Toward a theory of energetically optimal body size in growing animals

Our objective was to formulate a general and useful model of the energy economy of the growing animal. We developed a theory that the respiratory energy per unit of size reaches a minimum at a particular point, when the marginal respiratory heat production rate is equal to the average rate. This occurs at what we defined as the energetically optimal size for the animal. The relationship between heat production rate and size was found to be well described by a cubic function in which heat production rate accelerates as the animal approaches and then exceeds its optimal size. Reanalysis of energetics data from the literature often detected cubic curvature in the relationship between heat production rate and body size of fish, rats, chickens, goats, sheep, swine, cattle, and horses. This finding was consistent with the theory for 13 of 17 data sets. The bias-corrected Akaike information criterion indicated that the cubic equation modeled the influence of the size of a growing animal on its heat production rate better than a power function for 11 of 17 data sets. Changes in the sizes and specific heat production rates of metabolically active internal organs, and body composition and tissue turnover rates were found to explain notable portions of the expected increase in heat production rate as animals approached and then exceeded their energetically optimum size. Accelerating maintenance costs in this region decrease net energy available for productive functions. Energetically and economically optimum size criteria were also compared.