A Mathematical Model for Body Temperatures of Large Reptiles: Implications for Dinosaur Ecology

Abstract

A mathematical model for heat conduction through large reptiles is developed. The animal is approximated by a large cylinder with a central core of tissue kept at a uniform temperature by blood flow, surrounded by six layers of fat. An iterative mathematical procedure is used to solve equations for heat flowing into, heat flowing out of, and heat stored in each layer and the core during a specified time period. This yields the temperatures of the core and insulating layers at the end of the time period. Physiological and environmental parameters are incremented and calculations repeated for a new time period. These calculations show that a large reptile (D = 100 cm) would have a relatively constant high body temperature when exposed to warm, diurnally fluctuating environmental conditions, even with a low metabolic rate, as long as the average values of the physical parameters result in a body temperature within tolerable limits. Changes in fat thickness are of minor importance in determining the constancy of body temperature. If exposed to excessively hot or cold climates, large reptiles would have a constant excessively high or low body temperature. A time-constant equation is developed to describe the effect of size on the response of body temperature to environmental heat loads in small and large reptiles. Gigantism would be a very useful strategy for reptiles, providing a constant, equable internal temperature in a stable, warm climate. This strategy may have been selected for in dinosaurs, giving them a high stable body temperature without a high metabolic rate. Our calculations support the hypothesis that thermal stress resulting from decreased equability of climate may have been a primary factor in the extinction of dinosaurs during the late Cretaceous.