A Mathematical Model of Heat Flux Applied to Developing Endotherms

During postnatal development, young birds and mammals are neither strict ectotherms nor homeotherms. They have variable body temperatures (Tb) and high metabolic rates (Ṁ). Although Newtonian models for ectotherms and homeotherms are routinely applied to developing endotherms, they do not fit. Here, I apply a one-dimensional model of heat transfer to describe the thermoregulation of developing endotherms. This model, modified from a model for ectotherms, includes both heat storage and metabolic heat production terms critical to describing heat flux in endotherms. I rearrange the model to obtain an operational method to calculate the conductance of cooling endotherms: K0 = [Ṁ − (C · Ṫb)]/(Tb − Te), where Ṫb is the rate of body cooling, Tb is the operative environmental temperature, C is the heat capacity, and K0 is conductance. The model is combined with the Q10 relation for metabolic rate in an iterative procedure to predict cooling curves for endotherms. Validations were performed with the use of a series of measurements on thermoregulation in young western gull (Larus occidentalis) chicks. Conductances calculated for cooling chicks were statistically indistinguishable from minimum conductances determined by means of classical methods for homeothermic individuals. However, when classical methods were used to calculate conductance in cooling animals, K0 was underestimated by an average of 61%. Body temperatures predicted by the cooling model were not significantly different from measured values for the same birds. These models may be used to compare data obtained by means of diverse experimental protocols on the thermoregulatory performance of endotherms.