Pheromone trapping models for pest control: Effects of mating patterns and immigration

Summary Several models are presented which examine pest population behaviour with the release of female sex pheromones for the attraction and annihilation of males. These models include male polygamy and female monogamy, various mating frequencies, delayed mating of females, immigration of one or all individual types, and differential survivorship of males and females. In all the models there are two steady states, a stable s.s. at the origin and an unstable s.s. in the positive domain for a given value of pheromone release rate. In all the models, control relies on the reduced ability of males to fertilize virgin females following trapping and male annihilation. As such, control is very sensitive to mating frequency, being very difficult when males mate frequently. Control is also very difficult with the immigration of even a moderate number of fertilized females. Control is much easier when mating is delayed, especially if survivorship is low, or with density dependent population regulation.