Abstract
Many insects show discontinuous respiration with three phases, open, closed, and fluttering, in which the spiracles open and close rapidly. The relative durations of the three phases and the rate of fluttering during the flutter phase vary for individual insects depending on developmental stage and activity, vary between insects of the same species, and vary even more between different species. We studied how the rate of oxygen uptake during the flutter phase depends on the rate of fluttering. Using a mathematical model of oxygen diffusion in the insect tracheal system, we derive a formula for oxygen uptake during the flutter phase and how it depends on the length of the tracheal system, percentage of time open during the flutter phase, and the flutter rate. Surprisingly, our results show that an insect can have its spiracles closed a high percentage of time during the flutter phase and yet receive almost as much oxygen as if the spiracles were always open, provided the spiracles open and close rapidly. We investigate the respiratory gain due to fluttering for four specific insects. Our formula shows that respiratory gain increases with body size and with increased rate of fluttering. Therefore, insects can regulate their rate of oxygen uptake by varying the rate of fluttering while keeping the spiracles closed during a large fraction of the time during the flutter phase. We also use a mathematical model to show that water loss is approximately proportional to the percentage of time the spiracles are open. Thus, insects can achieve both high oxygen intake and low water loss by keeping the spiracles closed most of the time and fluttering while open, thereby decoupling the challenge of preventing water loss from the challenge of obtaining adequate oxygen uptake.