Transient dynamics in multilocus invasions by transgenic organisms

With recent advances in molecular genetics, it is likely that releases of genetically modified organisms will be used for a variety of purposes. In many cases, such systems would utilize organisms that have been modified on multiple genetic loci. Predicting the effect of such releases will require an understanding of the transient dynamics in the system. However, theoretical understanding of transient dynamics in multilocus systems is limited, particularly for early generations when gametic disequilibrium is still high. I derive approximate expressions for marginal allele frequency and marginal two-locus disequilibrium that are applicable in this initial period, assuming infinite population size, two alleles per locus, and weak viability selection. I then apply these results to exploring the effect of parameters on the frequency of the resident gamete type in a release of organisms carrying an autocidal allele on multiple loci. This leads to simple approximate expressions for the optimal number of loci carrying the autocidal allele (as a function of release size and the degree of natural selection against the alleles) and the size of release needed to overcome a given level of selection against the released alleles.