T H E W E I G H T - L E N G T H R E L A T I O N S H I P O F L A B E O R O H I T A ( H A M I L T O N ) A N D C I R R H I N A

M R I G A L A ( H A M I L T O N )

BY HAMID KHAN, M.Sc., LL.B. (PUNJAb), PH.D. (CANTAB.), F.A.Sc.

AND

AMJAD HUSSAIN, B .Sc . (HONS.)

Received July 24, 1944

IN other countries much work has been done on the correlation of weight and length in the various species of fish. Spencer (1898) mentions that " a fish which has doubled its length should have increased its weight eight times ". Fulton (1904) refers to the well-known law " that the volume of similarly shaped bodies of the same specific gravity: vary directly as the cube of the corresponding dimensions ". Crozier and He:'ht (1913) showed that the weight in the weak fish (Cvnoscion rezalis) increased approximately to the cube of its length. Reighard (1913) admitted that there existed a definite relation in length and weight but added that at some stage " the length increased much less rapidly than the weight" thus interfering with the rela. tion. Clark (1925) also pointed out a definite relation in the California sardina (Sardino caerulea).

In India. no such work has been conducted on the different species of fish. except on "Mahseer ", Barbu~ (Tor)putitora (Hamilton), for which Lacey a~d Cretin (1905), Skene Dh~T (1906), Trevenen (1925), and Spence and Prater (1933) have advanced some formulae. In these formulae 1�89 length of the fish in inches [Lacey and Cretin (1905)] or 1~: length of the fish [Trevenen (1925)], multiplied by the square of the girth izl inches and divided by !,000 gives the weight of the fish in lbs. When applied to other species of carp these formul0~ do not give accurate results.

In this article, results of observations made on the weight-length rela- tionship, in the two species of the carp,, namely Labeo roh#a (Hamilton) and Cirrhina mrigala (Hamilton) from the Departmental Fish Farm at Chhena- wan, during the years 1938 to 1942, are given as a guide to the anglers and to the pisciculturists in other parts in India.

a Keys (1928) mentions that great fluctuations in specific gravity are unlikely~ due to hydrostatic equilibrium that exists between the fish and its environment,

224

Weight-Length Relalio~zship o f L. rohita & C. mrigala 225

Method

Eight hundred and twenty-two fish, namely ~50 Rohu, Laheo rohita (Hamilton) and 472 Mori, Cirrhina mrigala (Hamilton) were studied. These fish were caught from the farm, and removed to the laboratory without much delay. Measurements were immediately recorded to avoid loss of weight from evaporation. The length was observed in centimetres and represented the total length from the tip of the snout to the end of the caudal fin. This was taken by placing the fish on the Fish Measuring Board 2 specially designed for the purpose. Tbe weight was recorded in 'Chhatanks ' from Salter's Improved Family Scale No. 50. Before the fish were weighed the surface water and mucus were removed. The increase in weight of fish during the spawning season has been discounted by omitting as far as possible data on all fish with ova, when calculating the average weight. The amount of undigested food was not always found sufficient to cause serious fluctuations in the average weight of fish. In all these cases the observations have been recorded at different times of the year but from the same locality.

The Length-Weight Relationship and its Factor

A detailed study of weights and lengths in the two species of hsh at Chhenawan, showed that these two units of measure were closely related. Since length is a linear measure and weight is a measure of volume, the latter would increase approximately to the cube of the length. This forms a mathematical equationfl namely W = xL "~ in which ' W ' represents the weight offish, ' L ' its length and ' x ' a constant, the value of which depends entirely upon the units of measare used, and on the species of fish. Such constants have been calculated at each centimetre, for each species of fish and their average has been worked "out. The standard deviation and the standard error of the mean of these constants have been calculated according to the following formulaz from Davenport and Ekas (1936).

0-- ~ Z (v N M)~ (l)

where 0- -S tandard deviation, v = individual measure, M = mean of the above value of measures.

2 A special board on which a scale and sliding metallic rod with a moveable pointer are fixed to record the various lengths.

s Clark (1928), Keys (1928) and Hile (1936) have developed this relation into tl~e equation W = xL '~, where the value of both ' x ' and ' n ' are determined empirically. After study of various formuke the equation W = xL '~ was found to be sufficiently accurate.

226 Hamid Khan and Amjad Hussain

(v -- M) ~ -~ Sum of squared deviations from the mean. N = Number of cases.

0 SEMi- ~ • ,

where

(2)

SEM ---Standard error of the mean 9 = Standard deviation.

N = Number of cases.

In accordance with these formulae the following table has been formu- lated which gives the weight-length factor, standard deviation, and standard error for the two species of fish mentioned in this paper.

TAnLE I. Showing the weight-length factor, standard deviation and standard error for the two species q f carp

Serml Species of fish I Weight-length Standard Standard No. [ factor deviation error

Labeo rohita "" "i .000238 Cirrhinamrigala .. .000180

.000022891

.00001714 .000003575 ,000002438

The equatic.n W =: xL a can now be applied with reference to tbe above table. If the length of fish is known, its approximate weight can be ascer- tained by multiplying the cube of length of fish with the weight-length factor for that particular species of fish. The average weight of fish under a given centimetre length is shown in Table II.

Conclusion

It will be seen from the tables that the weight for a given length differs in the twospecies considerably and so does the increment of growth for a certain ihcrease in length. The study gives the following results :--

1. The comparative increase of weight as compared to length is more in Labeo rohita than Cirrhina mrigala.

2. If form and specific gravity remain constant, the weight of certain species of fish tends to increase approximately to the cube of its length.

3. The weight (in chhatanks) of the following species of fish can be known at a certain length (in centimetres) by multiplying the cube of the length with the weight-length factor, which is approximately as under:

(i) Labeo rohita . . . . . . . . .000238 (ii) Cirrhina mrigala . . . . . . . . .000180

TABLI~ II. Showing average weight offish at each centimetre of le.,tgth for 822 fishes studied from March 1938 to December 1942

Species of Fish

T otai length Labeo rohita Cirrhina mrigala in

een.timetres Average No. of Average No. of weight in fish weight in fish chhatanks stu died chhatan ks studied

13 14 15 16 17 18 19 21 28 30 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 7O 71 72 73 74 75 76 77 78 80

.5 -7

1.0 . ~

~-o . .

~

. .

16:5 ~

~

16:o ~

~

o .

. ~

. ~

o .

2 i :0 27.0 28.0 29.0 29.8 33 -0 36.0 37.0 39 -0 42.0 43.0 45.0 48.0 49.0 53.0 53 -0 59.0 65.0 65 -0 71.0

7 i :9 77.0 90.0 95 .o 97 .o 99.8

lO2.O lO4.O 11o.o 116.o 128 .o

Total

2 2 1

. .

. .

. ~

. .

"i ~ 1 7 6

~

i ~ 1 7 6

. .

~ 1 7 6

. .

~

~

. ~

"i 6 3

16 25 33 29 12 22

3 12 13 13 13 14

6 10 5

17 8

14 13 9 3 5 7 6 3 5 3

350

'~62

i;o 1.0 l.O 1.0 1.5 3.5

~.o 6.0 7.4 8.1 8.3 8.9 9.2 10.0 11.0 12-3 12.8 13.4 15.1 16.9 17.4 18.0 18-6 20.6 21.5 24.0

. .

29:0 30.0 31-4 31.7 33.8 35.1 37.4 38 -3 39.1 41.9 43.6 46.7 53.4 54.2 58 -9 60.8 65.6 71.3 77.8

8 i :4

8fi:3 90-5

99:5

Total

i I 2 1 I 2

1 9

10 26 34 16 18 31 10 10 11 6 5 5 3 9 5 7 9

~

i 2

10 9 9 8

16 9

10 19 12 26 10

8 10 6

18 16 12

2 "i

472

228 Hamid Khan and Amjad Hussain

These observations are quite sufficient to show that there is a definite relationship in length and weight of the species of fish studied.

Crozier, W. J., and Hecht, S.

Davenport and Ekas

Fulton, T. Wemyss

Hile, Ralph

Hora, S. L.

REFERENCES

.. " T h e weight-length relationship on the California sardina (Sardina caerulea)," State o f California Fish and Game Commission, Fish Bull., 1925, 12. 5-59.

.. "Correlat ion of weight, length and other body measurements in the weak fish (Cynoscion regalis)", Bull. U.S. Bur. Fish., 1915, 33, 139-47.

.. Statistical Methods, 4th Edn., 1936, 29-37.

.. " O n the ra~e of growth of fishes," 22nd Annual Report o f Fisheries, Board of Scotland, 1904, 3, 141-240�9

.. " A g e and growth of the cisco, Leucichthys artedi Le Suer, in lakes of the North-eastern highlands, Wisconsion", Bull. 19 Bur. Fish., Washington, 1936, 48, 211-37.

�9 " T h e Game Fishes of India, Part VIII. The Mahseer or the large-scaled Barbels of India. The Putitor Mahseer, Barbus (Tor) putitora (Hamilton)," J. Bomb. Nat. Hist. Soc., 1939, 41, 272-85.

.. " T h e weight-length relation in fishes," Proc. Nat. Acad. o f Science, Washington, 1928, 12, 922-25.

. . The Angler's Handbook for India, 4th Edn., 1905, 74-75, Newman and Co., Calcutta.

.. " A n ecological reconnaissance of the fish of Douglas Lake," Contribution from the Zoological Lab. of the University of Michigan, 143, Bull. U.S. Bur. Fish., 1913, 33, 215--49.

. , Principles o f Biology, 1898, 1.

�9 The Mighty Mahseer and other Fish, Hints to Beginners on Indian Fishing, 2nd Edn., 1906, 193-94, Higginbotham & Co., Madras.

" G a m e Fishes of Bombay, the Deccan and the Neigbboutivg Districts of the Bombay Presidency," Jour. Born. Nat. Hist. Soe., 1933, 36, 29-66.

�9 "Fo rmu la for estimating weight of Mahseer," ibid., 1925, 30, 711-14.

. . The Rod in India, 3rd. Edn., 1898, Thacker Spink & Co., Calcutta.

Keys, Aneel B.

Lacey and Cretin

Reighard, Jacob

Spencer, Herbert

Skene, Dhu

Spence~ R�9 and Prater, S�9 H. . �9

Trevenen, W. B.

Thomas, H. S.

Clark, Francis N.