In a seminal study published nearly 70 years ago, Scholander et al. (Biol Bull 99:259-271, 1950) employed Newton's law of cooling to describe how metabolic rates (MR) in birds and mammals vary predictably with ambient temperature (T a). Here, we explore the theoretical consequences of Newton's law of cooling and show that a thermoregulatory polygon provides an intuitively simple and yet useful description of thermoregulatory responses in endothermic organisms. This polygon encapsulates the region in which heat production and dissipation are in equilibrium and, therefore, the range of conditions in which thermoregulation is possible. Whereas the typical U-shaped curve describes the relationship between T a and MR at rest, thermoregulatory polygons expand this framework to incorporate the impact of activity, other behaviors and environmental conditions on thermoregulation and energy balance. We discuss how this framework can be employed to study the limits to effective thermoregulation and their ecological repercussions, allometric effects and residual variation in MR and thermal insulation, and how thermoregulatory requirements might constrain locomotor or reproductive performance (as proposed, for instance, by the heat dissipation limit theory). In many systems the limited empirical knowledge on how organismal traits may respond to environmental changes prevents physiological ecology from becoming a fully developed predictive science. In endotherms, however, we contend that the lack of theoretical developments that translate current physiological understanding into formal mechanistic models remains the main impediment to study the ecological and evolutionary repercussions of thermoregulation. In spite of the inherent limitations of Newton's law of cooling as an oversimplified description of the mechanics of heat transfer, we argue that understanding how systems that obey this approximation work can be enlightening on conceptual grounds and relevant as an analytical and predictive tool to study ecological phenomena. As such, the proposed approach may constitute a powerful tool to study the impact of thermoregulatory constraints on variables related to fitness, such as survival and reproductive output, and help elucidating how species will be affected by ongoing climate change.
Keywords: Animal energetics; Bergmann’s rule; Geographic distribution; Macrophysiology; Metabolic rate; Thermal conductance; Thermal insulation.