Game theory approach to sterile release populations and replicator dynamics: Niche fragmentation and resilience

Abstract

The sterile release technique liberates infertile individuals who mate with wilds. Consequently, wilds have two mating options: sterile or fertile individuals. This choice process can be framed in a theoretical game, typical in economic studies, between two opponents with the appropriate payoff (fitness). The game matrix is constructed depending on parameters such as wild growth rates and the influx rate of sterile individuals. A technique using replicator dynamics allows the equilibrium points to be determined, particularly, the (Nash) equilibrium resulting from the influx of the sterile population. Moreover, when population diffusion is considered, the niche of wilds becomes partitioned, defining a criterion for protecting biodiversity. The medfly, Ceratitis capitata, is regarded as an explicit example for parameter evaluations and numerical simulations.