Modelling Allee effects in a transgenic mosquito population during range expansion

Abstract

Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.

Population Dynamics of Underdominance Gene Drive Systems in Continuous Space

“…[25][26][27]29 Hybrid zones between species have already provided demonstrations of such situations, 32 which often additionally involve Allee effects due to population suppression in such regions. 33,34 These models have also been successfully applied to Wolbachia systems, 35,36 which (when moderate to high fitness costs are present) are conceptually similar to underdominance systems in many aspects and also show frequency-dependent dynamics. 35,36,45,46,37−44 Taken together, the results from the study of bistable genetic systems in diffusion models clearly demonstrate that the dynamics of underdominance gene drive systems should be fundamentally different in spatially continuous populations compared to models of panmictic populations.…”

“…Diffusion theory has also provided analytical expressions for the expected rate of advance at which underdominance systems will spread in one- or two-dimensional space as a function of the fitness parameters of the system. , At the boundary where a region comprised primarily by drive alleles encounters a region comprised primarily by wild-type alleles, population density should be reduced due to the lower fitness of heterozygotes . Barriers to diffusion were found to stop propagation of the drive if strong enough, ,, while density gradients should generally assist diffusion of a drive allele from higher to lower density. , However, even with a boundary that is expected to be stable in a deterministic model, stochastic effects can shift this boundary. − , Hybrid zones between species have already provided demonstrations of such situations, which often additionally involve Allee effects due to population suppression in such regions. , These models have also been successfully applied to Wolbachia systems, , which (when moderate to high fitness costs are present) are conceptually similar to underdominance systems in many aspects and also show frequency-dependent dynamics. ,,,,− …”

Mathematical modeling of the performance of wild and transgenic mosquitoes in malaria transmission

“…Mathematical models describing the interaction between wild and genetically modified mosquitoes, as well as their spread, have been widely studied in the literature (see for example [24] and references therein). Recently, Wyse et al [25] presented a stochastic reaction-diffusion model with resistant allele dynamics based on the MCR technique.…”

Dynamics of a delayed predator‐prey model with Allee effect and Holling type II functional response

“…Here, breeding groups are less successful in producing and/or rearing young when small. In other works, such as Melody Walker et al, 26 studied the Allee effect in a transgenic mosquito population; as mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density.…”