly indebted to Dr. S. Jones and Shri S. K. Banerji for going through the manuscript and suggesting improvements. REFERENCES BEVERTON, R.J. H. AND S.J. HOLT. 1957. On the dynamics of exploited fish populations. Fish. Invest. Land., Ser. 2, 19: 533 pp. BRODV, S. 1945. Bioeiie'getics and growth. Reinhold Publishing Corporation, New York, 1023 pp. BROWN, M.E. 1957. Experimental studies on growth. In: The physiology of fishes, pp. 361-400. M.E. Brown (Ed.), Academic Press. New York. DHULKHED, M.H. 1963. The length-weight and volume relationship of the Indian oil saraine Sardinella longiceps Valenciennes. Indian J. Fish., lOA: 40-47. GANAPATI, P.N. AND K.S. RAO. 1957. On the bionomics of Sardinella gibbosa iB\kr) of Waltair coast. / . zool. S9C. India, 9: 162-182. LAGLER, K . F . 1952. Freshwater fishery biology. Wm. C. Brown Company, Dubuque, Iowa. LE CREN, E.D. 1951. The length weight relationship and seasonal cycle in gonad weight and condition in the porch (Perca fluviatilis). J. Anim. Ecol, 20 (2): 201-219. MiSRA, K.S. 1952. An aid to the identification of the fishes of India, Burma and Ceylon. Rec. Indian Mus., 50: 367-422. 174 K. V. SEKHARAN RiCKER, W.E. 1958. Handbook of computation for biological studies of fish populations. Bull. Fish Res. Bd Canada, 119: 300 pp. ROUNSEFELL, G.A, AND W.H. EvERHART. 1953. Fishery Science: its methods and applications. 444 pp. John Wiley and Sons Inc., New York. SEKHARAN, K.V. 1955. Observations on the Choodai fishery of Mandapam area. Indian J. Fish., 2: 113-132. SEKHARAN, K.V. 1959. Size-groups of Choodai taken by different nets and in different localities. Indian J. Fish., 6 (1): 1-29. 

Length-weight relationship in Sardinella albella (Val.)

and Sardinella gibbosa (Bleek.)

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Length-weight relationship in Sardinella albella (Val.) and Sardinella gibbosa (Bleek.)

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