A cascade of destabilizations: Combining Wolbachia and Allee effects to eradicate insect pests

The management of insect pests has long been dominated by the use of chemical insecticides, with the aim of instantaneously killing enough individuals to limit their damage. To minimize unwanted consequences, environmentally friendly approaches have been proposed that utilize biological control and take advantage of intrinsic demographic processes to reduce pest populations. We address the feasibility of a novel pest management strategy based on the release of insects infected with Wolbachia, which causes cytoplasmic incompatibilities in its host population, into a population with a pre-existing Allee effect. We hypothesize that the transient decline in population size caused by a successful invasion of Wolbachia can bring the population below its Allee threshold and, consequently, trigger extinction. We develop a stochastic population model that accounts for Wolbachia-induced cytoplasmic incompatibilities in addition to an Allee effect arising from mating failures at low population densities. Using our model, we identify conditions under which cytoplasmic incompatibilities and Allee effects successfully interact to drive insect pest populations towards extinction. Based on our results, we delineate control strategies based on introductions of Wolbachia-infected insects. We extend this analysis to evaluate control strategies that implement successive introductions of two incompatible Wolbachia strains. Additionally, we consider methods that combine Wolbachia invasion with mating disruption tactics to enhance the pre-existing Allee effect. We demonstrate that Wolbachia-induced cytoplasmic incompatibility and the Allee effect act independently from one another: the Allee effect does not modify the Wolbachia invasion threshold, and cytoplasmic incompatibilities only have a marginal effect on the Allee threshold. However, the interaction of these two processes can drive even large populations to extinction. The success of this method can be amplified by the introduction of multiple Wolbachia cytotypes as well as the addition of mating disruption. Our study extends the existing literature by proposing the use of Wolbachia introductions to capitalize on pre-existing Allee effects and consequently eradicate insect pests. More generally, it highlights the importance of transient dynamics, and the relevance of manipulating a cascade of destabilizatons for pest management.