Pest control by the release of insects carrying a female-killing allele on multiple loci

With recent advances in genetics, many new strategies for pest control have become feasible. This is the second article in which we model new techniques for pest control based on the mass release of genetically modified insects. In this article we model the release of insects carrying a dominant and redundant female killing or sterilizing (FK) allele on multiple genetic loci. If such insects are released into a target population, the FK allele can become widely spread in the population through the males while reducing the population each generation by killing females. We allow the number of loci used to vary from 1 to 20. We also allow the FK allele to carry a fitness cost in males due to the gene insertions. Using a model, we explore the effectiveness and optimal strategies for such releases. In the most ideal circumstances (no density-dependence and released insects equal in fitness to wild ones), FK releases are several orders of magnitude more effective than equal sized sterile male releases. For example, a single release of 19 FK-bearing males for every two wild males, with the released males carrying the FK allele on 10 loci, reduces the target population to 0.002% of no-release size. An equal sized sterile release reduces the target population to 5% of no-release size. We also show how the effectiveness of the technique decreases as the fitness cost of the FK alleles in males increases. For example, the above mentioned release reduces the target population to 0.7% of no-release size if each FK allele carries a fitness cost in males of 5%. Adding a simple model for density-dependence and assuming that each of the released males carries the FK allele on six loci, we show that the release size necessary to reduce the target population to 1/100 of no-release size in 10 generations of releases varies from 0.44:1 to 4:1 (depending on parameter values). We also calculate the optimal number of loci on which to put the FK allele under various circumstances.