The oxygen gain of diving insects

The gas gill of diving insects allows gas exchange with the surrounding water, thus extending diving time. Incompressible gas gills can potentially last indefinitely underwater, but compressible gas gills have a definite lifetime. Theoretical models of a dive event have reached opposite conclusions about the oxygen gain (G, the ratio between the duration of the diving event and the time that the initial oxygen content of the bubble would allow the insect to stay underwater). While some authors claim that G has a fixed value independently of the parameters of the dive (e.g. oxygen consumption rate) others claim the contrary. However, these claims are based on numerical solutions of the models. In this study we offer an analytical solution to the problem. The analysis of a model with constant area for gas exchange demonstrates that G cannot have a fixed value, for a fixed gain would imply in a P_O2 inside the bubble different from the one occurring as a result of physical constraints of the gas exchange process.