Body, weight, energetics, and the determination of body temperature.

An analysis of the influence of body weight on the energetics of endotherms has been proposed by McNab (1970). It was based on the observations that (1) when body temperature is constant heat production equals heat loss, and (2) heat loss may be described as the product of thermal conductance and the temperature differential between the body and the environment: M = C(Tb—Ta). This expression with some misfortune and inappropriateness has come to be called Newton's law of cooling. Its application means that the energetics of an endotherm has a limited number of degrees of freedom; at a particular environmental temperature, fixing two of the factors will determine the third. It was argued that thermal conductance and the rate of heat production vary with body size and with ecological conditions. Consequently, these factors are mainly responsible for setting the level 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).