Waves of extinction from sterile insect release.

Employing theoretical models, we show that the sterile insect release method (SIRM) can give rise to traveling waves of fertile insects. The velocity of these waves depends critically upon the density of sterile insects (and thus upon the rate at which sterile individuals are being released into the environment). When the sterile density is sufficiently low, the traveling wave advances, giving rise to an invasion. However, when the sterile density exceeds a critical threshold, the wave reverses direction, thereby retreating and giving rise to local extinction. Both analytical (regular perturbation) methods and numerical methods are used to determine wave velocities and wave profiles. This is the first time traveling wave solutions have been shown for the SIRM.