Spatially implicit approaches to understand the manipulation of mating success for insect invasion management

Recent work indicates that Allee effects (the positive relationship between population size and per capita growth rate) are critical in determining the successful establishment of invading species. Allee effects may create population thresholds, and failure to establish is likely if invading populations fall below these thresholds. There are many mechanisms that may contribute to Allee effects, but mate-location failure is a common cause in sexually reproducing insects. Consequently, mate-location failure represents a type of weak link that may be enhanced in order to achieve eradication of insect populations during the early stages of invasion. In this paper, spatially implicit models that account for mating behavior of both sexes are used to explore the enhancement of mate-location failure in pest eradication programs. Distinct from the previous studies, the Allee effect emerges from a mechanistic representation of mate-location failure in our model. Three specific eradication strategies, sterile insect release, mass-trapping, and mating disruption, are incorporated into the model and tested for their ability to depress population growth during the early stages of invasions. We conducted simulations with the model parameterized to represent two types of insects: Coleopteran-like insects which are long-lived and capable of multiple matings, but have low daily reproductive rates, and Lepidopteran-like insects which are capable of mating only once per generation, have an ephemeral reproductive stage, and have high reproductive rates. Simulations indicated that: (1) many insect pests are more likely to be eradicated than had been previously predicted by classic models which do not account for mate-finding difficulties, (2) for Lepidopteran-like insects, mass-trapping has the greatest potential for eradication among the three methods when a large number of traps can be installed, although mating-disruption will be the most effective if we can anticipate confusion or trail-masking mechanisms of disruption, and (3) populations of Coleopteran-like insects may be most effectively eradicated using the sterile male release method. Though more detailed models should be tailored for individual species, we expect that the spatially implicit approaches outlined in this paper can be widely adapted to study the efficiency of various eradication approaches in sparse conditions.