1. Male Ligia oceánica were used in an investigation of the relationship of body size to rate of oxygen consumption and pleopod beat.

  2. Animals varied in weight from 0·04 to 1·03 g. and from 0·95 to 3·1 cm. in length.

  3. Body shape does not change significantly over the size range, for length and breadth both increase at the same rate, and pleopod dimensions bear a constant relation to body length.

  4. Specific gravity also is constant, for the relation of body weight to the cube of body length shows no trend with increasing size.

  5. Oxygen consumption per gram decreases with increasing size and is proporitional to the –0·274 power of body weight. Total oxygen consumption is therefore proportional to the 0·726 power of body weight; but this value does not differ significantly from two-thirds.

  6. As shape is constant, surface area is proportional to the square of a linear dimension. It is shown that oxygen consumption per unit of length2 is constant over the size range. Although body length was measured far less accurately than body weight it is shown that it assesses ‘body size’ more accurately.

  7. Rate of pleopod beat was measured at 15 and 25° C. ; it decreases with the size of the animal. At 15° C. time per beat varies as the 0°66 power of body length, and at 25° C. as the 0·59 power; neither of these values differs significantly from 0·5. Despite the fact that pleopod movement is heavily damped, the rate therefore varies like that of a pendulum.

  8. Theworkof Fox (1936–9) and Fox et al. (1937a) on the rate of oxygen consumption of animals from cold and warmer seas and from different habitats is considered. It is suggested that many of their comparisons are invalidated by differences in body size of the animals concerned, and that, in relation to environment, no basis, theoretical or experimental, has been established for a distinction between ‘non-locomotory’ and ‘activity’ metabolism.

The experiments on which the present paper is based were completed in 1938 at University College, London, but for a variety of reasons it has been impossible to prepare the results for publication until now. I had just completed an investigation of the oxygen consumption of prepupae of Drosophila melanogaster and had demonstrated the inadequacy of ‘body-weight’ as a standard of comparison; in fact, the rate of oxygen consumption was shown to be proportional to the surface area (Ellenby, 1937, 1945 a). It seemed desirable to examine this relationship in other poikilothermal animals ; there are numerous cases in which workers have commented on a fall in metabolic rate with increasing body size, but extremely few in which the relationship has been investigated. Clearly, if it is general for the metabolic rate of cold-blooded animals to vary with the size of the animal, it is important for an understanding of metabolic processes that the relationship should be investigated; it might also be of importance for an understanding of aspects of mammalian physiology. Moreover, if the phenomenon were general, control of the ‘size factor’, rarely considered, would be a first demand in work in which the metabolic rates of different animals are compared. It is for these reasons that the present work was originally undertaken; despite the lapse of time and in spite of the excellent work in this field of Weymouth and his school (Weymouth, Crismon, Hall, Belding & Field, 1944), it is felt that these arguments have lost little of their force.

Ligia oceanica is a very convenient animal for an investigation of this sort. It has a simple shape, can be kept relatively easily in the laboratory, and, for an isopod, has a large size range. The movement of its pleopods has been studied by a number of workers (Nicholls, 1931; Numanhoi, 1933, 1937; Fox & Johnson, 1934; Johnson, 1936), but in no case has the effect of size been investigated. As it was noticed that the rate of beat varied with the size of the animal, it was thought that such an investigation would be of interest in relation to the distinction drawn by Fox (1936) between ‘non-locomotory’ and ‘activity’ metabolism of animals from northern and temperate waters.

The specimens were obtained from Drake’s Island, Plymouth.* In the laboratory they were kept in small groups in covered finger-bowls, with seaweed and a piece of cotton-wool soaked in sea water; the bowls were kept in semi-darkness. Like Numanhoi (1933) I found that animals would survive under these conditions for a considerable time. To avoid complications due to possible sex differences only males were used in the experiments described ; they reach a larger size than females.

Linear dimensions

Primarily the object of this research was to assess the relative values of ‘body weight’ and ‘surface area’ as standards for comparing the oxygen consumption of animals of different size. The ‘surface area’ it may be possible to measure, however, will differ considerably from the true ‘surface area’ (Ellenby, 1945a); what is measured is something porportional to the true surface. To use the two-thirds power of the body weight for estimating surface area would be to assume that the animals were constant in shape and specific gravity over their size range. If their shape is constant, however, the task is much simpler, for ‘surface area’ will then be proportional to the square of a linear dimension.

Accordingly, the ‘length’ and ‘breadth’ of experimental animals were measured; ‘length’ excluding uropods and antennae, and ‘breadth’ being the greatest width of the fourth segment. The animals were measured live as they are flaccid when dead, a lantern slide of a piece of millimetre ruled paper constituting both ruler and method of holding the animal; it could be swivelled round until squared up and the dimensions then read off to the nearest mm.

Pleopods of other animals were measured. The ventral ramus of the right third pleopod was mounted in Euparal, and the greatest distance across its short axis measured with a calibrated eyepiece micrometer. As the pleopod is normally held at right angles to the axis of the body, the dimension measured corresponds to the effective length of the beating organ, although, in fact, it is the morphological breadth.

Oxygen consumption

Animals were starved overnight prior to measurement of oxygen consumption. Measurements were made with an apparatus of the Haldane constant-pressure type already described (Ellenby, 1938) in which 1 cm. of the scale was equivalent to 0·0146 c.c. of dry oxygen at S.T.p. The pots, however, were considerably larger than in the earlier model and accommodated the animals on their floor. A tube cemented to each stopper was flanged and turned back at its distal end to form a shallow trough; a strip of Whatman no. 40 filter-paper wound round each tube rested in some potassium hydroxide in the trough and presented a large absorptive surface close to the animal.

The animals normally remained still in the humid atmosphere of the respirometer. In nature they tend to nestle quietly in crevices, and to encourage this during the respiration measurements a small cellophane shelter was provided in each pot. Each was rather like a table with two legs removed on one side; large holes were bored in the ‘table-top’ so that gaseous exchanges could take place freely. Experiments were carried out at 25 ± 0·2° C., each usually lasting an hour varying somewhat with the size of an animal. Animals were weighed on an Oertling automatic balance, and their length and breadth then measured as described.

Pleopod beat

Two series of measurements were made. The first series, at 25° C., was made on animals used in the respiration experiments. Each was dropped into a small glass cell of sea water immersed in the water-bath, and, after a few minutes acclimatization, the time for 20 beats was measured with a stop-watch; this was repeated two or more times.

Other animals were used for the second series, all of them in the same open dish of sea water at a room temperature of 15° C. Each animal was confined to a small numbered perforated cage and the cages shuffled after each determination. By this second method three determinations were made on each of twenty-five animals in less than an hour.

Body form and increasing body size

An animal may remain more or less of the same shape, and yet one part of it may change in proportions. For example, in Carcinus moenas (Huxley, 1932) the relationship of carapace length and carapace width remains constant over a wide range of body sizes; yet both frontal width and dentary width change in proportion to carapace length (Williams & Needham, 1941). In the present case the relationship of body length and width is considered, and then the relationship of body length and pleopod width; this will not show that there is no change in shape, but it will at least show whether it remains reasonably constant with increasing size.

Fig. 1, a double logarithmic plot, shows the relationship of length and breadth for eighty male Ligia ranging in body length from about 1 cm. to just over 3 cm. The regression coefficient for the straight line fitting the data, calculated by the method of least squares, is + 1·027 ; the dimensions kept exactly in step the slope would be 1·0, With a standard error of regression of ± 0·072, P, the probability is, 0·7, a very high value indeed; the difference from 1·0 is therefore not statistically significant.

Fig. 1.

Body length and breadth on a double logarithmic grid. The slope of the line does not differ significandy from 1·0, showing that both dimensions increase at the same rate.

Fig. 1.

Body length and breadth on a double logarithmic grid. The slope of the line does not differ significandy from 1·0, showing that both dimensions increase at the same rate.

In Fig. 2 values for the ratio of pleopod breadth to body length are plotted against body length for twenty-eight animals. Change in shape would be shown by change in the values of the ratio, and the line which fits the data would not be horizontal ; in fact, however, values keep fairly parallel to the abscissa, and analysis gives a regression coefficient of + 0·0147. With a standard error of regression of ± 0·092, P is greater than 0·1, showing that the line does not differ significantly from the horizontal. In this respect also therefore, male Ligia show no significant change in shape with increasing size.

Fig. 2.

Pleopod dimensions in relation to body size. Values of the ratio of pleopod breadth to body length show no significant tendency to change with increasing body size.

Fig. 2.

Pleopod dimensions in relation to body size. Values of the ratio of pleopod breadth to body length show no significant tendency to change with increasing body size.

It may be of interest to mention another example of the constancy of form of this animal. For another purpose, the surface area of the pleopod was investigated. They were projected so that their images could be outlined. It was found that if the degree of magnification of the projector was adjusted so that in a series of animals it was in proportion to body length, the images of their pleopods coincided exactly.

Both analyses, then, show that it is reasonable to assume that male Ligia remain the same shape with increase in body size ; surface area will therefore be proportional to the square of a linear dimension.

Oxygen consumption per unit of weight

Fig. 3 shows the values for oxygen consumption of eighty male Ligia, in mm.3 per mg. wet weight per hour, plotted against body weight; the animals range in body weight from 0·042 to 1 ·027 g. There is considerable variation in the data, but, clearly, on a weight basis, small animals consume very much more oxygen than large animals, the smallest animal examined having a rate of oxygen consumption about three times that of the largest. The curve of Fig. 3 was fitted to values estimated from a linear regression equation calculated from the data by means of a logarithmic transformation. The analysis gave a regression coefficient of –0·274, showing that oxygen consumption, per mg., is proportional to this power of the body weight, or that total oxygen consumption is proportional to the 0·726 power.

Fig. 3.

Oxygen consumption and body weight, arithmetic plot; curve fitted by means of a logarithmic transformation which showed that oxygen consumption per mg. was proportional to the – 0·274 power of the body weight.

Fig. 3.

Oxygen consumption and body weight, arithmetic plot; curve fitted by means of a logarithmic transformation which showed that oxygen consumption per mg. was proportional to the – 0·274 power of the body weight.

Body weight as such, therefore, is unsatisfactory as a standard ; oxygen consumption is proportional not to weight itself but to its 0·726 power.

Oxygen consumption per unit of surface

It has already been shown that surface area is proportional to length2; accordingly values for oxygen consumption, per unit of length2 per hour, were calculated, and these are plotted against body weight in Fig. 4. As in the case of the weight data, there is considerable variation in the data ; but the values apparently keep parallel to the abscissa, that is, they show no tendency to increase or decrease with increasing body size. This the regression analysis confirms, for the regression coefficient is only 0·002, or almost zero. In fact, the standard error of regression is ±0·0019, giving a value for P of 0·3 ; the line fitting the data therefore does not differ significantly from the horizontal.

Fig. 4.

Oxygen consumption and surface area. Values for oxygen consumption, per unit of length2, show no significant tendency to change with increasing body size.

Fig. 4.

Oxygen consumption and surface area. Values for oxygen consumption, per unit of length2, show no significant tendency to change with increasing body size.

Oxygen consumption, then, is proportional to ‘surface area’. On the other hand, results evaluated on a weight basis show that it is proportional to the 0·726 power of the body weight. In view of the variation in the data, the discrepancy between the two findings, for an animal of apparently constant shape, need not be taken too seriously; nor is it necessarily unresolvable. Surface area often varies as some power of body weight other than two-thirds ; sometimes the value may be below two-thirds, as in the case of the bean aphid (Simanton, 1933) or fruit-fly prepupae (Ellenby, 1945 b), but more frequently it is found to be above 0·7.

Surface area is proportional to length2 if shape is constant and to body weight if both shape and specific gravity are constant. As shape is constant, ‘volume’ will be proportional to length3; substituting ‘body-weight’ for ‘volume’ will therefore show whether specific gravity is constant. Values for the ratio of body-weight to length3 are plotted against body weight in Fig. 5; they show no trend. As the regression coefficient is only 0·00003,test of its significance is hardly necessary. Clearly there are no grounds for assuming that specific gravity changes with the size of the animal.

Fig. 5.

Values for the ratio of body weight to the cube of body length show no significant tendency to change with increasing size showing that specific gravity is constant.

Fig. 5.

Values for the ratio of body weight to the cube of body length show no significant tendency to change with increasing size showing that specific gravity is constant.

As both shape and specific gravity are apparently constant, surface area will be proportional to the two-thirds power of the body weight. There is, therefore, an apparent contradiction in the fact that oxygen consumption has been shown to be proportional both to length2, or ‘surface’, and also to the 0·726 power of the body weight. Fortunately, it is possible to estimate whether the difference is statistically significant.

The regression analysis carried out with the logs of values for oxygen consumption per mg. and body weight gave a regression coefficient of –0·274. Does this differ significantly from the value 0·333 necessary if the two-thirds power relationship is valid? Since the standard error of regression is ±0·041, t will equal 0·059/0·041, or 1·42; with 78 degrees of freedom, the value for P, the probability, lies between 0·1 and 0·2. There is therefore no statistically significant difference between the value obtained and –0·333.

Pleopod beat

In Figs. 6 and 7 the time for a complete pleopod beat is plotted against body length, for experiments at 15 and 25°C. respectively. Comparison of the mean values for each curve gives a temperature coefficient of 1·36, a value somewhat lower than that obtained for L. exotica (Numanhoi, 1933). The most interesting aspect of the results, however, is the variation in rate of beat with size of animal, pleopods of small animals beating faster than those of larger ones. Though the total oxygen consumption of a small animal is less than that of a large one, it is higher per unit of weight. In the case of the pleopod beat, however, the difference between animals differing in size is an absolute one. Oxygen consumption and pleopod beat vary at different rates with increasing body size.

Fig. 6.

Pleopod beat and body size, 15°C.

Fig. 6.

Pleopod beat and body size, 15°C.

Fig. 7.

Pleopod beat and body size, 25°C.

Fig. 7.

Pleopod beat and body size, 25°C.

D’Arcy Thompson (1942) has compared the rate of movement of a limb to that of a pendulum, the time of swing of which varies as the square root of the pendulum length; this comparison was first made, according to him, by the brothers Weber in 1836. The movement of a pleopod will, of course, be heavily damped by the water in which it is swinging. Nevertheless, it seemed interesting to consider pleopod beat from this point of view. Accordingly, values for time of swing and body length, the latter already shown to be proportional to ‘pendulum length’ (Fig. 2), were converted to logs and the regression coefficient calculated by the method of least squares. At 25°C., time of swing is proportional to length0·69, and, at 15° C. to length0·66. The first value does not differ significantly from 0·5, the value for a pendulum ; the second value differs rather more and, although statistical analysis shows that the difference is not significant, it approaches very close to it, for P is only slightly greater than 0·05. Nevertheless, in spite of the damping, the Ligia data give surprising support to D’Arcy Thompson’s contention that the pendulum theory, ‘with proper and large qualifications’, is ‘substantially true’.

The results clearly show that the rates of both oxygen consumption and pleopod beat vary with the size of the animal. The total oxygen consumption of small animals is less than that of large ones, but they consume more per unit of weight; on the other hand, the pleopods of small animals beat actually faster than those of large animals. Pleopod beat varies very much like that of a pendulum, the time for a complete swing of which is proportional to the square root of pendulum length; the values actually obtained were 0·66 and 0·59 at 15 and 25° C. respectively, neither of which differed significantly from the 0·5 power. Total oxygen consumption is proportional to length2 or to the 0·726 power of the body weight, but the latter value does not differ significantly from the two-thirds power.

There are examples from most invertebrate phyla where metabolism has been shown to vary with the size of the animal ; in some cases it has been suggested that it varies with surface area. (For references see Wingfield, 1939; Whitney, 1942.) Weymouth et al. (1944) have recently investigated the rate of oxygen consumption of the kelp crab, Pugettia producta. Total oxygen consumption varied as the 0·798 power of body weight, ‘weight-specific’ oxygen consumption, that is, oxygen consumption per unit of body weight, as the –0·198 power of body weight. Considering the results of other workers on Crustacea, principally Montuori (1913), they show that, interspecifically, the results for twenty-three species show total oxygen consumption proportional to the 0·826 power, a value which does not differ significantly from 0·798 obtained for the kelp crab. The individual results used in the interspecific comparison must be taken with reserve, for they are derived from experiments carried out under different conditions, particularly of temperature; it is doubtful, for example, whether a temperature coefficient, calculated for temperatures up to 17°C., is valid for temperatures up to 24·5° C. But, nevertheless, the agreement between the exponents of body weight is remarkable. Apparently the relationship holds good both interspecifically, for mature individuals of different species, and intraspecifically, for individuals differing in maturity.

Kleiber (1947) considers the application of a power law in intraspecific comparisons of mature mammals differing in size. For mice, rabbits and dogs, the only forms for which material was available covering a sufficient size range, he concludes that it is reasonable to adopt the same standard for both intraspecific and interspecific comparison; but the same standard does not apply among mammals, for example, human beings, differing in maturity (see DuBois, 1936).

Though the values for the kelp crab and the other Crustacea do not differ significantly from each other, both differ significantly from a two-thirds power relationship.

The exact value of the exponent has some importance in relation to theoretical considerations of factors influencing metabolic rate. The two-thirds power of the so-called surface-area law associated with the name of Rubner (1883) has long been applied in studies of the metabolism of mammals. There is, of course, no evidence that the actual surface of the animal is causally related to metabolic rate; indeed, the problem of the rabbit’s ears, amusingly posed by Kleiber (1932), is almost sufficient on its own to dispose of such a view. Moreover, as shown by Kleiber (1932, 1947), Benedict (1938), Brody (1945) and many others, the metabolic rate of mammals is more nearly proportional to some power between 0·73 and 0·76, and Weymouth considers some such power to apply in the case of invertebrates. Although I do not believe that there is a causal surface relationship, some of the arguments used in dismissing a surface law seem faulty.

‘Surface’ is dismissed because the values obtained differ from two-thirds. I have already pointed out (Ellenby, 1945 b) that the surface area of a series of animals need not be proportional to this power. The surface area (5) of any particular body will be proportional to the two-thirds power of its volume, or ; as for a particular body, volume will be proportional to weight, . If the argument is extended from one particular body to a series of particular bodies of different sizes, there is no a priori reason why the same relationship should hold good; but it will if the shapes of the bodies are similar and if specific gravity remains constant. As Weymouth et al. (1944) point out, the two-thirds power is a mathematical fiction; in fact, in the comparatively few cases in which surface area measurements have actually been made values different from two-thirds have usually been obtained ; for example, 0·63 and 0·60 for the German cockroach and the bean aphid (Simanton, 1933), 0·515 for Drosophila prepupae (Ellenby, 1945 b), and values over 0·7 are common for mammals (Cowgill & Drabkin, 1927).

The rejection of a two-thirds power is justified if an alternative value is more suitable; but the rejection of a surface law is not justified unless surface area has actually been measured, or there is strong evidence that neither specific-gravity nor body shape changes with body size. Such evidence is rarely advanced. In fact, it is well known that shape rarely remains constant and, as Meeh already showed for man in 1879, specific gravity may also vary with body size.

For Ligia, body shape and specific gravity do not change significantly with increasing size; surface area is therefore proportional to the square of a linear dimension. If rate of oxygen consumption is calculated per unit of length2, it is found that the values are constant over the entire size range. Oxygen consumption is therefore proportional to ‘surface area’ estimated in this way. On the other hand, oxygen consumption was proportional to the 0·726 power of the body weight, a value much closer to the 0·74 derived by Weymouth from Benedict’s data (1938), than the 0·798 of Weymouth et al. (1944), the 0·734 of Brody et al. (1934), or the three-quarters power of Kleiber (1947) ; but it does not differ significantly from two-thirds. Kleiber (1947) shows that it is impossible, with his mammal data, to distinguish statistically between a two-thirds power and 0·75 with a weight range less than ninefold. The Ligia body weights range from 0·04 to 1·03 g., a 25-fold increase; nevertheless, the two values do not differ significantly. This may be due to the large variation in the data; but there is certainly no reason, at the moment, for assuming anything other than a surface relationship for Ligia.

It is interesting to note that values calculated per unit of length2 agree among themselves somewhat better than values calculated on the basis of weight to the 0·726 power. The standard deviation, or the standard error of estimate, is about 24% of the mean value in the first case, and about 33 % in the second case. This, of course, does not mean that one basis is more ‘correct’ than the other, for ‘length’ and ‘weight’ are measured by different techniques; but it is rather salutary, to say the least, to find that a technique in which length, measured with a millimetre rule with an error of about ±2%, should provide a better basis for comparing rate of oxygen consumption than live weight determined with an accuracy of about 0·04% with an expensive analytical balance.

Whatever the explanation of the decrease in rate of oxygen consumption per unit weight with increase in body size, there is no doubt that body size is one of the most important variables in metabolic studies. Weymouth and his colleagues estimate from their data that no less than 96% of the variance in oxygen consumption is associated with variance in body weight and only 4% with the variance in all other factors; they obtain very similar figures for the other Crustacea and mammals they consider. There is little doubt of the ‘hopelessness of analysing other factors unless size is eliminated’.

In a series of papers beginning in 1936, Fox and his co-workers have considered ‘activity’ and ‘metabolism’ in relation to animal distribution. A large number of poikilothermal animals from cold waters are compared with related forms from warmer water, occasionally with members of the same species. Rates of oxygen consumption are measured and also the rates of various other activities used as indicators of ‘general activity’. It is claimed (Fox & Wingfield, 1937) that when two species within a genus are compared, the relation of oxygen consumption to temperature can be expressed by a single curve. At the higher temperatures at which it lives, an English species consumes more oxygen than an arctic species of the same genus in the colder water of its habitat, although the locomotory activity of the former is no greater. ‘It is suggested’(Fox, 1936)’that the similar locomotory activities of the two species require approximately equal amounts of oxygen, but that the non-locomotory oxygen consumption of the warm-water species is higher than that of the cold-water species.... The respiratory movements of the Crustacea formed a striking contrast to their oxygen consumption. The relation of rate of respiratory movements to temperature, for each of three pairs of comparable species did not form a single curve but two roughly parallel curves; at the temperature of its habitat, the respiratory appendage of each English species moved no faster than that of its arctic cousins living in colder water. This was true even within a single species of prawn (Pandalus montagui) inhabiting the two regions.’

The distinction between the ‘activities’ measured and oxygen consumption can hardly be sustained; activities such as heart beat, or movements of a respiratory appendage, are surely ‘basal’ rather than indicators of ‘general activity’. Moreover, rate of pleopod beat and oxygen consumption have been shown, for Ligia, to be activities taking place on different planes. The most serious question, however, is the validity of the method used to compare the rate of oxygen consumption or heart beat of two different organisms. This is hardly considered. Oxygen consumption is calculated per unit of weight, and the various activities are recorded on a time basis; these standards are perfectly suitable, but only if other things are equal. Rate of movement of the similar respiratory appendages of a pair of animals will be reasonable indicators, of the amount of work involved in moving the appendages; but if the appfendages are of different sizes, the comparison is much more difficult and some basis for the comparison must be found.

It is well known that northern forms are usually larger than similar forms from warmer waters (see Sverdrup, Johnson & Fleming, 1942); but Fox rejects the possibility that the metabolic differences may be due to the size difference. In a footnote (1936, p. 950) he states: It might be suggested that the smaller size of the English species noted above was responsible for their greater oxygen consumption, but within any one species I found no correlation between individual size and oxygen intake….’ Correlation coefficients are cited ranging from –0·2 to +0·13, and a similar value is also given in later experiments with other forms (Fox & Wingfield, 1937). But the correlations evaluated appear to be between oxygen consumption, per unit of weight, and body weight; these would be spurious. As pointed out by Weymouth et al.(1944), body weight will already have entered into the ratio with which it is correlated; if there is a positive correlation between total oxygen consumption and body weight, as seems likely, the resulting negative correlation for the ‘weight-specific’ rate will be lowered. But, in any case, as the numbers are small, comparison of correlation coefficients alone is hardly adequate for such important conclusions. Moreover, it is doubtful, to say the least, whether, even if the correlation test is accepted, it is sound to extrapolate from one group to another differing from it in size much more than the range of size within the original group.

It is interesting to compare the values obtained in a similar analysis carried out with the Ligia data. In order to compare them with those of Fox, the correlation coefficient was calculated for the first fifteen values for oxygen consumption per milligram, a number similar to the number in Fox’s tests. This gave a coefficient of +0·10. On the other hand, when the correlation coefficient was calculated for all the data, the value obtained was –0·69. Clearly, a size effect in a small group of animals which do not differ greatly in size would have great difficulty in manifesting itself. If it is incorrect to extrapolate from a restricted size range to the whole size range, it is even more incorrect to extrapolate from a restricted size range of one form to another form of larger size.

Fox claims that the ‘activity’ of related forms from northern and southern waters is apparently the same, each at its own normal temperature, and that this is shown by the rate of movement of their respiratory appendages, etc. For a pair of forms, therefore, two parallel curves relate rate of beat and temperature, while the results for both forms will fit a single curve relating temperature and rate of oxygen consumption per gram. But the northern forms are larger. If oxygen consumption varies with body size and is proportional to surface or some such function of body weight, oxygen consumption per unit of surface will be higher for the northern forms than for corresponding southern forms, as, per gram, it is claimed that they have the same consumption. A pair of forms will therefore give two curves relating oxygen consumption per unit of surface and temperature, just as in the case of the relationship for rate of movement of a respiratory appendage. There will therefore be no grounds for assuming that the warmer water species show environmental adaptation in having a higher rate of ‘non-locomotory’ metabolism.

That a size factor may, in fact, be operating to obscure other relationships is suggested by a comparison of the different English species of Crustacea (Fox, 1936; Fox & Wingfield, 1937). Four species were examined at 10°C., Pandalus montagui, Pontophilus norvegiens, Pandalina brevirostris and Spirontocaris cranchi. With mean body weights of 2·2, 0·3, 0·15 and 0·04 g. respectively, their rates of oxygen consumption, in mm.3/g./hr., are 106, 87, 119 and 141; values therefore tend to increase with decreasing body weight. But there is no such tendency in the case of three corresponding northern forms examined at 6·5° C. ; with body weights of 9·2, 4·4 and 1·8 g. the rates of oxygen consumption are 75, 82 and 77. Pandalus montagui, which occurs in both localities, has a mean weight at Kristineberg of 3·2 g. and at Plymouth of 2·2 g. ; the rates of oxygen consumption at 10° C. and 123 and 106 respectively. This form, however, does not fit Fox’s general scheme; it gives ‘parallel’ oxygen consumption curves with temperature, and he suggests that it has a higher locomotory metabolism at Kristineberg than at Plymouth.

Fox claims that the rate of scaphognathite beat does not vary with the size of the animal. As before, however, the claim is based on a correlation test on a small group of limited size range. This is supported for pandalus borealis by Abercrombie & Johnson (1941), but it is interesting to note that their specimens varied in size only from 11 to 16 cm. ; clearly, if variation between individuals is large, as they in fact found, a size effect could easily be obscured. It must again be pointed out that the apparent absence of a size effect in a group of animals of restricted size is no valid basis for the assumption that there is no such effect between two species differing in size to a much greater extent.

As recently shown for fish by Peiss & Field (1950) there may be striking metabolic adaptations to life in cold waters; but Fox’s comparisons are unfortunately invalidated by lack of consideration of the factor of body size. This is also true of the interesting investigation of the response of ephemerid nymphs from different habitats to change in oxygen tension (Fox, Wingfield & Simmonds, 1937a). It is most unfortunate that more attention was not paid to control of the factor of body size, particularly in view of the care taken in previous papers in this series (Fox & Simmonds, 1933; Fox, Simmonds & Washbourn, 1935). Their general conclusion that forms from fast-flowing streams respond to a reduction in oxygen consumption much more rapidly than forms from less highly oxygenated habitats may prove to be justified, but it cannot be said that this paper has established the point.

Rate of oxygen consumption was measured for each form at a number of different oxygen tensions; but different specimens were used at each oxygen tension, and, unfortunately, the mean weight often varied from tension to tension, sometimes in a systematic fashion,

Baetis sp. appears to show the most rapid response to lowered oxygen tension. At oxygen concentrations of 14· 6, 12·3, 7·7, 5·3 and 4·0 c.c./l., the rates of oxygen consumption, in mm.3/g./hr., were 4000, 4100, 2700, 1670 and 1350 respectively. Mean dry weights for the specimens examined at these tensions were, respectively, 10·0, 11·0, 15·7, 21·7 and 17 mg.; weight, therefore, increases more or less regularly with decreased tension and oxygen consumption. The position is slightly different in the case of Leptophlebia vespertina, which appears to show a response only at the two lowest levels of oxygen tension. Mean weights, in order of decreasing oxygen tension, were 27·7, 33, 37, 27, 41·2 and 54 mg.; size differences are therefore slight, until the two lowest levels of oxygen tension, where the rate of oxygen consumption also shows the most striking fall.

The size distribution is satisfactory in the case of Ephemera vulgata, a form which shows marked response to falling oxygen tension; but this species lives buried in mud and the response is not considered adaptive.

Clearly it is impossible to obtain a clear picture of the true response to lowered oxygen tension, for the differences of the mean weight of the animals in the different groups would itself influence the level of oxygen consumption.

A better conclusion to this section could hardly be found than that of Dreyer, Ray & Ainley-Walker (1913): In recent years it has become increasingly evident that many of the most important problems of physiology and experimental pathology cannot be investigated in a satisfactory manner until accurate data have been made available regarding the quantitative differences which are exhibited by the organs, tissues and fluids of normal animals of different species and varying weights. Results obtained with animals of different species and any given weight cannot be applied even within one and the same species, to yield conclusions regarding animals of different weight until it has been determined with precision how the various organs and tissues of the body are related to the size of the individual. Moreover, it will only be possible to compare one species with another, or to apply the results deduced from any given species to any other species of animal, until we have established some kind of quantitative correlation between the measurements in the different species.’

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*

I am very grateful to the officers of the Plymouth Marine Laboratory for the special efforts they made to obtain animals extending over a wide range of body sizes.