Body-Weight, Energetics, and the Determination of Body Temperature

Calder & King (1972) have just published a note disputing this analysis. A few comments on their evaluation might be of value. (1) They point out that the proposed analysis assumes a Newtonian model of heat exchange. The verification of the Newtonian model of heat exchange does not depend upon biologists; it is a question for physicists. The only question that biologists must answer is which physical model of heat exchange can most appropriately describe heat exchange in animals. There seem to be three schools of thought: (a) no model need be used (for whatever reason), (b) a sophisticated heat-transfer model should be used, and (c) a compromise Newtonian or Fourierian model must be used. The first view need not be answered, since thermoregulation is obviously a problem of heat transfer and thus a quantitative physical analysis is appropriate. The difference between the views of position b (e.g. Birkebak, 1966; Porter & Gates, 1969) and position c (e.g. Scholander et al. 1950; McNab, 1970; Yarbrough, 1971) is simply a question as to the physical sophistication employed in the model. Group b clearly has the most elegant and ‘correct’ formulation of the physics of heat exchange; however, it is very difficult to apply this analysis to live animals, except possibly in special climatic chambers. For example, what is the effective surface area of an animal? This question is exceedingly difficult if not impossible to answer, especially since there are separate surface areas associated with each mode of heat transfer and an animal can change them with great facility. These frustrations- not theoretical elegance- have led to the advocacy of a Newtonian compromise. It is not surprising that in their papers members of group b are heavily orientated towards theory, while those who advocate position c have been preoccupied with measurements on living animals. Newton’s law is clearly imperfect; some of the limits to its use have been examined by McNab (1970).

(3)In a point that is related to (2) Calder and King have referred to the empirical nature of the weight-dependent equations for the basal rate of metabolism and thermal conductance. They note that it is inconsistent to bring empirical expressions into an otherwise theoretical analysis. Their point is well taken, but until someone can give a theoretically ‘pure’ analysis of the influence of body weight on physiological functions we shall simply have to live with such imperfection. It should be noted, however, that these physiological empiricisms work reasonably well, both in fitting the relationship of metabolism and other functions to weight, and consequently in such derivative relationships as the relation of body temperature to weight

(4)Calder and King suggested that most - if not all - of the graphs are arbitrary and that ‘in several cases...[cited]...the lines do not fit the circled data points’. It is indeed gratifying that only a minority of points do not conform to expectations, e.g. about 3 out of 28 in Fig. 2, 6/38 in Fig. 3, and 2/12 in Fig. 9. They conclude: ‘The points seem to be random patterns, a portion of which happen to fall near a preconceived line.’ We have already agreed that the majority of points appear to agree rather well with several families of ‘preconceived’ lines, although it must be admitted that there are few statistical tests which will examine the validity of such a complex family of curves simultaneously. The concept of ‘preconceived’ seemingly fits with the attempt at making predictions from an idea and trying to see whether the data are compatible with such an idea.

(5)The authors proceed to point out the erroneous nature of assuming that the lower limit of thermoneutrality is a constant, which of course should not be done and is normally incorrect. They fail, however, to note three factors: (a) it was never assumed, (b) the statement is a conclusion under the condition that body temperature is a function of body weight, and (c) this conclusion is substantiated by observations (see Fig. 5).

(7)Calder and King point out that the ratio (M_b/C)_r must be inversely related to (M_b/C)_e, since the first ratio was in fact derived by dividing observed values by the latter ratio. The authors fail to understand that the inverse relationship holds only when all of the animals in the set maintain a high, regulated body temperature ; then their argument is correct. However, if endotherms allow body temperature to vary with body weight, this inverse relationship need not hold. For example, frugivorous bats of the genus Artibeus have (M_b/C)_r constant in reference to weight, but the body temperatures of large species are higher than those of small species (McNab, 1969).

There are two errors in the paper by McNab that were not discovered by Calder and King, but which should be corrected. On page 335 equation (6) should read (M_b/C)_r,. =11· 5/ (M_b/C)_e On page 338 the word independent should appear: ‘If, however, T_b is independent of weight, then from equation (5b).

The use of quantitative physical models often will permit insights into biologically important behaviour that might otherwise not occur by the simple contemplation of data alone. Such modelling will normally show that most systems, especially those associated with the maintenance of a steady state, have a limited flexibility, the limitations resulting from the finite number of important factors that determine the steady state. Ecologically important limitations to the steady state are dictated by an environmental influence upon the parameters of the system and therefore upon their resultant interactions.

This paper is in reply to criticisms of an earlier paper (McNab, 1970).

I should like to thank the National Science Foundation (GB-3477) for supporting research that led to this analysis.