## ABSTRACT

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 animal’s 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 (*δx*/*δt*) 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 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.

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 10° 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 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. at the middle of the period (71st day) ; in other words, the velocity of growth reaches 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.

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 very 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 represents 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 is normal in all respects except that it is consistently smaller than it would have been had the full amount of yolk been available.

*δx/δt*) is proportional to its dry weight

*(x)*and to the amount of dry yolk (

*y*) available

*k*

_{1}per gm. of embryo

^{1}, then the rate of disappearance of yolk (

*δx/δt*) is given by equation (ii)

*y*

_{0}is the total yolk in the unfertilised egg,

*x*

_{0}is very small so that, if

*k*

_{2}=

*k*

_{1}

*/k*, equation (iii) can be written and at the end of incubation when

*y*= o the weight of the embryo is given by equation (v) and from this

*k*

_{2}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 terms of yolk.

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 1·56*k*_{2},^{1} after which the wet weight of the whole larva will decrease although that of the embryo continues to increase. At 10° C. *k*_{2} = 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 1·10 gm.

Again, if the initial assumptions are sound, the size of the embryo at the end of incubation will decrease with increasing values of *k*_{2}. Now it is very unlikely that both *k* and *k*_{1} 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 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 10° C. a batch of eggs from a selected female was divided into two groups; one of these was incubated at 15° C., the other at 10° 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 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 *k*_{2} is increased, or in other words the temperature coefficient of the process of maintenance is higher than that of actual growth.

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.

It has now been shown that the assumed proportionality of the specific growth-rate to the amount of yolk in the yolk sac is in harmony with two distinct pieces of qualitative evidence, (i) the maximum wet weight of the larva is reached before the embryonic growth cycle is completed, (ii) the final size of the embryo varies with the temperature of incubation. We may now proceed to inquire how far the observed growth-rate of the larva runs parallel to the observed amount of yolk available.

## CORRELATION OF SPECIFIC GROWTH-RATE WITH AMOUNT OF YOLK AVAILABLE

It has already been shown that the maximum growth-rate of the embryo is attained at about the 71st day of incubation at 10° C., and when the embryo is about 70 per cent, of its final size. If equation (i) is correct, then the product of dry yolk and dry weight of embryo should also reach a maximum on the 71st day. The two variables were measured by direct experiment and the results are recorded in Table VII.

The parallel between the total growth-rate and the product of embryo × yolk is illustrated in Fig. 4. It is clear that both these values reach their maximum when the embryo is about 70 per cent, of its full size, at about 7ist–73rd day of incubation. It should, however, be noted that precise determinations of growth during short periods of time are not easy to obtain.

The asymmetrical nature of the growth-curve is readily seen in Fig. 5 where the growth-rate is plotted as a function of the size of the embryo. The dotted curve is that derived from Robertson’s formula ; it is symmetrical and reaches a maximum when the embryo is half its full size. The curve derived from equation (iv) on the other hand fits the observed data and reaches a maximum when the embryo is 70 per cent, completed (*x* = 1·65).

## THE “EFFICIENCY” OF DEVELOPMENTAL PROCESSES

_{0}= 3·36 and

*k*

_{2}= 1 =·0 (the approximate value characteristic of incubation at 15° C.) we get

The fall in the “efficiency” with advancing periods of development is seen when the values are calculated for successive periods (Table VIII). Thus for the first half gram of yolk which is used, there are formed 0·38 gm. of embryo giving an efficiency of 76 per cent., whereas for the last half gram of yolk used there are only 0·095 gm. of embryo formed with an efficiency of 19 per cent. In actual practice it is doubtful how far the available data are sufficiently accurate to calculate these percentages for short periods with any degree of precision. It is quite clear, however, that no single value can represent the efficiency of development at all periods of incubation. The facts simply indicate that development is an extremely efficient process (not much less than 100 per cent.—see Gray, 1926) and that, owing to the necessity for maintaining the embryo once it is formed, only two-thirds of the original yolk in the fertilised egg is actually converted into embryonic tissue.

## DISCUSSION

The available facts indicate the possibility that the growth-rate of the trout’s embryo is proportional to its mass and to the amount of yolk in the yolk sac. This conclusion is based on three main facts. Firstly, the final size of the embryo at the end of larval life is determined by that quantity of yolk in the newly fertilised egg which will not be required for maintaining the embryo during its period of life. At any instant, the growth-rate per gram of embryo is proportional to the amount of yolk available (Fig. 6). Secondly, the very characteristic decline in the wet weight of the whole larva which is shown to occur towards the end of incubation furnishes independent, although not conclusive, evidence that the decline in the growth of the embryo during this period is the result of a diminished supply of yolk. Thirdly, when incubation is carried out at higher temperatures the final size of an embryo is less than that of an egg incubated at lower temperatures. It is interesting to note that the growth-rate during larval life is determined for any given temperature by food supply, just as is the case during post-larval life.

The facts described in this paper show a striking parallel between the processes of growth of a fish embryo with those displayed by a culture of bacteria. In both cases we are dealing with an increasing population of cells growing at the expense of a limited amount of food. The food is being used for two purposes—the maintenance of the growing cells and for the production of new cells or tissue. If, in either case, the expenditure of food for the purpose of maintenance is made more intense by raising the temperature, the less food is available for the production of new tissue and the smaller is the amount of new cells or tissue formed before all the food has been utilised. In order to produce the maximum amount of tissue, incubation should be effected slowly by lowering the temperature.

Although the known facts clearly harmonize with the simple assumptions here made, there are certain criticisms which cannot be ignored. Firstly, it is by no means obvious why the growth-rate should be proportional to the total weight of the yolk in the yolk sac. Very little is known of the mechanism of yolk absorption except that it appears to be effected by the syncytial wall of the yolk sac and the nutritive material conveyed to the embryo by means of the large vitelline vein. One would have expected that the amount of yolk reaching the embryo would be determined by the mass of the syncytium and not of the yolk; if the thickness of the absorptive membrane remains constant, the amount of yolk reaching the embryo might well be proportional to the surface of the yolk rather than to its mass. Since the yolk sac does not remain spherical and no pertinent information is, as yet, available concerning the syncytial wall, the validity of this criticism is not easy to assess. Secondly, when the embryo is large and the amount of yolk is small, there is little doubt that the growth-rate falls for lack of food, but it is not altogether clear why this should also be the case when the embryo is very small and the amount of yolk large. One would expect, in the latter case, that food is present in excess and is not a critical factor controlling the specific growth-rate. Here, again, it is not easy to test this suggestion since determinations of the growth-rate of very small embryos are not easy and the error introduced by a factor which varies with the amount of yolk is not large until the embryo is of a considerable size. Finally, it must be remembered that the quantitative analysis carried out in this paper assumes that the rate of growth is also proportional to the weight of the whole embryo. In other words it is assumed that, although all the tissues are not growing at a uniform rate, the proportion of one tissue to another does not change materially throughout development. This, of course, is only true within limits. Until further data are available one can only suppose that the errors due to the three above causes are either small or cancel one another, leaving the possibility of correlating the growth-rate with the simple variables expressed by the total amount of yolk available and by the weight of the whole embryo.

Two secondary points may now be considered. Firstly, it will be noted that the departure of the observed growth-curve from the type advocated by Robertson is due to the fact that all the yolk is not converted into embryonic tissue. That the observed curve of growth cannot be expressed by Robertson’s formula is clearly established, and the fact that the growth-rate rises again as soon as the larval fish takes in extraneous food makes it unnecessary to postulate any fundamental difference between the factors controlling larval and post-larval growth. Secondly, the specific growth-rate when plotted against age does not fall with decreasing acceleration as was suggested by Minot and later implied by Murray (1925) for chick embryos. The specific growth-rate falls first with increasing acceleration and then with decreasing acceleration giving a sigmoid curve illustrated by Fig. 7. It would be interesting but difficult to confirm this conclusion by direct observation of the rate of growth in the very early stages of segmentation. If the present analysis is sound, the potentialities for growth of embryonic fish tissue do not materially decrease with age. The specific growth-rate of the embryo decreases because there is a reduction in the rate at which the tissues are supplied with the raw materials for manufacturing new tissue. It is possible, however, that there may be also a slow decline in the true potentiality for growth the effect of which is swamped by the much greater effect exerted by a declining supply of yolk. From a preliminary study of post-larval growth it would appear that such a decline in potential growth-rate occurs in later life.

## SUMMARY

The growth-curve of the embryo of

*Salmo fario*is asymmetrical and inflects when the embryo has completed approximately 70 per cent, of its development.For any given temperature of incubation the final size of the embryo is proportional to the total amount of yolk present in the newly fertilised egg. If the amount of yolk is reduced experimentally the final size of the embryo is reduced, but its morphological form is normal.

- The growth-rate of the embryo is shown to be proportional to its own size and to the amount of yolk in the yolk sac. Assuming that the amount of yolk required for the maintenance of a gram of embryo at all periods of its life is constant, the dry weight of the embryo
*(x)*can be expressed in terms of the yolk in the yolk sac*(y)*by means of the equation where*y*_{0}= the dry weight of yolk in the newly fertilised egg, and where is a constant which alters with the temperature of incubation. On theoretical grounds there should be a period towards the end of incubation when the total wet weight of the larva is decreasing, whereas the wet weight of the embryo is still increasing. This is shown to be the case.

If the temperature is raised, the final size of the embryo at the end of incubation is reduced. This fact is also deducible from the initial assumption that the specific rate of growth is proportional to the amount of yolk available.

The factors controlling the specific rate of growth of a fish embryo are, therefore, (i) temperature, (ii) food,

*i*.*e*. the amount of yolk in the yolk sac. These two factors operate in precisely the same way as on a culture of bacteria, and it may be concluded that the processes of metazoon growth*in vivo*are similar to those of bacteria.The so-called “efficiency” of development falls as incubation proceeds, and no single figure holds good over more than very limited periods.

## Bibliography

*Journ. of Hygiene,*

*Brit. Journ. Exp. Biol.*

*Brit. Journ. Exp. Biol.*

*Journ. Gen. Physiol.*

*Chemical basis of growth and senescence.*

^{1}

The rate of oxygen consumption per gram of embryo is constant from 40th–7oth day of incubation at 10°, after which it declines under the particular conditions which existed during the measurements (Gray, 1926).

^{1}

If then *z* reaches a maximum value when . In equation (vi)*a* =6·25, *b* =3·81, hence *x* is a maximum when *y* =1·56 *k*_{2}.