31. Relative Growth in Amphibia
Authors: March F. 
Published: August 2010

Summary.
The length of the hind limb of R. temporaria bears to the body length a linear relationship, which can be expressed by the equationy=ax+b.There is a change in the value of the constants a and b at a point which marks the onset of puberty in the female.
The weight of amphibians as deduced from mean group measurements of R. temporaria, T. cristatus, S. maculose, A. tigrinum, and R. esculenta tadpoles, can be expressed in terms of length by the equation y=bxα, where y=weight, x=length, and b and α are constants.Puberty is again clearly indicated, especially in the female frog,*by a change in the constants, giving a sudden upward inflection to the curves, and by an increase in the form index, 3√w/L.
This equation is not a cubic function, though during certain phases of development in the frog it may approximate to one. Animals become relatively stouter or heavier, or alternatively slimmer and lighter, with increase in absolute size, according as to whether the exponent a exceeds or falls short of 3.
Regression of weight on length, as expressed by the formula y=bxα, is not a case of simple allometry, but it may be regarded as the compounded result of the sum total of allometries concerned in the growth of individual parts, organs, and tissues.
Close calculations of the weight appropriate to a given length can also be made on the basis of the compound interest law, y=bpx, in which y=weight, x=length, and b and p are constants. The equation is really an exponential function in time, but since time observations were impossible under the conditions of experiment, length was substituted in the formula on the assumption that the length of an animal is approximately proportional to its physiological age. The close agreement between actual and calculated values in all the species examined supports this inference, and suggests that the law itself is valid over the central and longest phase of active growth.
The greater gross weight of the female frog, both absolutely and relatively to length, as compared with the male is due to the enormous development of the ovaries and oviducts after puberty. When the weight of the reproductive organs is deducted a length‐by‐length comparison shows that on net body weight the male is heavier than the female.
The weight of R. temporaria is subject to a seasonal fluctuation which is correlated with the physiological condition and the sex cycle. It is at its maximum immediately after hibernation, and least in summer during the period of greatest activity. The variation in weight is due in the main, though not entirely, to changes in the reproductive organs. The season itself exercises a direct influence on the condition of the animals, which is evidenced by changes in liver weight and in residual body weight after subtracting the weight of the reproductive organs. The cycle closely parallels that of the cod gs worked out by Graham (1923).
SUMMARY.
The seasonal fluctuation in the body weights of amphibians, previously noted, extends to the weights of the viscera. All organs examined, with the exception of the testis, are heaviest in spring and lightest in summer. The testis reaches maximum weight in autumn, i.e., just before hibernation. After the breeding season the reproductive organs of both sexes regress to juvenile proportions. It is suggested that the exception in the case of the testis is due to the transference of spermatozoa to the seminal vesicles in early spring.
There is a sex difference in the weights of liver and kidney. In Rana both organs are slightly larger in the female; in Triton and Salamandra livers are markedly heavier in the female and kidneys in the male.
The increase in the weights of testis, ovary, oviduct, ovary and duct together, kidney, and liver relative to increase in net body weight is fairly represented by the equation for simple allometry, y=bxα.
The mature reproductive organs show distinct positive allometry in Rana, Triton, and Salamandra, whilst allometry is negative for immature and spawned ovaries in the frog. The relative growth‐curve for mature ovaries after involution is continuous with that for immature ovaries, and the same equilibrium constant applies. The number of ova produced increases with the size of the animals in an allometric manner, and the higher equilibrium constant for mature unspawned ovaries is traceable to this cause.
The growth of liver and kidney over the ranges covered by the data is virtually isometric with that of the body in the frog. In newts the kidney shows negative, and in salamanders positive allometry; whilst allometry of the liver is positive for the males and negative for the females. In both species the relative growth‐rates of liver and kidney with respect to body growth appear to be higher in the male.
The onset of puberty is clearly delineated by changes in the slopes of the curves for limb‐length/body‐length and weight/length by wide and sudden upward leaps in the allometry graphs for the reproductive organs of the female, and by an increase in the form index. This occurs in Ram at round about, 7 gm. body weight and 11.5 cm. total length.
The allometry constants b and α as employed in the regression formulæ of weight/length as well as in the allometry equations proper show both sex and seasonal variation.
Hersh's equation b=Bεrα, connecting these constants, is found to hold in respect to the weight/length relationship of the frog.
Certain theoretical aspects of the allometry equation are discussed.
Summary.
Under conditions of partial or total inanition the behaviour of amphibians in respect to weight reduction is, during the earlier phase, as though the total weight could be resolved into wasting and non‐wasting fractions, the decrease in the former following a logarithmic curve of the typey=bpx, or y=bε‐ax,where y=the magnitude of the wasting component at any time, b=its initial weight,p=the daily decrement factor, and x=time in days.
The value of the non‐wasting fraction (K) is higher for partially fed than for completely starved animals and for large than for small frogs.
After the first few weeks there is apparently an acceleration in the rate of weight loss, and the possible biological significance of this is discussed.