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THE GROWTH OF FISH

II. THE GROWTH-RATE OF THE EMBRYO OF SALMO FARIO

BY J. GRAY

King's College, Cambridge.

(From the Zoological Laboratory, Cambridge.)

{Received July 7th, 1928.)

(With Seven Test-figures.)

ACCORDING to Minot (1908) the amount of new tissue formed per gram of mammalian embryo per unit time falls with decreasing velocity as the embryo gets older, so that for very young embryos this specific growth-rate is astonishingly high, whilst the decrease in its value is not in any obvious way associated with a scarcity of the raw materials for growth. How far such an inherent decline characterises the specific growth-rate of a cold blooded animal is entirely unknown. Within more recent years, Robertson (1923) has suggested that the growing period of an animaFs life can be resolved into one or more independent cycles and during each of these cycles the growth-rate is controlled by two factors. One of these factors is always proportional to the size of the organism, and therefore constantly increases; the other factor is a linear function of the size of the organism, but decreases as the animal grows, so that the rate of growth (Bx/St) is proportional to x (a -- x) where x is the weight of the organism and a is a constant representing the maximum weight reached by the animal at the end of a particular phase of growth. If this be so, it follows that the growth-rate must reach a maximum when the animal is half grown.

Since the larvae of the trout can be obtained in very large numbers and can be incubated under strictly controlled conditions, they provide a most suitable material for investigating the precise nature of a growth-curve as far as this is a practicable operation (see Gray, 1928).

The material for each experiment in the present work consisted of carefully selected ova of Salmo fario all of which were of approximately the same size and all of which were fertilised on the same day and incubated under strictly controlled conditions of water supply and temperature. For the determination of each observation in Fig. 1 and Table I 100 eggs were removed from the hatchery at various moments, anaesthetised with ether, dried on filter paper under standard although arbitrary conditions and weighed. The embryos were then carefully dissected away from the yolk sac and weighed separately. For observations of the weight of the embryo prior to hatching it was found necessary (owing to the fragility of the embryos) to harden the eggs for some hours in dilute formalin

The Growth of Fish

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before starting a series of observations; after hatching only fresh material was used. Since the percentage of water in the embryo remains constant at about 16 per cent., and that in the yolk at 41 per cent. (Gray, 1926), it was deemed unnecessary to determine the dry weight of embryos by direct methods. As the size of an embryo depends on the size of the whole egg, it was thought desirable to test the variability of the material by selecting from time to time 100 larvae, and weighing the embryos in ten samples of ten each. In this way it was found that when calculated from the mean weight of 100 embryos, the weight of a single embryo could be assumed to be correct to the third place of decimals. For the sake of convenience all the weights given in this paper represent those of 100 individuals selected at random.

0 10 20 30 40 50 60 70

100

Days after fertilisation

Fig. 1. Growth-curve of embryo of Salmo fario incubated at io? C. The ordinates represent the wet weight in grams of 100 embryos.

A consideration of Fig. 1 reveals the fact that the growth-curve is not symmetrical about its central point (i.e. when the embryos are half grown and weigh approximately 7-0 gm. per 100). It is obvious that for approximately 55 days (when incubated at io? C.) the curve is markedly convex to the time axis; it then remains more or less linear until 80 days, after which it suddenly becomes concave until development is complete at 100 days after fertilisation. The details of this curve are best seen from Table II and Fig. 2, in which are plotted the successive four-daily increments at different periods; it will be noticed that the period of maximum

J. GRAY

growth-rate occurs between 69th and 73rd days, since 100 embryos form 1*7 gm. of new tissue during this period, and at that time they weigh approximately 9-5 gm.

Table I.

Days after fertilisation. T=io?C.

28

34

42

47

5i

57

61

65 69 73 77

81

85 89

92 100

1

Wet weight of 100 embryos

in grams

0-438 0-869 1-254 2-060 2-861 4-135 5-654 7-026 8-567 10-274 n-6o6 12-675 13-294 13-438 13-840 13-983

100l-

0 10

70 80 90 100

Days after fertilisation

Fig. 2. The increment in wet weight of 100 embryos in successive periods of four days. Note that the curve is asymmetrical, reaching a maximum about 71 days after fertilisation.

at the middle of the period (71st day); in other words, the velocity of growth reaches

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a maximum when 70 per cent, and not 50 per cent, of the total growth has been accomplished.

As explained elsewhere (Gray, 1928) it is exceedingly dangerous to base a conception of the factors controlling growth on the form of the growth-curve. In this particular case, however, it is possible to proceed to some extent from first principles.

Table II.

Increment in grams wet weight

of embryo in four days

Day

Absolute

% maximum

increment

increment

30

43

47

51

\

55

59

63

67 71

75

79

83

87

91

O'2

12

o-5

30

0-7

40

o-8

47

i-o

59

i'3

77

1-4

82-5

1'5

88

1-7

100

1'3

77

1-1

69

c-6

35

O-2

12

O-2

12

The increments are those observed during the two days prior to and succeeding the days given in column i.

There are two obvious variables during incubation, (i) the increase in size of the

growing embryo, (ii) the decrease in the amount of available yolk. During larval

life all the tissues are growing, and although they are not all growing at the same

relative rates, the changes in the proportions of the various organs do not appear to be

great except where the total weights of the organs are veiy small. The muscles, skin

and cartilaginous skeleton all maintain roughly the same proportions during the period

of larval life here considered. If this be true, we can look upon the embryo as a system

whose heterogeneity is not changing very markedly (see Gray, 1928) and which repre-

sents therefore a natural entity of growth, whose growing powers are proportional to

the total size. As the embryo grows, so the amount of yolk in the yolk sac decreases,

and it is clear that the period of slow growth between the 80th and 100th day is

characterised by a small yolk sac which is rapidly decreasing in size. It is, therefore,

conceivable that the rapid decline in growth-rate towards the end of incubation is

correlated with a scarcity of the raw materials for growth, this suggestion being

supported by the fact that the growth-rate rapidly rises again as soon as the young

fish begins to take in extraneous food. Confirmatory evidence correlating growth-

rate with the amount of yolk available is derived from the fact that the absolute size

of an embryo at a given age is dependent on the size of the newly fertilised egg.

Small eggs give small embryos, large eggs yield large embryos. If a fine ligature is

attached to the posterior end of the yolk sac, the position distal to the ligature

becomes opaque and falls off; the resultant larva completes its development and

o

BJEB'Vlil

?

GRAY

is normal in all respects except that it is consistently smaller than it would have been

had the full amount of yolk been available.

At any particular moment the yolk which is passing into the embryo is being

used for two distinct processes, (i) to maintain the respiratory and other katabolic

processes of the tissues, (ii) to form new tissues. Let us assume for the moment

that the rate of growth of the embryo (Bx/St) is proportional to its dry weight (x)

and to the amount of dry yolk (y) available

$x ,

...

?t = k.x.y

(l).

If, however, the amount of yolk required for maintaining the embryo has an

average value of k? per gm. of embryo1, then the rate of disappearance of yolk

(-- Syfit) is given by equation (ii)

i

If x = x0 when y = y0, then equation (ii) can be integrated in the form of equation (iii)

k(x + y) k(x + y) fclog ? ^

At the beginning of development when y0 is the total yolk in the unfertilised egg, x0 is very small so that, if k^ = k^k, equation (iii) can be written

~ ge

y i

and at the end of incubation when y -- o the weight of the embryo is given by

equation (v)

x = yQ-k2\ogey? , 2

(v),

and from this k2 can be calculated.

If the underlying assumptions are justified, it follows that it is possible at any

moment during development to express the weight of embryo in terms of the

amount of yolk remaining in the yolk sac, or (what is more useful) the weight of

the whole larva in terms of this yolk or in terms of embryo. The dry weight

of the whole larva is obviously x + y, and if we substitute for x the value given in

equation (iv) we get a value for the dry weight of the larva in terras of yolk.

If, instead of calculating the dry weight of the larva, we determine its wet

weight, then

Wet weight ot larva = -?- -\

?

Substituting for x the value given in (iv)

io 41

yo -- y -- h logye ^+5 ? + 2-443;

= 6-25^0 - 3-813/ - &2$h k g ^ r n r

1 The rate of oxygen consumption per gram of embryo is constant from 46th~7oth day of incubation at io?, after which it declines under the particular conditions which existed during the measurements (Gray, 1926).

The Growth of Fish

115

Equation (vi) is of importance because, if the initial assumptions underlying equation (ii) are sound, it shows that the wet weight of the larva should reach a maximum before the embryonic growth cycle is completed; there ought to be a period towards the end of the larval life when the wet weight of the larva is decreasing although the wet weight of the embryo is still increasing, whereas during the major portion of incubation the wet weight of both will increase. From equation (vi) it follows that the wet weight of the larva will increase as the embryo grows until the wet weight of yolk left in the yolk sac is reduced to i*56^2,1 after which the wet weight of the whole larva will decrease although that of the embryo continues to

15-0r-

10 20 30 40 50 60 70 80 90 100 Days after fertilisation

Fig. 3. Growth-curve of the whole larva (embryo + yolk). The ordinates represent the wet weight in grams of 100 larvae. Note that the larva reaches a maximum weight at about the 85th day of incubation whereas the embryo continues to increase in weight until 100th day (see fig. 1). The curve indicates the theoretical values obtained from equation (vi). The dots are observed values.

increase. At io? C. k2 = 0*55, so that the maximum weight of the larva should be reached when there are o-86 gm. of yolk still unconsumed; the amount actually observed was I-IO gm.

Again, if the initial assumptions are sound, the size of the embryo at the end of

1 If z =ay0 --by --ak^ log^eyr^r* then z reaches a maximum value when y = - ^ -- h - *n equation (vi) a =6*25, b =3-81, hence x is a maximum when y =1*56 k%.

8-2

n6

J. GRAY

incubation will decrease with increasing values of k2. Now it is very unlikely that both k and kx will be equally affected by changes in temperature, so that if the temperature be changed there ought to be a measurable difference in the size of the young fish at the end of the larval phase. We have, therefore, two definite qualitative tests of the hypothesis that the rate of growth of a unit weight of embryo is proportional to the amount of yolk available.

The wet weight of the whole larva as determined by direct observation is shown in Fig. 3 and Table III. It is quite clear that the larva attains a maximum weight

Table III.

Days after fertilisation

34 42

47

5i

57

61

65

69 73

77

81

85.

92

100

Wet weight of 100 larvae

8-75

9-20 9-40 10-04 10-27 10-39 11-98 12-77 13-84 I4-25 14-56 14-63 14-22 13-98

Wet weight of 100 embryos in gm.

0-87

1-25 2-06 2-86

413

5-65

7-03 8-57 10-27

n-6r

12-67 13-29 J3'44 13-98

about fifteen days before the embryo itself ceases to grow. This period represents a time when the wet weight of the yolk being used up for maintaining the embryo is greater than the wet weight of larva being formed. The observed facts give, therefore, a considerable measure of support to the original assumptions here made; this support is increased by what follows.

EFFECT OF TEMPERATURE ON THE FINAL SIZE OF THE EMBRYO.

After forty-three days of incubation at io? C. a batch of eggs from a selected female was divided into two groups; one of these was incubated at 150 C , the other at io? C. The temperature of each hatchery was maintained at the required level by a supply of water running from a suitable thermostat, and contained the bulb of a recording thermometer. As soon as the larvae ceased to show a tendency to orientate themselves away from the light but swam actively in the hatchery trays they were removed and weighed in batches of ten. The results are recorded in Table IV.

A confirmatory experiment was carried out with another batch of eggs incubated at three different temperatures (Table V). The mortality was high at 17-5? C , whereas at lower temperatures it was negligible.

It is clear that the higher the temperature the smaller is the final size of the embryo at the end of incubation, although at the higher temperature the process of incubation is markedly accelerated (see Gray, 1928 b). This result is obviously

The Growth of Fish

117

in harmony with the assumption that the rate of growth of the embryo is proportional to its size and to the amount of available yolk. By raising the temperature the value of 1% is increased, or in other words the temperature coefficient of the process of maintenance is higher than that of actual growth.

Table IV.

Wet weight in grains of different samples of 10 fish at the end of incubation

15? C.

io?C.

1-420

1-3667 1-387 i*3oo i'245 i-3oo I-35O 1-306 1-3^5 1-360 1-230 i'35? i*3O5

i'33O 1-370

i*37o

1-482 1-605

1-623 1-464 1-426 1-426 1-503 i*495 i*535 1*485 1-480

1-546

1-520 1*466

1-467

Mean weight of 100 fish

13*35 dbo?i6

15*07 -fco'i8

Table V.

Temperature of incubation

Wet weight of 100 larvae at the end of incubation

5?C

13*3

9?C.

11-6

17*5? C,

9'2

Table VI.

Temperature

Maximum density of bacteria

Time in days required to teach. maximum density

i7?C.

18,272,000

8

15,164,000

5

37?

10,448,000

3

These results form a striking parallel to those observed by Graham Smith (1920) for the effect of temperature on the rate of growth and maximum density of a culture of bacteria. The higher the temperature, the lower is the maximum density reached in a given culture medium, although the characteristic maximum is reached more quickly at the higher temperatures (Table VI). The value of this maximum depends also on the concentration of nutrient material in the medium.

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