Insect eggs at a transition between diffusion and reaction limitation: Temperature, oxygen, and water

In diverse animal taxa, eggs and embryos are incapable of transporting oxygen by convection. In such cases, internal oxygen distributions are determined jointly by rates of oxygen consumption and diffusive transport. Here we develop a mathematical model of oxygen consumption and transport in insect eggs, with the goal of understanding—for eggs in variable-temperature environments—the interactive effects of the two processes on development. We fit the model to previously published data on development time of eggs of a sphingid moth, Manduca sexta. The fitted coefficients suggest that eggs develop at a transition point between reaction- and diffusion-limitation. We test then this conclusion with independent data on development times of eggs distributed across a set of temperatures generated by a thermal gradient bar. Finally, we develop an extension of the model that considers tradeoffs between oxygen transfer to eggs versus water loss from them. The model results provide both a rationale for why development is often mass-transfer limited and a set of new predictions about oxygen–water tradeoffs.