Gas exchange in the tissues and lungs is accurately described by simple equations, and mathematical models of O(2) transport play a paramount role in the conceptual understanding of respiratory physiology. In the present paper, we review an integrative approach to describe maximum oxygen uptake in animals with tidally ventilated lungs. Further, we expand the analysis by including a central vascular shunt compartment to mimic the cardiovascular anatomy of embryonic birds and mammals as well as many ectothermic vertebrates. Finally, we predict the effects of right-to-left and left-to-right cardiac shunts on maximal oxygen uptake and present a new hypothesis that relates the interaction of metabolic rates and central shunts in air breathing ectothermic vertebrates.