ABSTRACT
The thermal status of an animal is the result of a combination of physical and physiological factors. In poikilotherms, it may be possible to separate these more easily than in homeotherms, where the presence of control mechanisms can mask the processes occurring. The thermal time constant of a poikilotherm has been shown to be a useful measure of its thermal behaviour, and to vary with the physiological status of the animal. A simple model is developed to show how the thermal time constant is related to the physics of heat exchange. The derived thermal time constant is shown to scale as body mass raised to the power 2/3, and this is compared with results on lizards heating and cooling in water, taken from the literature.
When heat exchange in air is considered, the concept of boundary layer resistance leads to a useful simplification. The thermal time constants in air taken from the literature show that the boundary layer resistance is approximately constant.
1. INTRODUCTION
Although poikilotherms are normally considered incapable of maintaining a constant body temperature, it is now recognized that reptiles can and do regulate their physiology and behaviour to optimize body temperature (see reviews by Templeton, 1970; Cloudsey-Thompson, 1971; and White, 1973). Physiological control enables the animal to vary the rate at which it heats or cools in a fluctuating environment, probably by varying the blood supply to the periphery (Morgareidge & White, 1969; Grigg & Alchin, 1976). The study of this control requires that it be quantified in such a way that the index produced is easily related both to the physics of heat exchange and to the biology of the animal. Spotila et at. (1973) have proposed the use of the ‘thermal time constant’, and this is now used by most experimenters (Smith, 1976; Grigg, Drane & Courtice, 1979; Boland & Bell, 1980; Bartholomew, 1966). This concept has proved to be very useful, facilitating comparisons between experiments and between species.
Models of the thermal behaviour of lizards have been proposed which relate the thermal time constant to the physics of heat exchange (Spotila et al. 1973 ; Grigg et al. 1979). These models are rather complex and this can obscure the important principles which underlie thermo-regulation. This note presents a simple model based on the physics of heat conduction in solids, which still allows the derivation of a thermal time constant that has a scaling law very similar to that observed for lizards. The mathematical details of this model will be presented elsewhere.
2. THE MODEL
This model is basically a simplification of those of Spotila et al. (1973) and Grigg et al. (1979). It is equivalent to a single layer of insulating fat with no heat storage in the former, and letting the heat capacity of the insulating layer go to zero in the latter paper.
3. RESULTS
This prediction can be tested by comparing thermal time constants measured for lizards heating and cooling in water, a close approximation to an isothermal environment. Fig. 1 shows published values of τ plotted on a log-log scale against the corresponding body mass for lizards between 150 g and 30 kg. The differences between heating and cooling time constants are quite marked. The slope of the regression line fitted to the data for cooling agrees well with the prediction, but that for heating is significantly different at the 95 % level.
Log-log plots of thermal time constant against mass for various lizards heating and cooling in water. The data have been taken from the literature, and in many cases have been calculated from the rates measured at the midpoint of the heating or cooling curve. The species involved are: ▽, Crocodylus johnstoni (Grigg & Alehin. 1976); •, Alligator missiuippiensis (Smith, 1976); □, Physignathus lesueurii (Grigg et al. 1979); ○, Crocodylus porosus (Boland & Bell, 1980); ▴, Amblyrhynchus cristatus (Bartholomew, 1966; Bartholomew & Lasiewski, 1965). The lines are the least squares regression lines of log time constant on log mass. The uncertainties given are the 95 % confidence limits. The theoretical value of this slope is 0·67.
Log-log plots of thermal time constant against mass for various lizards heating and cooling in water. The data have been taken from the literature, and in many cases have been calculated from the rates measured at the midpoint of the heating or cooling curve. The species involved are: ▽, Crocodylus johnstoni (Grigg & Alehin. 1976); •, Alligator missiuippiensis (Smith, 1976); □, Physignathus lesueurii (Grigg et al. 1979); ○, Crocodylus porosus (Boland & Bell, 1980); ▴, Amblyrhynchus cristatus (Bartholomew, 1966; Bartholomew & Lasiewski, 1965). The lines are the least squares regression lines of log time constant on log mass. The uncertainties given are the 95 % confidence limits. The theoretical value of this slope is 0·67.
It thus appears that this simple model can account for the increase in the thermal inertia of lizards with increasing mass, but that in order to get full quantitative agreement, a greater understanding of the physiology and a correspondingly more complex model may be needed.
.Fig. 2 shows that rs appears to be constant, and approximately the same for heating and cooling. As rs is proportional to the Nusselt number, it could be expected to vary with the linear dimension of the animal, and so vary with mass (Monteith, 1973). However, at the high air velocities used in these experiments (typically 2—3 m s−1), the boundary layer will have a thickness of only a fraction of a millimetre, probably of the same order as the surface roughness of the skin. In this case the overall dimension of the animal will be unimportant, and the surface roughness will maintain rs, above that predicted for a smooth surface.
Log-log plots of the component of the thermal time constant in air due to the boundary layer, against mass for both heating and cooling. This component has been calculated by subtracting the time constant in water derived from the regression equations found previously from the value of the time constant in air in the literature. This difference was then normalized to an air velocity of 3 m s−1 using a correction proportional to the square root of the air velocity in the particular experiment (Monteith, 1973). Only experiments where the air velocity was greater than 1·5 ms−1have been used. The species are: •, Alligator mississippiensis (Smith, 1976); ◼, Var anus spp. (Bartholomew & Tucker, 1964); ▾, Disposaurus dorsalis (Weathers, 1970); △, Amphibolurtu barbatus (Bartholomew & Tucker, 1963); ◊, Tiliqua tcincoidet (Bartholomew et al. 1965). The regression lines shown do not differ significantly from lines of slope 0·33, indicating that heat loss in air is proportional to the area to volume ratio, and that the boundary layer resistance is constant.
Log-log plots of the component of the thermal time constant in air due to the boundary layer, against mass for both heating and cooling. This component has been calculated by subtracting the time constant in water derived from the regression equations found previously from the value of the time constant in air in the literature. This difference was then normalized to an air velocity of 3 m s−1 using a correction proportional to the square root of the air velocity in the particular experiment (Monteith, 1973). Only experiments where the air velocity was greater than 1·5 ms−1have been used. The species are: •, Alligator mississippiensis (Smith, 1976); ◼, Var anus spp. (Bartholomew & Tucker, 1964); ▾, Disposaurus dorsalis (Weathers, 1970); △, Amphibolurtu barbatus (Bartholomew & Tucker, 1963); ◊, Tiliqua tcincoidet (Bartholomew et al. 1965). The regression lines shown do not differ significantly from lines of slope 0·33, indicating that heat loss in air is proportional to the area to volume ratio, and that the boundary layer resistance is constant.
4. DISCUSSION
For smaller lizards heating and cooling in air, the boundary layer resistance is much larger than that of the insulating layer. As mass increases, the former becomes less important, and the resistances become equal at a mass of about 7 kg for heating and 4 kg for cooling. For masses much larger than these, the boundary layer resistance can be ignored, and lizards will heat and cool equally in air or water.
The largest animals appearing in these results are small crocodiles of around 20 kg mass. These had time constants for cooling of about 2 h, thus allowing considerable freedom of movement in adverse environments before basking would be necessary. If we extrapolate the results presented here, we can predict that a large crocodile of mass 400 kg will have a thermal time constant for cooling of about 12 h. It will therefore have a high degree of thermal stability, its body temperature varying by only a few kelvins between night and day. If we extrapolate even further, it can be seen that larger lizards such as dinosaurs would have even greater thermal stability. For instance, a 2000 kg lizard is predicted to have a thermal time constant of almost 48 h. As has been pointed out by Spotila et al. (1973) and others, such a massive creature would feel little effect of the diurnal cycle in ambient temperature, and be able to remain quite active during cool periods for some time.
ACKNOWLEDGEMENTS
I wish to thank Gordon Grigg for a preprint and Jerry Clark for his helpful comments.
